Doctoral Dissertation
博士論文

Suppression of γ-ray backgrounds forthe highest sensitivity of µ+ → e+γ searchin MEG II experiment（MEG II 実験における最高感度での µ+ → e+ γ 探索を可能にする背景
γ 線抑制）A Dissertation Submitted for the Degree of Doctor of Philosophy
December 2021
令和 3 年 12 月博士（理学）申請

Department of Physics, Graduate School of Science,
The University of Tokyo東京大学大学院理学系研究科物理学専攻

Rina Onda
恩田

理奈

i

Abstract
The µ → eγ decay, which is one of the charged lepton flavor violating decays, can be strong
evidence of physics beyond the standard model. In 2016, the MEG experiment set the moststringent upper limit for the branching ratio of the decay to be 4.2 × 10−13 (90% confidence
level). The MEG II experiment aims to search for the decay with a higher sensitivity by one
order of magnitude by updating the MEG detectors. The dominant background for the searchis the accidental coincidence between uncorrelated positrons and γ-rays, and thus it is essential
to improve detector resolutions in order to separate the signals from the backgrounds.
A liquid xenon γ-ray detector has been upgraded to measure γ-rays with better resolutions.
A higher granularity and a better uniformity of the scintillation readout were realized by tilingsilicon photomultipliers on the γ-ray entrance face, which results in better position and energy
resolutions especially for the shallow events. The performance of the detector was measured in aseries of pilot runs, and better position and energy resolution for the shallow events were proved
while there still remains an uncertainty for the evaluation of the timing resolution. Further
background suppression was found to be achievable by the methods developed in this work.
Pileup γ-rays aﬀect the γ-ray reconstruction especially for the energy measurement, and thus aseries of algorithms to eliminate the pileup γ-rays was developed and its background suppression
power was demonstrated.
A radiative decay counter (RDC) has been newly introduced in the MEG II experiment to
tag the γ-ray backgrounds. It identifies a γ-ray from a radiative muon decay, which is oneof the sources of the accidental γ-ray background, by detecting the positron emitted from thesame muon decay. The expected performance of the detector was confirmed using data in thepilot runs. In addition, the algorithm of the µ → eγ search analysis was updated to include theobservables of the RDC.
The branching ratio sensitivity of the MEG II experiment was estimated based on the measured detector performance and the improvement of the analysis. The pileup elimination for theliquid xenon γ-ray detector was found to improve the sensitivity by 22–26%. A further improvement of 8% was achieved by reducing the γ-ray backgrounds with the RDC. With the updated
performance and the algorithm, it was demonstrated that the sensitivity of 5.6–5.8 × 10−14 isachievable with three years of data-taking.

ii

Contents

Abstracti

Preface1
Search for µ → eγ

2

1.1

Physics motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2

1.2

Principle of µ → eγ search . . . . . . . . . . . . . . . . . . . . . . . . . . .

13

1.3

MEG experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

23

1.4

MEG II experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24

MEG II Experiment

26

2.1

Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

26

2.2

Pilot runs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

64

2.3

Detector simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

66

2.4

Statistical method for µ → e γ search . . . . . . . . . . . . . . . . . . .

71

2.5

Subject of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

76

Performance Evaluation of LXe Detector

79

3.1

Calibration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

79

3.2

Alignment of MPPCs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

90

3.3

Waveform analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

93

3.4

Position resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

95

3.5

Timing resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

98

3.6

Energy resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

Chapter 1

Chapter 2

Chapter 3

Chapter 4++

Performance Evaluation of Radiative Decay Counter

112

4.1

Calibration

4.2

Detector performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

Chapter 5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

γ-ray Background Reduction by Pileup Elimination

125

5.1

Sources of pileup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

5.2

Elimination algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

5.3

Performance evaluation with MC . . . . . . . . . . . . . . . . . . . . . . . 144

Contents
Chapter 6iii
γ-ray Background Reduction with RDC

159

6.1

Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

6.2

Procedure to make PDFs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162

6.3

Statistical limitation and its solution . . . . . . . . . . . . . . . . . . . . . 164

6.4

Uncertainty from PDF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

Chapter 7

MEG II Projected Sensitivity

171

7.1

Eﬀect of γ-ray pileup elimination . . . . . . . . . . . . . . . . . . . . . . . 171

7.2

Eﬀect of RDC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

7.3

MEG II projected sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . 174

Chapter 8

Conclusions

176

Appendix A

Lab Test for Downstream RDC

178

A.1

Timing counter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178

A.2

Calorimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

Appendix B

Resistive Plate Chamber

181

Appendix C

Study on Radiation Damage to VUV-MPPC

183

C.1

Radiation damage to SiPM . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

C.2

VUV photon irradiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184

C.3

Gamma irradiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189

C.4

Neutron irradiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191

1

Preface
Particle physics is a branch of physics that studies the elementary particles, which constitutethe Universe, and the law rules them. It aims to find an ultimate theory that can explain
everything in the Universe. The standard model is the most successful theory of today’s particle
physics though it is known that there are some phenomena the standard model cannot explainsuch as the origin of the dark matter. Therefore, new physics beyond the standard model isdesired and physicists in the field have searched for it.
In the past, the conservation of the lepton flavor was believed because no process that violates
the lepton flavor had been observed. In 1998, however, the violation of lepton flavor was discovered in the neutral lepton sector, which is called neutrino oscillation. This raised a doubt withrespect to the flavor conservation of the charged lepton sector. Many models of new physics
predict the charged lepton flavor violation can happen at experimentally reachable branchingratio. Therefore, various experiments have tried to find the violation.
The most stringent upper limit on the branching ratio of the µ → eγ decay, which is one of
the charged lepton flavor violating decays, is 4.2 × 10−13 (90% confidence level), which was givenby the MEG experiment [1]. The MEG II experiment is an upgraded experiment of the MEG
experiment and aims to search for the decay with a higher sensitivity by one order of magnitude.
To realize the target sensitivity, a suppression of the accidental backgrounds is essential since
the sensitivity of MEG was limited by the number of the accidental backgrounds.
This thesis focuses on a suppression of γ-ray backgrounds in the MEG II experiment from thetwo aspects: improvement of the pileup elimination for a γ-ray detector and development of amethod to tag the γ-ray backgrounds actively. Firstly, the physics motivation and the principleof the µ → eγ search are discussed in Chap. 1. Then, the MEG II experiment is explained in
Chap. 2. The analysis and the performance of the γ-ray detector are explained in Chap. 3
followed by those of the detector for tagging the γ-ray backgrounds in Chap. 4. The pileup
elimination algorithm and its performance for the γ-ray detector are described in Chap. 5.
Chap. 6 explains the study on how to integrate information from the background detector in
the physics analysis. Finally, the expected sensitivity of the MEG II experiment is discussed in
Chap. 7, and the thesis is concluded in Chap. 8.

2Chapter 1

Search for µ → eγ
In this chapter, an overview of the µ → eγ search is described. First of all, the physics
motivation for the µ → eγ decay search is introduced followed by the descriptions of the principle
and requirements for the search. Then, the MEG experiment is descried briefly as a preceding
work and upgrade concepts to the MEG II experiment are explained.

1.1 Physics motivation
1.1.1 The standard model
The standard model (SM) is the most successful theory in the particle physics, which describes
17 elementary particles and their interactions as summarized in Table 1.1. It is based on thegauge symmetry of SU (3)C × SU (2)L × U (1)Y , which gives three interactions of particles: thestrong, weak, and electromagnetic interactions.
Table 1.1 Particles in the SM.

Generation

QuarksFermions
Leptons

I

II

III

u

c

t

d

s

b

e

µ

τ

νe

νµ

ντ

g
Bossons

Gauge Bossonsγ
ZW

Scalar BosonH

The interactions are propagated via gauge bosons. Gluons take a charge of the strong interaction. W and Z bosons correspond to the weak interactions. The electromagnetic interaction
is propagated via photons. In addition to these bosons, there is a scaler boson called the Higgs
boson, which provides the mass of particles via the Higgs mechanism.
Fermions are the particles that constitute matter. They are divided into two groups depending
on how to interact with the gauge bosons: quarks and leptons. Quarks can interact via all thethree interactions while leptons can only interact via the weak and electromagnetic interactions.
The fermions have three generations which are distinguished with their masses and flavors.

Chapter 1 Search for µ → eγ
A variety of experimental results has proved the SM succeeds at a relatively low energy region
up to 100 GeV. Despite its success, the SM is not considered as the ultimate theory that can
explain everything but as an approximation of a more fundamental theory at the low-energy
scale due to the existence of several mysteries.
In the first place, the SM involves some theoretical problems. The three generations of thefermions are not explained; they are not theoretically required. We also have a lack of understanding for particle masses and mixing patterns, which results in the large number of underlying
parameters in the SM. In addition, all of the three interactions described in the SM are not unified
while the electromagnetic and the weak interactions have been unified into a single electroweak
framework. Moreover, the gravitational interaction is not even mentioned in the SM. Furthermore, there is the hierarchy problem, which is related to the huge diﬀerence of energy scales
between the weak scale of O(100 GeV) and Planck scale of O(1019 GeV), where quantum eﬀects
are dominant. At the high energy scale close to the Planck scale, the quadratic divergence inthe radiative corrections to the Higgs scalar mass becomes problematic, which requires a precise
fine-tuning between the bare mass and the radiative corrections to keep the electroweak scale.
There are also some experimental results that cannot be explained by the SM. The discoveryof the neutrino oscillation questioned the assumption that the neutrinos are massless. The
observation of the dark matter also contradicts the SM.
To compensate the incompleteness of the SM, a variety of physics beyond the SM (BSM) has
been proposed, and is under verification by various experiments.

1.1.2 Charged lepton flavor violation
Charged lepton flavor violation (cLFV) processes are good probes to search for BSM. In theSM, the flavor mixing is forbidden in the lepton sector while it is allowed in the quark sector via
the CKM matrix. However, the observation of the neutrino oscillation, which is the lepton flavor
violation in the neutral lepton sector, suggests the lepton flavor is also not conserved, and thus
the violation in the charged flavor sector is supposed to happen as well though such processes
have not been observed yet. Therefore, many experiments have searched for them.
Muon is a fermion in the second generation of charged leptons, which was discovered in 1937.
The search for the cLFV processes in muon decay channels started in 1947, and they have been
actively studied by many experiments improving their sensitivities. Fig. 1.1 shows the upper
limits of the branching ratios for cLFV processes from muon decay. As shown in this plot,
the three channels are often searched for in the field of cLFV search: µ → eγ, µN → eN andµ → eee. The branching ratios of these channels depend on the model of new physics. Therefore,
we can give constraints on the candidates by measuring the branching ratios of these channels.

1.1.3 µ → eγ decay in the SM
The µ → eγ decay is one of the cLFV muon decay channels. This decay is strictly prohibitedin the SM, but it can have a non-zero branching ratio taking the neutrino oscillation into account3

B(µ → e γ ) < 4.2 × 10

dom photon background.

at 90% confidence level (CL), based on the full data-set.
Currently, the upgrade of the experiment, known as the
Chapter 1 Search forMEGµ → IIeγexperiment, is in preparation aiming for a sensi-

90% C.L. Limit

History of CLFV experiments with muons
1µ → eγ10 −1µN → eN

10 −2µ → 3e

10 −3
10 −4
10 −5
10 −6
10 −7
10 −8
10 −9
10− 10
10− 1110− 1210− 1310− 14
1940 1950 1960 1970 1980 1990 2000 2010 2020
Year

Fig. 1 Figure
Chronology
upper limits
processes
1.1 of History
of on
thecLFVcLFVsearch [2].

The MEG experiment uses one of thcontinuous surface muon beams, withreasons expla
than 108 µ+ /s but, for 4
the stopping intensity is limited to 3 ×are stopped in a thin polyethylene targof the experimental set-up which inctrometer and a photon detector, as sh
Fig. 2.
The positron spectrometer consists
bers and scintillating timing countersconducting solenoid COBRA (COnswith a gradient magnetic field along t
from 1.27 T at the centre to 0.49 T at
antees a bending radius of positrons
the polar angle. The gradient field is alquickly spiralling positrons sweeping
trometer to reduce the track density iume.
The photon detector, located outs
a homogeneous volume of liquid xe
photomultiplier tubes (PMTs) subme
read the scintillating light from the L
measures the positron momentum ve
the LXe photon detector measures theas the position and time of its interacti
direction is measured connecting the i123

Figure 1.2 The µ → eγ process considering neutrino oscillation in the SM.

via the process shown in Fig. 1.2. Its branching ratio is calculated as follows [3]:B(µ → eγ) =3α ∑ ∗∆m2i1
Uµi Uei∼ 10−54 ,2
32π i=2,3MW

where α is the fine-structure constant and U is the PMNS matrix. Since the mass diﬀerenceof the neutrinos ∆m is small compared to the mass of W boson MW , the branching ratio issuppressed enough not to be observed experimentally in the near future.

1.1.4 µ → eγ decay in BSM models
In contrast to the SM, many BSM models predict the branching ratio of the µ → eγ decay islarge enough to be observed experimentally.

Chapter 1 Search for µ → eγ
A model-independent Lagrangian for the µ → eγ decay can be expressed as
GF
Lµ→eγ = − √ [mµ AR µ̄R σ µν eL Fµν + mµ AL µ̄L σ µν eR Fµν + (h.c.)],2where GF is Fermi coupling constant, and AR and AL are coupling constants corresponding toµ → eR γ and µ → eL γ process, respectively. This Lagrangian results in the diﬀerential angular
distribution given bydB(µ → eγ)= 192π 2 [|AR |2 (1 − Pµ cos θe ) + |AL |2 (1 + Pµ cos θe )],d cos θewhere θe is the angle between the muon polarization and the positron momentum in the muon
rest frame, and Pµ is the magnitude of the muon polarization. The coupling constants, AR
and AL , are found to give the dependence on the muon polarization from the equation. Since
they depend on the model, it is possible to restrict models by measuring the distribution of thepositron emission angle as well as by measuring the magnitude of the decay without relying on
the angle distribution.
The Supersymmetry (SUSY) model is one of the promising candidates for BSM [4]. In thismodel, the symmetry under the super-transformation between bosons and fermions is introduced. This symmetry requires a partner for each SM particle, and the divergence in theradiative corrections of the Higgs mass is cancelled out thanks to these SUSY particles, which
gives a natural solution for the hierarchy problem. In addition, the lightest SUSY particle canbe a candidate for the dark matter since it is electrically neutral and weakly interacts with thematter.
In the SUSY scenario, a particle and its super-partner should be degenerated and have thesame mass if the symmetry is exactly fulfilled. However, no SUSY particle with the same mass
has ever been observed, which indicates the symmetry should be broken. In this case, the massesof the SUSY particles are given by a term which breaks the super-symmetry so that the particle
pairs are disentangled. The LFV would be originated from the misalignment between particle
and super-particle mass eigenstate, and can be induced by the presence of nonzero oﬀ-diagonal
matrix elements in the mass matrix of slepton, which is super-partner of lepton, in the basis
where the lepton mass matrix is diagonalized. However, some experimental observations suggest
there are some mechanisms which suppress the matrix to be almost diagonal.
One of the possible mechanisms to explain the suppression is super gravity model (SUGRA).
In this model, all sfermions have the same mass and the mass matrix is diagonal, which restricts
the LFV completely at the Planck scale. This does not, however, necessarily imply that the
LFV should not exist in this model. In fact, if there is an interaction which breaks lepton
flavor conservation between the Plank and the electroweak scales, the LFV could be induced in
the slepton mass matrices through radiative corrections. Hereafter, two kinds of sources which
generate such eﬀects are introduced.

5

Chapter 1 Search for µ → eγ

6

SUSY seesaw
The seesaw mechanism provides a natural explanation of the tiny neutrino mass comparedto other fermions by introducing the Majorana mass term of right-handed neutrinos. In thistheory, left and right-handed neutrino masses are given by MD2 /MR and MR , where MD is the
Dirac mass and MR is the Majorana mass of the right-handed neutrino. This formula suggests
the left-handed neutrino mass is tiny when the right-handed neutrino mass is huge.
The SUSY seesaw model introduces the seesaw mechanism to the SUSY model. When the
Majorana neutrinos are included, a new Yukawa coupling matrix for the neutrinos yν is additionally included in the lepton sector. Since there are both of Yukawa coupling matrices forthe neutrino sector and for the charged lepton sector, the lepton flavor would no longer be conserved separately for each generation, which enhances the LFV decay. The Yukawa coupling
for the neutrinos couples the right-handed neutrino multiplets with the left-handed lepton doublets. This leads to the oﬀ-diagonal term proportional to (yν )∗ki (yν )kj in the mass matrix of theleft-handed slepton through radiative corrections as(m2l̃L )ij ≃ −1MP(yν )∗ki (yν )kj m02 (3 + |A0 |2 ) ln
,
2
8π
MR

(1.1)

where m0 is the universal scaler mass, A0 is the trilinear coupling, and MP is the reduced
Planck mass [5]. This mechanism is not eﬃcient to generate oﬀ-diagonal terms in the righthanded slepton mass matrix, and thus only the left-handed slepton contributes to the LFV.
If we assume that the neutrino mixing mostly originates from the neutrino Yukawa coupling
constants, the branching ratios of µ → eγ and τ → µγ decays can be evaluated by using theneutrino mixing parameters. Fig. 1.3 shows the correlation between those branching ratios inan example of this model. The neutrino mixing angle θ13 ∼ 9◦ [6] suggests a higher branchingratio for the µ → eγ decay.
SUSY GUTThe SU (5) SUSY GUT is the model in which the gauge groups of SU (3)C , SU (2)L and U (1)Yare unified into a single SU (5) group at the grand unification energy scale thanks to the SUSY
particles. The Yukawa coupling constant corresponding to the top-quark mass is large enoughto give the sizable soft SUSY-breaking mass terms. Since the right-handed sleptons are hosted
in the 10 representation as well as the top quark, the oﬀ-diagonal elements for them arise as(m2ẽR )ij ≃ −MP3(VR )i3 (VR )∗j3 |yu33 |2 m20 (3 + |A0 |2 ) ln
,
8π 2
MG

(1.2)

where VR is the mixing matrix of the right-handed slepton, yu is the Yukawa coupling constantfor up-type quarks, and MG represents the GUT energy scale. Fig. 1.4 shows the processes
induced by this oﬀ-diagonal elements. A higher branching ratio is expected with larger tan β,
where β = ⟨h2 ⟩ / ⟨h1 ⟩ is the ratio of the expectation values of two Higgs fields: h1 for down-type
quarks and leptons, and h2 for up-type quarks as shown in Fig. 1.5.
The SO(10) GUT models typically relate the up-quark Yukawa couplings with the Diracneutrino Yukawa couplings, and provide a natural setting for the seesaw mechanism with 16-

Chapter LEPTON
1 SearchFLAVOR
for µ →VIOLATIONeγ
IN THE SUPERSYMMETRIC …

7
PHYSICAL REVIEW
D 91

FigureCorrelation
the branchingµ→
and→τ μγÞ→ µγ
decaysin the case with ON ¼ 1. The S
FIG.1.3
3 (color
online). between(a) Correlation
betweenratios
Bðμ →ofeγÞ
andeγBðτin thedegenerate
MSSM
SUSY extension
thewestandard
withμ seesaw
mechanismðM 1=2(the; M 0minimum; A0 Þ are randomly
generated,ofandtake tan model)
β ¼ 30 and> 0. The
upper-right[7].
group of dots along each li
14 GeV, and the lower-left one corresponds to M
12 GeV. The results of NH and IH
~
~
M
¼
5
×
10
¼
7
×
10
The SUSY
parameters of tan β = 30 and µ > 0 are taken, whereN
N β is the ratio of the2 θ ¼ 0 are shown as indicated. The vertical and horizontal solid lines show the present
0.022–0.026
and ofwith
13 fields and µ is the higgsino mass parameter. The results
expectation
valuestwosinHiggs
Bðμ → eγÞ and Bðτ → μγÞ, respectively. The dotted lines indicate2expected sensitivities at SuperKEKB/Belle II andof the normal and inverted hierarchies (NH and IH) within sin
θ = 0.022–0.026 andratio 2Rτ=μ ¼ Bðτ → μγÞ=Bðμ → eγÞ for IH as a function of sin2 θ13 .13The gray region is the present experimental v
with sin θ13 = 0 are shown as indicated. The vertical and horizontal solid lines show the
branchingupperboundseach decay,
and the dotted
expected sensitivities
we discuss the correlation betw
muon gratio− 2 istoo small
toofexplain
the deviation
within ones
the are particular,at SuperKEKB/BelleII andother constraints. In
fact,MEG
in theII.allowed regions in Figs. 1
and Bðτ → μγÞ.

and 2, the contribution is suppressed. However, boththeoretical and experimental uncertainties are still signifi1. Degenerate casecant, and therefore the deviation is not conclusive. Thus, in
In Ref. [25], it has been found that
this study, we do not use the muon g − 2 as a constraint.2Bðτ→ eγÞ can be suppressed while keepin
The μ-e conversions in nuclei are also important procμγÞ
in the simplest degenerate case w
esses to search for evidence of the LFV. In the type-I
Eq. (24), if θ13 is chosen to be zero and n
SUSY seesaw model where the photon dipole operator3
are inversely hierarchical. This is because
gives dominant contributions, the rate of μ-e conversion−
elements of Y †N Y N are approximately writand μ → eγ is estimated, for example, as Bðμ Al →e− AlÞ=Bðμ → eγÞ ≃ 0.0026 [53]. Thus, we can easily
~N
Δm221
M
†
translate the constraint and prediction for μ → eγ into
ðY
Y
Þ
∝
·
;
N N 12;13
Figure 1.4 µ → eγ in the SU (5) SUSY GUT [9]v2 mν1 þ mν2
those for μ-e conversion.
Taking into account the present
upper bound on the μ-e conversion [54], the constraint from
~N
Δm232
M
†
Y
Þ
∝
·
ðY
the μ → eγ experiment is more important.
N N 23v2 mν2 þ mν3
dimensional representation. In the case of the SO(10) SUSY GUT, both left- and right-handed
2)ij , cancontribute to the LFV. Fig.for
sleptons, i.e. (m2ẽL )ij and (mB.
1.6θ shows
branchingsignalsẽR LFV¼ 0 thein thePMNS matrix. Thus,

13

ratio of the Weµ →investigate
eγ decay as
a functionof unified
mass
M1/2 andallowedparameterBðτ the→ eγÞ
are strongly
suppressed for thesignalsof LFVfor the gaugino
degeneratecasechical case.
Taking into account recent experimentneutrino experiments, we show the corre
2
There are several models where the deviation is explained in
Other models
Bðμ → eγÞ and Bðτ → μγÞ in the simplest
the SUSY model beyond the context of the minimal supergravity
2
withinθ13 ¼ 0.022–0.026
by splitting
themajor
mass spectrum
colored SUSY
particlesthat
In addition
to themodels ofmentioned
above,
manyandtheories
predict sin
observablerates of in Fig. 3(a).
2theresultwithsin
θ13 ¼ 0 for comparisonof sleptons, see e.g., Ref. [52].
the µ → eγ3Noticedecay withinreachofoflarge
MEG
extra-dimensions[11] [12] [13], left-rightthat in thethe casetanIIβ suchand assmallmass ofαν ¼ βν ¼ 0 for both the NH and IH ca
the[14]CP-oddHiggs
boson,
the Higgs[15] [16][17],and little
Higgsmediated[18] [19]loop[20] contribu[21].
symmetry
SUSY inputs, we randomly vary them wit
4

space [8].and the nondegenerate case in the neutrino sector. In

tions become significant and thus must be taken into account, seee.g., Ref. [53]. In the allowed regions in Figs. 1 and 2, such
0 < M0 < 8 TeV;
0 < M1=2 < 2 Tecontributions are small.
Summary4
The Higgs boson decay into a lepton-flavor-violating final−2 < A0 < 2;state suchtheas searchh → τμ foris alsoof eγ
theprocessinteresting
In conclusion,theoneµ→is aprocesses.
powerfulAprobe for BSM.
Pushing down
recent experimental study is given−14
in Ref. [55]. In the type-I
takingmany
the others
aswhichμ > 0, tan β ¼ 30. T
the sensitivityµ → model,eγ searchto O(10 ratio) levelis meaningful
to validate
theories
SUSY ofseesaw
its branchingis enhanced
compared
group
of
dots
along
each
line correspondswith one in the non-SUSY seesaw model, but it does not exceed
14−14~
mass MN ¼ 5 × 10 GeV, and thein the degenerate case [56].
∼10033007-9

20

10

22

10

Chapter 1 Search for µ → eγ

0200SU(5) A0 = 0 µ > 0

10

600

8

µ→eγ

µ→eγ
10

400
me~R

SU(5) A0 = 0 µ < 0

10

10

(a)

(b)

M2=150 tanβ=3
M2=150 tanβ=10M2=300 tanβ=3
M2=300 tanβ=101210M2=150 tanβ=3
M2=150 tanβ=10M2=300 tanβ=3
M2=300 tanβ=10

12

10

14

10

14

B(µ→eγ)B(µ→eγ)

10

16

10

16

10

18

18

10

20

10

10

20

10

22

10

22

10

0

200

400

600

0

m~eR

200

400

600

m~eR

µ→eγ

10

10

FIG. 10. Predicted branching ratios for the(b)µ+ → e+ γ decay in the SU (5) SUSY GUT baseon the minimal supergravity model as a function of the right-handed slepton mass for four differen(b)tanβ=3Figure1.5 Branching ratio
the
µ
→ eγ
decay
for (a)ofpositive
and(2)(b)negative
setsofMMof=150
the
SUSY
input
parameters
M2 (the SU
gauginomass)signand tan β (the ratio of the tw=150 tanβ=10
M =300 tanβ=3
Higgs
vacuumexpectation
values).
For
the
other
parameters,thetrilinearscalar coupling constanof the higgsino mass parameterµtanβasM =300=10 a function of right-handed selepton mass for four
A
=
0
and
m
=
175
GeV.
The
following
CKM
matrixelements
areused:|(VCKM )cb | = 0.04 ant of the SU (2) gaugino mass M and tan β in thediﬀerent sets of SUSY input0 parameters
2|(VCKM )td | = 0.01. (a) and (b) correspond to a positive and negative sign of the higgsino mas
SU (5) SUSY GUT [9]. The trilinear scalar coupling constant and the top-quark mass areparameter µ, respectively.
(a)A0 = 0 µ < 0
SU(5)

2
2

12

10

14

B(µ→eγ)1022

fixed to be A0 = 0 and mt = 175 GeV, respectively.

16

10

18

10

88

20

10

22

10

0

200

400

600

m~eR

(minimalfixed
β =tan
10 andUe3and(left)
the allowed
parametersin SUperGRAvity)
the ranges givenparametersin eq. (3.1)forand
fortanfixed= 10
Ue3and= 0.11(the lowest value
red and to PMNS
space
plane which
satisfy theThe
MEG
resultin 2012(right)[8]. The
allowedat in3 thebyMrecentobservation).
red(blue)
coloredpointscorrespond
0 –M1/2RENO
bluecase.
pointsDi↵erent
correspondto the maximal-mixing
scenario(PMNS)
the minimal-mixing(CKM)
horizontal
lines correspondto present
andandfuturebounds on BR(µ ! e ).
case,respectively.
The
region
below
the
red
line
is
excludedby the
LHCsatisfy the
The scenario
figure in(CKM)
the right
panel
shows
the
allowed
space
in
the
m
m
which
0
1/2 plane88
searches2012 [10].
current
MEGinbound.
The region below the red line is excluded by the current LHC searches [9].
Both the plots satisfy all the constraints in eq. (3.2).

predict the branching ratio of the decay at that level.

In figures 1 and 2 we present the constraints from BR(µ ! e ) on mSUGRA andNUHM1 parameter space for tan = 10 and 40 respectively. As can be seen, while only
1.1.5
Relation with other experimental searches
small part of the paramater space survives for tan = 10 in mSUGRA, it is completely
As discussed
the previous
section,the µregions→ eγ decay
is oneinteresting
channelsspectra,toruled
out for intan= 40. The
allowedfor low
tanof therequirevery heavyi.e. mfor
4 TeV
for smallM1/2 orotherM1/2& 2decay
TeV forsmallwhich
m0 . Whatis surprising
searchBSM.
Thereare, however,muonchannels
are sensitive
to BSM isasthat
0 &theasconstraint
on the inNUHM1
space is ofnotenergy
as weakas onemight expectwellτ decay channels
addition parameterto another approach
frontier
experiments.
In thisformeq. (2.6). As we can see from the figures even in the presence of partial cancellations,most of the NUHM1 parameter space is going to be explored by MEG. If one removes thelight Higgs mass constraint, points with stronger cancellations would be allowed, even withµ ! e rates below the MEG sensitivity. Thus points compatible with the Higgs mass
bound, eq. (3.2), do not allow strong cancellations in the flavor violating entry in eq. (2.6).

JHEP11(2012)040

FIG. 10. Predicted branching ratios for the µ+ → e+ γ decay in the SU (5) SUSY GUT based
the minimal supergravity model as a function of the right-handed slepton mass for four different
ts of the SUSY input parameters of M2 (the SU (2) gaugino mass) and tan β (the ratio of the two
ggs vacuum expectation values). For the other parameters, the trilinear scalar coupling constant0 = 0 and mt = 175 GeV. The following CKM matrix elements are used: |(VCKM )cb | = 0.04 and
VCKM )td | = 0.01. (a)andFigure(b)3.
correspondto ainpositiveandnegative
signeγtheof decaythe
higgsino
1.6 figure
Branchingratio
ofpanelthe µ→obtainedscanning
mSUGRA
Figure
The
the
left
shows
BR(µ
! emass) byobtainedby thescanning
the mSUGRA
arameter µ, respectively.

Chapter 1 Search for µ → eγ

9section, these experimental searches are described with their relations to the µ → eγ search.
1.1.5.1

cLFV search with other µ processes

Other cLFV channels of muon, which are complementary to µ → eγ decay, such as µN → eN ,µ → eee, also have been searched for actively.
The eﬀective Lagrangian*1 for the cLFV processes via muon can be written asL=mµκ
µ̄R σµν eL F µν +µ̄L γµ eL (f¯L γ µ fL ),2(κ + 1)Λ
(κ + 1)Λ2(1.3)

where f is the fermionic fields [22]. The coeﬃcients of the two types of operators are parametrizedby two constants: the mass dimension-one Λ parameter, which represents the eﬀective mass scaleof the new degree of freedom, and the dimensionless parameter κ, which governs the relative
size of the operators. The first term is the magnetic moment-type operator, which directly
mediates µ → eγ, µ → eee and µN → eN conversion in nuclei at order α. The second term also
mediates µN → eN at leading order and µ → eee at tree level in the cases that the fermion
is quark and electron, respectively, and µ → eγ is available at the one-loop level for the bothcases. For κ ≪ 1, the former dipole-type operator dominates cLFV phenomena while the latter
four-fermion operators are dominant for κ ≫ 1. Fig. 1.7 shows the sensitivity to Λ as a functionof κ for the processes, which illustrates the sensitivities of them depend on the magnitude of κ.
Although the coeﬃcients of the two operators depend on the model, many models including
the SUSY-seesaw/GUT models mentioned above predict the former operator is dominant. In
such a case, the branching ratios of the three muon processes have the following relations [9] [23]:B(µ → eee)
≈ 6 × 10−3 ,B(µ+ → e+ γ)
B(µ− N → e− N )≈ 2.6 × 10−3 (for N = Al).
B(µ+ → e+ γ)This means a search for µ+ → e+ γ decay with a sensitivity of ∼ 6 × 10−14 is competitive toother experiments planned in the coming years, which are introduced below.
On the other hand, searches for diﬀerent processes are important to restrict possible physics
models. In the case of a positive signal, the amount of information from one experiment islimited; a positive signal in a µN → eN conversion experiment cannot measure either Λ or κ
but only a function of the two, for example. Therefore, a combination with information fromother observables including those involving τ decays, studies of the electromagnetic properties ofcharged leptons, e.g. g−2, precision studies of neutrino processes, and searches for new physics
at the energy frontier, is necessary.
µ− N → e− N conversion
In the µN → eN conversion experiments, a negative muon is stopped in a thin target to forma muonic atom. In the SM, the muon decays in orbit as µ− → e− ν̄e νµ or is captured by a
*1 The most general eﬀective Lagrangian includes several other terms [9], but the subsets are suﬃcient forthe discussion here following the original notation in [22].

Chapter 1 Search for µ → eγ

10nucleus of the atom as µ− + N (A, Z) → νµ + N (A, Z − 1), where N (A, Z) represents a nucleusof the atom whose mass number is A and atomic number is Z. The µ− N → e− N conversion isa conversion process from a muon to an electron expressed asµ− + N (A, Z) → e− + N (A, Z).
The signal is characterized by a single electron with a monochromatic energy around 105 MeV,
which slightly depends on the target nucleus due to the diﬀerence of the binding energy ofmuon. The major backgrounds for the observation are the muon decay-in-orbit and the beam
contamination such as pions. Therefore, use of a pulsed muon beam can reduce the backgrounds
by searching for the conversion electrons in the bunch intervals since muonic atoms have lifetimes
ranging from hundreds of nanoseconds up to the free muon lifetime at low Z.
The current experimental upper limit of 7 × 10−13 (90% C.L.) was given by the SINDRUM II
experiment at PSI [24]. Further search for the µ− N → e− N conversion is planned by several
collaborations such as Mu2e and COMET. The Mu2e experiment in Fermilab will finish construction in 2023 followed by the physics data-taking for three years to reach the sensitivity of
8 × 10−17 (90% C.L.) [25] [26]. The construction of the COMET experiment at J-PARC is alsoin progress. It aims at the sensitivity below 7 × 10−15 (90% C.L.) with 150 day data-taking
at phase I in 2023 followed by one year data-taking to reach 6 × 10−17 (90% C.L.) at phase II,
which is expected to start in 2026–2027 [27].
µ → eee decay
The µ → eee decay is another LFV decay process. For κ ≪ 1, the µ → eγ search has anadvantage while it is opposite for κ ≫ 1.
The signal is characterized by three coincident electrons from the same muon. The backgroundin the search is an accidental background which consists of electrons from diﬀerent muon decays
and radiative decays with internal conversion with a small energy fraction carried away by
the neutrinos. Therefore, the good momentum, vertex and timing resolutions are required inaddition to a high rate capability to cope with the high intensity muon beam.
An experimental search for the µ → eee decay is planned by Mu3e collaboration at PSI [28].
It is expected to start the physics data-taking for 300 days aiming at a single event sensitivityof 2 × 10−15 at the phase I [29], and 7 × 10−17 at the phase II with 260 day data-taking.
Muon anomalous magnetic moment
The magnetic moment by muon spin is written by
Mµ =

g·e
s,
2mµ

where s is spin angular momentum and g is a factor to connect magnitudes of magnetic momentand spin. The factor g is exactly 2 when only tree-level process is considered, but it deviatesfrom 2 with higher order processes. Some experimental results deviate from the SM prediction
at the 3σ level.

NS60CH20-DeGouvea

ARI

21 September 2010

19:26

Chapter 1 Search for µ → eγ

11

a

4,000

b
B( µ → eee) > 10 –16

3,000
B( µ → eγ) > 10 –13

B( µ → e conversion in 48 Ti) > 10 –18

Annu. Rev. Nucl. Part. Sci. 2010.60:513-538. Downloaded from www.annualreviews.org
Access provided by 77.56.81.90 on 11/10/21. For personal use only.

10 4

B( µ → eγ) > 10 –14

B( µ → eγ) > 10 –13

B( µ → eee) > 10 –15

B( µ → eee) > 10 –14

B( µ → e conversion in 48 Ti) > 10 –16

Λ (TeV)Λ (TeV)

2,000

1,000
900
800
700
600
500
400

10 3

Excluded300

Excluded
10 –2

10 –1

10 0

κ

10 1

10 2

10 –2

10 –1

10 0

κ

10 1

10 2

Sensitivity of (a) a µN → eN conversion in 48 Ti experiment and (b) a(a)Sensitivityof a µ → ewith
conversion
in 48
experiment
thattocan
probe
capture10−16µ→
eee experimentthat ofa Tiµ→
eγ searchthenewnormalized
physics scaleΛ rates
as aoffunction
−18
−13
−14
and
of κ10[22]., and a µ → eγ search that is sensitive to branching ratios of 10 and 10 , to the new physics
Figure6 1.7
Figurescale " as a function of κ (Equation 7). (b) Sensitivity of a µ → eee experiment that is sensitive to branchingratios 10−14 , 10−15 , and 10−16 , and a µ → eγ search that is sensitive to a branching ratio of 10−13 , to thenew physics scale " as a function of κ (Equation 8). Also depicted are the currently excluded regions of both
spaces.
Theparameter
deviation
can be explained by introducing a contribution of new particles. The eﬀective

Lagrangian of the new physics contributions is given by [22]long as it is a couple of orders of magnitude more sensitive. Because it is, experimentally, very hardto achieve sensitivity to branching ratios formµµ → eγ smaller
than 10−14 (42), µ → e conversion
Lg−2 ⊃ 2 µ̄R σµν µL F µν .
searches—which are not expected to hit anyΛ“wall” before normalized rates of (at least) approximately 10−18 (42)—seem to be the most effective way of pursuing CLFV after the ongoing MEG
Even thoughthisis Lagrangianis flavor
conserving,
it is(41).
similar to Eq. (1.3) in the limit of κ ≪ 1.
experiment
done at the Paul
Scherrer
Institute (PSI)
In a SUSYin [30], the forbranchingratioµ→
eγ andthe captured
discrepancy
Wemodelcan askdiscussed
what the consequences
CLFV areif theofnew
physics
is bestby theof g iseffective Lagrangian:relatedfollowingasmµµ̄ σ e L F µν
LCLFV =
2 Rδaµν
µ
−4
(κ
+
1)"
B(µ → eγ) ≈ 10 ()2 |δ 12 |2 ,
κ 200 × 10−11 µ LL
µ̄ L γµ e L (ēγ e).
+8.
(1 + κ)"2

where δaµ is the diﬀerence between the theoretical value and the experimental observation of

Similar to the dimension-six operators in the second line of Equation 7, the dimension-six operator
in the second line of Equation 8 mediates µ → eee at tree level and µ → eγ at one-loop
whichlevel.
clarifies
thetocomplementarityof the two observations.
SimilarEquation 7, the dimensionlessparameter κ determines whether the dipole-likeor oftheE989four-fermion
interaction
is dominantin
when
it comes
CLFV. a greater value by
Theinteraction
first resultat Fermilab
was published
2021,
whichtoreports
The sensitivity to " as a function of κ for µ → eγ and µ → eee efforts is depicted in
BNL E821 [32], the new
3.3σ than the SM prediction [31]. Combining this to the result of −15
will probe " values
Figure 6b. Here, for κ # 1, an experiment sensitive to Br(µ → eee) > 10
experimental
averagebecame4.2σ.
of up to 1,800 TeV. As in the example depicted in Figure 6a, a µ → eee experiment is guaranteed
12aµ = (g −2)/2, and |δLL
| is a factor coming from cLFV coupling. Fig. 1.8 illustrates the relation,

1.1.5.2

cLFV search with τ decaywww.annualreviews.org • Fermilab’s Intensity Frontier525

The cLFV τ decay channels such as τ → ℓγ and τ → ℓℓℓ (ℓ = e or µ) have been searched for
as well. Many BSM models predict high branching ratios enough to be detected experimentallyChapter 1 Search for µ → eγ
FLAVOR PHYSICS AT LARGE TAN % WITH A . . .

PSfrag replacementsµ → e γ vs. τ → µ γ at tan β = 40

PMNS Ue3 = 0

MEG

10

BR(τ → µ γ) · 107

1
0.1
0.01

17
µ → e γ vs. τ → µ γ at tan β = 10100

µ → e γ vs. τ → µ γ at tan β = 10

µ → e γ vs. τ → µ γ at tan β = 40

cluding the see–saw mechanism. Moreover in the recent
years SO(10) SUSY models have spurred much interest as in this framework it is possible to build realistic
fermion mass model and to account for the proton lifetime bounds. In this paper we have addressed the issue
by a generic benchmark analysis, within the ansatz that
there is no fine–tuning in the neutrino Yukawa sector.

12

PHYSICAL REVIEW

Now

CKM
PMNS Ue3 = 0.07
PMNS Ue3 = 0

Now
SuperB
SuperF

0.001

e3
e3

BR(τ → µ γ) · 107

PSfrag replacements

PMNS Ue3 = 0µ → e γ vs. τ → µ γ at tan β = 10

BR(τ → µ γ) · 107e3e3

BR(τ → µ γ) · 107e3e3

PSfrag replacements

PMNS Ue3 = 0

PSfrag replacements

PMNS Ue3 = 0

12FIG.
6 (color
Expectations
B""of!µ e!$
anddecayB"( !
vs !a" of! muon"g" # gSM
From ouranalysis
weRelationcanstateonline).
that lepton
flavourvi- forFigure1.8
betweenthebranching
ratio
→ eγ
and"!$
deviation" $=2, assuming j'LL
#2
1e-05
−4the following ranges: 300 GeV * M ~ * 600 GeV, 200 GeV
olation experiments
be abletohavetell usbeen
much
about|δ 12employing
. The
plots
obtained
10should
anomalous
magnetic
momentassuming
obtained by scanning parameter ‘
LL | = 10
the structure of sucha SUSY–GUT
scenario.
If they
de500
GeV
*
"
*
1000
GeV,
10
*
tan%
*
50,
and setting AU ! #1 TeV, Mq~ ! 1:5 TeV. Moreover, the GU
1e-06
spaces[30].
tect LFV processes, by their rate and exploiting the inand Mexperiments,(red)
areas correspond to points within the funnel region which17
1e-07
3 ' 6M1 areweassumed.
terplay between different
would be The
able inner
1e-08
1e-06
1e-04
0.01
1
100
11 < 1:24, 0:8 < R
1:01→<
in Sec. III
B [B"Bs ! "% "# $ < 8 & 10#8 , BR(µBs!
B(& < 0:9, !MBs !
e γ)R
· 10
to get hints of theconstraints
structure oflisted
the unknown
neutrinos’µ → e γ vs. τ → µ γ at tan β = 40
er in the recent Yukawas. In this sense,µ → etheγ vs. capability
τ → µ γ at tan of
β =a10Super Flavour
1000
100
MEG
Now
Now mixing
CKM
ed much inter- factory to discriminate between MEG
CKM case
the minimal
PMNS U = 0.07
PMNS U = 0.07
PMNS U = 0
100
PMNS
U
=
0
build realistic and the U10e3 = 0 PMNS case is a most interesting feature.
the proton life1
Now
tween the ‘i ! ‘j ! transitions and !aGiven that both ‘i ! ‘j ! and !a" ! 10"g" # gSM" $=2 areessed the issue
SuperB1
Now
0.1
generated by dipole operators, it is natural to establish a
illustrated in Fig. 6. Since the loop fu
the ansatz that On thecontrary, in the case that both MEG andSuperB
SuperF
0.1
link
between
them.
To
this
purpose,werecallthedominant
processes are not identical, the correla
ukawa sector. a future0.01Super
Flavour factory happen not to see any
SuperF
contribution
to
!a
is
also
providedbythecharginoline; however, it is clear that the t
LFV process,only two possibilities should"be left: (i) a
0.01
0.001
the minimal mixing,
low
tan
β
scenario;(ii)
mSUGRA–
closely connected. We stress that th
exchange and can be written as
0.001
pton flavour vi- SO(10)1e-04see–saw without fine–tuned Yν couplings isshown in Fig. 6 have been obtained! the" stan2
us much about not a 1e-05
viable framework of physics beyond
g2c "M22 =M1e-04; "2 =M‘2~$
#
"M
~
2
2
mulas reported in Ref. [41] for the s‘2rio. If they de- dard model.
Moreover,
1e-05
tan%;
m"high sensitivity!aif"the! planned,
#
1e-06
2
2
2
ploiting the in- PRISM/PRIME conversion experiment,
4$ ablemtributions to both B"‘i ! ‘j !$ andto Ltest even "M2 # " $
1e-06
1e-07
would be able the minimal
1e-06
1e-04
0.01
1
100
10000
β region,
1e-08 mixing
1e-06low tan
1e-04
0.01 doesn’t1 manage
100toresultsin themass-insertion
approxim(17)
BR(µ → e γ) · 1011
BR(µ conclusion→ e γ) · 1011
own neutrinos’ find LFV evidences, the lattershould be the
(19)
have
been
shown
only
for the sµ →theree γ vs. shouldτ → µ γ atbetanno
β =room
40
Super Flavour most sensible
one andleft for theFIG.
14: ofComparison of µ → e γ and τ → µ γ as a probes of
1000
with
g
"x;
y$
defined
as
f
"x;
y$
in
terms
MEG
Now
c2
c2
CKM
(a)
(b)
dark-graymal mixing case no fine–tuning framework we studied in this paper.
AcSUSY–GUTs scenarios. The plotsinnerare doneby scanning(red)the areas are the
PMNS U = 0.07
PMNS U = 0
100
resting feature. tually one
fixed tan β. Thelines are are fulfilled. I
should remark that LFV experiments will be 2 LHC accessible parameter space atB-physics
constraints"3 # 4aa %2present
loga$
Correlation
between→%eγ→ µγbounds
forus(a)the τ
and(18)future sensitivities. Letnote that
10 Figureable to falsify
some1.9of theSUSYgGUT
scenarios µeven
in and: in SUSY-GUT(SO(10))
c2 "a$ !
constraints
3
theinterplay
between MEG and aB-physics
Super Flavour
factory will put a lower boun"a#1$
regions of1 tan
the
SUGRA
parameter
space
that
are
beyond
β
=
10
and
(b)
tan
β
=
40
[35].
The
plots
are
done
by
scanning
the
LHC
accessiNow
the funnel-region relatio
leave unscathed only the low tan βfore,
CKMthroughcase.
LHC experiments. In this sense, the power
oth MEG and the reach ofSuperB
space.
The inner among
(red)
areas
to points within the
funnel
0.1 ble parameterthenstraightforward
to deduce
the relation
Figs.
3 andregion4). As a result, the allowed
dif- correspond
not to see any of LFV experimentsItofistesting/discriminating
SuperFsatisfy
theresults
B-physics
GUTs
modelsvery constraints.
interesting andd be left: (i) a ferent SUSY
0.01 which$
B"‘RGENOTATION AND
EQUATIONS
3 # #!a APPENDIX:
i !‘j !$ are correspondingly low
B"‘! ‘j !$
tothei direct
searches at48$
the LHC.
" 2(ii) mSUGRA– highly complementary
0.001!
tary illustration of the interplay of Bν couplings is
B"‘i ! ‘j &‘i &" ‘j $G2F
m2"
1. The model
1e-04
dark-matter constraints, !a" , and LF
ond the stan−9−7aroundO(10)–O(10
)
[33].
The
τ
decay
channelsaretheoreticallyassociatedwith the µ
$
#
2
2
2
2
high sensitivity Acknowledgements
SKV
acknowledges
support1e-05
scenario—isshown in Fig. 7.9
f2c "M2 =M‘~The; " model=M‘~$consists
2
ij
2
in
a
supersymmetricSO(10)
frameble to test even fromIndo-French
Centrefor
PromotionofAdvanced
Re#4
&
j'
j
:
decay
in
scenarios
as shown inj'12
LL many
The normalizationu
1e-06 channels, and their branching ratios have
2 work2 correlations
2
2 following
LL j ! 10withthebreaking
pattern
1e-06
1e-04project 0.01
1
100
10000
"M
=M
;
"
=M
$
g
sn’t manage to search (CEFIPRA)
No: 2904-2 ‘Brane World
2c
~
~
2
‘
‘
11
BR(µ
→
e
γ)
·
10
corresponds
tothecentral
value
in
Eq.
should be the Phenomenology’.
Fig.
1.9. partially
In someparameter
haveMaGUhigher
sensitivity to
Fig. 1.3 and He
is also
supportedby IN-spaces, the τ channels
MXT
12
SO(10) −→SU(19)(5)RN −→RN
oom left for the TASFIG.
!
10GeV.(A.1)
This normalization
M&MSSM
grant,
CNRS
con- of
14: 03-51-6346,
Comparison ofµ → ePICS
γ and#τ 2530,→ µ γ RTN
as a probesRBSM.
his paper. Ac- tract
SUSY–GUTs
scenarios. The andplotsbyare
by scanning
MRTN-CT-2004-005104
a doneEuropean
Union the17 even pessimistic) c
rathernatural(orSO(10) is broken
at the scale MX = 5 · 10 GeV
To understandthe relativeof where
the correlation,in the
LHC accessible
parameter
space at fixed
tanLC,
β. Thelines
areriments will be Excellence
Grant,II
MEXT-CT-2003-509661.
AFsizeandplans
toforto theτ decayswithmediationa sensitivity
The
Belle
experimentat SuperKEKB
[34]
which
wesearchequate it
the SUSY
breaking
scale
present
boundsandfuturesensitivities.
Let
us
note
that
limit
of
degenerate
SUSY
spectrumwegetenarios even in AMthe
thank the PRIN ‘Astroparticle Physics’ of the Ital16
and
the
GUT
scale
is
M
=
2
·
10
GeV.
Below
the
GUT
−9
the
interplay
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APPENDIX: NOTATION AND RGE %EQUATIONS
2WSU(5)RN = Y10 ij 10i 10j 5H +ForR
1 &thank
10#4 j'12(" ! e);hes at the LHC. CPHT for hospitality. LC, AM and SKV also
LL jin grand unified th+Y1(20)+ Mij 1i 1j + µ5̄terms
ij 5̄i 1j 5H quark-induced
H 5H&
the CERN Theory Group for hospitality during various#5 23 2glected[43].
Asaresult,in many realis
1.
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model
2
&
10
j'
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!
"):
stages of this work. We thank U. Chattopadhyay, S. LL
While the corresponding soft SUSY
potentialiseasybreaking
to suppress
LFV entries
in the slepto
Kraml,S.
Profumo,
D.
P.
Roy
and
F.
Zwirnerfordiscusedges support#4 level [38].
the
10
A
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analysisofthestringentcorrelation
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in Gherghetta
a supersymmetricSO(10) frame- VSU(5)RN = (A10 ij 10i 10j 5H + A5 ij 10i 5̄j 5̄H̄
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Advanced Re- sions. The
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pported by INMX
MGU T
SO(10) −→SU (5)RN −→MSSMRN(A.1)
1e-04

Figure 5: Comparison between the ⌧ lepton mass measurement performed by Belle II
and the values obtained from previous experiments. ⌧ lepton mass average reportedby the PDG [5] is also displayed.
Chapter 1 Search for µ → eγ

13

Figure6:1.10
Upper90%
limitsfor upper
the branchingratiotheof LFVτ decayswith limits
expected
toFigureCurrent
C.L.
limits forbranchingfractionof LFV⌧ decays.
−1
beimposedby
BelleII
assuming
anintegrated
luminosity
of
50
ab
[36].
Limits imposed by CLEO, BaBar, Belle and LHCb are showed. Additionally, prospects
for limits to be imposed by Belle II are indicated with red circles, assuming an integrated luminosity of 50 ab 1 [6]. The last four decay modes also violates barion
1.1.5.3
Directsearch in energy frontier experiments
numberconservation.
The direct search for the SUSY particles is one of the attractive motivations for the en-ergy frontier experiments such as the large hadron collider (LHC) experiment. However, itsreachableenergy region
is decays
limited by the beam energy. Fig. 1.11 shows the mass reach of the
4.2
CP violation
in ⌧ATLAS experiment [37] for SUSY particles. It reaches 1–2 TeV scale. On the other hand, theThe decay of the ⌧ lepton to final states containing a KS0 meson will have a nonzero decay-rate
MEG II experimentcan byindirectly access SUSY particles’ masses around 10 TeV by searching forasymmetryA⌧ , defined−14
the µ → eγ decay at the sensitivity+of O(10) as shown in Fig. 01.12 [38]. In addition, cLFV¯⌧)(⌧ ! ⇡+ KS0 ⌫(⌧ ! ⇡ KS ⌫⌧ )searches are sensitive to particles
strongly interact suchas sleptons, which are notA⌧ = which do not(4)¯ ⌧ ) + (⌧ ! ⇡ KS0 ⌫⌧ )(⌧+ ! ⇡+ KS0 ⌫strongly constrained by the LHC results. Therefore, the two approaches are complementary to
due
to CP
violation
explorenew
physics.in the kaon sector. The SM prediction [12, 13] yields

AS⌧M = (3.6 ± 0.1) ⇥ 10 3 .

1.2 Principle of µ → eγ search

(5)

3.6

In a µ → eγ search, the decay mode is identified by detecting the decay products. Usually,
positive muons are used not to form muonic atoms; negative muons can be captured by nucleus
in target material. The decay from the muonic atom is no longer a two-body decay, which makes
the identification diﬃcult.

1.2.1 Signal
The signal µ+ → e+ γ decay is a two-body decay. In the rest frame of the muon, the muonemits a time coincident pair of a positron and a γ-ray with the energy of a half of the muon mass
mµ to the back-to-back direction. Therefore, the decay from stopped muons can be identified

Chapter 1 Search for µ → eγ

Figure 1.11 Mass reach of the ATLAS searches for SUSY in June 2021 [39]. A representative selection of the available search results is shown.

Figure 1.12 Branching ratio of µ → eγ decay as a function of the universal scaler mass m0
and tan β in the mSUGRA model [38]. Dark (light) green region satisfies 125 GeV < mh <127 GeV (124 GeV < mh < 128 GeV) and dashed two lines show 120 GeV < mg < 130 GeV.
The gray region is excluded by the non-perturbativity of the top Yukawa coupling.

14

Chapter 1 Search for µ → eγ

15

by the following conditions:• Ee+ = Eγ = mµ /2 ≃ 52.8 MeV,
• te+ γ = 0,
• Θe+ γ = 180◦ ,where Ee+ and Eγ are the energies of the positron and the γ-ray. te+ γ and Θe+ γ are the time
diﬀerence and the opening angle between the positron and the γ-ray, respectively.
The expected number of signals is the product of the branching ratio of the signal decay B
and the inverse of the single event sensitivity k, and thus it can be written as follows:
Nsig = B × k,
k := Rµ × T × Ω × ϵe+ × ϵγ × ϵcut ,(1.4)

where Rµ is the muon beam intensity, T is the total data-acquisition live time, Ω is the geometrical acceptance of the detector, ϵe+ and ϵγ are the detection eﬃciencies of the positron and
γ-ray respectively and ϵcut is the eﬃciency of the event selection. The increase of each of thefactors except for the branching ratio given by the nature results in a higher sensitivity.

1.2.2 Backgrounds
In the SM, the µ+ decays emitting a positron, neutrinos and a γ-ray as shown in Table 1.2.
The products from the SM decay modes can mimic the signal decay by satisfying the signal
event kinematics, and those events can be background events.
Table 1.2 Decay modes of muon [40].

Decay mode

Fractionµ → eννµ → eννγµ → eννe+ e−∼1(6.0 ± 0.5) × 10

−8(Ee > 45 MeV, Eγ > 40 MeV)

(3.4 ± 0.4) × 10−5

The background events in the µ+ → e+ γ search can be classified into two groups: physics
background and accidental background. The former one is from a radiative muon decay, whichemits a positron and a γ-ray at the same time, and the latter is given by the accidental coincidence of a positron and a γ-ray from diﬀerent muons. In principle, these background events
can be distinguished from the true signal event since they can have slight diﬀerences from thesignal event criteria. In reality, however, they are not necessarily distinguishable due to thefinite detector resolutions.
To discuss the expected number of background events, let’s introduce new quantities: thenormalized positron and γ-ray energies to the signal energy, x = 2Ee+ /mµ and y = 2Eγ /mµ ,and the opening angle, z = π − Θe+ γ . Using these quantities, the interesting region can beChapter 1 Search for µ → eγ
expressed as161 − δx ≤ x ≤ 1 + δx,1 − δy ≤ y ≤ 1 + δy,
0 ≤ z ≤ δz,−δte+ γ ≤ te+ γ ≤ δte+ γ ,where the variables with δ denote the ranges of the signal regions for the corresponding observables. The partial branching ratios in this region give the eﬀective number of the background
events.
Physics background
The radiative muon decay (RMD), µ+ → e+ νe ν µ γ, becomes a physics background. The
positron and the γ-ray from this decay are emitted simultaneously. In addition, when thetwo neutrinos carry little momentum, the energies of the positron and the γ-ray are close to
those of signals and they are emitted almost back-to-back: x ≈ 1, y ≈ 1 and z ≈ 0.
The diﬀerential branching ratio dB of the RMD can be written within the framework of theV–A interaction as
dB(µ+ → e+ νe ν µ γ) =αdyβdx dΩe+ dΩγ
364πy× [F (x, y, d) − β P⃗µ+ · p̂e+ G(x, y, d) − P⃗µ+ · p̂γ H(x, y, d)],(1.5)

where dΩe+ and dΩγ are solid angles of the emitted positron and γ-ray whose energy is in theinterval of dx and dy, respectively [9]. P⃗µ+ is the muon polarization vector. p̂e+ and p̂γ are unit
vectors of positron and γ-ray momenta, p⃗e+ and p⃗γ , in the muon rest frame respectively. β isdefined as β ≡ |⃗pe+ |/Ee+ . d is given by d ≡ 1 − β p̂e+ · p̂γ . The functions, F (x, y, d), G(x, y, d)and H(x, y, d), are given in Appendix A of [9]. From the four-body kinematics, the ranges of x
and y are limited as√√
2 r < x < 1 + r (0 < y ≤ 1 − r),√(1 − y) + r/(1 − y) ≤ x ≤ 1 + r (1 − r ≤ y ≤ 1 − r),(1.6)

where r = (me+ /mµ+ )2 .
In an approximation of the limit of x ≈ 1, y ≈ 1 and z ≈ 0, the diﬀerential branching ratio isexpressed asα[J1 (1 − Pµ+ cos θe+ ) + J2 (1 + Pµ+ cos θe+ )]d(cos θe+ ).
16π√
In the condition of the experiment in which the angular resolution meets δz ≤ 2 δxδy, J1 anddB(µ+ → e+ νe ν µ γ) =J2 are given by8δzδz
1 1 δz 8( ) ,(δx)3 (δy)( )2 − 2(δx)2 ( )4 +32
2
3 (δy)2 2
δz
δz
8 δz
J2 = 8(δx)2 (δy)2 ( )2 − 8(δx)(δy)( )4 + ( )6 .
2
2
3 2

J1 =

Fig. 1.13 shows a fraction of the µ+ → e+ νe ν µ γ decay for the given δx and δy values assuminga polarization of −0.86 measured in the MEG experiment [41] and δz ≈ 20 mrad. This figureδyChapter 1 Search for µ → eγ

17

0.05

0.045

1e-12

0.04
0.035
0.03
1e-13

0.025
0.02

1e-14

0.015

1e-15

0.01
0.005
0
0

0.01

0.02

0.03

0.04

0.05
δx

Figure 1.13 Eﬀective branching ratio of the physics background from theµ+ → e+ νe ν µ γ decay as a function of the positron energy resolution (δx) and γ-ray
energy resolution (δy).

indicates that both δx and δy on the order of 0.01 are needed to achieve a sensitivity limit at
the level of 10−15 .
The expected number of physics background events can be written by
NRMD = BRMD × Rµ × T × Ω × ϵe+ ,RMD × ϵγ,RMD ,(1.7)

where BRMD is the branching ratio of the background, which can be obtained by integrating
the diﬀerential branching ratio, and ϵe+ ,RMD and ϵγ,RMD are the eﬃciencies to detect the RMD
positrons and γ-rays, respectively.
Accidental background
The accidental background derives from a positron and a γ-ray originated from independent
muon decays. If a pair of the positron and the γ-ray with energies near those of the signals
is emitted simultaneously in the back-to-back direction, it can be regarded as a signal event.
The source of such positrons is a Michel decay (µ+ → e+ νe ν µ ). On the other hand, the γ-ray
background comes from an RMD and an annihilation in flight of a positron (AIF).
The eﬀective branching ratio of the accidental background Bacc can be expressed as
Bacc = Rµ × fe+ × fγ ×(δz)2× (2δte+ γ ),
4

(1.8)

where fe+ is the fraction of positrons which enter the signal energy region and fγ is that of
γ-rays.
fe+ can be given by the Michel positron energy spectrum. When the positron polarizationis neglected, the diﬀerential decay width of the Michel decay within the framework of the V–AChapter 1 Search for µ → eγ

18interaction in the SM has a simple form ofdΓ(µ+ → e+ νe ν µ ) =m5µ G2F 2
x [(3 − 2x) + Pµ cos θe+ (2x − 1)] dxd(cos θe+ ).
192π 3(1.9)

Fig. 1.14 shows the Michel positron energy spectrum obtained by integrating Eq. (1.9) over theangle assuming the polarization of −0.86. As the spectrum is almost flat in the signal region ofx ≈ 1, the integral can be approximated to befe+ ≃ 2δx.
fγ can be obtained by the combination of RMD and AIF γ-ray spectra. Fig. 1.15 shows thediﬀerential branching ratio of RMD as a function of the positron and the γ-ray energy obtainedby integrating Eq. (1.5) over the solid angles. The ratio is high for an energetic positron with asoft photon, where x ≈ 1 and y ≈ 0.
The γ-ray spectrum is obtained by integrating Eq. (1.5) over the positron energy and angles.
With ignorance of the terms suppressed by me+ /mµ+ , it is approximated bydB(µ+ → e+ νe ν µ γ)
1
= [J+ (y)(1 + Pµ+ cos θγ ) + J− (y)(1 − Pµ+ cos θγ )],dyd(cos θγ )y(1.10)

where θγ is the angle between the muon spin polarization and the photon momentum, and J+ (y)and J− (y) are defined by[]
1 − y 171−y
1 − y 13α(1 − y) (3 ln− ) + (−3 ln+ 7)(1 − y) + (2 ln− )(1 − y)2 ,J+ (y) =
6π
r
2
r
r
3
[
]
α
1 − y 93
1 − y 29
1 − y 552
2
J− (y) =(1 − y) (3 ln− ) + (−4 ln+ )(1 − y) + (2 ln− )(1 − y) .
6π
r
12
r
3
r
12
Fig. 1.16 shows the γ-ray spectrum, which is obtained by integrating Eq. (1.10) over the angle
assuming the polarization of −0.86. By integrating the spectrum over y, the contribution of the
RMD fγ,RMD can be given by the approximation in the signal region of y ≈ 1 with unpolarizedmuons asfγ,RMD ≃α(δy)2 {ln (δy) + 7.33}.
2π(1.11)

From the equation, fγ,RMD is roughly proportional to (δy)2 .
Although Eq. (1.10) is obtained by integration over the positron energy, the transition probability is high for the low energy positrons when the γ-ray energy is high. Fig. 1.17 shows
the positron energy spectrum obtained by integrating Eq. (1.5) over the solid angles and withrespect to the γ-ray energy from y = 0.9 to y = 1. It peaks at the positron energy region lower
than 8 MeV. This fact leads to an idea of the background suppression by identifying the RMD
γ-rays with detection of the low energy positrons which derive from the same muons, which will
be discussed in Sec. 2.1.3.3.
Some of the Michel positrons emit γ-rays via AIF and external Bremsstrahlung. The γ-rays
from the AIF can have high energies while the contribution from the Bremsstrahlung is negligibly
small in the signal region.

Chapter 1 Search for µ → eγ

19

The energies of two γ-rays, Eγ1 and Eγ2 , generated by the AIF are given byme+ (Ee+ + me+ ),Ee+ + me+ − pe+ cos θe+ γ1(Ee+ − pe+ cos θe+ γ1 )(Ee+ + me+ )Eγ2 =,Ee+ + me+ − pe+ cos θe+ γ1Eγ1 =where Ee+ and pe+ are the energy and magnitude of the momentum of the positron respectively,and θe+ γ1 is the direction of γ1 momentum with respect to the positron momentum direction.
Fig. 1.18(a) shows the energy distribution of the γ-rays from AIF as a function of θe+ γ1 whenx = 1. In most cases, either of the two γ-rays carries most of the energy in which the emission
direction of the γ-ray with higher energy is closely aligned to that of the original positron while
the energies of the two become equivalent otherwise.
The diﬀerential cross section for the annihilation of a positron is given by[dσ
e4 (Ee+ + me+ )
1
=−
dΩ
pe+
(Ee+ + me+ − pe+ cos θe+ γ1 )23me+ Ee+−
2me+ (Ee+ + me+ )(Ee+ − pe+ cos θe+ γ1 )]Ee+ + me+ − pe+ cos θe+ γ1,+2(Ee+ + me+ )2 (Ee+ − pe+ cos θe+ γ1 )2
in the laboratory coordinate system [42]. Fig. 1.18(b) shows the diﬀerential cross section as afunction of θe+ γ1 when x = 1. Combining Fig. 1.18(a) and Fig. 1.18(b), the energy spectrumof the γ-ray from AIF can be illustrated as Fig. 1.19, which indicates one of the γ-rays carries
most of the energy with high frequency.
The contribution from AIF depends on the material distribution of the experiment.
Fig. 1.20(a) shows the simulated energy deposit from a muon decay in the MEG II experiment.
The AIF spectrum decreases moderately as the energy gets higher while the RMD spectrum
decreases rapidly, which results in the high fraction of the AIF γ-ray in the signal region. For
instance, the fraction of AIF for Eγ > 48 MeV is 35%. Fig. 1.20(b) shows the integration of theenergy spectrum of the AIF γ-ray as a function of δy. From this figure, the fraction of the AIF
γ-ray fγ,AIF can be approximately represented as a square function of δy as well, which isfγ,AIF ≃ rγ,AIF (δy)2 .

(1.12)The normalization rγ,AIF is given by the fraction of the RMD and AIF contributions.
From the above results, the expected number of accidental background events can be writtenbyNacc = Bacc × Rµ × T × Ω × ϵe+ ,acc × ϵγ,acc(1.13)] (δz)2[α= Rµ2 × T × (2δx) ×(δy)2 {ln (δy) + 7.33} + rγ,AIF (δy)2 ×× (2δte+ γ )2π4∝ Rµ2 × T × δx × (δy)2 × (δz)2 × δte+ γ ,where ϵe+ ,acc and ϵγ,acc are the detection eﬃciencies of background positrons and γ-rays, respectively.

Differential Branching Ratio

Chapter 1 Search for µ → eγ

20

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0

0.2

0.4
0.6
0.8
1
Normalized Positron Energy (x)Figure 1.14 Energy spectrum of Michel positron. The muon spin polarization is set to −0.86.

×10−6
0.1
0.08
0.06
0.04
0.02
0
1

γ -r 0.8
ay
en0.6
erg 0.4y(y) 0.2

0.2

0.6

on
positr0.4

1
0.8 y (x)energ

Figure 1.15 Diﬀerential branching ratio of the RMD as a function of the positron and
γ-ray energies. The muon spin polarization is set to −0.86.

In addition to the RMD and AIF, there is a contribution from accidental pileup of multiple
γ-rays when the muon beam intensity is high. The eﬀect of the pileup will be discussed in
Chap. 5.
Fig. 1.21 shows the eﬀective branching ratio of the backgrounds as a function of the lower edgeof the integration regions with respect to Ee+ and Eγ in the MEG experiment. The eﬀective
branching ratio of the accidental background is larger than that of the RMD by one or two ordersof magnitude, and so the accidental background is a dominant background in this experiment.

Differential Branching Ratio

Chapter 1 Search for µ → eγ

21

1
10−1
10−2
10−3
10−4
10−5
0

0.2

0.4
0.6
0.8
1
Normalized γ -ray Energy (y)Figure 1.16 Energy spectrum of RMD γ-ray. The muon spin polarization is set to −0.86.

Differential Branching Ratio

−9

×10
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0

0.05

0.1
0.15
0.2
Normalized Positron Energy (x)dσ/dΩγ -ray energy (y)Figure 1.17 Diﬀerential branching ratio of the RMD as a function of the positron energy
with γ-ray energy of y = 0.9–1. The muon spin polarization is set to −0.86. The lower√
edge of the distribution is given by the kinematics of 2 r in Eq. (1.6).

1
0.8

1
10−1

0.6

10−2

0.4

10−3

0.2

10−4

0
0

0.2

0.4

(a)

0.6

0.8

1

cosθe+ γ

10−5
0

0.2

0.4

0.6

0.8

1
cosθe+ γ(b)

Figure 1.18 (a) Energies of γ-rays from AIF and (b) normalized diﬀerential cross section
as a function of the angle between the positron and one γ-ray directions (black) whenx = 1. That for the other γ-ray is also drawn in red.

Chapter 1 Search for µ → eγ

22

1

10−1

10−2

10−3

10−4

0.2

0.4

0.6

0.8
1
γ -ray energy (y)10

The Number of Events (a.u.)

probability /100 keV

Figure 1.19 Energy spectrum of a γ-ray from AIF when x = 1.

−3

10−4
10−5
10

−6

10−7
10

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1

−8

0

0.01

0.02

0.03

0.04

0
0

0.05
0.06
Eγ (GeV)

0.02

0.04

(a)

0.06

0.08

0.1
δy

(b)

Figure 1.20 (a) Simulated energy deposit from a muon decay on target for RMD decay(blue) and Michel decay (red) in the MEG II. (b) Integrated energy spectrum of AIF as afunction of δy obtained by integrating the spectrum of (a) with respect to y from 1 − δyto 1. The y-axis is normalized at δy = 0.1.

E γ ,min (MeV)

Page 21 of 30 434

53

53

(a)

52

10
-12

10

51

48
50

0.94

0.96

50
10-11

51

10-15
-14

10

51

50
49

(b)

52

-13

10-13
10-12

49
52

53

48
50

51

52
53
E e+,min (MeV)

Fig. 23 branching
Effective branchingof the two typesof backgroundFigure 1.21 Eﬀective
ratios ofratios(a) accidental
backgroundand (b) RMD back+
+
into
the
kinematic
windowdefinedbyE<E< 53.5|tMeV,| < 0.24 ns ande MeV,
0.98 ground
1 in Ee+ ,min < Ee+ < 53.5 MeV, Eγ,min <e E,min
<
53.5
γ
e+ γ
E γ ,min < E γ < 53.5 MeV, |te+ γ | < 0.24 ns and cos "e+ γ < −0.9996.
y Thresholdcos Θe+ γ < -0.9996.
The former
one wasevaluatedfromtheside-band.
timing side-banda Accidental
backgroundevaluatedfrom thetimingb RMD data and thebackgroundµ+ → formulae+ γ ν ν̄ calculatedwith detector
theoreticalresponses
formula [1].
latter was calculatedwith fromtheoreticalfolded withes) and AIF (green circles) photon backdetector estimated by a MC simulation
nt. The variable on the horizontal axis ise photon energy and m µ is the muon mass

kinematic end-point, a good energy
y the single photon background.

folded with detector responses

Bacc ∝ Rµ δ E e+ (δ E γ )2 δte+ γ δθe+ γ δφe+ γ ,where Rµ is the muon stopping rate and δq is the width ofChapter 1 Search for µ → eγ

1.2.3 Experimental requirements
In order to achieve a high sensitivity, Nsig should be maximized while NRMD and Nacc should
be minimized. This leads to the following requirements.
Firstly, a high-intensity direct-current (DC) muon beam is required. High muon statistics
results in the large number of signals from Eq. (1.4). However, the number of the accidental
backgrounds increases quadratically with Rµ while that of the signals increases linearly. Thus,
a DC muon beam is a better choice to acquire the same statistics with a lower beam intensity
than a pulsed beam.
Secondly, the improvement of the detector resolutions is essential for the high sensitivity. As
shown in Eq. (1.7) and Eq. (1.13), both of the number of the backgrounds depend on the energy
and opening angle resolutions, and that of the accidental backgrounds depends on the timing
resolutions as well.
Furthermore, the reduction of γ-ray backgrounds from AIF can be realized by minimizing thematerial throughout the positron path.

1.3 MEG experiment
The MEG experiment searched for the µ+ → e+ γ decay with the highest sensitivity in theworld. Fig. 1.22 shows the schematic of the MEG experiment. The world’s most intense DC
muon beam available in the Paul Sherrer Institut (PSI) in Switzerland was used in the experiment. Muons were stopped in a target, and then decayed into positrons and γ-rays. The tracks ofpositrons were bent into spirals in the magnet produced by a superconducting solenoid and their
momenta, vertices and timings were measured with drift chambers and timing counters. Theenergies, positions and timings of γ-rays were measured with a liquid xenon detector. Thanks
to the high performance of these detectors, the MEG experiment searched for the decay withthe sensitivity of 5.3 × 10−13 . Although the positive signal was not observed, the experimentsucceeded in setting the current upper limit on the branching ratio, B(µ → eγ) < 4.2 × 10−13(90% confidence level) [1].
Further enhancement of the sensitivity cannot be expected in the MEG experiment even withmore statistics. Fig. 1.23 shows the improvement of the sensitivities of the MEG thanks to thestatistics used for each analysis. The figure indicates the degree of the sensitivity enhancement by
an increased statistics becomes less with accumulation of the data. This is because the increaseof statistics contributes to the increase of the backgrounds as well. As shown in Fig. 1.21,
the eﬀective branching ratio of the accidental backgrounds in 52.5 MeV < Ee+ < 53.5 MeV
and 52.0 MeV < Eγ < 53.5 MeV is in the order of 10−13 in the MEG. Considering the energy
resolution of 330 keV (core) for positrons and 2.3% for γ-rays in the MEG, a fundamental
improvement of the detector performance is unavoidable to reach the sensitivity of O(10−14 ).

23

Chapter 1 Search for µ → eγ

ur. Phys. J. C (2018) 78:380

Page 3 of 60 380

g. 2 Schematic of the MEG
periment

CHAPTER 3. MEG II EXPERIMENT

15

Branching ratio

Figure 1.22 Schematic of the MEG experiment.
Xe photon detector with the positron vertex in the target
ferential branching ratio [4] over the appropriate kinematicbtained by extrapolating the positron track. All the signals
intervals, but there is no simple equation for NRMD . In
MEG, NRMD was more than ten times smaller than Nacc
e individually digitised by in-house designed waveform
MEG 2009[2]. Due to the dependence Nacc ∝ Rµ2 + , in comparison withgitisers (DRS4) [3].
coincidencesin MEG II, where
NRMD ∝ Rµ+ , the accidental
The number of expected signal events for a given branchObtained 90%
UL
MEGA
large
as in MEG, will dominate evenRµ+ is about twice as 90%
g ratio B is related to the rate of stopping muons R
UL sensitivity
µ+ ,
−11
10
e measurement time T , the solid angle Ω subtended bymore over the number ±of
1 σbackground events from RMD.
e photon and positron detectors, the efficiencies of these
It is clear from Eqs.±(1)2 σ and (2) that, for fixed experimenetectors (ϵγ , ϵe+ ) and the efficiency of the selection criteria
tal resolutions, the muon stopping rate cannot be increased
1:arbitrarily but must be chosen in order to keep a reasonable
signal to background
MEG 2011 ratio.
(1)
sig = Rµ+ × T × Ω × B × ϵγ × ϵe+ × ϵs .
After the five-year data taking of MEG, only a limited
he single event sensitivity (SES) is defined as the B forgain in sensitivity could be achieved with further statistics
hich the experiment would see one event. In principle−12thedue to the background (accidental) extending into the signal
10
west SES, and therefore the largest possible Rµ+ , is desirregion. Therefore, the data-taking ceased in 2013, allowing
ble in order to be sensitive to the lowest possible B. The
the upgrade program to proceed with full impetus.
umber of accidental coincidences Nacc , for given selection
Other cLFV channels, complementary to µ+ → e+ γ andMEG 2013
N →Finale− N , µ → 3e, τ → ℓγ
iteria, depends on the experimental resolutions (indicatedbeing actively pursued are: µ−MEG
and τ → 3ℓ (ℓ = e or µ).
∆) with which the four relevant quantities (E γ , pe+ , Θe+ γ ,+ γ ) are measured. By integrating the RMD photon andIn the µ− N → e− N conversion experiments, negative
Michel positron spectra over respectively the photon energymuons are stopped in a thin target and form muonic atoms.
nd positron momentum resolution intervals, it can be shown
The conversion of the muon into an electron in the field of the
−13
10
at:
nucleusresults in the200
emission of a300
monochromatic electron
0100
ofmomentum∼100
MeV/c,
depending222
Accumulated DAQ dayson the target nucleus
acc ∝ Rµ+ × ∆E γ × ∆pe+ × ∆Θe+ γ × ∆te+ γ × T. (2)used. Here the backgrounds to be rejected are totally dif+ γ case. The dominant backgroundhe number of RMD backgroundcal- sensitivities→ eandferent fromthe µ+
RMD can be
Figure events
1.23 N
Branchingratio(blackline)
upper limits (purple markers) of
Figure
3.7:
Sensitivity
improvement
in MEG. and those correlated
ulated by integrating the SM
calculation
contributions are muon decay-in-orbit
MEG
results. of the RMD difɹɹɹwith the presence of beam impurities, such as pions. In order
An usual selection criterion is to choose 90% efficient cuts on each of
to reduce these backgrounds the experiments planned at Fere variables (E γ , pe+ , Θe+ γ , te+ γ ) around the values expected for the
milab (Mu2e) [5,6] and J-PARC (COMET [7,8] and DeeMe
gnal: this criterion defines
to be ϵs = (0.9)4 .
1.4the selection
MEGefficiency
II experiment[9]) will use pulsed proton beams to produce their muons.
his kind of analysis in which one counts the number of events within
Since muonic atoms have lifetimes ranging from hundreds
me selection cuts and compares the number found with predictionsThe
II MEG/MEG
experiment,
upgradeof the MEG
was proposed
toconimprove theof nanoseconds
up toexperiment,
the free muon lifetime
at low Z, ther the background is named“ boxMEG
analysis”.
II adoptan
more
fined analyses which take into account the different distributions ofversionelectrons
aretherefore
searchedforintheintrabunch
sensitivity
one oderof magnitude[43]. Fig. 1.24 shows the schematic view of the MEG II exE γ , pe+ , Θe+ γ , te+ γ ) for
background by
and signal
type eventsby using
intervals.

aximum likelihood methods.
periment.

Muons are stopped in the target and emit positrons and γ-rays. The positrons arebent in a magnetic field produced by COBRA magnet, and then detected with the cylindrical123

drift chamber and the pixelated timing counter while the γ-rays are detected with the liquid24Chapter 1 Search for µ → eγ

Figure 1.24 Schematic of the MEG II experiment [2].

xenon detector. The radiative decay counter is newly installed for tagging γ-ray backgrounds.
The improvement in the sensitivity is achieved by upgrades of the detectors in two aspects.
The first strategy is to improve the detector resolutions, which is eﬀective to reduce theaccidental backgrounds. As shown in Eq. (1.13), the number of accidental backgrounds increases
with the resolutions. Therefore, the MEG II detectors were designed to achieve better resolutions
by a factor of two than the MEG detectors.
The second is an increase of the accumulated statistics. The muon beam rate in the MEG
experiment was limited to 3×107 µ+ stops/s, which is lower than a half of the maximum intensity,
due to the limited performance of the detectors; the drift chamber was not operational undera high intensity environment causing discharge, and the performance of the MEG detectors
can significantly deteriorate at the increased background level. Thus, an improvement of thedetectors to be tolerant toward an increase of the beam intensity enables a gain in the total
number of muons. In addition, the eﬃciency of the positron spectrometer is doubled by reducing
the material between the drift chamber and the timing counter, which causes positron scattering.

25

26

Chapter 2

MEG II ExperimentThis chapter begins with explanations about apparatus for the MEG II experiment. Then, theconfigurations of the pilot runs for the detector commissioning are summarized followed by thedescriptions about the detector simulation. Finally, the procedure for the µ+ → e+ γ analysis is
described.

2.1 Apparatus
In this section, the apparatus for the MEG II experiment is explained such as the beamline,
the detectors, the DAQ system.
Here we define a global coordinate system (x, y, z) as follows. The origin is defined at thecenter of the COBRA magnet and the muon stopping target is located there. The z-axis is
set parallel to the muon beam direction, and the y-axis is set vertical upward. The x-axis is
set horizontal, so that (x, y, z) forms a right-handed system. A cylindrical coordinate system√(r, θ, ϕ) is also defined as r := x2 + y 2 , θ := tan−1 (z/r), ϕ := tan−1 (y/x).

2.1.1 Beamline
The MEG II experiment uses the muon beam at PSI. Fig. 2.1 shows an overview of the beamline. The beam is transported along the arrows to the MEG II detectors placed in the πE5beamline.
Proton acceleration
The muon beam at PSI originates from protons. The protons from a hydrogen source areaccelerated in three steps. At the first step, a Cockcroft–Walton pre-accelerator shown in Fig. 2.2
accelerates them up to 870 keV [45]. The pre-accelerated protons are injected into a isochronous
cyclotron called Injector 2, which consists of four magnets, two radio-frequency (RF) cavities
operated at ∼ 400 kV and two third-harmonic cavities operated at ∼ 30 kV shown in Fig. 2.3.
This first cyclotron accelerates the protons up to 72 MeV and the beam is delivered to the second
cyclotron, the main ring cyclotron. The second cyclotron is composed of four main RF cavities
and eight magnets as shown in Fig. 2.4, and accelerates the beam up to 590 MeV. Table 2.1

the ⇡E5 beamline where the most intense DC µ+ beam up to 108 /s is available. The beam bunchinterval is ⇠ 20 ns (repetition rate 50.6 MHz), and is well shorter than the mean life of muon atrest state: 2.2 µs. Therefore, the beam can be considered as DC beam. Requirements for beam
property
the smalltransverse size, small momentum spread and small beam contamination.
Chapter are
2 MEG
II Experiment27!"#$%&#$'%()(*+,&+$,"&'-,%.

/.0%"&-"

Figure 2.1 Experimental hall in PSI [44]. The beam path is shown in arrows.

Figure 2.2: Top view of beam facility in PSI main experimental hall. The beam path is shownin arrows.
summarizes the characteristics of the main ring cyclotron.

2.1.1

PSI accelerator facility

Muon production

The accelerated protons are injected into two graphite targets called target M and target E+ beam withIn(Fig.
Figuremap5 ofis axis,shown.
PSI provides2.5), 2.2,
whicha have
mmPSI
andmain
40 mmexperimental
thickness alonghallbeam
respectively.
In theseµtargets,+
High
Proton[47].
HIPA consists
accelerators,
CockcroftpionsIntensity
are produced
andAccelerators
subsequently(HIPA)
muons areproducedby π + →ofµthreeνµ decay.
Pions havea
Waltonaccelerator,
Injector2
cyclotron
and
main
ring
cyclotron(Fig.
2.3(a))1.
The
energyoflifetime of ∼ 26 ns at the rest, which is long enough to regard the extracted muon beam as a

DC
eﬀectively.
1 Inbeam
operation
since 1974.
πE5 beamline22

πE5 beamline, where the MEG II experiment is conducted, provides the highest intensity
muon beam in the seven beamlines stretching from target E. This beamline has an angle of 166◦with respect to the proton beam direction in order to collect surface muons with magnets, which
originate from pions stopped in a thin region of the target surface. The surface muons can be
stopped on a thin target thanks to small momenta of ∼ 28 MeV/c with 5–7% (FWHM).

Chapter 2 MEG II Experiment

28

Chapter 2. MEG experiment setup

Figure 2.2 Cockcroft–Walton preaccelerator [46].

Figure 2.3 Injector 2 [47].

Chapter 2. MEG experiment setup
proton is 590 MeV and the nominal beam current at the year 2013 was 2.2 mA.
proton is 590 MeV and the nominal beam current at the year 2013 was 2.2 mA.

(a)
PSI2.4
protonmain
cyclotron
FigureMainringring
cyclotron[44].
(a) PSI proton main ring
cyclotron
Figure2.3(b) Target E. The outermost
part is graphite target.
(b)2.5Target
The outermost
FigurePionE.production
target [44].
part is graphite target.

Figure 2.3
The proton beam is lead to a production target made of carbon graphite with 4 cm length
along beam axis. The target
isin Fig. 2.3(b),theringwheel
keeps on rotating during the
2.1shown
the main
cyclotron
The proton beam Tableis leadtoCharacteristics
a productionoftarget
made ofcarbon[48].
graphite with 4 cm length
operation for cooling. The surface muon is produced from decay of positive pion (⇡ + ! µ+ ⌫ µ )along beam axis. The target isshownenergy
in Fig. 2.3(b),72thewheel keeps on rotating during the
Injection
MeV
which stopped near surface of the target. The energy of µ+ s is uniform (since the pion is stopped)
operation for cooling. The surface muonenergy
is produced fromdecay of positive pion (⇡ + ! µ+ ⌫ µ )and spin is completely polarized.Extraction
The surface muon beam590
is+MeV
contaminated with positron, which
which stopped near surface of the target.
The energy of1.2µGeV/cs is uniform (since the pion is stopped)
is needed to be removed beforeExtraction
it reachesmomentum
the MEG detector.
The ⇡E5 beam line is located atand spin is completely polarized. The surface muon beam is contaminated with positron, whichBeamcurrent
2.2–2.4
mAthe
DCtarget are extracted with an
166 from the original beam, where
surfacemuons [48]fromis needed to be removed before it reaches the MEG detector. The ⇡E5 beam line is located atarray of magnets. The main specification
the beam is 50.63
summarized in Table 2.1.
Accelerator of
frequency
166 from the original beam,
where surface
muons [48] MHzfrom the target are extracted with anTime
betweenpulses19.75
nsarray of magnets. The main
specificationof ofthe⇡E5beam
is summarizedin Table 2.1.
Table
2.1: Specs
beam
line
Bunch width

0.3 nsTable 2.1: Specs of ⇡E5 beam
line
Item
Value
momentumcenter
28 MeV/c
Item
Value
momentum spread (FWHM)
5-7%
momentum center
28 MeV/csolid angle
150 msrmomentum spread (FWHM)
5-7%
spot size (FWHM)
15 mm horizontal
solid angle
150 msr
20 mm verticalChapter 2 MEG II Experiment

Page 7 of 60 380

29

Page 7 of 60 380

Eur. Phys. J. C (2018) 78:380

Fig. 4 MEG Beam line with the π E5 channel and MEG detector system incorporated in and around the COBRA magnet

Figure 2.6 Schematic view of the πE5 beamline and the beam transport system in the
II system
experiment[2]. in and around the COBRA magnet
the π E5 channel and MEGMEG
detectorincorporated
2 Beam lineut

2.1 MEG beam line layout
The main beam requirements for a high rate, high sensitivity,
ultra-rare decay coincidence experiment such as MEG are:ents for a high rate, high sensitivity,– high stopping intensity (Rµ+ = 7 × 107 s−1 ) on target
nce experiment suchwith
as MEGare:high transmission
optics,– small beam spot to minimise the stopping target size,
Fig. 5 Measurement of the separation quality with the Wien-filter dur∆pµ+ / pµ+ ∼ 7% (FWHM) withing the 2015 Pre-Engineering Run
ty (Rµ+ = 7 × 10–7 larges−1 )momentum-byte
on target
an achromatic final focus, yielding an almost monochron optics,
matic beam with a high stop density for a thin target,
inimise the stopping
target size,– minimal
and well separated
backgrounds® withFig. Measurement
5beam-correlated
Measurementofof thequalitythe
Wien-filter
dur- at theMylardegradersystemis placed
Figure 2.7
theseparation
separation
qualitywith
the Wien-filter[2].central focus to min(FWHM)
withe ∆pµ+ / pµ+ ∼ 7% suchthe
as positrons
froming
Micheldecay
or π 0 -decay inRun
the 2015
Pre-Engineering
imise multiple Coulomb scattering. The degrader thickness
cus, yielding an almost
monochroproduction
target or decay particles from along the beamof 300 µm takes into account the remaining material budgetline
andgh stop density for a thin target,of the vacuum window at the entrance to the COBRA magnet– Fig.
minimisationof material
budgetalongline tobeamline
2.6 showsa schematic
viewtheofbeamthe πE5
andthebeam transportsystemtheinresidual
thethe central
heliumatmosphereinside, so adjusting
rated beam-correlated
backgrounds®
Mylarscattering
degradersystemisproplacedandat thefocus to minsuppress
multiple
Coulombandphotonrangeof themuonsIItobeamstop at the centre ofsystema 205 µmadthickin them Michel decay or
π 0 -decay
MEG
II experiment.
The multiple
muon beam
is delivered
toThe
the
MEG
Coulomb
scattering.
degraderthicknesstransport
duction, use of vacuumimiseor helium
environments
as faras◦ to the axis.
polyethylene
targetplacedat
20.5
ecay particles fromalong
themomentum
beam
of with300 µmtakes into
accountquadrupoles,
the remaining
materialbudgetjustingits
bendingmagnets,
hexapoles
andofslits
through
thepolarised
πE5
possible.
The residual
polarisation
the initially
100%
of
the
vacuumwindowattheentrance
to
the
COBRA
magnetmuonsquadrupoleat production has
been estimatedconsidering depobeamline. The transport system consists of the first
tripletmagnetby(Triplet1),arial budget along thebeam thelineMEGto COBRA
larising
effect at production,
during propagation and due to
Coupling
spectrometerand LXe phoand thehelium atmosphereinside,so adjusting
the residual
the second
triplet magnet(Triplet2),
andbeam transulomb scatteringWien-filterandphotonpro-π E5 channel,
stopping
target.
Thethenet polarisationis seenton
detector
to(Separator),
theendsquadrupolewithrange ofwhich
the muonsto thestoplastat themoderation
centre ofinathe205µm thickintheasymmetryoftheangulardistributionofdecay
Micheldipole magnet
shieldingwall,
isachievedwitham or helium environments
as ASC41
far (BTS)
as in the◦portsolenoidinthisorder.
The
muon
beam
contains
positroncontamination
whose
polyethylene target placed at 20.5 to the axis.
positrons from the target. The estimate is consistent with
Wien-filter (cross-field separator) and two sets of quadrupoleThe
residual
polarisationof the initially
100%from
polarised Michel decay of theamountis eight
times
higherthan
the muons,is derived
measurements
made usingthe
Michel positrons at the centre of
triplet magnets,
as shown
in Fig.
4. Thesefront-elementsof whichmuons
at production has optics
been estimatedby considering
depothe COBRA
spectrometer[89],after
where being
the energy-dependent
the MEGbeam
a maximalmuon
andthelineπ 0allowdecay
in the transmission
target. It is separated
with theseparatorsqueezedlarising
at production,
propagation
anddueanalysed.
to
OBRA spectrometerandtheLXepho- followed
angulardistributions
were
A high residual polarithroughseparator,
byeffectan achromatic
focus at during
withthe first
magnet,which resultsinpositronsof muons
(Fig.
2.7).
After
that,
+ = −0.86 is± seen0.02(stat.)+ 0.06− 0.05(syst.)
sationof polarisation
Pµ1%
the intermediate
collimatorsystem.
Herean stopping
optimalsepmoderationin thetarget.less
Thethannet
channel, which ends
withthe last
wasfound,
withthesinglelargestdepolarising
contribution
arationquality
betweensurface
muons
and
the
eight-foldmuon beam
again withsecondmagnet.of The
has a role of focusing
in the asymmetryof thetheangulardistribution
decayBTS
Michelhe shielding wall,theis achieved
with a is squeezed
coming fromthe cloud muoncontent of the beam. These arehigherbeam
positron contaminationfromMichelpositrons
positrons
fromthetarget.
The
estimateisconsistentwithparator) and two setsofquadrupole
thebeam derived
on a muontarget.
Thebeam ismuonscollimatedwithpiona collimator,
thenthethe0 -decay in thetarget andhavingderived fromdecay-in-flightand
in andaroundor positrons
from π stopping
measurements made using Michel positrons at the centre ofin Fig. 4. These front-elements ofthe correct momentum,
be achieved(seeFig. 5)targetMylarand inherently
have atolowmaximize
polarisation due
to the widely
momentaof muonscanare
adjusted
witha [1].
300Theµm-thickdegradera stopping
the COBRA
spectrometer
theacceptanceenergy-dependent
w a maximal transmission
optics adjustment
muon range-momentum
is madeat the centre[89],of wherediffering
kinematics. The cloud muon content ineﬃciencyin theat target.
AMeV/chigh residual
polarillowed by an achromaticfocus
the superconducting
beamangulartransportdistributions
solenoid BTSwere
whereanalysed.
athe 28surface muon
beam was derived from mea-

sation of Pµ+ = −0.86 ± 0.02 (stat.) + 0.06 − 0.05 (syst.)
tor system. Here an optimal sepwas found, with the single largest depolarising contribution
surface muons and the eight-fold
123
2.1.2 Muon stopping target
coming from the cloud muon content of the beam. These arentamination from Michel positrons
havingderivedfrompion
decay-in-flightand around
π 0 -decay in the target
The andmuon
beam muons
is injected
into
the
muon
stopping intargetplacedthe
at the center of the
an be achieved (see Fig. 5) [1]. The
target and inherently have a low polarisation due to the widely
MEG
II centre
detectors.
targetacceptanceneeds to kinematics.
have a highThemuon
stopping
eﬃciency
adjustment is madeat theof Thedifferingcloud
muon content
in with low material
m transport solenoid BTS where athe 28 MeV/c surface muon beam was derived from mea-

123

Chapter 2 MEG II Experiment
380 Page 16 of 60

30

Eur. Phys. J.

The double readout of the wires with the
charge division and of time propagation differ
with the ability to implement the cluster cotechnique [96], will further improve the long
dinate measurement.
The stereo configuration of wires gives a hfile to the active volume along the z-axis. T
The opticalmarkings
on the scintillator
target used
to test thecellFigure Fig.
2.8 23Muon
stopping
targetin the MEG
II experiment[2]. (see Fig. 25) is approximately square, 6
photogrammetric monitoring principle
innermost layer) to 9.0 mm (in the outermost oa 20 µm diameter gold plated W sense wire
– further investigations to understand the origin of the pre40 µm diameter silver plated Al field wires into avoid multiple Coulombvious
scatteringof distortion
the emitted
positrons,
andproduction of γ-ray
MEG target(e.g. radiation
damage,brit-the For
equalising the gains of the innermost anddue to dry He-environment);
backgrounds from positrontlenessbremsstrahlungor annihilation. In the MEG
experiment,
ers, two
guard wires thelayers (50 µm silver-pl– measurement of the target planarity both before and after
been added at proper radii and at appropriate
deformation of the target causeda large systematic uncertainty in the reconstructed positron
exposure using a coordinate measuring machine with a
total number of wires amounts to 13 056 for
precision
better than
50 µm;
direction, which resulted in
the largest
systematics
of 13%. Therefore,radiation
the MEGlengthIIpertarget
track turn of about 1.58 ×– determination of the target frame position in the experithe chamber is filled with an ultra-low mass
must be mechanically stable.
In addition, a monitoring system of the target deformation isment to a precision of ∼15 µm using a laser survey techhelium and isobutane (C4 H10 ) in the ratio 90
nique with low-mass corner-cube reflectors mounted on
introduced.
with 2.0 × 10−3 X0 in the MEG DCH [1]). T
the target frame;
ber is built by overlapping along the radius, al
In the pilot runs for the
MEG II experiment, a 174 µm thick plastic scintillating
film was– photogrammetric monitoring of target position, orientaBoards (PCB), to which the ends of the wire
◦ of printed patterns (dots) areand shape.
A 15seriesused as a target (Fig. 2.8). tion
It wasplacedslanted from the beam axis andto makeeﬀectiveto set the proper cell wi
PEEK®6anspacers,
optically monitored by CCD cameras viewing the target
the twelve sectors, between the spokes of the
thickness for the muon beam longer and that for the outgoing positron shorter. Optical markings
close to axially. Preliminary studies show a precision of
end-plate (see Fig. 26). A carbon fibre support∼10theirµm inpositions
the transverse
coordinate(x–y)withand ∼100µm camera
are printed on the target andweremeasureda CCD
to proper
monitorantees thewirethetension and encloses th
in the axial coordinate can be achieved. The current scinAt the innermost radius, an Al Mylar foil sep
deformation.
tillator target with its printed pattern is shown in Fig. 23.
chamber gas volume from the helium filled ta
Prototypes have been built [97] to demon
design single hit resolution of the chamber (σ2.1.3 Detectors
can be reached and the detector can be opera
4 Cylindrical drift chamber
particle flux environment of MEG II withou
2.1. asIndetailed
addition,a 4.7.
The MEG II detectors4.1
were
upgradedthe
MEG as discussed in Sec.
ageing,in Sect.
Cylindricaldrift fromchamber
overview

new detector for further background suppression is installed.

The MEG II Cylindrical Drift Chamber (CDCH) is a single
4.2 The choice of the filling gas
volume detector, whose design was optimized to satisfy thefundamental requirements of high transparency and low mul2.1.3.1 Positron spectrometer
CDCH uses a helium based gas mixture. The chtiple Coulomb scattering contribution for 50 MeV positrons,
is very
advantageous,
because of its large ra
The positron spectrometerin theMEG II
consists
Bending
RAdiusstopped of
on COnstanttarsustainableoccupancy(atexperiment∼7 × 107 µ+ /s(X0 ∼5300 m at STP), which ensures a smaget) magnet
and fast electronics
cluster timing
capabilities[96]. drift(COBRA) superconducting
to bend for
positrontracks,a cylindricalchamber(CDCH)
in terms
of multiple
Coulomb scattering, a v
Despite the fact that in MEG II the acceptance of the appafeatureinlow
momentumto track positrons and a pixelated
timingcounter(pTC)
to measuretimings. They were measurements.
ratus is dictatedby theC-shaped
LXe photon
detectorpositron(see
A small amount (10%) of isobutane is
Sect. 6), CDCHtohas
full highcoverage(2π in φ), andto avoid
non- detection
designed to satisfy the requirements
haveresolutions
a highandquenchereﬃciency,
to avoid self-sustaineddischarge. S
homogeneous and asymmetric electric fields.
age is sufficient as it raises the number of prim
to be tolerant of a high backgroundenvironment
fromMicheldecays.
The mechanical structure, shown in Fig. 24, consists of apairs to ∼ 13 cm−1 [98] though lowers the mi
1.91 m long cylinder, inner radius of 17 cm and outer radius
length to X0 ∼1300 m. Unfortunately, the useof 29 cm. It is composed of 10 concentric layers (see Fig. 25),
quencher also results in additional problems
COBRA magnet
azimuthally divided in 12 identical 30◦ sectors per layer, 16
to high radiation fluxes. The recombination
wide. Each drift solenoid
cell layer consistsof twofor
crissThe COBRA magnet drift
is a cells
superconducting
developed
the MEGand in the formation oorganicexperimentmolecules results
crossing field wires planes enclosing a sense wires plane atuidpolymers
whichaccumulate
on the anodes
reused in the MEG II experiment.
forms
a (approximately
gradient magnetic
field by placing coils withalternating signsIt
stereoanglesranging fromcontributing
totheageingofthechamber.
while radiusincreases)
respect
contigu- is 1.27 T at the center
6.0◦ to 8.5◦densities
2.9).withThe
fieldtostrength
diﬀerent radii and wire winding(Fig.
ous layers for a precise reconstruction of the z-longitudinaland decreasing to 0.49 Tcoordinate.
at the both ends. This gradient magnetic field6 isdesignedso thatPolyEther
Ether Ketone,
a colourless organic therm

positrons with the same momenta emitted from the target to have the same projected bending123
radii independent of theiremission angles (Fig. 2.10(a)). This enables us to detect positrons
with the high momenta selectively. Moreover, positrons can be swept away quickly even if they
are emitted almost perpendicularly to the beam axis because of the decreasing magnetic fieldChapter 2 MEG II Experiment

434 Page 4 of 30

31

Eur. Phys. J. C (2016) 76:434

sion polar angle θe+ (see Fig. 3a), even for positrons emittedwith substantial longitudinal momentum.
The central part of the coil and cryostat accounts for
0.197 X 0 , thereby maintaining high transmission of signal
photons to the LXe detector outside the COBRA cryostat.
The COBRA magnet is also equipped with a pair of compensation coils to reduce the stray field to the level necessary to operate the photomultiplier tubes (PMTs) in the LXe
Figure 2.9 Schematic view of the COBRA magnet [49].
detector.
(a)Eur. Phys. J.with
C (2016)
76:434The COBRA magnetic field was measured
a commercial Hall probe mounted on a wagon moving along z,
positrons emitted r and φ in the ranges |z| < 110 cm, 0◦ < φ < 360◦ and0 < r < 29 cm, covering most of the positron tracking volstat accounts for ume. The probe contained three Hall sensors orthogonally
mission of signal aligned to measure Bz , Br and Bφ individually. Because the
COBRA cryostat. main (axial) field component is much larger than the others,
th a pair of com- even small angular misalignments of the other probes could
o the level neces- cause large errors in Br and Bφ . Therefore, only the meaPMTs) in the LXe sured values of Bz are used in the analysis and the secondaryfrom the measured
components Br and Bφ are reconstructed(a)(b)
ured with a com- Bz using Maxwell’s equations(a)as(b)
moving along z,
Fig. 3 Concept of the gradient magnetic field of COBRA. The!
1 z ∂ Bz (z ′ , r, φ) ′positrons
follow trajectories
at constantradius have
weakly depen< φ < 360◦ and B (z, r, φ)Figure2.10
Principleof
COBRA
magnet[1].
(a) Positrons
with thesamebending
momentadz= Bφ (z B , r, φ) +φ
+ (a) and those emitted from the target
dent
on
the
emission
angle
θ
e
r
∂φ
tron tracking volzB
the same radius. (b)are swept awaywith
quickly.
small longitudinal momentum (θe+ ≈90◦ ) are quickly swept away
! z Positrons
sors orthogonally∂ Bz (z ′ , r, φ) ′from
the central region (b)dz .
ually. Because the Br (z, r, φ) = Br (z B , r, φ) + z∂rBer than the others,
The measuredof Br andtheBφ are2.10(b)).values
Therefore,
hitrequired
rate atonly
theatpositron detectors can be suppressed.
ther probes could (Fig.
re, only the mea- z B = 1 mm near the symmetry plane of the magnet where
The COBRA magnet was designed not to interfere γ-ray detection. It has a thin window withand the secondary the measured value of Br is minimised (|Br (z B , r, φ)| <as expected.
effectof the misalignment× 10−3 0T)thickness
om the measured 20.197X
at Thethe(b)
acceptanceregion of the γ-rays so that the signal γ-rays can penetrateof the Bφ -measuring sensor on Bφ (z B , r, φ) is estimated byit.Fig.The
used
forreconstructedtheγ-ray detectorarenot operational in magnetic field, and thus theBφ withchecking
thePMTsconsistencyof the3 Conceptof the gradientmagnetic fieldBrofand
COBRA.
The′ , r, φ)positrons follow
trajectories
at constantbending
weaklydepenMaxwell’sequations.
compensationcoils areplacedto radius
reducethestray field at the location of the PMTs from the
dz ′
dent
the emission
angle θe+field(a) andemittedthe targetφ
The oncontinuous
magnetic
mapthoseusedin the fromanalysisis◦+ ≈90 ) are quickly swept awaywith small longitudinal
COBRA
magnet momentum
down to(θe50
G.
obtainedinterpolating, φ) ′
from theby
centralregion (b) the reconstructed magnetic field atdz .
the measurement grid points by a B-spline fit [11].

required only at Cylindrical drift chamber
2.4 Drift chamber system
he magnet where
A new single-volume wire drift chamber was designed to have a high transparency for the(|Br (z B , r, φ)| <The DCH system [12] is designed to ensure precise meahe misalignment MEG II experiment since the positron detection eﬃciency
experiment
was
low
due
Fig. 4 View ofin
thetheDCHMEG
system fromthe downstreamside ofthe MEGsurement of the trajectory and momentum of positrons fromφ) is estimated by +detector. The muon stopping target is placed in the centre and the 16+ γ decays. It is designed to satisfy several requireeµto →the multiple Coulomb scattering at mechanicalDCH
supports
andelectronics
of thedrift chamber.
modules aremountedin a semi-circulararray
ed Br and Bφ withments: operate at high rates, primarily from positrons from+ decays
has a incylindricalshape
withtothe
innerradius of 17 cm, outer of 29 cm and the length of 191 cm
the target; have
low mass
improve
kinematicµIt
d in the analysis is27.9 cm (see Fig. 4). Each module has a trapezoidal shape
resolution (dominated by scattering) and to minimise promagnetic field at (Fig. 2.11). A low-density gas mixture of He and C4 H10 is enclosed in the volume with thewith base lengths of 40 and 104 cm, without supporting strucduction of photons by positron AIF; and provide excellent
fit [11].
ture on the long (inner) side to reduce the amount of material
resolution in the measurement of the radial and longitudinalintercepted by signal positrons. A module consists of twocoordinates.
independent detector planes, each consisting of two cathThe DCH system consists of 16 identical, independentode foils (12.5 µm-thick aluminised polyamide) separated
modules placed inside COBRA, aligned in a semi-circle withure precise mea- 10.5◦ spacing, and covering the azimuthal region between
by 7 mm and filled with a 50:50 mixture of He:C2 H6 . A plane
Fig. 4◦ View of the DCH
system from the downstream side of the MEG
of positrons from 191.25
and 348.75◦ and the radial region between 19.3 andof alternating axial anode and potential wires is situated mid-Chapter 2 MEG II Experiment32
Page 21 of 60 380

Eur. Phys. J. C (2018) 78:380

Counts [a.u.]

the acoustic method a periodic signal at a frequency close
to the wire resonance is measured in the readout circuit byapplying a HV difference between two adjacent wires andby using an acoustic source to excite the wires’ oscillation.
This system has the ability of measuringEur.
simultaneously
up78:380
380 Page 22 of 60
Phys. J. C (2018)
to 16 wires. In the electrical method the wire oscillation isforced by applying a HV signal at a known frequency. The
mutual capacitance variation between two adjacent wires isthen measured during a HV frequency scan on an external
auto oscillating circuit connected to the wires.
The drift chamber assembly is performed in safe conditions with unstretched wires: the distance between the endplates is fixed at 1906 mm, 6 mm less than the nominal length(1912 mm) and 2 mm less than the untensioned wire length.
The positioning of the wire trays on the drift chamber isdone in a well-constrained way using a rocker arm, shown in
Fig. 26.
The wire tray is first engaged to the rocker arm by meansof two precision pins fitting two PCB holes and a clip. The
rocker arm is then engaged to a support that leaves it free torotate and transfers the wire tray on the end-plates between
two spokes. The final positioning is driven by hand though
dedicated nippers. The wire PCBs are glued on the PEEK
spacers with double sided tape previously applied on the inner
layer. The PEEK spacers are needed to separate the layers at
the right distance. Two pressing arches are used for ensuring
Fig. 33 The entire drift chamber with all layers mounted. The hyperbolic profile of the chamber is visible
Fig. 32 A close view of an end-plate after assembling 80% of thea good adhesion of the tape.
of the layers is shown(a) 0.12we show the picture of the drift chamber after layers, in the insert the crossing(b)– Spectrometer acceptance: the well known Mott cross sec-In Fig. 32
assembled the 80% of the layers, the crossing of the layers
tion permits the direct measurement of the spectrometer
acceptance.
in the two stereo
views is shown in the box, while Fig. 33
0.1
the positron momentum very close to the µ+ → e+ γ signal– Independent check of the muon polarisation: the comshows the hyperbolic profile of the drift chamber with allenergy ( pe+ ∼53 MeV/c), a quasi-monochromatic intenseparison of the Michel versus Mott θe+ -distribution, afterlayers mounted.
7 +beam (σ pbeam
0.08+ ∼250, keV/c, Ie+ ∼10 e /s) can be Mott scattaking into account the θ cross-section dependence of theeMott events, allows a cross-check of the muon polarisatered on the light nuclei present in the muon stopping target,
4.6 Calibration and monitoringtion at the Mott positron energy.
providing a very useful e+ -line for a full understanding of
0.06– Positron momentum and angular resolutions: positron
the spectrometer from alignment to the positron kinematic
Michel events represent the natural way to continuously and −3
0 resolution.
momentum and angular resolutions are extracted using
variables’
fully characterise the spectrometer with dedicated pre-scaled
double-turn track events. The double-turn track is divided
0.04
The merits of the method, some of them unique, can betriggers. The
Michel positrons at the edge of the continuous−3
in two independent
listed as
0 tracks, the two tracks are propagatedenergy spectrum are actually used to perform the alignment
towards the target and the difference between the relevantof the spectrometer,
to define the energy scale of the detector
0.02
observable (i.e. the pe+ , φe+ or θe+ variable) is computed.
and to extract all the positron kinematic variable resolutions(energy, time and angular variable resolutions).
– Spectrometer absolute energy scale determination.
0
As final remarks it should be noted that the high Mott
40
42
44
46 48
50 52
54 56
58
60 – Spectrometer alignment:*1the alignment is performed as
positron rate enables for a fast calibration, the method does
Ee [MeV]
an iterative procedure on the residuals of the expected and4.6.1 The Mott monochromatic positron beam
not require a dedicated target (i.e. the Mott target is themeasured hits of the tracks. The alignment is executed
Fig. 34 The Mott scattered positron energy distribution in our specMEG II muon stopping target) and does not need additionalwith the detector under normal running conditions (i.e.
The continuous
Michelpositronmakes
cali+ = (51.840 ±trometer angular
acceptancewithspectrum
a mean valueat Ê ethebeam infrastructures.
with the magnetic field on) using curved tracks having
bration 0.003)
difficultandto significant
errors,
MeV.
Thesubject
comparison
between datasystematic(black dot points)
and MCThe potential of this method has been proven using dedsimulation (redmono-energetic
dashed area) is shown
monochromatic energy which simplify the procedure.
while delivering
positrons would bringicated beam tests performed at the π E5 beam line (i.e. the– Spectrometer checks: the well known relative depenimportant advantages.
MEG II beam line) with the MEG spectrometer in 2012.
Positrons
an abundantcomponentof the MEG/MEG
Theareabilityof performing
the spectrometeralignment◦ II and dence◦ of the Mott scattered +positron-momentum on the
Figure 34 shows the good agreement between the Mott e+ -surface
compobeam (eighttimesconsistent
more intense
thancanthebeµ+seenobtaining
resultsin Table
3 which angular variables φe+ and θe makes possible a detailed
line (black dot points) and the Monte Carlo (MC) simulanent,
but
they
are
normally
separatedandrejected).
Turninvestigationof the spectrometer, any distortion wouldshowsareconstructed
set
of
Mott
data
taken
in
2013
based
tion prediction (red dashed area). The data are fitted withmuon
beam into
a positron
beam
and tuning
the Michelalignment
versusMottlinealignment:
both the signal deviation from the expected detector behaviour.
a double Gaussian function: one taking into account ing
the theonmean energy and width are compared. The two data sets arecore of the distribution and one the low energy tail. Within good agreement. The two different methods allow different
the beam momentum slits virtually “fully closed” we get a123systematic errors to be identified.
line centred at Ê e+ = (51.840 ± 0.003) MeV with a width
=
(412
±
10)
KeV.
σ Ecore+Figure 2.11 (a) Overview and (b) an enlarged view of the end cap of the MEG II drift chamber [2].

proportion of 90 : 10. The total radiation length is 1.58 × 10
2.0 × 10X in a single turn while it was

X in the MEG drift chamber. The low material budget also reduces generation ofthe γ-ray backgrounds from the positron annihilation in flight.

The drift chamber consists of nine drift cell layers as shown in Fig. 2.12 . Sense wires made+of gold plated tungsten with the diameter of 20 µm are centered in each cells, and silver plated
aluminum field wires with the diameter of 40/50 µm surround the sense wires. Wire planes are
slanted at alternating signs stereo angles raging from 6.0 to 8.5 , which allows to reconstruct
the z-longitudinal coordinate precisely. The drift cells are almost square from 6.6 mm in the
innermost layer to 8.7 mm in the outermost layer. Each drift cell layer consists of two crisscrossing field wire planes enclosing a sense wire plane.
e123

Pixelated timing counterA pixelated timing counter is placed outside the drift chamber and measures the positron
timings. It is composed of an upstream and a downstream sector. The timing counter for
the MEG II experiment is a highly segmented scintillation counter made of BC422 fast plastic
scintillator (Saint-Gobain). It consists of 512 small scintillator tiles (Fig. 2.13(b)), 256 tiles
for each sector, while 30 scintillator bars with the size of 40 × 40 × 800 mm3 were used for
the MEG experiment (Fig. 2.13(a)). The size of the scintillation tiles is 40 × 120 × 5 mm3 or
50 × 120 × 5 mm3 depending on the position as shown in Fig. 2.14. The pileup probability canbe significantly reduced, which enables operation in a high-rate environment.
This segmented design enhances the timing resolution. The resolution of the MEG timing
counter was limited by a large variation in the optical photon path lengths due to the large
scintillator size, and thus the small dimensions of the single counter can make the timing resolution better. In addition, since each particle can hit multiple counters, nine hits on average*1 This figure includes ten layers though the most outer layer was removed in the real detector.

Chapter 2 MEG II Experiment

Figure 2.12 Drift cells configuration at the center of the drift chamber [2].

(Fig. 2.15(a)), the combined timing resolutions can be greatly better than the resolution of the√single counter; the resolution improves as σtsingle / Nhit , where σtsingle is the timing resolutionof a single counter, which includes the intrinsic resolution of a single counter, the error in timealignment over the counters, and the electronics jitter. Fig. 2.15(b) shows the dependence of the
combined timing resolution on the number of hits Nhit , which was measured for Michel positrons
in the pilot run. The resolution of 31 ps is achieved at Nhit = 9.
The silicon photomultiplier (SiPM) from AdvanSiD (ASD-NUV3S-P High-Gain (MEG)) is
used for the MEG II timing counter instead of the photomultiplier tube (PMT) for the MEG
because it is superior for the timing counter in the two aspects: the compactness and the highimmunity to magnetic fields; the degradation of the performance of PMTs in the magnetic field
deteriorated the timing resolution in the MEG. Each tile is readout by six series-connected
SiPMs attached to each end.
The scintillation tile is wrapped with an enhanced specular reflector (ESR) from 3M(Fig. 2.16). An optical fiber is inserted to the scintillator tile in order to inject a synchronous
laser signal for the timing alignment between tiles.
Expected performance
The performance of the spectrometer is evaluated with MC and the expectation is summarizedin Table 2.2.
2.1.3.2

γ-ray detector

The positions, timings and energies of γ-rays were measured with a liquid xenon (LXe) γ-ray
detector in the MEG experiment. LXe of 900 L was used as a scintillator and its scintillation

33

Chapter 2 MEG II Experiment

(a)

34

(b)

Figure 2.13 (a) The380
MEGPagepositron
26 of 60timing counter [1]. (b) The MEG II positron timing counter [2].

tion and hence the time resolution
was obtained with ESR film, whi
observed with Teflon tape (diffuse
reflector [115].

5.3.1.2 SiPM The photo-sensors
scintillation light in the near-u
Recently, several manufacturers ha
sensitive SiPMs based on ‘p-on-nfore, we tested a number of such NU
able as of 2013 from AdvanSiD (Aics, KETEK, and SensL.
Before the decision of SiPM m
W = 50 mm
the schemes of SiPM connection. I
W = 40 mm
small active area of SiPMs, multiin parallel for read-out. However, pparallel connection are: increase i
Figure 2.14 Designofthedownstreamtimingcounter.
Eachscintillation
counter
is 40andmmincrease in the parallel a
Fig. 39 Design of the downstream pTC super-module
width
or 50 mm wide depending on its position.
inate from the larger sensor capacit
the time resolution. We have exami
tion: series connection of multiple
5.3.1 Counter module design
light was detected by surrounding photosensors as shown in Fig. 2.17. PMTs
were40used
asa comparison of
Figureshows
and parallel
Theon
singleis composedof werea scintillator
tilewithand multiphotosensors and thosethecounter
γ-ray entrancefacereplaced
SiPMs inseries
the MEGII. connections. Se
tertime
resolutions
ple
SiPMs.
The
counterdimensionsaredefinedbythelengthIn the MEG experiment, 846 PMTs were installed on faces of the detector. The inner face at all over-vol
narrower output pulse shape beca
(L), width (W ), and thickness (T ) of the scintillator tile andwas covered by 216 described
PMTs withminimum
spacingMultiple
betweenadjacent
PMTs. sensor
However,since in the series c
capacitanceas La ×W × T below.
SiPMs
are optithe photo-cathode ofcallythecoupled
PMT hasa round-shape,
interval
among
is 63 mmcharge (gain)
is reduced to 1/NSiPM
to eachW × T side theof thescintillator.
Thethe PMTs
thesignalamplitude
signals
from
the
SiPMs
on
each
end
are
summedupandfedwhich is much larger than the diameter of the active area of the PMT, 46 mm (Fig. 2.18(a)). (pulse height)
times fast
pensated by the N
to one readout channel. The e+ impact time at each counter
This non-uniform PMT coverage caused an even-by-event fluctuation in collection eﬃciency of SiPM
conclude that series connection isis obtained by averaging the times measured at both ends.
2.18(b)showsantheextensiveeﬃciencyof scintillationlightcollection
as aWefunction
scintillation light. Fig. We
cation.
simply connect SiPMs
performed
study
to optimise thesinglecircuitdepends
board (PCB)
counter
design, startinga comparative
study
of scintil-eﬃciencyof the depth of the firstinteraction
for thefrom
signalphoton. The
collection
on while we adop
the
MPPCs
used
lator
material,
SiPM
models,numberof
SiPMs
percounter,the incident position: a high eﬃciency if γ-rays enter in front of the PMTs (case A) and a lowin LXe photon deFor each type of SiPM, we mand connection scheme. Then, an optimisation of the scineﬃciency otherwise (caseB).
This
deteriorates
theenergyandpositionresolutions,especiallyacteristics(such as dark count ratillator geometry was performed to find the best compro2.19,
thisfor shallow events. Sincemany γ-rays
interactin thedetection
shallow region
as shown
inFig.and
PDE,
temperaturedependencemise between
the total
resolution,
efficiency
andwhen coupled to a scintillator. Th
required number of channels. The results are reported inin Fig. 41. The best time resolutio
detail in [115–118] and summarised below.
from Hamamatsu Photonics, whic
This result indicates that the time r
5.3.1.1 Scintillator The choice of the scintillator material
predominantly limited by the pho
is crucial to optimise the time resolution. The candidates

Chapter 2 MEG II Experiment

35
100

1
9.281

Resolution (ps)Frequency (a.u.)

Mean

0.5

0
0

5

10
Nhit

15

(a)

20

80

χ2 / ndf

8.537 / 3

single92.62 ± 0.6224

const

0 ± 3.032

60

40
20

2

4

6
N hit

8

10

(b)

Figure 2.15 (a) Expected number of hits for a signal positron from the simulation [2]. (b)The timing resolution measured in the pilot run 2016 as a function of the number of hits√
Nhit [2]. The red curve shows the best fit by a function of σsingle / Nhit ⊕ σconst .

Figure 2.16 Scintillation counters of the MEG II timing counter [2]. Each scintillator has
the size of 40, 50 × 120 × 5 mm3 . Scintillation light is read out by the six series connected
SiPMs attached to the both sides. The fiber inserted in the right scintillator is used forthe timing alignment.

fluctuation is a crucial problem.
The main upgrade of the LXe detector for the MEG II experiment is to improve this nonuniform response by replacing the 216 PMTs on the inner face with 4092 SiPMs as shown in
Fig. 2.20. Thanks to the square shape of the photosensor, the inner face can be covered uniformly
by the sensitive area. Moreover, the higher granularity (Fig. 2.21) leads to better energy andposition resolutions of the shallow events.
The SiPM has further advantages compared to the PMTs. Its insensitivity to magnetic fields
and photoelectron counting capability enable an easier and more reliable calibration of thedetector. Less material budget in the entrance face increases the detection eﬃciency by 9%. Its
lower bias voltage, typically under 100 V, also makes the operation easier.
In addition to the photosensor replacement, the layout of the PMTs is modified to make thebest use of them based on MC. The inner face is extended horizontally by 10% to each side
(Fig. 2.22). The PMTs on the lateral faces are tilted so that all the photo-cathodes lie in thesame plane. The extended volume and the sensor configuration reduce the eﬀect of leakage dueChapter 2 MEG II Experiment

36

Table 2.2 Positron detector performance [50].

MEG (measured)

MEG II (simulated)

Ee+ resolution (keV)

380

100

θe+ resolution (mrad)

9.4

6.7

ϕe+ resolution (mrad)

8.7

4.9

te+ resolution (ps)

107

40

2.4/1.2

1.7/0.83065vertex resolution (ze+ /ye+ mm)
eﬃciency (%)

Figure 2.17 Overview of the LXe detector in MEG. A γ-ray enters to the inner face of thedetector and scintillation light induced by the γ-ray is detected by photosensors.

to shower fluctuations for events near the lateral walls, which improves the energy resolution
especially for those events. The PMTs on the top and the bottom faces are also rearranged togain uniform response for the events near the top or the bottom face (Fig. 2.23).
Geometry
Fig. 2.24 shows the overview of the LXe detector. The detector has a C-shape with six faces
called inner, outer, upstream, downstream, top and bottom face. The distance between theChapter 2 MEG II Experiment

37

62 mm

57 mm
sensitive area
PMT
46 mm

(a)

(b)

Figure 2.18 (a) Layout of the PMTs on the inner face in MEG. (b) Simulated photon
collection eﬃciency as a function of the conversion depth of signal γ-rays in MEG [2].

450
400
350
300
250
200
150
100
50
0
0

2

4

6

8

10

12

14

16 18 20depth (cm)Figure 2.19 Simulated distribution of the conversion depth for the signal γ-rays [2].

Figure 2.20 The inner face of the LXe detector for the MEG II experiment.

Figure 59 illustrates the modified layout viewed on a r -z section. The inner face extends along z, outside the acceptanceregion by 10% on each side. The extended volume reduces
the energy leakage for events near the lateral walls. The PMTs
Chapter
2 facesMEG
II Experimentonthe lateral
are tilted
such that all the photo-cathodes
1200

100
80

100

60

80

40

60

20

40

0

There are several issues to be addressed concerning the detection of LXe scintillation light by MPPCs.
The first issue is the photon detection efficiency (PDE)
for VUV light. There are two types of layer structures for38
1200

100
80

100

60

80

40

60

20

40

0

20

494

203

84

20
0

-60
-100
-100

100

200

14

-60

5

-80

2

0

2

-100
-100

300

z

34

-40

5

-80

84

-20

14

-40

203

0

34

-20

494

0

100

200

300

z

1

1

Fig. 58 Example of scintillating light distributions detected by photo-sensors in case of (left) PMTs and (right) smaller photo-sensors (12 × 12
2.21for the
Examplescintillating light distributions in MEG II (left) and MEG (right)mm2 ) on Figure
the inner facesame MCof
event

for the same MC event [2].

123

Figure 2.22 Layouts of the PMTs on the lateral faces of the LXe detector for MEG (left)
and MEG II (right) [2].

115

115

110

110

105

105

100

100

95

95

90

90

85
80

85

r

80

75
70

75

z

70
−40

−20

0

(a)

20

40

r
z

−40

−20

0

20

40

(b)

Figure 2.23 Layouts of the PMTs on the top and the bottom faces of the LXe detector in(a) MEG and (b) MEG II.

inner face and the beam axis Rinner is 64.84 cm for MEG II such that the detector subtends∼11% of the solid angle. The thickness of the active volume is 38.5 cm, which corresponds to
13.8X0 , to capture the whole electromagnetic shower from the signal γ-ray.
The development view with the definition of the local coordinate system is illustrated inFig. 2.25. A local coordinate (u, v, w) is defined to describe a position of a γ-ray vertex in theChapter 2 MEG II Experiment

39

Figure 2.24 Overview of the LXe detector for the MEG II.

detector asu = z,
v = tan (−y/x) × Rinner ,√w = x2 + y 2 − Rinner ,where u and v correspond to the horizontal and vertical coordinates on the inner face, respectively, and w is the depth from the inner face. The active volume of this detector, where γ-ray
hits are analyzed, is defined as |u| < 23.9 cm, |v| < 67.9 cm and 0 < w < 38.5 cm.
The detector cryostat consists of an inner and an outer vessel to keep xenon in liquid state. The
layer between the two vessels is in vacuum state to thermally insulate the inner vessel filled withliquid xenon, and super insulation sheets are installed between the vessels to prevent a radiantheat. An entrance window γ-rays go through is required to be thin to suppress their conversions
before the active volume. It is composed of a honeycomb-structure aluminum window covered
with a carbon fiber plate resulting in material thickness of 0.081X0 radiation length. The totalmaterial budget of the γ-ray entrance window is 0.110X0 including that of the photosensors,
0.029X0 .
Liquid xenon
Liquid xenon is used as a scintillator for several advantages. Table 2.3 summarizes its properties. Thanks to the large atomic number and high density, LXe has a high stopping power,
which allows a compact detector with a reasonable detection eﬃciency. The high light yieldprovides a good detector resolution. The fast decay time of the scintillation is suitable for an
operation in a high pileup environment. In addition, a liquid scintillator is easier to obtain aChapter 2 MEG II Experiment
top

100
80

40
1300.00

downstream

upstream

1001118.14
60

80

40

60

20

40

0

20
0
−20

962.26806.38v-axis650.50u-axisw-axisinner

468.64−40−60

312.76−80

156.88

−100
−100

0

z

bottom

100

200

300
outer

1.00

Figure 2.25 Development view of the LXe detector for the MEG II. The red axises show
directions of the local coordinate on the detector.

uniform response than a crystal scintillator.
Table 2.3 Properties of LXe.

Item

Value

Atomic Number

54

Density

2.953 g/cm3 [51]Radiation length2.872 cm [51]Moliere radius

5.224 cm

Scintillation Wavelength (mean)

174.8 ± 0.1(stat.) ± 0.1(syst.) nm [52]Scintillation Wavelength (FWHM)

10.2 ± 0.2(stat.) ± 0.2(syst.) nm [52]Decay time (fast)

4.2 ns [53]Decay time (slow)

22 ns [53]Decay time (recombination)

45 ns [53]W-value for electron

21.6 eV [54]W-value for alpha17.9 eV [54], 19.6 eV [55]Refractive index (for λ = 175 nm)

1.65

Critical energy

14.5 MeV [56]Another advantage is its transparency against its own scintillation light. When a particle
deposits its energy in LXe, scintillation light is produced by the self-trapping of excited xenon
atoms (Xe∗ ) in two processes: direct excitation (Eq. (2.1)) and recombination of electron-ion
pair (Eq. (2.2)). They create excited atoms, which combine with a neutral ground-state Xe
atom to form the molecular dimer Xe∗∗ . The dimer decays to the monatomic ground state via
emission of a vacuum ultraviolet (VUV) photon. Since the scintillation light is generated via
the excimer not via the excited xenon atom itself in LXe, the yielded light is not absorbed byChapter 2 MEG II Experiment

41

Figure 2.26 LXe scintillation decay time for each particle [53].

LXe.
Xe∗ + Xe + Xe → Xe∗2 + Xe

(2.1)

Xe∗2 → 2Xe + hν

Xe+ + Xe

→ Xe+
2

−
Xe+
→ Xe∗∗ + Xe
2 +eXe∗∗ → Xe∗ + heatXe∗ + Xe + Xe → Xe∗2 + Xe

(2.2)

Xe∗2 → 2Xe + hνThe decay of the excimer, Xe∗2 → 2Xe + hν, has two decay time constants since the excimer
has mainly two excited molecular states of singlet and triplet; the decay time of the singlet stateis much shorter than that of the triplet state. As shown in Fig. 2.26, the scintillation decay
times are diﬀerent depending on particles, which can be used for a particle identification.
On the other hand, LXe has disadvantages as well. Firstly, LXe is expensive. Secondly, since
the wavelength of its scintillation light is in the VUV region, photosensors sensitive to light inthis region are required. Thirdly, the detector operation is diﬃcult because LXe must be kept

Chapter 2 MEG II Experiment42

Figure 2.27 Phase diagram of xenon.

free from contaminations in liquid state. Fig. 2.27 shows a xenon phase diagram. To keep liquidstate, only a small temperature region is allowed around the atmospheric pressure. Therefore,a precise temperature control is essential. Moreover, impurities in LXe results in a reduced
light yield since a oxygen or a water contamination can absorb scintillation light and a nitrogencontamination can quench the xenon scintillation by the following process:Xe∗2 + N2 → 2Xe + N2 .
When a γ-ray is injected into material, three types of reactions occur, i.e. photoelectric absorption, Compton scattering and pair creation. Fig. 2.28 shows the cross section of xenon, whichindicates pair creation is dominant process around the energy of the γ-ray from the µ → eγ.
Fig. 2.29 illustrates the development of the electromagnetic shower when a signal γ-ray enters
the LXe detector; the γ-ray firstly converts, and a positron and an electron are emitted by thepair creation. They fly emitting γ-rays by bremsstrahlung, and the γ-rays travel in the detector
depositing their energies by Compton scattering. The cross section of the Compton scattering
for the γ-ray of 1 MeV is 0.052 cm2 /g resulting in mean free path of 6.5 cm, where most of thegenerated γ-rays has the energy below 1 MeV. Fig. 2.30 shows the averaged shower profile alongwith the transverse direction and the longitudinal direction. The shower spread is limited withinO(1) cm, which can be understood by the mean free path.
Photosensors
The photosensors for the LXe detector must be sensitive to the VUV light and operational at
the low temperature. A new type of PMT was developed for the MEG and that of SiPM forthe MEG II which fulfill these requirements. Hereafter, the properties of the photosensors areFigure 2.8: Phase diagram of xenon
Chapterand
2 MEG
II Experiment43
scatteringpair creation
are dominant. Therefore the gamma-ray around the signal energy
makes electromagnetic shower starting from the first conversion by scattering or creation.

Figure2.28 Photon
crossassectionof xenonFigure 2.9: Photon
interaction
in LXea functionof[57].
photon energy [58].

y (cm)

Some part of the deposited energy in the liquid xenon is used to emit scintillation photon.
The scintillation photons are generated from two reaction paths [53]. The first path is excitation
as follows,
3
1
27
2.8
0.9
2.6

0.8

2.4

0.7

2.2

0.6

2

0.5

1.8

0.4

1.6

0.3

1.4

0.2

1.2

0.1

1
−80

−78

−76

−74

−72
x (cm)

0

Figure 2.29 Development of electromagnetic shower in LXe simulated with GEANT 4 (version 10.4 [58]). Particle tracks of γ-rays, positrons and electrons are shown as lines in black,
red and green, respectively. The original signal γ-ray from a muon comes from the right.
The energy deposit on each point is overlaid. The scale of the bar is in the unit of MeV.

44

5

10

4
3

1

2

y (cm)y (cm)

Chapter 2 MEG II Experiment

5
3

1

2
1

1
10−1

0
−1

−1
−2

10−2

−3

10−1

0

−2

10−2

−3
−4

−4
−5

10

4

−4

−2

0

2

4
z (cm)

10−3

−5

0

5

(a)

10

10−3

15
x (cm)(b)

Figure 2.30 Shower profile from a signal γ-ray along with (a) the transverse direction and(b) the longitudinal direction simulated with GEANT 4 (version 10.4 [58]). Mean of energy
deposits in the area of 0.1 cm square over O(100) events is shown, where the first conversion
points of each event are aligned to be the origin. The scale of the bar is in the unit of MeV.

Figure 2.31 VUV-sensitive PMT (R9869) [59].

discussed.
PMT
A new PMT which satisfies the requirements was developed in collaboration with Hamamatsu
Photonics (Fig. 2.31). Table 2.4 summarizes the properties of the PMT (R9869). For thesensitivity to the VUV light, Bialkali (K-Cs-Sb) is used as a photo-cathode and a quarts window,
which is 80% transparent for λ ∼ 178 nm, is adopted. For the operation at the low temperature,
the photo-cathode has aluminum strips to avoid the increase of the sheet resistance. In order tostabilize the gain at high-rate environment, Zener diodes are inserted in parallel to the last twostages of the resistive divider for twelve-step dynodes and keep a voltage around 85 V (Fig. 2.32).
In total, 668 PMTs are installed in the detector: 234 on the outer face, 144 on each of the
upstream and the downstream faces, and 73 on each of the top and the bottom faces, respectively.

Chapter 2 MEG II Experiment45

Table 2.4 Properties of VUV-sensitive PMT (R9869).

36
K

Size

57 mm ϕActive Area

45 mm ϕ

PMT length

32 mm ϕPhoto-cathode material

K-Cs-Sb

Dynode type

Metal channel

Number of dynode12

Typical HV

900 V

Typical gain

1 × 106

Typical QE

15%

Rise time

2 ns

Typical Transit time

12.5 ns

3. Detector
and Transit
Setup Time Spread
Typical0.75 ns

DY1

DY11

R1

DY2

R2

DY3

R3

DY4

R4

DY5

R5

DY6

R6

DY7

R7

DY8

R8

DY9

R9

DY10

R10

P

DY12

R15

R16

R12

R13
Z1

R19

R17

R14
R11

R20

C4

R21

Z2
C5

C1

R1,R12,R13 : 2MΩ 1%, 1/8W
R2-11 :
1MΩ 1%, 1/8W
R14-R16 :51Ω 1%, 1/8W
R17 :10kΩ 1%, 1/8W
R18 :10kΩ 1%, 1/4W
R19-R21 :100kΩ 1%, 1/8W

C1-C3 :
C4, C5 :
Z1 :
Z2 :

C2

C3

0.022µF, 1kV
0.01µF, 2kV

R18

+HV
(RG-188A/U)

RD68S
RD82S

SignalOutput(RG-196A/U)

Figure 3.36: Divider circuit of photo-multiplier tube.
Figure 2.32 Bleeder circuit of PMT (R9869) [60].

field was measured by three directions shown in Figure 3.37, because the PMTs aremounted on six different faces. There are larger decreases on lateral faces than others but
VUV-sensitiveMPPC
no significant
change on inner face as displayed in Figure 3.38. The measured decrease ofgains from COBRA off to on is about 10% on average and sufficiently small.

Since standard SiPMs are not sensitive to VUV light, a VUV-sensitive MPPC (Multi-Pixel
Relative output [%]Photon Counter, S10943-4372) was developed*2 for the LXe detector of the MEG II experiment
140

x-axisY

Entries2846
PMTs(Fig. 2.33). One MPPC package has a size of 15 × 15 mm. It
distinctfour bareMean
0.911consists of allZ

y-axis120

z-axisX

50

RMS

0.10096
MPPC chips with the active area of 5.95 × 5.85 mm2 for Underflow
each. Eachchip contains 13925 microOverflow
2
100

40

cells with pixel pitch of 50 µm. The four chips are glued on a ceramic base with conductive
80

30

adhesive.

PMTs (Inner face)

60

20

40

A high sensitivity to VUV light is achieved by optimizing
the design: removing the protection
10
20

coating, optimizing the optical matching between LXe0 and the chip surface, and thinning down
0
-300

-200

-100

0

100
200
300
Magnetic flux density [ Gauss]

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

Gain (COBRA
ON) / Gain
(COBRA Off)the top contact layer. In the standard SiPMs, there is a protection
layerof epoxyresin at thesurface of the sensor. This layer is removed since it disturbs VUV photons to enter the sensitive
Figure 3.37: Response of PMT against mag- Figure 3.38: PMT gain ratios for CO-

region due
to field.
the absorption,
anda 0.5 mmthick VUV-transparent
window
is mounted
netic
Relative gain
decreaseis shown
BRA magnetic fieldquartz
on / off.
The ratioby three axes with different magnetic flux
densities.

is measured with LEDs and shown by all
PMTs. The gains of PMTs in the inner*2 MPPC is the product name of SiPM device produced by Hamamatsu Photonics.
face have small changes as shown by asuperimposed distribution around 1.

Chapter 2 MEG II Experimenton the package instead. There is a thin gap of 0.5 mm between the window and the chips. It
is filled with LXe when the MPPC is operated in the LXe detector. The refractive index of
the quartz, 1.60, is close to that of LXe, 1.65, which reduces the reflection at the boundary.
In addition to the removement of the protection coating, the top contact later of the chip isthinned down to reduce absorption. Even with these optimizations, VUV light can be absorbed
in the top contact later since the attenuation length of VUV light in silicon is only 5 nm, whichis still shorter than the thickness of the layer. Nevertheless, VUV light can be detected in theway that a part of charge carriers generated in the contact later drifts to the active layer andtriggers an avalanche. To enhance this process, further improvements are applied. The dopant
concentration in the contact layer is adjusted to have a low electric field, which helps the carriers
to drift to the active layer. The processing of the contact layer is optimized to minimize thelattice defects not to trap the carriers.
To suppress the number of readout channels, an enlargement of a sensitive area is also requiredsince the sensitive areas of the standard SiPMs are typically 3 × 3 mm2 . This is realized by anenlargement of the MPPC chip and the design that the MPPC package includes four chips. In
original, the four chips can be read out individually, but they are connected inside a PCB, which
results in the active area of 12 × 12 mm2 per channel. There are, however, two issues caused by
the enlargement of the chip: an increase of dark noise and a longer decay time due to a larger
capacitance. The first issue is not a problem for the LXe detector since it is caused by a thermal
excitation, and thus it can be greatly suppressed at LXe temperature. The second issue can besolved by connecting them in series, which reduces the capacitance (Fig. 2.34). Thanks to thelarge sensitive area, the inner face of the LXe detector of 0.92 m2 is tiled with 4092 MPPCs witha total active area of 0.57 m2 .
The performance of the VUV-sensitive MPPC was measured in LXe and proved to have an
excellent performance such as a high photon detection eﬃciency, a high gain, a low probability ofthe optical crosstalk and the after-pulsing and a low dark count rate as summarized in Table 2.5.
The mass production of 4200 MPPCs including spares was performed by Hamamatsu Photonics, and they were produced in four batches called lot A, B, C and D. Before the installation,
all MPPCs were tested at room temperature. I-V curves were obtained to identify bad MPPCs,
and some MPPCs were removed due to strange current values. The waveforms were also measured with a pulsed LED light. Fig. 2.35 shows the measured decay time of each MPPC. The
production lot dependence was observed due to diﬀerent after-pulsing probabilities. This kind of
lot dependence is also observed in the LXe detector, and so it is corrected for the reconstruction.
The MPPCs are mounted on PCB strips as shown in Fig. 2.36. Each PCB strip has 22
MPPCs, and two PCBs are installed in a line along the z-axis with 93 lines covering the innerface of the detector. The electrode pins of the MPPCs are inserted into sockets on the PCBs
(Fig. 2.38(a)). The four MPPC chips in each package are connected in series inside a circuit of
the PCB. Instead of a simple series connection, the chips are connected with so-called hybrid
connection shown in Fig. 2.37. There are a decoupling capacitor and resistors in-between, whichenable to connect the signal line in series and the bias line in parallel. Thanks to this connection

46

Chapter 2 MEG II Experiment

47

215

low-level light pulses from the blue LED for the four chips connected in series
operated in LXe at

V = 7 V. The photoelectron peaks are clearly resolved

with a single photoelectron resolution as good as 12%. Fig. 12 shows the gain
computed from the single photoelectron charge measured as a function of theVoltage [mV]over-voltage.
(a)

215

10

(b)

low-level light pulses from the blue LED for the four chips connected5 in series

Figureof VUV-sensitive
MPPC
developed for MEG II (S10943-4372,
operated in LXe at
V =2.33
7 V. Overview
The photoelectron
peaks are clearly0 resolved
Hamamatsu
Photonics)[61].as 12%. Fig. 12 shows the gain
with a single photoelectron
resolution
as good−5−10 of thecomputed from the single photoelectron charge measured as a function−15

Voltage [mV]

Voltage [mV]over-voltage.
10
5
0

−200

0
Time [nsec]

−600

−400

−200

0
Time [nsec]

10
5
0

−10

−10

Voltage [mV]

−400

−5

−5

−15

−600

−15
−600

−400

−200

0
Time [nsec]

(a)

10

(b)
Figure 10: Typical waveforms for the signal with two photoelectrons (primary photoelectron

5

Figure 2.34 Typical waveforms ofoverlapped
the MPPC
with two photoelectrons, i.e. primary single
with optical cross-talk) from the VUV-MPPC with the four chips connected inwith optical crosstalk. The four chips in the−5 photoelectron signal from LED overlapped
parallel (top) and in series (bottom). The VUV-MPPCs were operated in LXe.
−10 MPPC are connected in (a) parallel and (b) series [61].
0

−15
−600

220

−400

−200

The energy resolutions of the large-area VUV-MPPC were measured for vis-

0Time [nsec]

ible light and LXe scintillation light. The sensor was illuminated by light pulses
Pulse decay time (ns)from a blue-LED with a constant intensity and the resolution was measured as
Figure 10: Typical waveforms for the signal with two
photoelectrons (primary photoelectron70

the standard deviation of the Gaussian function fitted to the charge distribu-

overlapped with optical cross-talk) from the VUV-MPPC with the four chips connected intion. The measurement was repeated for di↵erent light intensities by varying

60

parallel (top) and in series (bottom). The VUV-MPPCs were operated in LXe.
50

225

the voltage to the LED to study the dependence of the resolutions on the num-

40

220

The energy resolutions of the large-area VUV-MPPC
measured for visber wereof photoelectrons.
The sensor was operated at a low over-voltage of 1.5 V
30ible light and LXe scintillation light. The sensor was illuminatedlightpulsesto eliminatebythee↵ectof the worsening of the resolution due to the correlated
20

from a blue-LED with a constant intensity and the resolution
was13measured
noises. Fig.
shows theasmeasured resolutions as a function of the detected num10

Lot A

Lot B

Lot C

Lot D

the standard deviation of the Gaussian function fitted to the charge distribu0
0

1000

2000

3000

4000

5000

6000

MPPC serial number
tion. The measurement was repeated for di↵erent light intensities by varying

225

15

the voltage to the LEDFigure
to study
the Pulse
dependence
the ofresolutions
on the2.35
decay oftimeeach MPPC
as numa function of serial number [61].
ber of photoelectrons. The sensor was operated at a low over-voltage of 1.5 V
to eliminate the e↵ect of the worsening of the resolution due to the correlated
noises. Fig. 13 shows the measured resolutions as a function of the detected num-

15

Chapter 2 MEG II Experiment48

Table 2.5 Properties of VUV-sensitive MPPC (S10943-4372) [61].

Size

15 × 15 mm2Eﬀective photosensitive area

12 × 12 mm2

Pixel pitch

50 µm

Typical HV

55 V per chip

Typical gain

5 × 105

Typical PDE

15%

Typical dark count rate

5 Hz/mm2

Correlated noise probability< 30%

Figure 2.36 PCB for the MPPCs.
Coaxial cable (~12m)

2k
22nF

+HV

1k
1k
22nF
1k
1k
22nF
2k

MPPC

PCB

Figure 2.37 Hybrid connection used for the MPPC [61].

method, the applied high voltage is smaller than the case of a simple series connection. To avoid
electric noise, a coaxial-like signal line structure is implemented in the PCBs.
The PCBs are aligned on structures made of Carbon Fiber Reinforced Plastic (CFRP), andthey are fixed on the cryostat as shown in Fig. 2.38(b). The PCBs are mounted on four separate
CFRP structures. The temperature coeﬃcient of the CFRP is adjusted to be consistent withthat of the PCBs to meet the thermal contraction at LXe temperature. A spacer made of FR4
is inserted in the gap between the MPPCs and the PCBs to prevent LXe from filling the gap,
and another spacer is inserted between the PCB and the CFRP since the CFRP is conductive.

Chapter 2 MEG II Experiment

49

MPPC Support structure

Prototype for the spacer
bw/ MPPC and PCB

(a)

•

(b)

Any space between
Figure MPPC
2.38 MPPC support structure [62].
and Cryostat wall cause
detection inefficiency

Xenon handling system• Need to fill the gap with
Fig. 2.39 shows a whole xenon control system. Besides the LXe detector cryostat, auxiliary

light material

components are connected to control, store and purify xenon.
Since xenon has a narrow liquid state range at the operation pressure, the temperature and the12pressure of LXe must be well controlled for the safe and stable operation. A 200 W pulse-tube
refrigerator [63] is mounted on the top chimney of the detector, and a heater is installed in thedetector. A 400 W Giﬀord-McMahon (GM) refrigerator [64] is newly introduced to the MEG II
to compensate the heat from the increased number of cables. Cooling pipes with liquid nitrogenattached to the outside of the inner vessel also contribute to cooling. The temperature is kept
with a precision of 0.1 K, and the pressure is within 0.8 kPa.
There are two types of xenon storage. The 1000 L storage tank stores LXe during short-term
maintenance of the LXe detector. The pressure and temperature can be controlled with anindependent liquid nitrogen cooling system. The high pressure tanks keep gaseous xenon duringlong-term detector maintenance. The storage consists of eight tanks with 250 L capacity andtolerance to 8 MPa pressure.
To keep the high purity of xenon, purification systems in liquid phase and gaseous phase areused. The liquid purifier filters water with molecular sieves. The gaseous purifier can absorb
most kinds of molecules except for rare gas with a metal-heated getter.
2.1.3.3

Background detector

A radiative decay counter (RDC) is newly installed in the MEG II experiment to reduce
γ-ray backgrounds. As described in Sec. 1.2.2, the dominant background is the accidental
coincidence between a positron from Michel decay and a γ-ray from AIF and RMD. Thanks
to the reduction of the CDCH material in MEG II, γ-rays deriving from AIF is expected tobe suppressed compared to the MEG experiment. On the other hand, the number of RMD
backgrounds does not change, and the fraction of background γ-rays from RMD can be 65% forChapter 2 MEG II Experiment50

Eur. Phys. J. C (2018) 78:380

Fig. 77 Sources of the background photons (E γ > 48 MeV) in acciFigure 2.39 Xenon control system in MEG II.
dental background events for MEG and MEG II

Fig. 79 Simulated time differences bet
detectors for accidental background even
events (blue)

78 Schematicview
the detectionof RMD
RDC
Figure 2.40 Fig.
Schematic
view oftheofRMD
detection
withwith
thethedownstream
RDC [2].

the RMD photon background does not change. Therefore, it
is important to identify these events. According to simulaFig. 2.40 describestions,a conceptof canthe detect
RMD∼detection
theRDC.backSince the RMD events
the RDC
42% of thewith
RMD
photonwith high energy γ-raysemitevents
low energy
positrons
simultaneously,
those events
can be identified
MeV), (theproduct of the fractionofground(E γ > 48
positronsThegoing(∼ 48%)follow
and thepositronby detecting the positrons.
lowdownstream
energy positrons
anRDC
almosthelical trajectories with
detection efficiency (∼ 88%, see Table 8)) thus improving
small radii along the beamline due to the+COBRA
magnetic field, and thus the RDC is placed
the sensitivity of the µ → e+ γ search by 15%.
Fig. 80 Expected energy distribution a+ stoppingon the beam axis. TheThe
RDC
canupstream
anddownstream
target,RDC
willbebeinstalled
installed bothdownstream
the µ
E γ of> the
48 MeV(red) and for the Michel
shown inare
Fig.emitted,
78. A fractionof the RMD events
where 52% and 48% targetof theaspositrons
respectively.
can bebe identified
identified bya low-energy
positron intime the RDC and the
The RMD events canby tagging
taking thetime coincidence
betweencoincidence with the detection of a high energy photon in theenergy since they typically have h
LXe detector. The LXe
red histogram
in low-energy
Fig. 2.41 shows
theofsimulated
distribution of the time
detector. This
positron
1–5 MeV (withFig. 80. Hence, the RDC consist
diﬀerences between theaccidental
background
events whileblue
is forfortiming and a LYS> 48 MeV)forfollows
an almosthelical trajectorywith the tor
E γ detectors
barsone
(PS)
+
+
small
radiusaroundthe
B-field
lines.
Therefore,
it
can
be
energymeasurements.
µ → e γ signal events. The peak in the red histogram corresponds to the RMD
events.
Thereseen by a small detector with a radius of only ∼ 10 cm, placed
Figure81shows a schematic v
are also flat regions in both histograms, which derive from background Michel positrons. Theyon the beam axis. There is an option to install a detector also
12 plastic scintillator bars in thecan be distinguished,upstream,
however,by measuring
theirpositrons
as describedin Sect.
7.6. energies since the Michelthe
positrons,have
and 76 LYSO crysta
relatively high energies as shown in Fig. 2.42.
ter for energy measurement. In o
7.2 Detector design
positrons from Michel ones, bot
calorimeter are finely segmented.
The red histogram in Fig. 79 shows the expected distriburate is larger close to the beam ax
tion of the time difference between RDC and the LXe phothe central region is 1 cm while it
ton detector for accidental background events (with photons
The size of each LYSO crystal is 2
The PS shown in Fig. 82 consfrom RMD or AIF), while the blue histogram is the dis++read out by SiPMs. The design
tribution due to µ → e γ signal events. The peak in the
red histogram corresponds to the RMD events, while the flatto that of the pTC (Sect. 5). In o
Eγ > 48 MeV.

Chapter 2 MEG II Experiment

Page 45 of 60 380

ground photons (E γ > 48 MeV) in acciMEG and MEG II
Fig. 79 Simulated
time differences
between
RDC
andtheLXeLXephotonFigure 2.41 Simulated
time diﬀerences
betweenthe theRDC
anddetector for acci++
detectors for accidental background++ events (red) and µ → e γ signal
dental background events (red) and µ → e γ signal events (blue) [2].
events (blue)

he detection of RMD with the RDC

und does not change. Therefore, ithese events. According to simula∼ 42% of the RMD photon backMeV), (the product of the fraction ofam (∼ 48%) and the RDC positron
8%, see Table 8)) thus improving→ e+ γ search by 15%.Figure 2.42 Simulated
Fig. 80 Expecteddistribution
the RDC
eventswithenergy energy
distributions
of at
RMD
forfor
EγRMD
≥ 48
MeV
(red) and Michel
alled downstream the µ+ stopping
E
>
48
MeV
(red)
and
for
the
Michelevents(blue)
γ(blue) positrons detected by the RDC [2].
78. A fraction of the RMD events
ing a low-energy positron in timection of a high energy photon in theenergy since they typically have higher energies as shown innergy positron of 1–5 MeV (withFig. 80. Hence, the RDC consists of fast plastic scintillaDownstream
an almost helicaltrajectory withRDCtor bars (PS) for timing and a LYSO crystal calorimeter for
B-field lines. Therefore,
it caninstalledbe
The RDCin themeasurements.
downstream side consists of a timing counter and a calorimeter asenergyith a radius of only∼
10cm,
placed81 shows
a schematicof the RDC
detector:shown in Fig. 2.43. ItsFigure
geometricalacceptancetoview
the RMD
positrons
emitted to downstreams an option to install a detector also
12 plastic scintillator bars in the front detect the timing ofside is 88%. Since the Michel positrons hit the RDC at the frequency of about 10 MHz, both
Sect. 7.6.
the positrons, and 76 LYSO crystals behind are the calorimethe timing counter andtheenergy
calorimeterare finely
12 plastic
scintillator bars for theter formeasurement.
In segmented:
order to distinguish
RMD
Michel ones,
both theYttrium
PS and the
LYSOtiming counter and positrons
76 LYSO from
(Cerium-doped
Lutetium
Orthosilicate)
crystals for thecalorimeterarefinelysegmented.
Becausethebackgroundcalorimeter.
g. 79 shows the expected distriburate is larger close to the beam axis, the width of the PS in
Hereafter, the designs of the timing counter and the calorimeter are described. The measuree between RDC and the LXe phothe central region is 1 cm while it is 2 cm at the outer part.
3.
A.
ments
in photons
lab for the The
performance
evaluation
are explained
Appendixl background events(withsize of each
LYSO crystal
is 2 × 2 × 2incm
The PS shown in Fig. 82 consists of plastic scintillators
ile the blue histogram is the dis+ γ signal events. The peak in theread out by SiPMs. The design of the PS is very similar
Timing counters to the RMD events, while the flatto that of the pTC (Sect. 5). In order to have good timing
The timing
counteris composedof 12 must
fast plastic
scintillators
corresponds to background
Michelresolution,
scintillators
have a highlight yield(BC-418,
and short Saint-Gobain) withr is placed on thediﬀerent
beam-axis,
thererise time.
BC-418Saint-Gobain[119]
wascharacteristics
selected as it for a high timing
2.44.from
The
scintillators
have
sizes
as shown
in Fig.
7+
ichel positrons (∼10 e /s). They
satisfies these requirements. The scintillation light is read out
RMD positrons by measuring theirby SiPMs at both ends of each scintillator. SiPMs are compact

123

51

Chapter 2 MEG II Experiment52

Figure 2.43 Design of the downstream RDC.

Table 2.6 Properties of BC-418 (Saint-Gobain) [66].

Light Output, %Anthracene

67

Rise Time

0.5 ns

Decay Time

1.4 nsWavelength of Max. Emission

391 nsresolution with a high light yield and fast rise time as described in Table 2.6. The thicknesses of
all the scintillators are 5 mm. The widths of the six scintillators at the center are 1 cm becauseof a higher hit rate while those for the others are 2 cm. The lengths are 7, 11, 15 and 19 cm inthis order from an outer side. The scintillation light is read out with SiPMs (S13360-3050PE,
Hamamatsu Photonics) at both ends of each scintillator. Two or three SiPMs are used for
scintillators with 1 cm or 2 cm widths, respectively. The SiPMs have a high detection eﬃciency
at the wavelength of the scintillation light (Table 2.7). The SiPMs on each face are connected inseries to reduce the number of readout channels. The series connection is superior to the parallel
connection for the timing counter since a rise time of the waveform is shorter as the capacitanceof the sensor gets smaller. They are mounted on PCBs by soldering. Six SiPMs on the central
three scintillators are mounted on a single PCB together due to the limited space while others aremounted every scintillator (Fig. 2.45). The SiPMs are coupled to the scintillators with opticalcement. The scintillators are wrapped with reflectors of aluminized mylar, and then shieldedwith black sheets from Tedlar (Fig. 2.46). The timing resolution was measured to be better than
90 ps with a 90 Sr source, which is good enough for the RMD detection [65].

Fig. 81

Schematic view of the RDC. The horizontal long plates in

Chapter 2 MEG II front
Experiment
are the plastic scintillator bars, and the cubes behind are the LYSO

Fig. 83 LYSO crystals with the SiPMs

53

crystals

As described in Sect. 7.4, this in
be used for an energy calibratio
crystal is measured to be smal
not affecting the detection of pos
LYSO crystal is connected to one
side (see Fig. 83). A SiPM wit
25 µm (S12572-025 from Hamama
selected as it has good linearity fdent scintillation light. The SiPM
tact to the crystal, using opticalglued. Therefore, it is possible tocrystal.
Fig. 82 Plastic
scintillatorof timing
the RDC.
SiPMs areFigure2.44 bars
RDC
counter[2].connected tothe scintillator bars at both ends

7.3 Tests and construction in the laandTable
operatemagnetic
fields, (S13360-3050PE)
and so are suitable[67].
for the
The characteristics of each SiPM
2.7in highPropertiesof SiPMRDC having many readout channels in a limited space. The
before construction. The breakdow
Pixel
pitch
50
µm
MPPC S13360-3050PE from Hamamatsu Photonics [143]each SiPM from the measuremen
2
Eﬀective
3.0mm
was selected
forphotosensitive
the SiPM for PSarea
becauseof×
its3.0
high
gain
and
response curve. SiPMs with the bhigh photonNumber
detectionofefficiency.
In
order
to
detectasmuch
to each other are grouped together
pixels3600
scintillation light as possible, multiple SiPMs (two for theAfter the construction of the PS,
Fill factor
74%
central part and three for the outer part) are attached to botheach counter is measured to be le90
Peaksensitive
wave
length450nm
Sr source.
ends of the scintillators. The SiPMs are connected in series
The LYSO crystals are also teston the readout printed circuit boards (PCBs) to reduce thesured the light yield and the energy
number of readout channels and to reduce the rise time of thetals by using a 60 Co source. The en
signal due to the reduced capacitance. They are glued to thesured to be ∼ 6% at E γ = 1 MeV
scintillators by optical cement. Each scintillator is wrappedhigh rate environment, energy reswith a 65 µm thick reflective sheet (ESR from 3M) to increaseby the “afterglow” effect of LYSO
light yield and to provide optical separation as well as black
light emission of crystals with very
sheets of Tedlar for light shielding.
ically few hours). This effect was
The calorimeter is made of 76 LYSO crystals (Shangcrystals to a 90 Sr source. The incre
hai Institute of Ceramics). LYSO crystals have a highFigure 2.45 PCB for scintillators
with
a
2
cm
width
(left)
and
a
1
cm
width
(right).
afterglow was measured with the Si
light yield (3 × 104 photon/MeV) and a short decay time
constant (42 ns). These characteristics are suitable fortals. According to this measureme
the measurement of positron energy in a high rate enviof the current in the MEG II beam
176
Lu, whichronment. LYSO contains the radio isotope
to be ∼ 10 µA at maximum. The
decays to 176 Hf with emission of a β − (with end-point
resolution is expected to be less tha
10energy of 596 keV and half life of 3.78 × 10 years),
The support structures of thefollowed by a cascade of 307, 202 and 88 keV γ -rays.
calorimeter are constructed with

123

Figure 2.46 RDC timing counter after shielding [2].

Chapter 2 MEG II Experiment

Figure 2.47 RDC calorimeter.

54

Figure 2.48 LYSO crystal. Each crystal
is wrapped with the reflector.

Calorimeter
The calorimeter is composed of 76 LYSO crystals (Shanghai Institute of Ceramics) in the
shape of a 2 cm cube as shown in Fig. 2.47. Each crystal is wrapped with a 65 µm thick reflector(ESR, 3M) [68]. Table 2.8 summarizes the properties of the LYSO crystal. The LYSO crystal
has a high light yield and a short decay time constant, which are suitable for the measurementof energy in a high rate environment. LYSO contains the radio isotope 176 Lu (2.59% naturalabundance), which decays to 176 Hf with emission of a β − , followed by a cascade of 307, 202 and88 keV γ-rays (Fig. 2.49). The decay rate per crystal was measured to be small enough (∼ 2 kHz)not to aﬀect the RMD positron detection. The energy spectrum has a peak at 596 keV as shownin Fig. 2.50, which can be used for the energy calibration.
Each crystal is read out with a single SiPM (S12572-25P, Hamamatsu Photonics). SiPMs withmany pixels are desirable in order to avoid the saturation of the pixels due to the high lightyield of the crystals. On the other hand, the pixel size of such SiPMs is small, and thus they
have small capacitance. This results in a worse energy resolution due to a low gain. SiPMs with15, 25 or 50 µm pitch were compared in terms of the energy resolution and linearity for incident
scintillation light, and those of 25 µm pitch were selected [65]. In addition, the eﬀect of thesaturation can be suppressed to some extent by reducing the operation voltage resulting in the
low after-pulsing and crosstalk probability. The SiPMs are mounted on PCBs with soldering.
As shown in Fig. 2.51, the PCBs have flexible branches where the SiPMs are placed. The SiPMs
are pressed against each LYSO crystal with springs and coupled using optical grease. This
removable attachment enables a replacement of the SiPMs or the crystals for maintenance. Theenergy resolutions of most crystals were measured to be ∼ 6% at 1 MeV with a 60 Co source,which is good enough for the background separation [69].
Support structures
The support structures for the RDC are constructed with non-magnetic materials (Fig. 2.52).
To fix the timing counter, a stainless steel plate is placed in the front of the timing counter.
The center of the timing counter is not covered to minimize the amount of material. In orderChapter 2 MEG II Experiment55

Table 2.8 Properties of the LYSO crystal [70].

Density

7.4 g/cm3

Radiation length

1.14 cm

Decay constant

42 ns

Emission peak

420 nsLight yield

30000 p.h./MeV

Q.E.(%)

Anode Signall (50 ohm, normalized)

PreLudeTM420 Scintillation Material

Lu.

26

Figure 2.50 Energy spectrum of the int (ns)trinsic
radioactivity of LYSO [71].
Q.E.(%)

Figure 2.49 Decay scheme of

176

Anode Signall (50 ohm, normalized)

PreLudeTM420 Scintillation Material

Figure 2. PreLudeTM 420 response to
511 keV with R3241 PMT

Chapter 3. Radiative Decay Counter(The curve is for 1µs. The curve for 12µs is i
Wavelength (nm)1.1

Figure 2. PreLudeTM 420 response to
511 keV with R3241 PMT

TM
Figure420 Emission & ETI 92
1.0 3. PreLude(Q.E. data courtesy of Electron Tubes,
0.9

25 µm
E (keV)Eﬀective photosensitive area

3.0 × 3.0 mm2

Number of pixels

14400

0.8

RPH
PHR

Counts/s/keV/cc

Table 2.9 Properties of S12572-25P[72].
t (ns)

Pixel pitch

Wavelength (nm)Figure 3. PreLudeTM 420 Emission & ET
(Q.E. data courtesy of Electron Tube

0.7

0.6
(The curve is for 1µs. The curve for 12µs is iden

Figure 3.13: Decay scheme of
[18].

176

0.4
1.0 0.2

65%

E (keV)

0.9

Figure 4. Beta distributions

-100

-50

0

Lu and energy spectrum of the LYSO intrinsic radioactivity

50

100

Temperature ((ºC)
oTemperature
C)

0.8

RPH
PHR

Fill factor

Counts/s/keV/cc

0.5
1.1 0.3

Figure 5. Temperature respon

0.7
0.6
0.5
0.4
0.3
0.2
-100

-50
0
50
150
Absorption
Efficiencyof 100
PreLudeTemperature (ºC)

Temperature (oC)

Figure 4. Beta distributions

Figure6. Gamma
and X-ray response
absorptio
Figure5. Temperature
various thicknesses of PreLude 420 m
Data compiled by C. M. Rozsa (presen
Crystals brochure “Efficiency for Selec

Absorption Efficiency of PreLude®42

Figure 3.14: PCB in the calorimeter.
½ mm

6. Gamma and X-ray absorption e
Figure 2.51 PCB for the RDC calorimeter. The SiPMs are mounted on the each branchFigure
various thicknesses of PreLude 420 mate
Therefore, the optical coupling of the crystals and the SiPMs need to be optimized. The detail
Data compiled by C. M. Rozsa (presented(left). The SiPMs
are inpressedfrom the backside with springs (right).
Crystals brochure “Efficiency for Selected
is describedchapter 4.3.
Energy (keV)

In order to absorb the stress of the springs (⇠2.5 kg in total), several support plates areinserted (Figure 3.15). The material thickness has to be as small as possible between theProperty
PreLude 420
BGO
crystals and the timing counter. Therefore, the support plate consists ½ofa thick Rohacell platemm(3.3 mm) and two thin carbon fiber plates (CFRP : 0.2 mm ⇥ 2). In addition, a thinDensity
aluminum[g/cm3]
7.1
7.1
Table comparing principal properties
plate (0.1 mm) is inserted for the light shield of the crystals.
On the other side of the crystals,
Attenuation length for 511 keV (cm)1.2
1.0
of PreLudeTM 420 versus BGO and LSO
a carbon fiber plate and two Derlin plates are inserted.
Energy (keV)
Decay
41
300
The springs are fixed on a chassis (Figure 3.16). After cabling, all the cables are
fixedtimeon [ns]the chassis not to touch the springs. For light shielding, an aluminum holder is equippedtoEnergy resolution
8.0
12.0
Property
PreLude 420
BGO
cover the whole calorimeter (Figure 3.17).
Light output, photons per keV
32
9Density [g/cm3]
7.1
7.1
Table comparing principal properties
Average temperature coefficient-0.28
Attenuation
1.2
1.0-1.2of PreLudeTM 420 versus BGO and LSO
25 to 50oClength(%/oC)for 511 keV (cm)R
Decay time [ns]41300

to absorb the stress of the springs (∼ 2.5 kg in total) with the minimum amount of material,a 2 mm thick Rohacell plate sandwiched with CFRP layers with a thickness of 0.2 mm each isinserted between the timing counter and the calorimeter. In addition, a 0.1 mm thin aluminum

plate is inserted behind the Rohacell plate (Fig. 2.53) and the side is covered with an aluminum
frame for light shielding of the calorimeter (Fig. 2.55). Two 0.2 mm plates made of Delrin⃝ andEnergy resolution

8.0

one CFRP plate are placed behind the calorimeter (Fig.2.54). TheProtectedsprings
are
fixed
onkeV
a chassis 32
Light under
output,photonsperpatents:
US6624420,
US6921901

12.0
9Management Systems of Saint-Gobain Crystals (Scintillation Products) in Ohio (U.S.A
Averagetemperatureregistered
to ISO
9001:2008. coefficient
-0.28
-1.2
o
Manufacturer
25 to 50reserves
C (%/otheC)right to alter specifications.

made of brass (Fig. 2.56). The cables are fixed on the chassis not to touch the springs (Fig. 2.57).

is a registered trademark of Saint-Gobain Ceramics & Plastics, In®420

Saint-Gobain Crystals
www.crystals.saint-gobain.com

Manufacturer reserves the right to alter specifications.
©2004-2016
Saint-Gobain
Ceramics& Plastics, Inc. All rights reserved.
Protected
under patents:
US6624420,
US6921901

Management Systems of Saint-Gobain Crystals (Scintillation Products) in Ohio (U.S.A.),
registered to ISO 9001:2008.
Manufacturer reserves the right to alter specifications.

is a registered trademark of Saint-Gobain Ceramics & Plastics, Inc.

®420

Saint-Gobain Crystals

Chapter 2 MEG II Experiment

56

Figure 2.52 Outlook of the RDC.

Figure 2.53 Rohacell plate and aluminum plate inserted between the timing
counter and the calorimeter.

Figure 2.54 Delrin and CFRP plates inserted behind the RDC calorimeter.

Figure 2.55 Aluminum frame for the
RDC calorimeter.

The backside of the calorimeter is covered with an aluminum holder for light shielding (Fig. 2.58).
The RDC is mounted on a moving arm system attached to the end-cap of the COBRA magnet
as shown in Fig. 2.59. The moving arm enables the RDC to be moved away from the beam-axis
when a calibration target for the LXe detector is inserted from the downstream side (Fig. 2.60).
It can be controlled remotely by water pistons made of plastic. The shaft is made of titanium
to work under heavy loads and other parts are made of aluminum. The position of the detector
can be monitored with two end-switches. Since the end-cap of the COBRA separates the innervolume from the outside, SiPM signals are transmitted via feed-through PCBs attached to theend-cap. The design of the PCB is the same as that used for the LXe detector, which is describedin Sec. 2.1.3.2.
Control system
Two thermometers (PT100) are installed in the RDC; one is near the SiPM of LYSO crystal
around the center and the other is placed outside the main frame. Signals from the sensors areread out via the feed-through PCB.

Chapter 2 MEG II Experiment57

Figure 2.56 Springs to fix the SiPMs for
the RDC calorimeter.
Figure 2.57 Brass chassis to fix the springs.

Figure 2.58 Aluminum holder for the light shielding of the RDC calorimeter.

(a)

(b)

Figure 2.59 RDC mounted on a moving arm viewed from (a) front and (b) back sides.
Compressed air is provided through the blue tube.

Chapter 2 MEG II Experiment

(a)

58

(b)

Figure 2.60 RDC at (a) parking position and (b) measurement position.

The moving arm is controlled by pneumatic system. When pressurized gas of 7–8 bar is
supplied to the pipes connected to the water piston, the RDC is inserted to or moved out fromthe beam-axis. Compressed air is supplied as the pressurized gas source and its flow is controlledwith remote valves.
The two end-switches are the physical switches installed to monitor the position of the RDC.
One of them is placed to be on when the RDC is at the measurement position and the other isat the parking position. Current is supplied and read out via the feed-through PCB. When theswitches are not pressed, the electric path is disconnected.
Upstream RDC
The RDC for the upstream is under development. The requirement for the detector is more
stringent than the downstream since the µ beam needs to pass the upstream RDC. Firstly,
the material thickness must be small enough not to aﬀect the beam, and thus a calorimetercannot be placed. Secondly, the detector must be finely segmented and have a fast response todistinguish the RMD positrons from beam muons. Thirdly, radiation hardness is required forthe operation under the muon beam.
Various detectors have been tested such as scintillating fibers, a diamond detector and a silicondetector, but they cannot satisfy the requirements. A resistive plate chamber, a type of gaseous
detectors, has been investigated as a candidate, which will be described in Appendix B.
Since this thesis focuses on the downstream RDC and the performance of the upstream RDC
has not been fixed yet, only the downstream RDC is taken into account hereafter. The upstream
RDC will be installed after the development, and a further improvement of the sensitivity is
expected.

2.1.4 Trigger and data acquisition
The DAQ system is also upgraded for the MEG II experiment. In the MEG experiment, thedetector signals were actively split and then sent to the trigger and DAQ systems as shown inChapter 2 MEG II Experiment

Figure 2.61 Designs of electronics for the MEG (left) and the MEG II (right) [74].

Fig. 2.61. However, due to the limited space for the electronics in the experimental area, adopting
such a scheme is impossible with the increased number of channels in the MEG II experiment
by a factor of three. Therefore, a new simplified and compact system called WaveDAQ wasdeveloped which integrates the trigger and DAQ functionalities onto the same electronics board,
the WaveDREAM board (WDB).
The WaveDAQ crate contains the crate management board (CMB), 16 slots for WDBs andtwo slots for so-called concentrator boards, the trigger concentrator board (TCB) and the data
concentrator board (DCB) as shown in Fig. 2.62. The CMB supplies power to all the boardsin the crate and manage the slow control system. The TCB generates a trigger. The DCB
configures all boards inside the crate, distributes the master clock and trigger signals, andreads out waveform data. The whole of the system is controlled by Maximum Integration Data
Acquisition System (MIDAS) [73].
WaveDREAM boards
The WDB has multiple functions such as a signal amplification and shaping, a HV supply
and a signal digitization. Fig. 2.63 shows the schematic view of the WDB. Two DRS4 (Domino
Ring Sampling) chips [74] are connected to two 8-channel ADCs, which are read out by a FieldProgrammable Gate Array (FPGA). The output stream of the ADCs is used in the FPGA to
perform complex trigger algorithms.
The DRS4 chip digitizes input waveforms with a maximum sampling speed of 5 GSPS. In
the pilot runs, the sampling frequency of 1.2 GHz was used for the LXe detector and the RDC
instead of 1.4 GHz planned in the physics data-taking. This is because of the trigger latency

59

Chapter 2 MEG II Experiment60

3 The WaveDAQ Trigger and Data Acquisition System������������

�����������

������������

Figure 2.62 Sketch of WaveDAQ crate with WDBs (green), DCBs (violet), TCBs (blue)
and Ancillary board (red) [75].
Figure 3.7: Data flow and trigger signals flow in the multi-crate WaveDAQ system:
WaveDREAMs in green, TCBs in blue, DCBs in violet and Ancillary board
in red.

of ∼ 680 ns, which is reduced by replacing the ADC for the final system [75]. Fig. 2.64 showsa readoutevents,
mechanism
thechip.to random
The amplitudesof theIn waveforms
are stored
on thewhile ID ofcode
63 DRSis reserved
pedestal trigger.
between increasingID
code is assigned
to looser
conditions
usedto acquiredetector
events. switches
1024 capacitors
called DRS
cells.trigger
A logic
wave, socalledDominowave,calibration
opens analogue
The condition ID code identify the “Trigger Type” which is used to trace back theat the inputof theDRS
cells
each Together
channel.withAntheon-chip
lockedloop (PLL)
condition
which
fired
the oftrigger.
Triggerphase
Type anprogressive“Event locks the
Number”
assignedwave
to eachby the master
TCBclock.
for unambiguous
identification.
generationof the is
Dominoto event
an externalreference
The samplingis stopped when atrigger is fired, and then the stored charges are read out by the ADCs in the order of the DRS

3.4 Trigger Signals Distribution

cells via a shift register. One DRS chip includes eight readout channels and one clock channela trigger
as shownWhen
in Fig.
2.65. is generated it is distributed back to all the boards through the connections marked in orange in figure 3.7: a fanout system made by custom designed Ancillary

A reference
80 MHzis distributed
to eachonthereDRS chips inboardsclock(figureof3.8),
placedsine
in awavededicatedcrate, is used.
Apartclockfrom channel
the trigger,others to be
distributed:
order to aresynchronize
channels,
which enables the precise timing alignment with oﬄine analysis.
copy ofmain
low waveform,
jitter 80 MHz
referenceclock toused
for chips
DRS sampling
A sine wave •isafitted
tothe
each
clock
and
the timings
ofbe
the
DRS
are aligned based
and trigger data transmission;

on zero-crossing times extracted by the fitting. The precision of the synchronization between
the chips was evaluated as follows; pulses were input into channels in diﬀerent chips whichwere divided from a single signal generated with a function generator. The pulse timings were71

extracted by waveform analysis. The time jitter between the chips was given by the standard
deviation of their timing diﬀerence, which was 45 ps.
The WDB provides variable amplification and flexible shaping of a waveform. Two stage
amplifiers and a programmable attenuator are implemented on the analog frontend of the WDB,
which enable to select the gain from 0.5 to 100. The shaping is available with a programmablepole-zero cancelation. In the pilot runs, an electronics amplifier of 2.5 was adopted for thephotosensors of the LXe detector. The signals of the RDC timing counter were amplified by afactor of 100 and shaped with pole-zero cancellation while neither amplification nor shaping was

Chapter 2 MEG II Experiment61

第 2 章 MEG II 実験

15

Figure 2.63 Schematic view of WaveDREAM board [2].
Rotating
signalInverter "Domino" Chain
Input

OutputShift Register
図 2.16 DRS の動作原理
Figure 2.64 Mechanism of DRS4 [74].

applied to the RDC calorimeter.
The voltages for sensors up to ∼ 240 V can be supplied with a Cockcroft–Walton (CW) voltage
multiplier on the WDB. Channel by channel tuning of the applied voltages is possible thanks

Branching ratio

to a 5 V digital-to-analog converter (DAC), which is mounted after the CW voltage multiplier.
The currents are measured with a precision of 1 nA.
Trigger-11

Obtained 90% UL
90% UL sensitivity

MEGA

1σ
10MEG II experiment is required to±collect
The trigger in theµ+ → e+ γ-like events suppressing
2σ the eﬀective DAQ and the reduction
the backgrounds by almost six orders of magnitude ±for
3σ discoveryof the overall data size. The information from the pTC
and the LXe detector is used for theon-line trigger, while the signals from CDCH is not used due to its slow response. Hence, theobservables of Eγ , te+ γ and Θe+ γ are reconstructed on-line on the FPGA.
Eγ is reconstructed by summing up weighted waveforms over MPPCs and PMTs in the LXedetector. The weights-12are defined to compensate the diﬀerence of the waveform shape between

10

the MPPCs and the PMTs, and the photosensor performance such as the gain and the photon

MEG 2013

detection eﬃciency. Events whose amplitudes of the summed waveforms exceed a certain threshold are selected as signal-like events. A veto threshold is also available to reject high energy

10-13
0

100

200

300

Chapter 2 MEG II Experiment

62
487

S. Ritt et al. / Nuclear Instruments and Methods in Physics Research A 623 (2010) 486–488
PLLOUT PLLLCKDSPEEDREFCLK
LVDS

PLL

WSRIN
DENABLEDWRITE

DTAP A0 A1 A2 A3DOMINO WAVE CIRCUITENABLEAGND AVDDMUXMUXOUT /OUT0

IN1

CHANNEL 1

OUT1

IN2

CHANNEL 2OUT2CHANNEL 3OUT3CHANNEL 4OUT4CHANNEL 5OUT5CHANNEL 6OUT6CHANNEL 7OUT7CHANNEL 8OUT8CHANNEL 9OUT9STOP SHIFT REGISTER

BIAS
ROFS

IN3
IN4
IN5
IN6
IN7
IN8

WRITE SHIFT REGISTERCHANNEL 0

WRITE CONFIG REGISTER

IN0

IN9
WSROUTRSRLOADREAD SHIFT REGISTER

SRIN
SRCLK

MUX

SROUT

CONFIG REGISTER
DVDD DGND

Fig. 1. Functional block diagram of the DRS4 chip.

100

Figure 2.65 Brock diagram of DRS4 chip. Eight readout channels and one clock channel
are mounted in a chip [74].LVDS
clock
IN0+
50

100

ADT1-1WT
Rterm
VDD
1k

...

IN0IN1+IN1IN2+IN2IN3+IN3IN4+IN4IN5+IN5IN6+IN6IN7+IN7IN8+IN8-

A0-A3
DWRITE
DENABLEDTAPPLLLCK
SRIN
SRCLK
SROUT
RSRLOAD

DRS4

FPGA

REFCLK+REFCLK-

100

other

inputs

100nF

1k

background events originating from the cosmic rays.

LVDS

ROFS

...

DSPEED

similarly

PLLOUTte+ γ is reconstructed from the on-line timing of the pTC and the LXe detector using comOUT0+OUT0-

VIN+ CLK D0-D13
VIN-

parators on the WDBs coupled to each input signal with the time-of-flight correction from the
PLL
LOOP
FITER

AD8061

VDD

AD9245target to each detector. While being straightforward in the case of the LXe detector, the curved
Fig. 2. Typical mode of The
operation timingof the DRS 4chip.
tracks of positrons make it more complicated.
of the pTC is extracted from a single

counter placed
atis themostz ofallreadhitTheof bethetrack
concurrent writing
and correction
reading. The chip canconfigured
as alength is
If dead-time
an issue,all eightinner
data channels
can beout counters.
in parallel and digitized simultaneously, using modern octal ADCs

single channel with eight analogue buffer segments of 1024 cells

region-of-interest readout mode, only the part of the stored

while the previous segment is read out and digitized. For Poisson-

applied based
onAD9222
the from
positionof theCDCH
is unavailable,
there
each.theIf a trigger
occurs, information
the next segment is activatedfor writing
such as theAnalog Devices,
Inc. counter.
Using a specialSince
distributed
events,techniquereducethe dead-timeof thewaveform ofofinterest
can be readof
outpositronand digitized.
The
is an ambiguity
the number
turns;
thetimeof thisflightcancanbe
diﬀerent
dependingon
DAQ system significantly.
digitization time is then n ! 30 ns, where n is the number ofsamples of interest. For short PMT pulses of 10 ns width sampled
the number
positronthewith 5ofGSPS,
the readoutturnsof all 50 evensamplesthoughtakes then 50! 30selected counter is the same as shown in Fig. 2.66.
ns ¼1.5 ms, allowing for acquisition rates of several 100 kHz.

This resultsin acascading
relatively
widetime window.
A flexible
scheme has
been implemented,
with which
one can configure the DRS4 chip to have deeper sampling depths at

3. Application in the MEG experiment

The MEG experiment at PSI, Switzerland, uses 3000 channels

the cost of fewer
channels.
the extreme
the chipbeequippedwith DRS chips
digitize
all detector
signals, including
The pixelated
designofIn thepTCcase,andthecanhigher
granularity
oftotheLXe
detector
give a tighter
PMTs from the calorimeter and timing counters, as well as drift
configured as a single channel with 8192 sampling cells. Furthermore, several DRS4 chips can be daisy-chained to form a channel
chamber anode and cathode signals. All pre-amplifiers used areangle constraint
than thatMEG.
Θe+ γ is theestimatedby theso first
hitoriginal
pixelof thefrom
pTC
voltage sensitive,that thewaveforms
the and thewith virtually unlimited
samplingof
depth
without compromising
bandwidth, given that the analogue signal is externally split and fed

detectors are preserved. This allows techniques such as shaping,peak position
on ofthefaceAnotherof thedetectora look-up
createdbased
on afiltering using
and integration
to be applied tableoffline, either
by softwareinto all channels
each innerchip in parallel.
optionLXe
is to havesimulation.
Thanks to the improvements in the on-line reconstruction resolutions, the trigger rate is
expected to be ∼ 10 Hz, which is comparable with that of the MEG in spite of the increased
beam rate.
Not only the µ+ → e+ γ trigger but also a variety of trigger logics is implemented for thedetector calibrations. Hereafter, the triggers used for this thesis are described.
EGamma trigger
The background γ-ray and the 17.6 MeV γ-ray data are taken based on the on-line
reconstructed energy of the LXe detector. This trigger is fired when the amplitude of
the sum waveform exceeds a given threshold, which is generated by summing up the
waveforms of each channel with a weight given by the calibrated sensor performance.

Chapter 2 MEG II Experiment

Figure 2.66 Time of flight of positrons to each pTC tile [76]. Clusters which derive fromthe diﬀerence of the number of positron turns can be seen.

CEX trigger
The trigger for calibration data taken with the charge exchange reaction of a π − beam(Sec. 3.1) requires the coincidence hits in the LXe detector and a reference counter.
For the LXe side, an excess of the amplitude of the sum waveform is required to obtainhigh energy γ-ray events as well as the EGamma trigger. For the reference counter,an excess of the amplitude of the sum waveform of the calorimeter part is required forthe energy measurements as well. Coincidence hits whose pulse amplitudes are higher
than a threshold in two timing counters are required for the timing measurement.
Alpha trigger
The trigger to take α events from the calibration source (Sec. 3.1) is also fired based on
the sum of the sensor waveforms, but only the PMTs around each α source wire shownin Fig. 2.67 are used to have a better signal-to-noise ratio. To remove a contaminationfrom γ-rays and cosmic rays, a particle identification based on charge-to-height ratio
is also implemented.
RDC LYSO trigger
Calibration data of the RDC calorimeter uses a self-trigger of each channel, and thetrigger is fired based on the waveform amplitude of a single channel (Sec. 4.1).
Random trigger
Data can be acquired by firing the trigger at random timings, which are used to monitor
the performance of electronics such as noise level and event-by-event fluctuation of thebaseline. They are also useful to take γ-ray data without trigger bias.

63

Chapter 2 MEG II Experiment

64

100
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40Wire 1

20

Wire 20
20

Wire 3

40
60

Wire 4

80
100
100

50

0

50

100

150

200

250

300

Figure 2.67 PMTs used for the alpha trigger. Only 32 PMTs around each wire are used
for the trigger [62].

2.2 Pilot runs
The commissioning of the LXe detector and the RDC have been carried out since 2017 after
the detector construction and the installation in the MEG experimental area. The configurationsof each year data-taking are summarized in this section.

2.2.1 Run configuration
Pilot run 2017
The pilot run 2017 is the first operation and data-taking with the muon beam for the LXedetector. Data of γ-rays from the muon beam stopped on the target placed at center of the
MEG II detector was accumulated for the LXe detector and the RDC. The beam intensity was
adjusted to 3.2 × 107 µ+ stops/s to keep the induced current on the RDC in the dynamic rangeof the readout, which has been extended since the run 2018. The construction of the CDCH
had not been finished, and so a mechanical mockup was installed instead, which had no wire,
no electronics and a thinner aluminum end-cap of 2 mm thickness.
Pilot run 2018
In the pilot run 2018, the background γ-ray data from the muon beam were taken at a
reduced beam intensity of 0.7 × 107 µ+ stops/s and the so-called MEG II beam intensity of 7 ×
107 µ+ stops/s for the study on the background γ-ray spectrum. An unexpected hit rate and hit
position distribution were observed with the RDC, and it was found that the hit timings werecorrelated to the cyclotron acceleration. This implies the beam was contaminated with positrons
which should be eliminated with the separator (Sec. 2.1.1). In order to avoid the high current
and the radiation damage, data for the RDC were taken only with the lower beam intensity.
The data suﬀers from an instability in terms of the monitoring the LXe detector performance
because the DAQ configuration and the beam intensity were often switched. There is anotherreason that the BTS magnet was not stable due to an instability of the liquid helium supplyChapter 2 MEG II Experimentfrom the PSI.
In addition to the background γ-rays, the 17.6 MeV γ-rays from the nuclear reaction of Li
were measured to evaluate the energy resolution of the LXe detector. The position resolution
was also measured by placing a lead collimator in front of the detector.
Pilot run 2019
There was an indication of the degradation of the sensitivity to the VUV light of the SiPMs
installed in the LXe detector in the run 2018 data. Since it was diﬃcult to conclude thedegradation due to the instability of the 2018 data, dedicated data were taken for the LXedetector in 2019. The detector was operated under the MEG II intensity muon beam, and thephotosensor performance was often measured to monitor the degradation.
It was found that the muon beam intensity seemed to be 10–20% higher than expected, which
was suggested from the observation of the detector hit rates. This was likely due to a problem
on the beam blocker during a beam intensity measurement.
Pilot run 2020
In the pilot run 2020, the background γ-rays were measured with the LXe detector. Higher hit
rates than expected from the measured beam intensity were observed again with all the detectors,
and thus the beam intensity was tuned referring to the detector hit rates. The background γray data were accumulated at beam intensities of 1.6 × 107 µ+ stops/s and 7.7 × 107 µ+ stops/s,
which were calculated by the comparisons between the detector hit rates and the beam intensity
measured in the run 2021.
The quasi-monochromatic γ-ray of 54.9 MeV using the charge exchange reaction from a π −beam was also measured to evaluate the energy resolution and the timing resolution of the LXedetector near the signal energy.
Run 2021
In the run 2021, all the detectors were installed and they were read out with the full electronic
channels. Although data under the muon beam were accumulated, only the noise data are usedin this thesis.

2.2.2 DAQ system
Since the full DAQ system was not available due to the delay of the development, a prototype
system was used for the data acquisition in the pilot runs [75].
The number of readout channels were limited in the pilot runs due to the lack of the WDBs,
and only a quarter of the LXe channels was read out (Table 2.10) while the RDC channels were
fully read out until the run 2020. Fig. 2.68 shows the channel assignment of the LXe detector
for each run. The readout area on the inner face was concentrated while that of the PMTs
was widely distributed. This is because local information around the γ-ray hit position on the65Chapter 2 MEG II Experiment66

entrance face is important for the reconstruction of the position and the timing, and the wide
coverage of the PMTs is required to achieve a reasonable uniformity of reconstructed energy.
Only the events in which γ-rays hit the central part of the readout area are selected in theanalysis.
Table 2.10 Number of readout channels of the LXe detector for each year.

Yearnumber of SiPM channel

number of PMT channel

Typical DAQ rate

2017

704

192

∼ 3 Hz

2018

640

378

∼ 3 Hz

2019

640

378

∼ 10–25 Hz

2020

720

378

∼ 20 Hz

2021

4092

668

∼ 6–25 Hz

2.3 Detector simulation
A framework for the detector simulation is developed to gain more insight into the detector
performance and backgrounds. It consists of several steps as shown in Fig. 2.69. Firstly, eventsin the simulation are generated in “gem4” based on Monte Carlo simulation software, GEANT 4(version 10.4 [58]), and interactions of particles in the detectors are simulated and recorded in“sev” files. Then, “bartender” mixes the events of multiple event types at a certain event rate
to simulate pileup eﬀects and the results are recorded in “sim” files. A electronics simulation is
also performed and the simulated waveforms are recorded in “raw” files with the same format
as the real data. Finally, “analyzer” analyzes the waveforms with the same algorithm as data.
The bartender and the analyzer are based on the ROME framework [77].

2.3.1 Event generation and interaction
At the event generation stage of gem4, the primary particles and their kinematics can be
specified. The event types used in this thesis are listed in Table 2.11.
The MEG II apparatus is implemented in the gem4. Physics interactions of generated particles
with materials are simulated in the framework of the GEANT 4 and the hit information such asenergy deposits is recorded once the particles interact with a detector sensitive volume.
When a particle enters the scintillator part of the LXe detector, it produces electromagnetic
showers, which are also simulated by GEANT 4. Based on the property of LXe (Table 2.3), scintillation photons are generated at each energy deposit point of the electromagnetic shower. The
number of generated scintillation photons is calculated with the W-value considering a Poisson
fluctuation and the generation timings are given by scintillation time constants. Propagation of
scintillation photons is simulated considering an absorption by impurities, the Rayleigh scattering and a reflection on the detector material. If scintillation photons reach a sensitive volume
of a photosensor such as a photo-cathode of the PMT and a silicon surface of the MPPC, theChapter 2 MEG II Experiment

67

100
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40
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(b)
100

2.00

80

100

60

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40

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1.87

1.75

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1118.14962.26806.380650.50−20468.64−40−60

312.76

−80
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156.88

0

100

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200

300
1.00

Figure 2.68 Readout channels of the LXe detector in (a) the run 2017, (b) the run
2018/2019, the run 2020 and (d) the run 2021. The non-readout channels and the deadchannels are shown in gray.

Chapter 2 MEG II Experiment

68

Experimental
raw waveform

Result of analysis
Event reconstruction

online DAQ.midanalyzerrec

Simulated
raw waveform

raw
gem4

sev

Detector simulation

bartendersim

Event mixing
Waveform simulation

Simulated MC truth

Figure 2.69 Framework of MEG II simulation software.

timings and the total number of incident photons in the volume are recorded. The fired pixel
and the incident angle of the photon are also recorded for the MPPCs to be used in the following
waveform simulation.
In the case of the RDC, such a dedicated simulation is skipped and only the hit informationin the scintillator volume is recorded.
Table 2.11 Event types in gem4.

ID

Description

Generated particle(s)2

SM decay of µe+ and γ-ray from the SM decay on the target

21

Signal γ

52.8 MeV γ on the target

12

Michel decay of µe+ from the Michel decay on the target

22

Radiative decay of µe+ and γ from the RMD on the target

30

Muon beamµ+ injected from 564.70 cm upstream of the target *3

63

Alpha

5.5 MeV α from 241 Am inside LXe detector

64

CW-Li

17.6 MeV γ from the target

0

67

π 2γ

76

Uniform γ

two γ-rays from π 0 decay (pπ0 = 27.62 MeV) on the target
γ-rays from the target whose energies are uniformly selectedfrom a certain energy range

2.3.2 Event mixing
Since the gem4 simulates a single event of a specific event type, mixing of events is necessary
to know the pileup eﬀects. In the bartender, events of diﬀerent event types can be mixed at a
certain rate. An event with pileups was generated by mixing pileup events at a random timing
assuming a Poisson distribution to a main event whose timing was fixed to zero.

*3 The generation point corresponds to just after the last magnet of Triplet2.

Chapter 2 MEG II Experiment69

2.3.3 Waveform simulation
The bartender simulates waveforms of photosensors after the event mixing based on therecorded information in gem4.
For the waveform simulation of the LXe detector, the waveforms are generated from the single
photoelectron response of each sensor as shown in Fig. 2.70. The waveform of the MPPC is
obtained from the single photoelectron events acquired using an LED while that of the PMT is
obtained from deconvolution of γ-ray waveforms with an exponential function of the scintillation
time constant since the single photoelectron peak cannot be resolved in the charge distribution.
The MPPC characteristics are also simulated. When one pixel is fired, the crosstalk is simulated by firing another pixel with a certain probability and the after-pulsing is by firing the same
pixel with certain probabilities with given time constants. Two time constants with diﬀerent
probabilities are introduced for the better description of the after-pulsing [78]. The dark noiseis added with a given rate. To simulate the saturation, when more than one photon enter thesame pixel, waveforms from the second photon are reduced according to the elapsed time fromthe prior photons; the posterior photons are ignored if they enter in a dead time, otherwise
amplitudes of their waveforms are reduced with a time constant. The parameters used for the
waveform simulation are summarized in Table 2.12.
For the simulation of the RDC waveforms, the waveforms are generated from the energy
deposits of the hits since optical photons are not simulated in the previous step. Both for thetiming counter and the calorimeter of the RDC, template waveforms and typical energies forthe templates are obtained from µ beam data (Fig. 2.71). The template waveforms are scaled
based on the energy deposits of the hits.
At the end of the simulations, electronics responses are simulated. A white noise is added toreproduce the noise observed in data. The simulated waveforms are digitized by the sampling
frequency of 1.2 GHz, and the waveforms outside the dynamic range of the electronics are cut.
To make the noise simulation more realistic, a method which directly uses noise data is also
implemented. The noise waveforms obtained with the random trigger without signals are added
to the simulated waveforms without the white noise. Since the noise waveforms were taken at
the sampling frequency of 1.4 GHz in the run 2021, the digitization is carried out at the same
frequency for the simulation with the full readout channels.
Table 2.12 Parameters used to simulate MPPC characteristics for the LXe detector [61].

Parameters

ValuesDead Time

1 ns

Recovery Time Constant

38 ns

Crosstalk Probability

0.15

After-pulsing Probability

0.1 / 0.05

After-pulsing Time Constant

5 ns / 200 ns

Dark Current Rate

500 Hz70

×10−3

amplitude (V)amplitude (V)Chapter 2 MEG II Experiment

0

−0.05

0.004
0.002
0

−0.1

−0.002−0.15−0.004

−0.2
0

0.1

0.2

×10−6
0.3
(s)

−0.006
0

0.05

0.1

×10−6

0.15
(s)

(a)

(b)

amplitude (V)amplitude (V)Figure 2.70 Single photoelectron response used for the waveform simulation of the LXe(a) MPPCs and (b) PMTs.

0
−0.1
−0.2

0
−0.02
−0.04
−0.06

−0.3

−0.08

−0.4

−0.1

−0.5

−0.12
−6

−0.6

×10
0

0.1

0.2

−0.14

×10−6
0

0.1

0.2

(s)

(a)

(s)

(b)

Figure 2.71 Template waveforms used for the waveform simulation of the RDC (a) timing
counter and (b) calorimeter.

2.3.4 Background γ-ray
For the simulation of the background γ-rays from the muon beam, a dedicated operation is
performed since its computational cost is too high to generate enough γ-ray events from muon
decays due to a very small probability of having a high energy γ-ray from a muon decay. Firstly,background γ-ray events are classified into three groups by their sources as follow, and eventsof each group are simulated separately.
• AIF : γ-ray originating from a Michel muon decay stopped on the target. High energy
γ-rays mainly come from the annihilation in flight of Michel positrons.
• RMD : γ-ray from a radiative muon decay stopped on the target.
• DIF : γ-ray from a muon decay in flight (i.e. not on the target).
Then, the generated events are mixed with each event rate calculated from the probability tohave a hit in the LXe detector to produce the original background γ-ray event set.

Chapter 2 MEG II Experiment71

Since only γ-rays with high energy above 20 MeV are important, simulations of particles below
20 MeV are skipped. The phase spaces of the muon decay for the AIF and the RMD event
generation are restricted to Pe+ > 20 MeV and Eγ > 20 MeV, respectively. For the further
reduction, once positrons in the AIF reach more than 16 cm away from the target along beamaxis, their simulations are stopped because such positrons are found not to produce the highenergy γ-rays arriving at the LXe detector. Thanks to these reduction methods, events roughly
corresponding to one day data-taking were simulated for 50 days with 200 physical cores of therecent CPUs as summarized in Table 2.13.
Table 2.13 Simulated number of events.

Event type

The number of simulated events

AIF∼ 1.3 × 105

RMD∼ 1.3 × 106

DIF∼ 4.8 × 105

2.3.5 Pileup mixing for uniform γ-ray
The uniform γ-ray events were used to train a deep learning model for the pileup elimination(Chap. 5). The pileup events of the uniform γ-rays were generated by mixing only a light
distribution measured with the photosensors in the LXe detector. Waveforms of an event was
digitized as a single γ-ray event, and they were converted to the number of photons of eachphotosensor with waveform analysis. For the pileup events, the light distributions of the pileup
γ-rays were added to those of the uniform γ-rays.

2.4 Statistical method for µ+ → e+ γ search
In the µ+ → e+ γ search, the number of signal events Nsig and its confidence interval are estimated with a maximum likelihood method. The likelihood function is composed of probability
density functions (PDFs) of signal, RMD and accidental background. The estimated Nsig isconverted to the branching ratio B with the normalization factor, which is given by the accumulated number of muon decays. The branching ratio sensitivity is defined as the median of the
90% confidence upper limits of pseudo experiments.

2.4.1 Likelihood function
The likelihood function L for target parameters θ is given byL(θ|X) =

N
obs
∏
i

p(xi |θ),(2.3)

Chapter 2 MEG II Experiment72

where Nobs is the total number of events, xi is a set of observables of i-th event, and X is anarray of the observable sets (x1 , x2 , ..., xN ). The probability density function p(xi |θ) shows
the probability to find xi under a condition of θ. The best estimate θ̂ is defined such thatmaximizes the likelihood function with a given set of observables.
This likelihood function can be extended to take the statistical fluctuation of Nobs in a Poisson
distribution into account, that is,obs
N Nobs e−N ∏L(θ|X) =p(xi |θ),Nobs !
iN(2.4)

where N is the sum of the expected numbers of events [79].
In this context, the parameters to be estimated are the expected numbers of the signal, theRMD and the accidental background events, namely
θ = (Nsig , NRMD , Nacc ).

(2.5)

Then, N can be written by the sum of the numbers of the three event types:
N = Nsig + NRMD + Nacc .

(2.6)

From the definition of PDF, there are relations bellow:
p(sig) + p(RMD) + p(acc) = 1,

(2.7)

p(sig|xi ) + p(RMD|xi ) + p(acc|xi ) = 1,

(2.8)

where p(sig), p(RMD) and p(acc) are the PDF of signal, RMD or accidental background event,and p(sig|xi ), p(RMD|xi ) and p(acc|xi ) are the PDF of signal, RMD or accidental background
event after the observation of xi . From the Beyes’ theorem, the following relation is completed:p(x|xi ) =p(xi |x)p(x),p(xi )(2.9)

where x = sig, RMD or acc. Thus, the PDF can be written asp(xi |Nsig , NRMD , Nacc ) = p(xi |sig)p(sig) + p(xi |RMD)p(RMD) + p(xi |acc)p(acc). (2.10)
Since p(x) is the probability to be the event type x, they are given byp(x) =

Nx.
N(2.11)

Therefore, the PDF can be
Nsig
NRMD
Nacc
· S(xi ) +· R(xi ) +· A(xi ),(2.12)N
N
N
where S(xi ), R(xi ) and A(xi ) are the PDF for signal, RMD and accidental background event,p(xi |Nsig , NRMD , Nacc ) =respectively.
Since the NRMD and Nacc can be estimated also from the sideband of the fit region, constraints
can be added as−µRMD )
(N−µacc )
e−N − (NRMD
− acc
2
2σ 2
2σacc
RMD
e
e
Nobs !
2

L(Nsig , NRMD , Nacc |X) =
×

N
obs
∏
i=1

2

(Nsig S(xi ) + NRMD R(xi ) + Nacc A(xi )),(2.13)

Chapter 2 MEG II Experiment73

where µx and σx (x = RMD or acc) are the means and the uncertainties of the estimation.

2.4.2 PDF
The PDFs are defined as functions of the observables xi asdsds
xi = (Eγ , Ee+ , te+ γ , ϕe+ γ , θe+ γ , tus
rdc , trdc , Erdc ).

(2.14)

Eγ and Ee+ are the reconstructed energy of the γ-ray and the positron, respectively. The time
diﬀerence of the positron and the γ-ray te+ γ is calculated from the measured timings considering
the propagation times from the decay vertex. The relative azimuthal and polar angles of the
flipped positron direction with reference to the γ direction (ϕe+ γ , θe+ γ ) are calculated using thereconstructed positions and the decay vertex. The positron timing and energy measured withds
ds
the RDC (tusrdc , trdc , Erdc ) are used to enhance the discriminant power of accidental background.

As discussed above, three types of PDF are considered: S, R and A representing signal, RMD
and accidental background, respectively.
Signal PDF
The PDF for the signal event is defined as
ds
ds
S(Eγ , Ee+ , te+ γ , ϕe+ γ , θe+ γ , tus
rdc , trdc , Erdc |rγ , yi ) = S(te+ γ |Eγ , Ee+ , yi )× S(Eγ |rγ )× S(Ee+ |yi )× S(ϕe+ γ |rγ , yi )× S(θe+ γ |rγ , yi )dsds
× S(tusrdc , trdc , Erdc ),where rγ is the first conversion point of a γ-ray and yi is a set of reconstructed positron variables
such as direction, decay vertex, and tracking quality.
The signal PDF of the γ-ray energy S(Eγ ) is defined by the detector response to the signal
γ-ray. It is created from the simulated energy distribution for the signal γ-ray smeared withan additional Gaussian to match the measured energy resolution*4 . The Ee+ PDF is given by
the detector response to the the signal positron. The signal PDF for the relative timing of apositron and a γ-ray is defined by a combination of the the timing resolutions of them*5 . The
angular PDFs are given by the γ-ray position resolution, the positron vertex resolution and thepositron direction resolution. The signal PDF of the RDC observables is created by the timing
and energy distribution of Michel positrons as will be discussed in Sec. 6.2.1.

*4 The signal Eγ PDF will be generated from the energy distribution for 54.9 MeV γ-ray in CEX calibrationin the analysis of real data.
*5 The t + resolution will be evaluated with the timing coincidence hits to the detectors from the RMD ine γ

the analysis of real data.

Chapter 2 MEG II Experiment74

RMD PDFThe PDF for the RMD event is written asds
ds
R(Eγ , Ee+ , te+ γ , ϕe+ γ , θe+ γ , tus
rdc , trdc , Erdc |rγ , yi ) = R(te+ γ |yi )× R(Eγ , Ee+ , ϕe+ γ , θe+ γ )dsds
× R(tusrdc , trdc , Erdc ).

The RMD PDF for te+ γ is also given by the combination of the timing resolutions. The variables, Eγ , Ee+ , ϕe+ γ , θe+ γ , are correlated with each other, and the relation can be calculated
theoretically in the standard model. Therefore, the RMD PDF of the variables is obtained byconvoluting the theoretical spectrum with the detector response functions for each observable.
The RMD PDF for the RDC observables is the same as the signal PDF since only accidental
hits from Michel decays are expected.
Accidental background PDF
The PDF for the accidental background is defined asds
ds
A(Eγ , Ee+ , te+ γ , ϕe+ γ , θe+ γ , tus
rdc , trdc , Erdc |rγ , yi ) = A(te+ γ |Eγ , Ee+ , yi )× A(Eγ |rγ )× A(Ee+ |yi )× A(ϕe+ γ |rγ )× A(θe+ γ |rγ )dsds
× A(tusrdc , trdc , Erdc |Eγ ).

The te+ γ distribution in accidental background events should be flat by definition, and thus its
PDF is given by a uniform distribution. The Eγ is generated from the simulated background
spectrum with the Gaussian smearing*6 . At the same time, the accidental background PDF for
the RDC observables is created as a function of Eγ with the smeared spectrum to include its
energy dependence as will be discussed in Sec. 6.1.2. The other PDFs are generated based on
the resolutions of each variable.

2.4.3 Analysis Region
In this thesis, the likelihood fitting is performed in the analysis region defined as follows:• 48 MeV < Eγ < 58 MeV,
• 52.2 MeV < Ee+ < 53.5 MeV,
• |te+ γ | < 0.25 ns,• |θe+ γ | < 40 mrad,• |ϕe+ γ | < 40 mrad,• −20 ns < tus
rdc < 28 ns,*6 The accidental background Eγ PDF will be generated using the timing sideband data in the analysis ofreal data.

Chapter 2 MEG II Experiment75• −20 ns < tds
rdc < 28 ns,
ds• 0 MeV < Erdc
< 50 MeV.

2.4.4 Normalization
Since the likelihood fitting provides the number of the signal events, it needs to be convertedwith a normalization factor to obtain the branching ratio of the µ+ → e+ γ decay. The normalization factor k is given by the accumulated number of muon decays as Eq. (1.4). In the analysis
for the µ+ → e+ γ search, it is computed from a combination of the detected number of events
for two independent datasets: Michel decay events and RMD events.
In this thesis, the nominal value of the normalization factor is estimated based on the original
DAQ plan of the MEG II experiment and the simulation at the design stage except for ϵe+ , which
was updated to be more realistic based on the observation in the pilot runs [50]. Table 2.14
summarizes the values used for the calculation. As a result, the total number of muon decays
is k = 9.38 × 1013 . All of the sensitivity estimations are performed by scaling these values asnecessary.
Table 2.14 Nominal settings for the normalization of the MEG II experiment.

Variables

ValuesRµ

7 × 107 µ+ stops/s

T

Three years with 20 week data-taking per year including 84% live fraction

Ω

10.8%

ϵ e+

65%

ϵγ

69%

ϵcut

91% (same as the first half of MEG)

2.4.5 Sensitivity calculation
The branching ratio sensitivity is defined as the median of the upper limits at 90% confidence
level for pseudo experiments with a background-only hypothesis. In this thesis, the upper limit
is calculated by asymptotic formulae in which the profile likelihood ratio is approximated by thechi-square distribution [80].
An ensemble of pseudo experiments are generated from given PDFs assuming a backgroundonly hypothesis; Nsig is fixed to be zero. The pseudo experiment is a statistical simulation,
which simulates a statistical behavior of observables based on their distributions and correlations
including the detector response. A fluctuation of the number of events is also simulated following
Poisson distribution with mean values of expected numbers of NRMD and Nacc . The projected
sensitivity is calculated from O(1000) pseudo experiments.

Chapter 2 MEG II Experiment

2.5 Subject of this thesis
This thesis focuses on a suppression of γ-ray backgrounds in the MEG II experiment withtwo methods: the elimination of pileup γ-rays and the identification of the background γrays. The former one was achieved by developing the pileup elimination algorithms for the LXedetector, and the latter was by introducing the RDC. Thus, the analysis and the performance ofthe detectors and the background suppression methods are discussed in the following chapters.
Hereafter, statuses and updates for the two detectors are summarized, and the MEG II projected
sensitivity without any updates in this thesis is described.

2.5.1 Status and update for LXe detector
The LXe detector had been developed by the liquid xenon group of the MEG II collaboration.
Its construction was finished in 2017, and installed to the MEG experimental area followed by
the commissioning of the detector. The detector performance was measured with the muon
beam and other γ-ray sources, which are explained in Sec. 3.1.2. The position and energy
resolutions were evaluated using the data taken in 2018 and 2019, and were reported in [62],which are summarized in Sec. 3.4 and Sec. 3.6, respectively. The timing resolution was alsomeasured with γ-rays from the muon beam and reported in [62]. It was updated in this thesis
using the other γ-ray source. The author contributed to the development of a reference counterfor the measurement, the timing calibration of the detector and the evaluation of the resolution
as described in Sec. 3.5.
Since an unexpected degradation of the MPPC performance was observed under the muon
beam, the radiation damage on the MPPC was investigated. The author was responsible for thelab test, which was carried out to understand the observed degradation in the detector. The
measurements and the results are explained in Appendix C.
Since pileup γ-rays increases the number of background events in the signal energy region,
the further background suppression can be achieved by eliminating them. The algorithm usedin [62] tries to find out the pileup γ-rays by searching for the excess of a measured waveformfrom a template waveform (Fig. 2.72). This method is sensitive only to the pileup γ-rays whose
hit timings are far enough from the main γ-ray since their waveforms cannot be separated fromthat of the main γ-ray. The author developed a series of the pileup elimination algorithms todeal with all of the pileups, and succeeded in achieving better performance, which is discussed
in Sec. 5.

2.5.2 Status and update for RDC
The RDC had been developed by the RDC group of the MEG II collaboration. It was tested
with the muon beam in 2016 after the construction followed by the performance measurementwith the LXe detector from 2017. The author has taken responsibility all of the operation,
calibration and performance evaluation of the RDC from 2017, which are described in Chap. 4,

76

77

chi2

amplitude (V)Chapter 2 MEG II Experiment

0

−0.2

103

102

−0.4
10
−0.6

−0.8

1

−1
−6

−0.05

0

0.05

0.1

0.15

0.2

0.25

0.3
time (sec)

×10

10−1

−6

−0.05

0

(a)

0.05

0.1

0.15

0.2

0.25

0.3
time (sec)

×10

(b)

Figure 2.72 Pileup elimination by waveform for a typical waveform with pileups [62]. (a)The original PMT waveform (black) is unfolded to three identified pulses (red, blue, andgreen). (b) Chi-square of this event assuming (black) signal γ-ray, and (red) three γ-rays.
The pileups are found by searching for the excess in the chi-square.

in addition to the development of the procedure to introduce the RDC information to theµ+ → e+ γ analysis as discussed in Chap. 6. These works confirmed the background suppression
power with the RDC and the improvement of the sensitivity.

2.5.3 MEG II projected sensitivity without updates in this thesis
Here, we define the parameters used for the sensitivity calculation as the nominal setting, which
are summarized in Table 2.15. In addition to the designed beam intensity of 7 × 107 µ+ stops/s,
the case at a half intensity, 3.5 × 107 µ+ stops/s, is calculated as a possible scenario to copewith the PDE degradation of the LXe MPPCs. The positron resolutions are updated from thedesign values based on the observations [50]. The γ-ray resolutions at the MPPC PDE of 6%
are used, and the timing resolution is assumed to be consistent with the MC expectation. The
nominal branching ratio sensitivity before applying any updates in this thesis was calculatedwith the updated nominal parameters at 7 × 107 µ+ stops/s; the γ-ray pileup elimination usedin [62] was applied, and the RDC was excluded. For the generation of the Eγ PDF, simulated
data with a real noise taken in 2021 were used. The sensitivity was calculated to be 7.8 × 10−14
for three-year data-taking.
This value is, indeed, worse than the previously reported values in [62], i.e. 6 × 10−14 . The
discrepancy partly comes from an increase of the number of high energy γ-rays resulting fromthe consideration of the real noise situation; only a Gaussian white noise was included for the Eγ
PDF generation in the previous estimation*7 though there are some new observations such as acoherent noise in reality as will be discussed in Sec. 5.3.2. Fig. 2.73 shows the energy spectra
generated with the simulated noise and the real noise. The events in 51.5–54 MeV increases
by 28% due to the real noise from the simulated one. Another cause is an increase of positronineﬃciency due to the higher noise level than the original expectation: k = 1.03 × 1014 in the*7 The performance was validated with data in the run 2019, and its consistency with the simulated noise

dataset was proved. However, only the limited channels were used in the run, which led an underestimationof the eﬀect of the real noise.

event rate (Hz)

Chapter 2 MEG II Experiment

78

102

10

1

10−1

10−2
48

50

52

54

56
58
Eγ (MeV)Figure 2.73 Energy spectra of the simulated background γ-rays with the simulated noise(black) and the real noise (red) after applying the elimination algorithm in [62].

past.
Table 2.15 Parameters for sensitivity calculation as the nominal setting.

Variables

Values+7 × 10 µ stops/s

3.5 × 107 µ+ stops/s

σpe+

100 keV/c

90 keV/cσθe+

6.7 mrad6.2 mradσϕe+

4.9 mrad4.7 mrad

7

σEγ

1.7%

σuγ

2.5–8.1 mm (for diﬀerent wγ )σ vγ

2.5–7.4 mm (for diﬀerent wγ )σwγ

2.4–13.9 mm (for diﬀerent wγ )σte+ γ

70 ps

68 ps

ϵe+

65%

74%

ϵγ
k

69%
9.38 × 10

13(for three years)

5.34 × 1013 (for three years)

79

Chapter 3

Performance Evaluation of LXe Detector
The LXe γ-ray detector measures γ-ray energy, position and timing. This detector was developed for the MEG experiment and upgraded for the MEG II experiment in order to achieve
better performance as mentioned in Sec. 2.1.3.2. In this chapter, the descriptions of several calibration methods and sensor alignment are given firstly. Then, the performance of the detector
in terms of the position, timing and energy resolution is also discussed in this order.

3.1 Calibration
The LXe detector requires precise calibration to achieve the aimed resolutions. Therefore,
many calibration methods are developed as summarized in Table 3.1.
Table 3.1 Calibration tools for the LXe detector [2].

Category

Process

EnergyCharge exchange reaction

π− p → π0 n55, 83 MeV photons

π → γγ0Li(p, γ)8 Be

14.8, 17.6 MeV photons

11

B(p, γ)12 C

4.4, 11.6, 16.1 MeV photons

Neutron generator

58

59

Am source

241

Proton accelerator

7

Ni(n, γ) Ni
Am(α, γ)237 Np

LED

9 MeV photons
5.5 MeV αsblue-UV region

3.1.1 Sensor calibration
For the event reconstruction, the number of photons Npho on each photosensor is calculated
from the observed charge q as

Npho = q/Rsensor /e,(3.1)

where Rsensor is a sensor response, which must be measured correctly for the precise reconstruction.

Chapter 3 Performance Evaluation of LXe Detector

80

Top

Outer
old LED
from MEG
new LED
from MEG II

DS

BottomUSz axisFigure 3.1 Installed positions of the LEDs [84].

Top

Outer
α source
4

3

2

1

0

Wire0
9

8

7

6

14 13 12 11 10

19 18 17 16 15

24 23 22 21 20

DS

Bottom

US

5

Wire1
Wire2
Wire3
Wire4

z axisFigure 3.2 Installed positions of the alpha sources [84].
Satoru Kobayashi

28

The response of the photosensors is calibrated using blue-light LEDs and α sources installedin the detector as shown in Fig. 3.1 and Fig. 3.2. The LEDs on the lateral face (Toyoda Gosei
E1L49–3B1A–02. [81]) are reused from the MEG, and used for the PMTs (Fig. 3.3(a)). The
LEDs (Kingbright KA-3021QBS-D. [82]) on the outer face are newly installed for the MEG II
for the MPPCs, which are covered with a Teflon sheet to diﬀuse the light for a uniform light
distribution (Fig. 3.3(b)). The α sources, 241 Am, are installed by being crimped on tungsten
wires with 100 µm diameter as shown in Fig. 3.3(c) [83]. Five wires are stretched between the
upstream and the downstream faces, and each wire includes five sources at intervals of 12.4 cm.
The activity of the sources is 200 Bq at most, which is low enough not to aﬀect the beam datataking.

Chapter 3 Performance Evaluation of LXe Detector

(a)

(b)

81

(c)

Figure 3.3 Sensor calibration sources. (a) LEDs on the lateral face. (b) LEDs on theouter face. (c) α source crimped on a wire.

PMT
The sensor response term of the PMTs RPMT can be written as

RPMT = Gain × CE × QE.

(3.2)

The Gain includes the sensor gain and the amplifier gain of the electronics. The QE is thequantum eﬃciency, which is a probability of the incident photon conversion, and the CE is thecollection eﬃciency, which is a probability where the converted photoelectrons reach the active
region of the sensor.
The PMT gain is calculated using the Poisson statistics of the number of photoelectronsobserved with a PMT Nphe for a constant intensity light as22σN= µNphe + σnoise
,
phe

(3.3)

where σNphe and µNphe are the standard deviation and the mean of Nphe , respectively, and σnoise
is a noise contribution. Using this equation, the relation between the standard deviation σq andthe mean µq of the measured charge can be written as2
σq2 = Gain × (µq + Gain × σnoise
),

(3.4)

since the charge can be converted from the number of photoelectrons with q = Gain × Nphe × e.
The calibration data are taken with the LEDs changing the intensities as shown in Fig. 3.4.
The PMT gain is extracted by fitting a linear function to the mean–variance relation of themeasured charge as its slope corresponds to the objective value. The PMT gain needs to becalibrated periodically because the value continuously decreases during the data-taking with theµ beam probably due to the degradation of the dynode material.
The other terms of the PMT response, i.e. the QE and the CE, can be calculated by comparing
the observed charge for the scintillation light from the α sources with that of MC simulation.
MC
The observed charge q can be written with the expected number of photons Nphoas

Variance^2 [10^18 e^2]

Chapter 3 Performance Evaluation of LXe Detector

82

0.00220.002
0.00180.00160.00140.00120.001
0.00080.00060.0004run 353696
PMT 41300.0002
0

0.2

0.4

0.6

0.8

1

1.2
Charge [10^9 e]

Figure 3.4 Relation between charge mean µq and charge variance σq2 measured with different LED intensities [62]. The gain is calculated from the fitted slope.

q = Gain × CE × QE × Npho × e,

(3.5)

MC
= Gain × CE × QE × Npho
× LY × e,

where LY is a relative level of the light yield normalized to 1 for the MC. From the direct
observation, we can know the product of the response parameters as

MC
CE × QE × LY = q/Gain/Npho
/e.

(3.6)

The precision of the measurement was estimated to be 4% [85].
MPPC
Similarly to the PMTs, the sensor response term of the MPPCs RMPPC can be written as

RMPPC = Gain × P DE × ECF,

(3.7)

where P DE is the photon detection eﬃciency. The P DE is a product of the quantum eﬃciencyof silicon, the avalanche initiation probability and the geometrical fill factor, which is a fractionof the sensitive microcells over all cells. ECF is the excess charge factor.
The MPPC gain is calculated with a single photoelectron peak obtained using an LED light.
Fig. 3.5 shows an example of the measured charge distribution. The gain is extracted fromthe diﬀerence between the mean of zero photoelectron and single photoelectron peaks obtainedby fitting two Gaussians. Fig. 3.6(a) shows the measured MPPC gains. The distribution is
suﬃciently uniform though there is a slight lot dependence. The precision of the measurement
was estimated to be 2.5% [85].
The ECF , which is a factor to correct the measured charge for the eﬀects of correlated noises,
is also calculated with the LED data assuming a Poisson distribution. If there is no correlated

Chapter 3 Performance Evaluation of LXe Detector

83

noise, the number of photoelectrons follows a Poisson distribution Pλ (x), where λ is the Poissonmean. Since the number of the zero photoelectron events is not aﬀected by the correlated noise,
λ can be obtained by a fraction of such events f0 as
f0 = Pλ (0) = e−λ .

(3.8)

If there is the correlated noise, the mean of the distribution µ deviates from the expected mean,and so the ECF can be calculated as ECF = µ/λ. Fig. 3.6(b) shows the ECFs of the MPPCs.
A large production lot dependence is observed. The precision of the measurement was estimatedto be 1.4%.
The P DE, which is defined by Nphe = Npho × P DE, is measured using the α sources bycomparing the measured number of photoelectrons with that of MC similar to the PMT asMC
P DE × LY = q/Gain/ECF/Npho
/e.

(3.9)

The PDEs measured at the beginning of the run 2019 are shown in Fig. 3.7(a). The precisionof the measurement was estimated to be 3%. The average PDE is 7%, which is much lower
than that measured at the lab (∼ 15%). It is suspected that this discrepancy is caused by PDE
decrease due to the exposure to the µ beam. Fig. 3.7(b) shows the PDEs as a function of theincident angle from each α source to each MPPC. A larger angular dependence was observed
than that expected from the reflection, which is consistent with the observation at the lab [62].
Fig. 3.8 shows the MPPC response, i.e. RMPPC × LY , to the VUV light and the visible lightaveraged over all MPPCs during the run 2019. The response to the VUV light was found to
decrease by 11% correlated to the beam exposure. If the decrease comes from the gain or the
ECF, the response to visible light should decrease to the same level. However, it decreased only
by 1%, and thus that is not the case. To test the contribution of LY , the PMT response to
the VUV light except for the gain, i.e. CE × QE × LY , was also measured and the result isshown in Fig. 3.9. It also decreased, but only by 4%, which means the degradation of the MPPC
response cannot be explained by the decrease of the xenon light yield. Therefore, it is concluded
that the degradation of the MPPC response mainly comes from the PDE. This degradation was
confirmed with other variables such as charge for background γ-rays and current measured with
the MPPCs under the µ beam [62].
Since the degradation is correlated with the beam usage, the PDE decrease can be caused byradiation damage. The possible irradiation sources are γ-rays, neutrons and VUV photons, andtheir fluence during the run 2019 are summarized in Table 3.2. Since the dose levels of the γ-ray
and the neutron are much less than the levels at which the performance of the MPPC can beaﬀected according to previous studies [86] [87] [88] [89] and the damage due to the VUV photon
has not been reported, the PDE degradation was unexpected.
A possible cause of the degradation is a surface damage by the VUV photon irradiation. In thesurface damage, the oxide charges are accumulated near the interface between the silicon layer
and the passivation layer, and they can distort the electric field around it. Since the collection

Chapter 3 Performance Evaluation of LXe Detector
eﬃciency for the VUV light is enhanced by the electric field as described in Sec. 2.1.3.2, it canbe aﬀected by the distortion while that for the visible light is hardly aﬀected.
The eﬀect of the radiation damage was investigated at the lab. Although the degradation
observed for the MPPCs in the LXe detector was not reproduced completely, the PDE degradation due to the VUV photon irradiation was observed with much slower decreasing speed aswill be described in Appendix C. The result suggests that the PDE can be saturated around
10% of the original value, which corresponds to the PDE of 2%.
If the degradation is due to the surface damage, a thermal annealing can recover the degraded
PDE by the release of the accumulated charges by the thermal excitation. The eﬀect of theannealing was tested for a small number of MPPCs in the LXe detector after the run 2018. LXe
was transferred to the storage tank, and the detector was filled with gaseous xenon at room
temperature during the annealing. The MPPCs were heated up by the sensor current when
they were illuminated by intense LED light. The annealing was performed for six MPPCs with
diﬀerent conditions: the induced current from 17 to 24 mA and the duration of 23 or 38 hours.
The temperature of the MPPCs was not directly measured, but it is expected be about 70◦ C
according to a lab test performed under the same condition. Fig. 3.10(a) shows the degree of
PDE recovery for VUV light after the annealing. It was significantly recovered to the samelevel observed at the lab test before installation, i.e. ∼ 17%. The dependence on the annealing
strength of the recovery was also observed, which supports it resulted from the annealing. Not
only the PDE for VUV light but also that for visible light recovered as shown in Fig. 3.10(b)though the recovery was much smaller than that of VUV light since the PDE for visible light
was not reduced so much.
The signal amplification is useful to compensate the decreasing PDE during data-taking since
the annealing is not possible so frequently. In the original plan, the PDE of ∼ 15% is assumed,
and the amplifier is not used to avoid the signal amplitude of the MPPCs exceeding the dynamic
range of the readout, but it can be increased depending on the PDE as shown in Table 3.3.
Although the MPPC PDE can be recovered by the thermal annealing, the degradation limits
the continuous operational days without any annealing in the middle of the beam time. Fig. 3.11
shows the history of the averaged PDE on the readout MPPCs measured in the pilot runs from2017 to 2019, and its extrapolation to the future. Since the speed of the degradation were
measured to be gradually slowing down, there is a large uncertainty in the extrapolation.
In the worst case, the PDE will be zero after a 70–100 day beam usage at the MEG II beam
intensity (7 × 107 µ+ stops/s) while the original plan is 120 day data-taking per year. Therefore,
detector operation to survive with reasonable performance must be considered. The following
three scenarios were considered in [62]. The first scenario is just to shorten the DAQ time per
year. The LXe detector can be operated for 60 days with a full PDE recovery at the beginningof the year’s DAQ. The second scenario is to reduce the beam intensity by a factor of two,
which enables the detector operation for 120 days. Since the accidental backgrounds increase√
according to the beam intensity, the significance Nsig / NBG gets better than the first scenario.
In addition, pileup conditions are improved by the reduced beam intensity resulting in a better

84

Events

Chapter 3 Performance Evaluation of LXe Detector

300
250
200
150
100
50
0
−0.1

0

0.1

0.2

0.3
0.4
Charge[10 9 e]

Figure 3.5 Charge distribution of an MPPC obtained using a weak LED light. The redline is a sum of fitted Gaussians [62].

background suppression performance. The third scenario is to have an annealing not only atthe begging of each year, but also during the beam time. In total, it will take about 60 days
to finish all the annealing processes, and thus the remaining 80 days can be used for the DAQ.
This results in a higher statistics and a higher PDE than the former two scenarios. These three
scenarios were compared in terms of the branching ratio sensitivity, and it was found that thehighest sensitivity is achievable with the second scenario.
To be optimistic, the PDE can be saturated around 2% based on the observation at the lab*1 .
In this case, the detector is operational even at the MEG II intensity for 120 days though the
PDE is kept low after the saturation. This enables to accumulate the highest statistics in the
scenarios.
The two scenarios, the halved intensity in the pessimistic case and the MEG II intensity inthe optimistic case, are discussed in Sec. 7.3. Note that other scenarios with the intermediate
beam intensity are also possible. It can be optimized to maximize the accumulated statistics
and detector performance.
Table 3.2 Expected irradiation fluence in run 2019 corresponding to 160 hours in the
MEG II beam intensity [62].

irradiation source

dose/fluenceγ

0.01 GyVUV photon

4.6–5.8 × 1010 /mm2

neutron

2.9 × 106 n/cm2*1 The PDE degradation was supposed to be saturated around 6% in an optimistic scenario in [62] based on theobservation of a lab test; saturation around 35% for the wavelength of 190 nm had been observed. However,it was found that the saturation level is lower for the wavelength of 150–180 nm with the subsequent
measurement (Appendix C).

85

1800 ×10

86

3

ECF

Gain

Chapter 3 Performance Evaluation of LXe Detector

2.4
2.2

1700
2
1600
1.8
1.6

1500

1.4
1400
1.2
1300
1
1200
0

1000

2000

3000

4000

5000
6000
MPPC serial number

0.8
0

1000

2000

(a)

3000

4000

5000
6000
MPPC serial number

(b)

0.18

Normalized PDE

VUV PDE

Figure 3.6 (a) Gain and (b) ECF of the MPPCs at the over voltage 7 V [62].

2

1.8

0.16

50

Measured in actual machine
Measured in large prototype

1.6

0.14

40

1.4

0.12

1.2

0.1

30

1

0.8

0.08

20

0.6

0.06

0.4

0.04

10

0.2
0.02
0
0

0
0
1000

2000

3000

4000

(a)

5000
6000
MPPC serial number

20

40

60

80

0

Incident Angle[deg](b)Figure 3.7 (a) PDE of each MPPC at over voltage 7 V measured at the beginning of therun 2019 [62]. (b) MPPC VUV PDE as a function of the incident angle [84]. The individual
diﬀerence of PDE of each MPPC is corrected using the data point of the smallest incident
angle.

3.1.2 Detector calibration
Proton accelerator
A CW proton accelerator is located at the downstream side of the πE5 beamline (Fig. 3.12).
Accelerated protons are injected into a target made of Li2 B4 O7 placed at the center of the
COBRA magnet [48]. The nuclear reactions both of Li and B produce γ-rays: 14.8 MeV
and 17.6 MeVγ-ray from 73 Li(p, γ)84 Be at Ep = 440 keV, and 4.4 MeV and 11.7 MeVγ-ray from11
12
5 B(p, γ)6 C at Ep = 163 keV.

The γ-ray with 17.6 MeV from the lithium excitation is used not only for the energy calibration
but also for the evaluation energy resolution of the LXe detector since its energy spread is smallenough (12 keV). The other γ-ray with 14.8 MeV is not used due to the large decay width andthe overlap with a lower energy tail of the 17.6 MeV peak. From the boron excitation, γ-rays of

MPPC Response (a.u.)

Chapter 3 Performance Evaluation of LXe Detector

87

MPPC Response under muon beam

1.06
1.04
1.02
1
0.98
0.96
0.94
0.92
0.9

Response to LED light

0.88

Response to VUV light

Accumulated Beam Exposure (hour)

0.86

200

19/10

180

26/10
Exposure to muon
beam

02/11

160
140
120
100
80
60
40
20
0

10/19

10/26

11/02

Month/Day

PMT Response (a.u.)

Figure 3.8 Averaged MPPC response to the VUV light from the α sources (blue) and thevisible light from the LEDs (red) during the run 2019 (upper), and the accumulated beam
usage (lower) [62]. The values are normalized by the first measurement points.

1.06
1.04
1.02
1
0.98
0.96
0.94
0.92
0.9
0.88
0.86
10/19

10/26

11/02
Month/Day

Figure 3.9 Averaged PMT response to the VUV light from the α sources divided by thegain, i.e. CE × QE × LY , during the run 2019 [62].

4.4 MeV and 11.7 MeV are emitted simultaneously, which can be used for timing alignment of
the LXe detector and the pTC.
CEX
The Charge EXchange reaction (CEX) of π − on proton is used to calibrate energy and timing
and to evaluate the performance with quasi-monochromatic γ-rays with energies near the signal
γ-ray energy. A π − beam with the momentum of 70.5 MeV/c is injected into a liquid hydrogentarget, and then π 0 produced by the CEX immediately decays to two γ-rays as

Vis PDE recovery by annealing.

VUV PDE recovery by annealing.

Chapter 3 Performance Evaluation of LXe Detector

2.2
2
1.8
1.6
1.4

2.2
2
1.8
1.6
1.4

1.2

1.2

1

1

0.8

88

0.8

Not annealed

2802

2712

2672

2789

2700

2658 MPPC id

Not annealed

2802

(a)

2712

2672

2789

2700

2658 MPPC id(b)

Figure 3.10 Recovery of the PDE (a) for VUV light, (b) for blue LED light due to theannealing [62]. Non-annealed MPPCs are also shown for comparison. The MPPC ids inthe x-axis are in an ascending order of the annealing strength. The error bar of the nonannealed MPPCs shows the 1σ spread of the PDE ratio distribution of the non-annealed
MPPCs.
Table 3.3 Amplifier gain to be used for diﬀerent PDEs.

PDE

amplifier gain

8% < P DE ≤ 22%

1

4% < P DE ≤ 8%

2.5

2% < P DE ≤ 4%

50% < P DE ≤ 2%10

π − + p → π 0 + n → γ + γ + n.

(3.10)The γ-rays are emitted back-to-back with the energy of 67.5 MeV in the rest frame of the π 0 :Eγrest =mπ 0≃ 67.5 MeV.
2

(3.11)In the laboratory frame, they are boosted by π 0 momentum and their energies can be written
by

Eγ =

mπ 0
γ(1 ± βcosθrest ),2(3.12)

where β is the velocity of the π 0 (≃ 0.2), γ is the Lorentz factor and θrest is the emission angle
in the rest frame. Therefore, the γ-ray energy ranges from 54.9 MeV to 82.9 MeV depending on
the angle. The quasi-monochromatic γ-rays of 54.9 MeV and 82.9 MeV are available by selecting
back-to-back events. The energy spread can be narrower than 0.2% if the events with opening
angle above 175◦ are selected, which is suﬃcient to measure the energy resolution of 1%.

Chapter 3 Performance Evaluation of LXe Detector

Figure 3.11 Measured PDE history measured in the pilot runs from 2017 to 2019, and its
extrapolation. The x-axis is the usage time of the MEG II beam. Blue band shows a linear
extrapolation of the 9 ± 2% degradation observed in the run 2019 [62].

Figure 3.12 Location of the CW proton accelerator [90].

In order to select such events, a reference counter is placed in the opposite side of the LXedetector (Fig. 3.13). It is composed of a timing counter and a calorimeter. The calorimeterconsists of a 4 × 4 arrayed Bismuth Germanium Oxide (BGO) crystals sized 46 × 46 × 200 mm3(Fig. 3.14(a)). Each crystal is read out with a PMT (H8409-70, Hamamatsu Photonics) attachedon the back (Fig. 3.14(b)). The timing counter is placed in front of the calorimeter (Fig. 3.15).
It consists of two plastic scintillator counters, which are placed to be orthogonal to each other,and a lead converter with 4 mm thickness placed in front of them. The thickness of the converter
was optimized to maximize the eﬃciency based on the simulation. The scintillators (EJ-230) aresized 80 × 175 × 5 mm3 , and read out with 16 SiPMs (S13360-3050PE, Hamamatsu Photonics)
coupled to each side. To reduce the number of readout channels, the adjacent four SiPMs areconnected in series, and thus 16 channels are read out in total.
The reference counter is mounted on a mover to scan the whole LXe detector acceptance89

Chapter 3 Performance Evaluation of LXe Detector

90

πReference counterγγ

Liquid hydrogen target

LXe detector
Figure 3.13 Overview of the CEX measurement.

(a)

(b)

Figure 3.14 BGO calorimeter for CEX calibration [44]. (a) 16 crystals are installed in a
detector holder. (b) Each BGO crystal is read out with a PMT.

(Fig. 3.16). It can be moved in ϕ (vertical) and z (horizontal) directions, and rotated in orderto face the liquid hydrogen target.
In the run 2020, the CEX data-taking was performed. The LH2 target was installed to z ∼ 7 cm
due to a mechanical conflict though it would be the center. The position of the reference counter
was shifted by 7 cm accordingly. In this thesis, only the timing calibration and resolution are
discussed with the CEX data.

3.2 Alignment of MPPCs
The γ-ray hit position is reconstructed using the detected charge distribution and the positionsof MPPCs, and thus the MPPCs must be well aligned. In order to achieve the aimed position

Chapter 3 Performance Evaluation of LXe Detector

Figure 3.15 Timing counter for CEX calibration.

Figure 3.16 Mover for the reference counter. The arrows shows the degree of freedom [44].

resolution of 2 mm, a precision of 0.5 mm is required for the measurement of the MPPC positions.
This was realized by combining two independent measurements.

3.2.1 Measurement with laser scanner
The surfaces of the installed MPPCs were surveyed with a three-dimensional laser scanner(FARO Edge ScanArm) during the detector construction (Fig. 3.17(a)). Edges of MPPC chips
and MPPC packages can be seen in the data as shown in Fig. 3.17(b). The gaps between the91

Chapter 3 Performance Evaluation of LXe Detector
four chips were fitted, and the position and the normal vector of each MPPC were reconstructed.
Since the space between the inner and the outer faces of the cryostat is limited, the data quality
only for ∼10% of MPPCs was good enough to reconstruct the positions. Therefore, those of theother MPPCs were interpolated by the reconstructed ones assuming the MPPCs on the same
CFRP are well aligned with a good precision.

3.2.2 Measurement with γ-rays
Since the positions of the MPPCs are aﬀected by the thermal contraction of the PCBs and the
CFRPs, a complementary measurement was performed at the LXe temperature. The γ-rays of
120 keV from a 57 Co (Fig. 3.18(a)) were injected into the LXe detector and interact with the LXe
within 3 mm. The γ beam was collimated with a brass collimator to be a size of 1.5 × 40 mm2
on the MPPC surface. The whole inner face of the LXe detector was scanned by changing
the position and the direction of the beam with moving stages. The movement was monitoredwith an optical laser and a bubble level [91], which enables to align the beam with precisions of
30 µm in z and 80 µm in ϕ direction. Since the scintillation light is localized thanks to the shortattenuation length for 120 keV γ-ray, an excess of the event rate can be observed when a γ-ray
hits above the MPPC (Fig. 3.18(b)), from which the MPPC position is reconstructed.

3.2.3 Combined analysis
A three-dimensional position of each MPPC at the LXe temperature was calculated by combining the two measurements; the laser scanner measurement provides a three-dimensional position
at room temperature, and the γ-ray measurement provides a two-dimensional position at the
LXe temperature. The reconstructed position in the γ-ray measurement was fitted by the measured position with the laser scanner ⃗xlaser with a transformation, Euler rotation R(α, β, γ) andoﬀset ⃗coﬀset , and a thermal contraction a asx⃗′ laser = (1 − a)R(α, β, γ)⃗xlaser + ⃗coﬀset .
The fitted thermal contraction rate was found to be consistent with that of the detector material(16 ppm/K). The fitted laser positions and the γ-ray positions were in agreement within an
accuracy of 0.3 mm, which fulfills the requirement of 0.5 mm.
The results suggest that the MPPCs deviate from the designed positions from −4.1 mm to+0.3 mm along with the r direction and −3.1 mm to +0.5 mm along with the z direction mainly
due to a curvature of the CFRPs (Fig. 3.19). In this thesis, the correction was not applied, but
the eﬀect is limited since only a part of channels, which concentrate in the center of one CFRP,
is used.

92

Chapter 3 Performance Evaluation of LXe Detector

93
MPPC Surface
1.5

1

0.5

0

−0.5

−1

(a)

(b)

Figure 3.17 (a) MPPC position measurement by a laser scanner [91]. (b) Example ofmeasured MPPC surface by laser scanner [84]. Color shows the coordinate of perpendicular
direction. The red region corresponds to the ceramic package of each MPPC, and the blue
region corresponds to the gap between four chips on a package (Fig. 2.33).

Laser Emitter
Rotation Stageφ motion
BubbleBeamCollimatorz motion
Linear Stage
(a)

(b)

Satoru Kobayashi

Figure 3.18 (a) Apparatus for MPPC alignment with85γ-rays [84]. (b) The γ-ray event
rate of an MPPC as a function of z position of the beam [91].

3.3 Waveform analysis
Signals of the photosensors are recorded with the waveform digitizer. Fig. 3.20 shows typical
waveforms of the LXe detector for a γ-ray event. The information of the signals such as timings
and charges is extracted by analyzing them.
The pulse timing is defined by the timing when the waveform crosses a certain thresholdvoltage given by the product of the signal amplitude and a constant fraction. This method
has an advantage of the time walk suppression compared to using a constant threshold. The
constant fraction is optimized to have the best timing resolution for the MPPCs and the PMTs,
individually. The resolution can be better with a lower threshold due to the smaller statisticalfluctuation for the first arriving photon timing while it can be more sensitive to the noise andthe transit time spread. The optimal fraction was measured to be 5% for the MPPCs and 10%
for the PMTs.

Chapter 3 Performance Evaluation of LXe Detector

94

0.05
60

0.05
60

-0.01
40

-0.01
40

-0.08

20

-0.14

-0.08

20

-0.14

0

-0.20

0

-0.20

−20

-0.26

−20

-0.26

-0.33

−40

-0.33

−40

-0.39
−60

−20

-0.39
−60

0

20

40

−20

0

20

-0.45
∆r (cm)
(a)

40
-0.45
∆z (cm)(b)

Figure 3.19 Deviation of MPPC positions from the design along with (a) r and (b) z
directions. The four gaps along with the x-axis are due to the diﬀerent CFRPs. The
central slit along with the y-axis in (b) is due to the diﬀerent PCBs.

Since the timing extraction is sensitive to high frequency noises, a noise reduction algorithm
is appleid to the original waveform. Such noises come from the system clock of the readout
electronics, they are synchronized to the phase of the clock. Therefore, they can be reduced bysubtracting template waveforms generated using random trigger events. For further reduction,a moving average filter of adjacent three points is also applied for the MPPC waveforms. The
application of the digital lowpass filter is a trade-oﬀ between a reduction of the high frequency
noise and a smearing of the sensor waveforms, and thus the strength of this filter was optimized
to get the best timing resolution.
The charge of each photosensor is obtained by integrating each waveform over 300 ns arounda common reference timing. The reference timing is extracted from a sum waveform of the
MPPCs based on the constant fraction method. The baseline is calculated by taking a mean of
amplitudes before the charge integration region. The charges are converted to the number ofphotons using the calibration parameters.

amplitude (a.u.)

amplitude (a.u.)

Chapter 3 Performance Evaluation of LXe Detector

0
−0.2
−0.4

95

0
−0.2
−0.4

−0.6

−0.6

−0.8

−0.8

−1

−6

0

0.2

0.4

×10
0.6
(s)

−1

−6

0

0.2

(a)

0.4

×10
0.6
(s)

(b)

Figure 3.20 Typical waveforms of (a) MPPC and (b) PMT. Each color in (a) corresponds
to each production lot: Lot A (black), Lot B (red), Lot C (green) and Lot D (blue).
The variety of the MPPC waveforms comes from the diﬀerent correlated noise probability(Sec. 2.1.3.2).

3.4 Position resolution
The hit position of the γ-ray is reconstructed using the light distribution on the inner face,
and thus the improved granularity thanks to the replacement of the PMTs on the inner faceto the MPPCs is expected to make the position resolution for the shallow events better. Thiswas verified by taking γ-ray data with a collimator and comparing the reconstructed position
distribution with MC.

3.4.1 Position reconstruction
The position of the γ-ray conversion is reconstructed from the light distribution on the innerface. Firstly, initial position is computed from the mean of MPPC positions weighted by thedetected number of photons Npho . Then, a fitting is performed to minimize the diﬀerence
between the detected number of photons and the expected one from the solid angle Ω of each
MPPC from the γ-ray hit position ⃗x assuming the scintillation photons are isotropically emitted
from one point as2χ :=∑ ( Npho − C × Ω(⃗x) )2MPPC

σ(Npho ),where C is a normalization of the light distribution, which is estimated in the fitting as a
nuisance parameter. σ(Npho ) is the uncertainty of the Npho of each channel, which is given by
the statistical fluctuation of the number of photoelectrons as

Chapter 3 Performance Evaluation of LXe Detector

96

outer faceHit
position

U_fit - U_mc (cm)Fittedposition

Residual of U vs. U

inner face

5

45

4

40

3

35

2

30

1

25

0

20

1

15

2

γ

u

w

3

10

4

5

5
40

30

20

(a)

10

0

10

20

30
40
U_fit (cm)0(b)

Figure 3.21 (a) Schematic of the u correction [62]. A bias in the reconstruction (red arrow)is corrected by the reconstructed γ-ray position (blue arrow). (b) Correlation between thebias and the reconstructed position in MC.

σ(Nphe )
,
P
DE
√
Nphe
=
.
P DE

σ(Npho ) : =The estimated position is biased to the direction of shower development due to the assumptionthat all the scintillation photons come from one point since they are emitted from each point of
the electromagnetic shower in reality. To reduce this bias, only the limited number of MPPCs
around the hit position is used in the fitting. In addition, two corrections are applied whoseparameters are derived from the MC simulation. The first type corrects a global bias withrespect to u direction. The direction of the shower development tends to be similar to the γray incident direction. This causes the reconstructed u position to be larger when a γ-ray hits
at large |u| position as shown in Fig. 3.21. This dependence is corrected as a function of thereconstructed u position. The second type corrects an eﬀect of even-by-event fluctuation of theshower direction. Even for the events with the same hit position, the shower direction can be
diﬀerent due to the fluctuation. In order to correct the dependence on the shower direction, it
is reconstructed by performing the position fitting for several fitting regions utilizing the factthat the reconstruction bias becomes larger for a wider fitting region (Fig. 3.22).

3.4.2 Performance Measurement
Measurement with 17.6 MeV γ-ray
The position resolution was evaluated with the CW-Li γ-rays in the run 2018. A 25 mm thicklead collimator was placed in front of the LXe detector, which had several slits of 5 mm width at

Chapter 3 Performance Evaluation of LXe Detector

outer face

97

Residual of U vs. Difference of U b/w different Fitting Range

U_fit - U_mc (cm)1

FittedpositionHit
position

inner face

50

0.8
0.6

40

0.4
0.2

30

0
0.2

20

0.4

γ

0.6
u

w

10

0.8
1
0.2

0.15

(a)

0.1 0.05
0
0.05
0.1 0.15
0.2
Difference of U b/w different Fitting Range (cm)0(b)

Figure 3.22 (a) Schematic of the shower correction [62]. A bias in the reconstruction(red arrow) is corrected by the diﬀerence of the reconstructed position using diﬀerent
fitting ranges (blue arrow). (b) Correlation between the bias and the diﬀerence of thereconstructed position in MC.

intervals of 50 mm. The resolution was evaluated with the width of the reconstructed position
distribution of the slits. An excess of the event rate corresponding to each slit was fitted witha simulated hit position distribution smeared by a Gaussian. The resolution was defined by thesigma of the Gaussian.
The γ-rays from the RMD were not used because the spot size of the muon beam is 1.2 cm
for the vertical direction and 4 cm for the horizontal direction, which can smear the position
distribution to the extent being not negligible. That of the proton beam is small enough, which
is 0.6 mm for the vertical direction and 0.8 mm for the horizontal direction. In addition, theposition resolution does not depend on the energy since the resolution is not dominated by thestatistical fluctuation according to MC.
The estimated resolution is shown in Fig. 3.23 as a function of the reconstructed conversion
depth. The improvement of the resolution in the shallow region is observed as expected. On theother hand, that in the deep region is measured to be slightly worse than the expectation. Thiscan be because of a contribution of the noise, but it has not yet been understood quantitatively.
An angular dependence of the MPPC PDE which cannot be explained by the Fresnel reflection
was found as described in Sec. 3.1.1, and the PDE for the larger incident angle is lower thanthat for the smaller incident angle. This leads to a bias of the position reconstruction; theconversion depth is biased to be shallower since the light distribution on the MPPCs becomes
sharper. Although the bias can be corrected by the measured angular dependence, it canbecome systematic uncertainty if we misunderstood the angular dependence, and thus its eﬀect
was investigated. As a result, it was found that even if the angular dependence is totally
misunderstood, the angular resolution of Θe+ γ increases only by 1.2%, which results in 0.6%
degradation of the branching ratio sensitivity at most.

0.9

resolution (cm)resolution (cm)

Chapter 3 Performance Evaluation of LXe Detector

0.8
0.7
0.6

98

0.9
0.8
0.7
0.6

0.5

0.5

0.4

0.4

0.3

MEG II. Data

0.3

MEG II. Data

0.2

MEG II. MC

0.2

MEG II. MC

MEG.

0.1

MEG.

0.1
0
0

2

4

6

8

10
12
depth (cm)

0
0

(a)

2

4

6

8

10
12
depth (cm)(b)

Figure 3.23 Position resolution for 17.6 MeV γ-ray as a function of the conversion depthfor (a) horizontal u-direction, and (b) vertical v-direction. The resolutions in MEG are
also shown for comparison.

The eﬀect of the position resolution on the branching ratio sensitivity was investigated. For
the calculation, the resolutions except for the position resolution were fixed to the measured
resolution in the pilot runs. The improvement in the shallow region leads to a 30% better
sensitivity than MEG. On the other hand, the sensitivity is worse by 4% compared to the MC
expectation due to the worse resolution in the deep region. In total, therefore, a 26% sensitivity
improvement is achieved compared to MEG.
Eﬀect of PDE degradation
The increase of the statistical fluctuation due to the reduced PDE can increase the fitting uncertainty for the position reconstruction, which results in the worse position resolution. Fig. 3.24
shows the position resolution simulated assuming various MPPC PDEs. The degradation of theresolution was observed in the deep region, where the fitting uncertainty can be larger due to thesmaller number of photoelectrons on the inner face. The noise eﬀect is negligible for the position
resolution since it was proved that the position resolution measured with the 17.6 MeV γ-ray
from the CW-Li at the 7% PDE is not aﬀected, whose signal-to-noise ratio is equivalent to thatat the 2.3% PDE for the signal γ-ray.
Fig. 3.25 shows the eﬀect on the branching ratio sensitivity from the degradation of the position
resolution. It was found to be less than a few percent.

3.5 Timing resolution
The hit timing of a γ-ray is reconstructed using the extracted timings of each channel. An improvement of the timing resolution is also expected thanks to a better estimation of a correction
parameter resulting from the better position resolution. The timing resolution was measured
with a high energy γ-ray from the CEX reaction.

PDE 16 %0.9
PDE 8 %
0.8
0.7
0.6

PDE 4 %

1
PDE 16 %0.9
PDE 8 %
0.8
0.7

PDE 2 %

99

resolution (cm)1resolution (cm)resolution (cm)

Chapter 3 Performance Evaluation of LXe Detector

0.6

0.5

0.5

0.4

0.4

0.3

0.3

0.2

0.2

0.1

0.1

PDE 16 %1.6
PDE 8 %
1.4

PDE 4 %

PDE 4 %
1.2

PDE 2 %

PDE 2 %
1

0.8

0.6

0
0

2

4

6

8

0.4

0.2

0
0

10
12
depth (cm)

2

4

6

(a)

8

0
0

10
12
depth (cm)

(b)

2

4

6

8

10
12
depth (cm)(c)

Branching ratio sensitivity (a.u.)

Figure 3.24 Position resolution in the simulation as a function of the conversion depth atvarious PDE for (a) u, (b) v, and (c) w direction [62].

1.25

1.2

1.15

1.1

1.05

1

0.95

0.9
0

2

4

6

8

10

12

14

16

18

20

22

24

PDE (%)

Figure 3.25 Eﬀect on the branching ratio sensitivity from the position resolution degradation at diﬀerent MPPC PDEs [62]. The values are normalized by that of 8% PDE.

3.5.1 Timing reconstruction
The hit timing of a γ-ray is reconstructed based on the weighted mean of the sensor timings.
Firstly, initial timing is extracted from the channel whose detected number of photons is the
maximum on the inner face. Then, a fitting is performed to minimize the diﬀerence between
the hit timing tγ and each photosensor timing as

χ2 :=

∑

χ2pm,i ,pm

χ2pm,i :=(tpm,i − tcorr,i − tγ )2
,
2
σpm,i

tcorr,i := tprop,i + twalk,i + toﬀset,i .

Chapter 3 Performance Evaluation of LXe Detector

100

Here, tpm,i is the extracted timing of each photosensor. tcorr,i is a correction term, which consistsof the propagation time from the reconstructed γ-ray hit position to each photosensor tprop,i , thetime walk eﬀect twalk,i and the time oﬀset toﬀset,i coming from the diﬀerence of the cable lengthand electronics. σpm,i is the precision of the timing information. The fitting is iterated until
χ2 /ndf gets lower than 10. To eliminate the pileup eﬀect, the photosensors whose χ2pm,i are morethan 10 are removed from the reconstruction. The rests can contribute to the reconstruction,but only a part of them has a suﬃcient timing resolution to aﬀect the reconstruction in practice.
Typically, contributions from channels below 100 photoelectrons are negligible though channels
above 50 photoelectrons are included.

3.5.2 Performance Measurement
The timing resolution was evaluated using the γ-rays from the CEX reaction (Sec. 3.1.2) in
2020. The reference detector was placed at the opposite side of the readout area of the LXedetector.
Performance of timing counter
The reference timing was measured with the timing counter. It is defined by the mean of thetimings measured with the two scintillator counters, where the timing of each counter is definedby the mean of the timings of the readout channels as

tfront + tback,
2∑
1
tfront,back =ti ,Nchtref =(3.13)i∈front,backwhere tref is the reference timing, tfront and tback is the timing of the scintillator counter in thefront and the back side, respectively, and ti is the timing of each readout channel. The numberof the channels Nch is eight for each scintillator.
The hit position xref on the timing counter is also computed by the timing diﬀerence of thechannels attached on each side, tleft and tright , asxref = (tleft − tright ) × veﬀ ,∑2
tleft,right =
ti ,
Nch

(3.14)i∈left,rightwhere veﬀ is the eﬀective velocity of scintillation light, which is measured to be ∼ 12 cm/ns.
Since the two scintillators are arranged to be orthogonal to each other, the positions along withthe vertical and horizontal axis can be obtained. The events in which the reconstructed position
satisfies |xref | < 4 cm for both is used for the analysis. More than a half of the total energy
deposit in the center 2 × 2 crystals was also required for the BGO calorimeter.
The timing resolution of the timing counter σtref was obtained during the CEX data-taking

2time walk (ns)time walk (ns)

Chapter 3 Performance Evaluation of LXe Detector

1.5
1
0.5

101

10
9
8
7

0

6

−0.5

5

−1

4

−1.5

3

−2
0

0.05

0.1

0.15
1/ Npe

2
0

(a)

0.05

0.1

0.15
1/ Npe(b)

Figure 3.26 Measured time walk of (a) MPPC and (b) PMT. Each color corresponds toeach group; MPPC Lot A (black), Lot B (red), Lot C (green) and Lot D (blue) in (a), andPMT outer (black) and lateral (red) in (b).

by taking the timing diﬀerence of the two counters as
σtref =

σ(tfront − tback ).
2(3.15)

It was estimated to be 38(0.4) ps.
Calculation of calibration parameters
The calibration parameters were calculated using the reference timing. The timing resolutionof each channel σpm and the time walk twalk were estimated from the spread and the meanof tpm − tprop − tγ,exp , where tγ,exp is the γ-ray hit time on the LXe detector expected fromthe timing counter and the time-of-flight, i.e. tγ,exp = tref − T OFref + T OFγ . These TOF arecalculated from the reconstructed positions on each detector assuming the vertex is the center of
the target. The propagation time tprop is calculated from the distance between the reconstructed
position and each photosensor divided by the eﬀective velocity of light in LXe.
Fig. 3.26 and Fig. 3.27 show the obtained twalk and σpm as a function of an inverse of squareroot of the number of photoelectrons, respectively. These functions are extracted for eachproduction lot for the MPPCs because they have diﬀerent shapes of a waveform due to thediﬀerent after-pulsing probabilities. The PMTs are grouped by those on the outer face andthe others since their time walks and resolutions were found to be diﬀerent. The mean of this
distribution has a channel-by-channel diﬀerence, which is interpreted as a time oﬀset of eachchannel toﬀset . The distribution of the measured time oﬀset for the PMTs was found to be wider
than that for the MPPCs as shown in Fig. 3.28. This is likely due to the individual diﬀerence ofthe cable length since the cables for the PMTs are reused from MEG with some modifications.

3

timing resolution (ns)timing resolution (ns)

Chapter 3 Performance Evaluation of LXe Detector

2.5
2
1.5

102

3
2.5
2
1.5

1

1

0.5

0.5

0
0

0.05

0.1

0
0

0.15
1/ Npe

0.05

(a)

0.1

0.15
1/ Npe(b)

Figure 3.27 Measured timing resolution of (a) MPPC and (b) PMT. Each color corresponds to each group; MPPC Lot A (black), Lot B (red), Lot C (green) and Lot D (blue)in (a), and PMT outer (black) and lateral (red) in (b).

50
40
30
20
10
0
−3

−2

−1

0

1

2
3
time offset (ns)Figure 3.28 Measured time oﬀset of the MPPCs (black) and the PMTs (red).

Detector resolution
There are two variables which describe the detector timing resolution. One is the absolute
resolution which is a spread of the diﬀerence between the reconstructed γ-ray timing and thereference timing. This is the resolution directly related to the physics analysis, and can bemeasured in the CEX run using the reference timing as the true value. The other is the intrinsic
timing resolution estimated from an even-odd analysis. In the even-odd analysis, the photosensors are divided into two groups, e.g. sensors with even channel numbers and odd channel
numbers (Fig. 3.29), and the timing is reconstructed independently for both groups. The intrinsic resolution is estimated from the diﬀerence of them. This resolution can be better than theabsolute one since some eﬀects fluctuating the reconstructed timing are canceled by the even-odd

Chapter 3 Performance Evaluation of LXe Detector

103

subtraction, such as a precision of the propagation time given by the hit position resolution anda coherent noise from the electronics.
The absolute timing resolution is calculated by subtracting possible uncertainties from thetiming diﬀerence between the LXe detector and the timing counter as

σtγ = σ(t′γ − t′ref ) ⊖ σtref ⊖ σtvertex ,t′γ = tγ − T OFγ ,t′ref = tref − T OFref .

(3.16)

The contribution from the vertex uncertainty σtvertex is estimated to be 48(2) ps using MC fromthe measured beam size of 6.5 mm and 5.5 mm along with the x and y direction. Fig. 3.30(a)shows the timing diﬀerence between the two detectors after the TOF correction. The absolutetiming resolution was evaluated to be 81(3) ps for 54.9 MeV. The intrinsic timing resolution was
also evaluated using the same data to be 38(0.7) ps (Fig. 3.30(b)), which is consistent with thatmeasured using background γ-rays in the pilot run 2019 [62].
The measured resolutions and their MC expectation are summarized in Table 3.4. To makethe simulation realistic, the noise obtained by firing trigger randomly was added to the simulated waveforms. In addition, precisions of the timing calibration of the electronics and thesynchronization between the WDBs were added based on the measured values, 25 ps and 45 ps,
respectively. The measured absolute resolution was found to be much worse than the MC expectation while the intrinsic resolution was consistent with each other. As a result, the discrepancy
between the absolute and intrinsic resolution, 72(3) ps, was found to be much larger than the
expectation, 30 ps.
The timing resolution for 82.9 MeV γ-rays is also evaluated. The absolute timing resolution
was 80(3) ps while the intrinsic resolution was 31(0.4) ps, which is slightly better resolution
than that for 54.9 MeV due to the higher photoelectron statistics. The diﬀerence between
the absolute and intrinsic resolution was 73(3) ps, which is consistent with that observed for54.9 MeV. This indicates the term causing the additional deviation does not depend on thephotoelectron statistics.
Fig. 3.31 shows the timing resolutions as a function of the reconstructed conversion position.
Both of them have almost flat distributions and the discrepancy remains independent of theposition. Fig. 3.32 shows the timing resolution as a function of the number of photoelectrons.
The improvement of the resolution due to the increased number of photoelectrons was observed
for both resolutions.
There are two types of candidates to explain the discrepancy: the eﬀect canceled by theeven-odd subtraction and the eﬀect added to the calculation of the absolute resolution. In theformer type, the precision of the propagation time, the coherent noise eﬀect, the precision ofsynchronization are included. Indeed, however, these eﬀects are included in the simulation, andthus they are almost excluded. There is also possibility that the analysis causes some kinds ofbias which can be reduced by the subtraction. An overestimation of the timing resolution of theChapter 3 Performance Evaluation of LXe Detector

104

timing counter belongs to the latter case. However, it is not likely since its resolution was alsomeasured with a 90 Sr source in advance, and the result was consistent with each other. There isanother possibility that the estimation of the vertex uncertainty is wrong. Since its estimation
totally relies on the measured beam size and the simulation, it can be underestimated due toan error of either. Fig. 3.33 shows a relation between the beam size and the simulated vertex
contribution. It is obvious that the vertex contribution can be easily misunderstood if there
is an error in the measured beam size. Indeed, the measured beam size in 2020, (σx , σy ) =(6.5 mm, 5.5 mm), is much smaller than that measured in MEG, (σx , σy ) = (1 cm, 1 cm), and if
the measured value is wrong for some reasons and the true size is the same as that in MEG,
the observed discrepancy can be almost explained. Therefore, it turned out to be important toestimate the vertex contribution in another way in order to certify the estimation.
A dedicated data-taking is planned to measure the vertex contribution directly. The measurement uses γ-rays from the CEX. An additional timing counter whose design is the same as
the reference timing counter is placed in front of the LXe detector and the timing of one of the
γ-rays is measured with it instead of the LXe detector. Since we know the timing resolutions ofboth timing counters, the vertex contribution can be estimated in the same way as Eq. (3.16).
This measurement will be performed in the CEX run 2021, and the absolute timing resolution
will be re-evaluated using the measured vertex uncertainty.
Note that the te+ γ resolution for the µ+ → e+ γ analysis will be evaluated from the RMD
data; a peak in the timing diﬀerence between the positron timing measured with the pTC andthe γ-ray timing measured with the LXe detector is fitted with a double Gaussian. This allows
us to check the consistency of the measured resolutions and gain information about the causeof the unknown contribution: whether it derives from the systematics of the CEX measurement
or whether it is related to the detector performance itself.
The eﬀect on the branching ratio sensitivity is evaluated. If the unknown contribution is
explained by the error of the vertex uncertainty estimation, a timing resolution of ∼ 50 ps
is achieved, which results in the sensitivity improvement of a few percent from MEG. If theunknown contribution remains even with the improved estimation of the vertex contribution,
the timing resolution is worse than the MC expectation by 27 ps resulting in a 13% worse
sensitivity.
Table 3.4 Comparison of the detector timing resolution between MC and data.

VariableMC

data

Absolute resolution

55 ps

81 ps

Intrinsic resolution

40 ps

38 ps

Eﬀect of PDE degradation
The timing resolution can be worsen both by the lower signal-to-noise ratio and the larger
statistical fluctuation, which are expected at lower PDE. The former contribution can be com-

Chapter 3 Performance Evaluation of LXe Detector

105

100

1300.00

80

100

60

80

40

60

20

40

0

20

1118.14962.26806.380650.50−20468.64−40−60

312.76−80
156.88

−100
−100

0

100

200

300

z

1.00

Figure 3.29 Assignment for even (gray) and odd (red) channels in the even-odd analysis.

500

400
350

400

300
250

300

200
200

150
100

100

50
−9

0
−2

−1

×10
1
2
t'γ - t'ref (s)

0

0

−9

−0.4

×10

−0.2

0

(a)

0.2
0.4
(tγ , even - tγ , odd)/2 (sec)(b)

Figure 3.30 Measured timing diﬀerence between (a) the LXe detector and the timing
counter and (b) the even and odd timings. σ of the fitted Gaussian is 102 ps and 38 ps,
respectively.

−9

0.12
0.1
0.08

−9

×10

timing resolution (s)timing resolution (s)timing resolution (s)

−9

×10
0.14

0.14
0.12
0.1
0.08

×10
0.14
0.12
0.1
0.08

0.06

0.06

0.04

0.04

0.04

0.02

0.02

0.02

0
−10

−5

0

(a)

5

10
uγ (cm)

0
−30

0.06

−25

−20

(b)

−15

−10

−5
vγ (cm)

0
0

2

4

6

8

10
12
wγ (cm)(c)

Figure 3.31 Position dependence of absolute (black) and intrinsic (red) timing resolutionfor (a) u direction, (b) v direction and (c) w direction.

Chapter 3 Performance Evaluation of LXe Detector

106

timing resolution (sec)

−9

×10
0.14
0.12
0.1
0.08
0.06
0.04
0.02

×10
60
80
100
total number of photoelectrons

3

0

40

σvertex (ps)Figure 3.32 Absolute (black) and intrinsic (red) timing resolution as a number of total
number of photoelectrons. The spectrum of the total number of photoelectrons is also
shown (gray). The two peaks correspond to the energies of 54.9 MeV and 82.9 MeV, respectively.

100
90
80
70
60
50
40
30
20
10
0

0.6

0.8

1

1.2

1.4
σx, σy (cm)Figure 3.33 Simulated vertex contribution as a function of a beam size. The sizes alongwith x-axis and y-axis are assumed to be the same.

pensated to some extent by amplification since the noise level is not proportional to the gainof the amplifier as shown in Table 3.5. The timing resolution at lower PDE was simulated byadding the pedestal data taken at each gain to the simulated waveform. The precisions of thetiming calibration and synchronization of the electronics were added as well. Fig. 3.34 shows
the simulated timing resolution and the eﬀect on the sensitivity. Since energy dependence of
the unknown term causing the discrepancy is not observed, its eﬀect is constantly added to theestimated resolutions. The eﬀect of the PDE degradation was found to be up to 5% for the

90
80
70

Branching ratio sensitivity (a.u.)

resolution (ps)

Chapter 3 Performance Evaluation of LXe Detector

MEG II design

MEG LXe

60
50
40
30
20

1.25
1.2
1.15
1.1
1.05
1
0.95

10
0
0

107

5

10

15

0.9
0

20
PDE (%)

5

10

15

20
PDE (%)(b)(a)

Figure 3.34 (a) Simulated absolute (black), intrinsic resolution (red) and absolute resolution including the unknown term of 72 ps (blue). (b) Eﬀect on the branching ratio
sensitivity as a function of the MPPC PDE assuming the simulated absolute timing resolution (black) and that with the unknown contribution (blue). The values are normalized
by that of 8% PDE in the former case.

expected resolution.
Table 3.5 Noise level (RMS of pedestal waveform) at each amplifier gain in the run 2019.

amplifier gain

1

2.5

5

10

Noise level

0.7 mV

0.8 mV

0.9 mV

1.3 mV

3.6 Energy resolution
The energy of a γ-ray is reconstructed from the detected number of photons. In MEG, theenergy resolution in the shallow region was worse than that in the deep region due to the
non-uniformity of scintillation light collection, which can be improved thanks to use of the
MPPCs. The energy resolution measured in MEG was worse than the expectation by 1.5%.
The reason of the disagreement is not understood yet, and it can also remain in MEG II. Since
the energy resolution in MEG II is expected to be 0.7% according to the simulation, the unknown
contribution can be dominant. The resolution was measured using several γ-ray sources.

3.6.1 Energy reconstruction
The energy of a γ-ray is reconstructed from the weighted sum of the detected number ofphotons on each sensor as

Eγ = C ×∑

Npho,i × wi ,pm

Npho,i = qi /Gaini /ECFi /QEi .

(3.17)

Chapter 3 Performance Evaluation of LXe Detector

108

The number of photons Npho,i detected with each photosensor is computed from the integrated
charge qi . The weight wi is the correction for the sensor coverage, which is given by the size ofthe insensitive area around each sensor divided by the size of the sensitive area in order to realize
uniform response in the whole detector. The factor C converts the sum of the number of photons
to the energy, which is calculated using the monochromatic γ-ray sources. A further correction
is applied to reduce the position dependence of the reconstructed energy, which reflects possible
errors in the photosensor calibration and the position dependence of photon collection eﬃciency.
This is also measured using the monochromatic γ-ray sources.

3.6.2 Performance Measurement
The energy resolution was evaluated in the pilot run 2019. In spite of the limited numberof readout channels, it was found in simulation that the same energy resolution as with fullelectronics was achievable as shown in Table 3.6 by applying the event selection as• |u| < 9 cm,• |v + 17| < 9 cm,• |w| < 12 cm.
The third selection was applied to reject the very deep events since scintillation light from thedeep conversion depth distributes wider than the MPPC readout area. In addition, a selectionof Eγ,MPPC > Eγ,PMT /6 was used to reject cosmic-ray events since the cosmic rays do not enter
the detector from the inner face and thus a fraction of the energy measured with the MPPCs issmaller than that of γ-ray.
Table 3.6 Energy resolution estimated with MC simulations in MEG II for the signal 52.8 MeV γ-ray

Full channel readout

Limited channel readoutw < 2 cm

0.72(1)%0.73(1)%

w > 2 cm

0.70(1)%0.76(1)%

Measurement with 17.6 MeV γ-ray
The energy resolution at 17.6 MeV was measured using CW-Li. Fig. 3.35 shows the reconstructed energy distribution after the non-uniformity correction is applied. The energy resolution
was evaluated to be 3.1% at 17.6 MeV, which is much worse than the expected resolution of 1.0%
from the MC. A part of the diﬀerence between the MC and the data comes from an electronics noise, which is estimated to be 1.2% from the reconstructed energy distribution of pedestal
data. The rest part can result from the unknown contribution observed in MEG since the energy
resolution excluding the noise eﬀect is 2.8%, which is consistent with the resolution measured
in MEG for the deep events (w > 2 cm). This term worsens the energy resolution independentof the conversion depth. The reconstructed energies only with the MPPCs and the PMTs werecompared between the MC and the data, and the discrepancy is consistently observed for both.

Chapter 3 Performance Evaluation of LXe Detector

109

450
400
350
300
250
200
150
100
50
0
12

13

14

15

16

17

18

19
20
Energy (MeV)

Figure 3.35 Reconstructed energy spectrum of 17.6 MeV γ-ray from CW-Li [62].

Measurement with background γ-ray
The energy resolution near the signal energy was evaluated using the background γ-rays fromthe muon beam. It was extracted by fitting an expected spectrum to the measured one with abinned-likelihood method. The likelihood L(p), and its negative log likelihood nll are definedasL(p) :=

N
−1
∏
b=0

fb (p)hb e−fb (p),hb !

nll := − ln L(p) = −N−1∑{hb ln fb (p) − fb (p)} + const. ,b=0where {hb |0 ≤ b < N } is a N -bin histogram of the measured spectrum, and {fb (p)|0 ≤ b < N }is that of the expected spectrum given by convoluting the simulated spectrum fMC with anadditional resolution σ as∫f (x|p) = R ×

fMC (x/S + s)e−s /2σ ds + fCR (x).
22An energy scale S and an overall rate R are also considered as nuisance parameters. A non-beam
contribution fCR is also included based on the spectrum measured without muon beam*2 .
The measured background spectra at the reduced intensity (0.7 × 107 µ+ stops/s) and at the
MEG II intensity (7 × 107 µ+ stops/s) are shown in Fig. 3.36, together with the expected spectra.
A pileup elimination was applied in which sum waveforms of the MPPCs and the PMTs are
unfolded by fitting template waveforms [62]. The best estimate of the fitting parameters are

S = 1.013(3), R = 1.16, σ = 1.6(2)% (for reduced intensity),
S = 1.007(1), R = 1.13, σ = 1.5(1)% (for MEG II intensity).
The larger uncertainty of the reduced intensity is due to the limited statistic. The energy scales
agree with that of the CW-Li γ-ray within 1% precision. The event rate was 10–20% higher*2 It mainly comes from cosmic rays, and neutrons from the accelerator captured by the LXe.

Measured spectrum

1Best Fit. MC convoluted by 1.6% gauss
MC convoluted by 0.7% gauss
MC convoluted by 2.2% gauss

10

1

Event rate (Hz)Event rate (Hz)

Chapter 3 Performance Evaluation of LXe Detector

10 2

10

Measured spectrum

10Best Fit. MC convoluted by 1.5% gauss
MC convoluted by 0.7% gauss
MC convoluted by 2.2% gauss

1

10 1

3

42

110

10

44

46

48

50

52

54

56

Energy (MeV)

2

42

44

(a)

46

48

50

52

54

56

Energy (MeV)(b)

Figure 3.36 Measured energy spectra of the background γ-ray and the best fit result (a)at the reduced intensity, (b) at the MEG II intensity [62]. The expected spectrum at better
and worse resolution than best fit are also shown for comparison.

than that expected from the beam intensity. This is likely due to the higher beam intensity than
the setting as mentioned in Sec. 2.2.1. The energy resolution can be obtained by combining thefitted σ and the 0.7% energy resolution in the simulation, and it was estimated to be 1.7(2)%for the reduced intensity and 1.7(1)% for the MEG II intensity. The noise contribution was only
0.4% for the signal energy γ-ray, and thus it is negligible.
Fig. 3.37 shows the depth dependence of the energy resolution. An improvement in the shallow
region, where many γ-rays interact as shown in Fig. 2.19, was observed though it was worse thanthe expectation due to the unknown contribution.
The expected sensitivity was evaluated with the measured energy resolution. The improvement for the shallow events results in the 15% improvement compared to MEG. The sensitivity
improvement from MEG is 10% smaller than the design value since it was calculated assuming
only a half of the unknown contribution remains though it was found to completely remain.
Although the cause of the unknown term has not been understood yet, there are several possibilities to explain it. One possibility is a problem of the detector system such as a convectionof LXe in the cryostat. Another possibility is an event-by-event fluctuation of the shower development which is not correctly simulated for some reasons. An intrinsic property of the LXescintillation is also a candidate; a part of the energy deposit in LXe can be used for a generationof the charged carries or an emission in infrared, which may cause an event-by-event fluctuationof the energy used for an emission of the VUV light. Further studies are necessary for a better
understanding.
Eﬀect of PDE degradation
The energy resolution can be aﬀected both by the statistical fluctuation and the noise on
the signals. Fig. 3.38(a) shows the simulated energy resolution of the signal γ-ray with thecontribution for the statistical fluctuation. It was found to increase the resolution by 0.15% atResolution (%)

Chapter 3 Performance Evaluation of LXe Detector

3111

MEG measured
MEG II measured
MEG II expected

2.5

2

1.5

1

0.5

0
0

2

4

6

8

10

12

Conversion depth (cm)2.4
Energy resolution + 1.5%

2.2
2
1.8
1.6
1.4

1.25

1.2

1.15

1.1

1.05

1

0.95

1.2
1
0

Branching ratio sensitivity (a.u.)

resolution (%)

Figure 3.37 Energy resolution as a function of the conversion depth estimated from background γ-rays at MEG II intensity [62].

2

4

6

8

10

12

(a)

14

16

18

20

22
24
PDE (%)

0.9
0

2

4

6

8

10

12

14

16

18

20

22

24

PDE (%)(b)

Figure 3.38 (a) Expected energy resolution for the signal γ-ray as a function of the PDE
including the unknown contribution of 1.5%. (b) Eﬀect on the branching ratio sensitivity
from the energy resolution degradation at diﬀerent MPPC PDEs [62]. The values arenormalized by that of 8% PDE.

the PDE of 2%. The noise contribution was simulated using the noise level measured in thepilot run 2019, and it is found to be less than 0.6% at 2% PDE by applying the amplification.
As a result, the sensitivity can be degraded by 4% as shown in Fig. 3.38(b).

112Chapter 4

Performance Evaluation of Radiative
Decay Counter
The downstream RDC has been tested with a µ beam. In this chapter, the calibration is
described followed by the discussion on the performance measured with the µ beam.

4.1 Calibration
The energy of the RDC calorimeter is converted from charge as
E = q × Scalo ,Scalo = (Scalib + ftemp × ∆T )/fbias ,

(4.1)
(4.2)

where q is the charge, Scalo is an energy scale conversion factor of the calorimeter, Scalib is thefactor obtained from calibration, ftemp and fbias are correction factors of temperature and bias,∆T is a diﬀerence between temperatures at the time of calibration and the measurement.
Fitting function
The energy of the RDC calorimeter is calibrated using the intrinsic radioactivity of LYSO. The
highest energy peak of 596 keV (88 + 202 + 307 keV) is fitted with a function of the theoreticalenergy spectrum including γ-rays and β decays convoluted with a gaussian function (Fig. 4.1),
that is,∫f (x) =

Gaus(x/p7 − E, σ(E, p8 , p9 )) × Decay(E)dE,

Gaus(x, σ) = exp(−x2 /2σ 2 ),2σ(x, σenergy , σnoise ) = x × σenergy + σnoise,6∑

pi × BetaDecay(x/p7 − Ei ),Decay(x) =i=0

BetaDecay(x) = Norm ×√
x2 + 2x × me c2 × (Q − x)2 × (x + me c2 ),

(4.3)
(4.4)
(4.5)
(4.6)
(4.7)

where Norm is normalization constant, me is the mass of an electron, c is the velocity of light,
and Q is a Q-value of β decay. p0 − p9 are fitting parameters; p0 − p6 are amplitudes of theChapter 4 Performance Evaluation of Radiative Decay Counter

220
200
180
160
140
120
100
80
60
40
20
0
0

0.2

0.4

0.6

0.8
1
charge (a.u.)

Figure 4.1 Example of the measured energy spectrum of the LYSO intrinsic radioactivity
and the fitting function.
Table 4.1 Parameters of the fitting function for the LYSO intrinsic radioactivity spectrum.

p0

Amplitude of the γ-ray peak of 88 keV

p1

Amplitude of the γ-ray peak of 202 keV

p2

Amplitude of the γ-ray peak of 307 keV

p3

Amplitude of the γ-ray peak of 88 + 202 keV

p4

Amplitude of the γ-ray peak of 88 + 307 keV

p5

Amplitude of the γ-ray peak of 202 + 307 keV

p6

Amplitude of the γ-ray peak of 88 + 202 + 307 keV

p7Conversion factor from charge to energy

p8Energy resolution

p9

Noise

γ-ray peaks, p7 is a conversion factor from charge to energy, p8 is the energy resolution, and p9
corresponds to noise as summarized in Table 4.1. The energy is calibrated using the conversion
factor p7 obtained by fitting, i.e. Scalib = p7 .
Since the fitting function has many parameters, the fitting results was found to be unstable;
the results can easily change by fluctuation of data and a fitting range. Therefore, some fitting
parameters are fixed to expected values in order to reduce the degree of freedom. The parametersettings are written in Table 4.2. The amplitudes of γ-ray peaks except for the highest one are
set to reproduce the measured spectrum by hand due to a diﬃculty of estimation by the fitting
because the fitting is performed only around the highest peak. The energy resolution is set tothe measured value. The improvement reduces the instability.
The uncertainty from the fitting was evaluated by repeating the calculation with three diﬀerent
datasets obtained under the same condition, which was 1.2%.

113

Chapter 4 Performance Evaluation of Radiative Decay Counter

114

Table 4.2 Parameter settings of the fitting function for the LYSO intrinsic radioactivity spectrum.

Parameter

Value

p0

0

p1

0

p2

0

p3

0.5

p4

0.1

p5

0

p6

free

p7

free

p8

8%

p9

free
rec335421

rec335420

300

h_ch0
EntriesMean
Std Dev

180
160

4970
0.34710.1496h_ch0
EntriesMean
Std Dev

250

140

4950
0.51420.3127

200

120
100

150

80

100

60
40

50

20
0
0

0.2

0.4

0.6

0.8

1

0
0

0.5

1

charge (a.u.)

(a)

1.5

2
charge (a.u.)(b)

Figure 4.2 Energy spectra of (a) intrinsic radioactivity and (b) 88 Y with fitting results of each peak.

Bias correction
The calibration using the intrinsic radioactivity was verified by the measurement with 88 Y.
The source was attached to each crystal and its energy spectrum was obtained. Fig. 4.2 showsthe energy spectra of the same crystal. The peaks of the 88 Y were fitted with gaussian functions
and the conversion factors were calculated with the peak positions. The relation between thefactors obtained with the two diﬀerent methods is shown in Fig. 4.3. The factors of the intrinsic
radioactivity are consistently higher than those of 88 Y, which can be because of a bias from thefitting. Here, the factors calculated with the peak of 0.898 MeV are used as the result of 88 Y to
suppress an eﬀect from SiPM saturation. Therefore, the bias is corrected based on the fitting
result of a liner function: fbias = 1.122 ± 0.021.

intrinsic radioactivity

Chapter 4 Performance Evaluation of Radiative Decay Counter

115

2.1
2
1.9
1.8
1.7
1.6
1.5
1.4
1.4

1.6

1.8

88

2
Y (0.898 MeV)

Figure 4.3 Comparison between the conversion factors obtained from the intrinsic radioactivity (vertical) and 88 Y (horizontal) with a fitted linear function. The result of the
0.898 MeV peak is used as 88 Y.

(a)

(b)

Figure 4.4 (a) Measured temperature and (b) conversion factors during the monitoring offive weeks. The results of four channels are shown.

Temperature correction
Temperature correction is applied since a SiPM gain can change depending on the temperature
resulting from a change of its breakdown voltage. The temperature dependence was measured
by monitoring the conversion factors of four channels for five weeks as shown in Fig. 4.4. The
temperature coeﬃcient was obtained by fitting the relation with a linear function (Fig. 4.5),
that is ftemp = 0.114 ± 0.03.
Eﬀect on energy resolution
The uncertainties from the calibration parameters aﬀect the energy resolution. Their eﬀects
were estimated using the measured values and their uncertainties as summarized in Table 4.3.
The measured energy resolution of 6.5% with 88 Y was used as the energy resolution before theconversion to the energy. The mean of the measured energy scales with diﬀerent channels wasused as a representative. The temperature change was assumed to be 1%, which would be
expected in the experimental environment with an air conditioner. Including these uncertainties, the energy resolution was 6.9%, which is good enough not to worsen the branching ratio

energy scale

Chapter 4 Performance Evaluation of Radiative Decay Counter

116

2.5
2.4
2.3
2.2
2.1
2
1.9
1.8

ch18

1.7

ch43

ch33
ch57

1.6
1.5
18

20

22

24
temperature (°C)

Figure 4.5 Temperature dependence of the conversion factor. The results of four channels are shown.

sensitivity; it is not deteriorated at least up to 10% energy resolution [65].
Table 4.3 Parameter values and uncertainties used for the estimation of the energy resolution.

Parameter

Value

Energy resolution before conversion

6.5% (1.836 MeV)

Sself

1.83 ± 0.022

ftemp

0.114 ± 0.003

fbias

1.122 ± 0.021

δT

1◦ C

4.2 Detector performance
The performance of the RDC was evaluated with the data taken under the muon beam at
7.7 × 107 µ+ stops/s in the run 2020. In this section, the reconstruction algorithm for the RDC
is described followed by the discussion on the performance.

4.2.1 Reconstruction
Fig. 4.6 shows an overview of the RDC reconstruction chain. Firstly, the waveforms of thetiming counter are analyzed. Then, those of the calorimeters are analyzed with information of
the timings extracted in the timing counter. Hit reconstruction is performed at each detector,
and the reconstructed hits are clustered based on timings.

Chapter 4 Performance Evaluation of Radiative Decay Counter

117

Timing Counter
Waveform Analysis

Hit Reconstruction
Clustering

Hit Time
Calorimeter
Waveform Analysis

Hit Reconstruction

Figure 4.6 Overview of RDC reconstruction chain.

Waveform Analysis
Reconstruction starts from analyzing the raw waveform recorded with the waveform digitizer.
Fig. 4.7 shows typical waveforms of the RDC. The information of signals such as the timings
and charges is extracted by analyzing them.
To find the signals of the timing counter, a peak search is performed with a given threshold.
The baseline is calculated by taking the mean of the amplitudes before the found pulse timing.
The timing is extracted with the constant fraction method. The signal charge is obtained byintegrating the waveform for 20 ns around the pulse. Fig. 4.8(a) shows the hit rate of each plastic
scintillator. The maximum hit rate is about 1.2 MHz, which means one hit is expected in 830 ns
on average. This results in an overlap of pulses with the probability of 0.9% over all incident
hits since the pulses within 10 ns cannot be separated.
In the case of the calorimeter, the pulse timing is given based on the timings of found pulses inthe timing counter, and the charge integration is performed around the timing since some signals
are too small that they cannot be found by peak search. Fig. 4.8(b) shows the hit rates of eachcrystal. The center part has the highest hit rate of 0.6 MHz, which results in an overlap of pulses
with the probability of 10% considering the charge integration region of 250 ns. The eﬀect of
the overlapping pulses is eliminated as follows. If another pulse whose timing is in the baseline
calculation region of the pulse is found, the region is shifted to an earlier timing where no pulse
is found. If another pulse whose timing is in the charge integration range of the pulse is found,the charge is estimated from the pulse height by multiplying a conversion factor extracted froma template waveform. If the adjacent pulse is so close that it aﬀects the calculation of the pulse
height of the focusing pulse, i.e. the adjacent pulse timing is within the charge integration regionof the focusing pulse, the amplitude of the adjacent pulse at the timing of the height calculation
is estimated from the template waveform, and it is subtracted from the original height of the
focusing pulse. Then, the charge estimation is performed from the modified height.

amplitude (mV)

Chapter 4 Performance Evaluation of Radiative Decay Counter

118

0

−200
−400
−600
−800
−800

−600

−400

−200

0

amplitude (mV)

(ns)

0

−100
−200
−300
−400
−500

−800

−600

−400

−200

0
(ns)

2

y (cm)

hit rate (MHz)Figure 4.7 Typical waveforms of the RDC. The timing counter (top) and the calorimeter (bottom).

1.8

0.6

10

0.5

1.6
5

1.4

0.4

1.2
0

1

0.3

0.8

0.2

−5

0.6
0.4

0.1

0.2
0
−10

−5

0

(a)

5

10
y (cm)

−10
−10

−5

0

5

10
x (cm)(b)

Figure 4.8 Measured hit rates of each scintillator for (a) the timing counter and (b) the
calorimeter. The scale of the bar in (b) is in the unit of MHz. The depression at the centerin (a) is due to the diﬀerent scintillator sizes.

0Chapter 4 Performance Evaluation of Radiative Decay Counter119

Hit reconstruction
A hit in the timing counter is reconstructed by combining the information of two channels of
the same scintillator. The hit timing is defined as the average of the two channels ast=tleft + tright
,
2

(4.8)

where tleft and tright are the extracted timings of the left and right channels. The energy is givenby the geometric mean of the channels:E=√

qleft × qright × Stc ,(4.9)

where qleft and qright are the integrated charges of the left and right channels. Stc is an energy
scale conversion factor of the timing counter, which is calculated by comparing the peak energies
of Michel positrons of MC and data.
A hit in the calorimeter is reconstructed channel by channel. The energy of the hit is converted
from the charge, which is discussed in Sec. 4.1.
Clustering
Since a positron leaves several hits in the RDC, the reconstructed hits belonging to the same
positron should be combined. This clustering is performed based on the hit timings. If the hitson the timing counter are within 5 ns, they are regarded as the identical positron hits. Since
the hits of the calorimeter are already reconstructed based on the timings of the timing counter,they are automatically assigned to the same cluster with the seed hits. The fastest timing of
the clustered timing counter hits is adopted as the cluster timing while the energy is calculated
by summing up the energies of the members.

4.2.2 Performance
The performance of the RDC is characterized by the timing and energy distributions andextracted parameters from these distributions. Firstly, the event selection criteria are explained.
Then, the raw distributions are shown followed by the evaluation of the parameters; the RMD
fraction and the hit rate of accidental positrons. In addition, the eﬀect of the SiPM saturation
observed for the calorimeter is discussed.
Event Selection
To discuss the performance of the RDC, it must be ensured that the γ-ray energy is measured
correctly with the LXe detector since the detection performance of the RMD positrons relies
on it. The same selection as that for the evaluation of the γ-ray energy resolution (Sec. 3.6.2)
was applied. To reduce the pileup eﬀect, the pileup elimination based on the peak search andthe waveform unfolding is applied*1 , which will be explained in Chap. 5. The events whose
γ-ray energies are from 48 MeV to 58 MeV were used for the analysis. Fig. 4.9 shows the energy
spectra measured with the LXe detector. The data and MC were consistent with each other.
*1 The deep learning-based rejection is not used due to the limited number of channels.

event rate (Hz)

Chapter 4 Performance Evaluation of Radiative Decay Counter

10

1

10−1

data
MC

10−2
48

50

52

54

56
58
Eγ (MeV)Figure 4.9 Energy spectra of the background γ-ray measured with the LXe detector fordata at 7.7 × 107 µ+ stops/s in the run 2020 (black) and MC (red).

Measured timing and energy distributions
The distribution of the timing diﬀerence between the RDC and the LXe detector of the RMDlike hit, which is defined as a particle that hits the RDC at the closest timing to the center ofthe RDC and the LXe timing diﬀerence, is shown in Fig. 4.10(a). A clear peak together with a
low tail component was observed as expected, which correspond to the RMD positrons and theMichel positrons, respectively. The spread of the peak results from diﬀerent positron paths.
Fig. 4.10(b) shows the energy distribution. The low energy peak corresponding to the RMD
positron was observed. By selecting the events within ±8 ns timing window, the events comingfrom the RMD positrons and the Michel positrons can be roughly separated as demonstrated
in the figure. This means the RDC successfully detects both type of positrons, and they can be
distinguished by the RDC observables. Note that the low energy peak in the oﬀ-timing events
derives from γ-rays generated from Michel positrons.
RMD fraction
The RMD fraction fRMD is the most important parameter to describe the RDC performance,
which is the product of the detection eﬃciency and the fraction of the RMD events over the all
events. It is defined as the number of RMD positrons detected with the RDC NRMD divided by
the number of γ-ray events triggered with the LXe detector Nγ . The number of RMD positrons
can be calculated by counting excess of events over the expectation from the accidental hit rateof the background Racc assuming a Poisson distribution as

120

Chapter 4 Performance Evaluation of Radiative Decay Counter

121

800
2000
700

1800

600

1600

500

1400
1200

400

1000

300

800

200

600
400

100
0

−9

−40

×10

−20

0

20

40
t RDC - tLXe (s)

(a)

200
0
0

10

20

30

40
50
ERDC (MeV)(b)

Figure 4.10 (a) Timing diﬀerence between the RDC and the LXe detector under the muon
beam at 7.7 × 107 µ+ stops/s. (b) Energy distributions measured with the RDC for all
events (black), oﬀ-timing (red) and on-timing events (blue).

fRMD =NRMD,
Nγ

NRMD = Non-timing − Noﬀ-timing ×
NBG (tmin , tmax ) = A ×∫ tmaxNBG (tmin, on-timing , tmax, on-timing ),NBG (tmin, oﬀ-timing , tmax, oﬀ-timing )(4.10)

e−2Racc |t| dt,

tmin

where Non/oﬀ-timing is the numbers of events in the on/oﬀ-timing region from tmin, on/oﬀ-timing
to tmax, on/oﬀ-timing and A is normalization.
Overall fraction was evaluated to be 26.6(4)% with data, which is consistent with the MC
expectation of 27.2(4)%. To estimate the dependence on the γ-ray energy, the events weregrouped into several energy regions and the eﬃciency was calculated in the same way. As shownin Fig. 4.11, the values of data and MC were consistent with each other except for the highenergy region where statistics is limited. Therefore, it is confirmed that the RDC can detect theRMD positrons as expected.
Hit rate of Michel positron
The positron from the Michel decay is a background source for the RMD detection. The
increase of the backgrounds reduces the power of the RMD identification since the probability
to have a hit around the timing center in the non-RMD event gets higher.
The expected hit rate was estimated with MC. Fig. 4.12 shows the muon decay vertex alongwith the z-axis. The probabilities of Michel positron hit at the RDC with diﬀerent vertex
positions are summarized in Table 4.4. The hit probability becomes higher as the muon decays
at further downstream due to less interfering materials. Since the beam rate is usually definedas the stopping rate at the target, the probabilities over the total muon incidence from the

RMD fraction

Chapter 4 Performance Evaluation of Radiative Decay Counter

0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1

data

0.05

MC

0
48

50

52

54

56
58
Eγ (MeV)Figure 4.11 Dependence of RMD fraction on the γ-ray energy for data (black) and MC (red).

upstream should be corrected with the stopping eﬃciency at the target of 90.2(4)%. From thenumber of hits over all muon decay, the hit rate can be 10.4(1)% of the beam rate. Note that it
is 14.0(2)% for the run 2017 due to the less materials since the mockup was installed instead of
the real CDCH.
The hit rate was calculated by counting the number of events per unit time. In order toavoid including the RMD positron, the timing sideband from −40 ns to −20 ns in the timing
diﬀerence distribution was used for the estimation. The results measured in each year are listed
in Table 4.5. There is still a large uncertainty for the estimation mainly due to the uncertaintyof the beam rate as discussed in Sec. 2.2, but they imply the hit rate can be higher than the
MC expectation (Table 4.4) with up to 40% excess, which possibly because the material budget
from the target to the RDC is not correctly simulated; the less materials for the CDCH resultin the higher hit rate as seen in the diﬀerence between the mockup and the real CDCH cases,
for example.
Table 4.4 Hit probability to the RDC over the incident muons decaying at each position.

vertexhit probability to RDC

upstream of target

3.0(2)%

on target

9.4(1)%

downstream of target

16.0(6)%overall

9.4(1)%

122

entries

Chapter 4 Performance Evaluation of Radiative Decay Counter

123

104

103

102

10

1
−600

−400

−200

0

200
z (cm)

Figure 4.12 Simulated muon decay vertex along with the z-axis for all events (black) andevents with a RDC hit. Most muons decay on the target around zero. The sharp peak at
the downstream side corresponds to the surface of the RDC.
Table 4.5 Hit rate measured with the RDC. The data in 2018 is not included due to theserious beam contamination.

year

beam rate (µ+ stops/s)

hit rate (MHz)hit probability (%)

2017

3.2 × 1075.7

18

0.7 × 107

1.0

14

7 × 10710

14

1.6 × 1072.1

13

7.7 × 10

10

13

2019
2020

7

Saturation of SiPM for calorimeter
The SiPM used to read out the scintillation light of each LYSO crystal has a small pixel
pitch in order to avoid the saturation of the pixels as discussed in Sec. 2.1.3.3. Nevertheless, it
was found that the energy distribution measured with the calorimeter is greatly aﬀected by thesaturation eﬀect. Fig. 4.13(a) compares the energy distribution measured under the muon beamand the MC expectation. The shape in the high energy is deformed, which can be explained by
the underestimation of the energy due to the saturation. The SiPM has 14400 pixels for eachwhile about 1300 photons are generated per energy deposit of 1 MeV, and so the amount ofgenerated photons reaches a half of the number of the pixels with the energy deposit of 6 MeV.
In fact, the deformation of the waveform was observed as shown in Fig. 4.13(b). The diﬀerenceof the shape can reflect the fact that the amplitude around the peak becomes lower due to theChapter 4 Performance Evaluation of Radiative Decay Counter
LYSO energy (data)

amplitude (a.u.)

LYSO energy (data)

124

0.04
0.03

0
−0.2

0.05
0.04

−0.4 0.03

0.02−0.6 0.02

0.01−0.8 0.01

0
0

20

40

60

80
(MeV)

0
0

−1
0

20

40

0.1

60
0.2

80 ×10−6
(sec)

(a)

(b)

Figure 4.13 (a) Energy distribution under the muon beam of data (black) and MC (red).
(b) Template waveforms of the SiPM attached to the LYSO crystal averaged over the eventswith energy deposits below (black) and over (red) 10 MeV normalized by the pulse height.

saturation while that in the other region is not aﬀected since the amount of light is small enough.
No correction is applied for the energy reconstruction since it was found that the saturation
does not aﬀect the branching ratio sensitivity as will be discussed in Sec. 7.2.

125

Chapter 5

γ-ray Background Reduction by Pileup
Elimination
The energy, position and timing of γ-ray are reconstructed using the photosensor waveforms
as discussed in Chap. 3. In practice, however, multiple γ-rays can hit the LXe detector in theanalysis time window, which can aﬀect the reconstruction of γ-rays. The position and the timing
resolution are not aﬀected so much because they are reconstructed from the local information
only around the hit position as shown in Fig. 5.1. The reconstructed timings of some γ-rays arebiased by the pileup γ-rays as shown in the long tail of Fig. 5.1(b). This leads to an analysis
ineﬃciency for the signal events up to 3%. The most significant eﬀect from the pileup γ-rays isseen in the energy reconstruction because it is performed using global information. Thus, thischapter focuses on the pileup eﬀect on the reconstructed energy.
In Sec. 5.1, sources of pileup γ-rays are introduced. The pileup elimination algorithm is
explained in Sec. 5.2 followed by the performance evaluation in Sec. 5.3.

without pileup
10

10

3

3

with pileup

without pileup
with pileup

102

102

10

10

1

1
−10

−5

0

5

10

−2000

−1500

−1000

−500

0

u (cm) (reco. - truth)

(a)

500

1000

1500

2000

time (ps) (reco. - truth)(b)

Figure 5.1 Pileup eﬀect on the (a) position (u-direction) and (b) timing reconstruction of
the signal γ-rays in MC [62]. The diﬀerences between the reconstructed variable and its
truth are shown.

Chapter 5 γ-ray Background Reduction by Pileup Elimination

5.1 Sources of pileup
There are mainly two types of pileup γ-ray sources separated from the aspect of the origin; thepileup γ-ray originates from a diﬀerent µ or the same µ as the main γ-ray. Their characteristics
as a pileup γ-ray, i.e. the incident timings, are diﬀerent due to this diﬀerence of the origin, which
requires diﬀerent approaches to eliminate them. Hereafter, the detailed explanations for thesepileup γ-rays follow.

5.1.1 Pileup γ-ray from same µ decay
The first type of pileup γ-rays is a pileup γ-ray from the same muon decay. Such a γ-ray
originates from AIF.
Most of the Michel positrons are swept away by the gradient magnetic field of the COBRA,
but some of them interact with materials in flight, and two γ-rays are emitted being boosted
in the direction of the flight. Fig. 5.2 shows the interaction points of AIF from which γ-rays
deposit their energies to the LXe detector (Eγ > 20 MeV). About 42% of the AIF γ-rays are
emitted on the target, which is a central part in the figure, and most of the rests are emitted in
the drift chamber.
The background events with the AIF γ-rays reconstructed to be signal-like energy can beclassified into two event types shown in Fig. 5.3. The first type is the event in which only oneof the emitted γ-rays hits to the LXe detector with a high energy around the signal energy.
Since such a γ-ray carries most of the parental positron energy, the other γ-ray is emitted nearlybackward, and thus it cannot come to the detector. This type of event is called AIF 1γ event.
The second type is the event in which both of the emitted γ-rays hit the LXe detector, which iscalled AIF 2γ event. If their hit positions are too close to identify them, they look like a single
high energy γ-ray.
The latter type is the source of simultaneous pileup γ-rays. This AIF 2γ event has a large
contribution near the signal energy. Fig. 5.4 shows the energy spectra for diﬀerent sources ofthe background γ-rays from a single muon decay. The number of the γ-rays from RMD rapidly
decreases as the energy gets close to the signal energy while that from AIF decreases gradually
resulting from the Michel positron spectrum (Fig. 1.14). As a result, the fraction of AIF 2γ
events becomes dominant in the high energy region though this is moderated by the energy
resolution as shown in Fig. 5.5. At the currently achieved energy resolution of 1.7%, the AIF 2γ
contribution is 34% near the signal energy (51.5 MeV < Eγ < 54 MeV).
All of this type of pileup γ-rays hit the LXe detector at the same timing with each other.
Such γ-rays, namely on-timing pileups, cannot be found by a temporal search, and thus aspatial search is the only eﬀective way.

126

200

30

180
20

x (cm)y (cm)

Chapter 5 γ-ray Background Reduction by Pileup Elimination

160
140

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127

30
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20

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140

10

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120
0

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60
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40

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20

20
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−10

0

10

20

30
x (cm)

0

−30
−30

−20

(a)

−10

0

10

20

30
z (cm)

0(b)

Figure 5.2 Interaction points of AIF projected to (a) x–y axis and (b) z–x axis. The hot
region around the center corresponds to the target.

ν
γ

ν
γ

γ

e

(a)

ν

ν

e

γ

(b)

Figure 5.3 Two types of high energy background γ from AIF. (a) AIF 1γ and (b) AIF 2γ [62].

5.1.2 Accidental pileup γ-ray from a diﬀerent µ decay
The second type of pileup γ-rays is an accidental pileup γ-ray from a diﬀerent muon decay. In
the MEG II experiment, 7×107 muons decay on the target per second. Some of them emit γ-raysin the radiative muon decay, and some of the Michel positrons emit γ-rays via the interactions
with materials. The energy spectra of these γ-rays are given in Fig. 1.20(a). A single muon
decay emits a γ-ray which deposits energy in the LXe detector with a probability of 1.3%, andthus one pileup γ-ray enters the LXe detector at 0.7 MHz on average (Eγ > 0.2 MeV*1 ).
*1 Only the γ-rays whose energy deposits are larger than 0.2 MeV are included since the energy lower than

the threshold is too small to aﬀect the reconstruction.

Fraction

event rate (Hz)

Chapter 5 γ-ray Background Reduction by Pileup Elimination

AIF 2 gamma102

AIF 1 gamma

1.2

AIF 2 gamma
AIF 1 gamma
RMD

1

RMD

10

128

0.8

0.6

1

0.4
10− 1
0.2
10

−2

42

44

46

48

50

52

54

0

56
energy (MeV)

42

44

(a)

46

48

50

52

54

56
58
energy (MeV)(b)

Fraction of AIF two gamma

Figure 5.4 (a) Simulated energy deposits of the background γ-rays in the LXe detector
for each event type. Events above mµ /2 come from muon decays before stopped on thetarget. Muon momentum can boost decay products in these events. (b) Fraction of the
background γ-rays of each type calculated from (a) [62].

0.9resolution 0.6%

0.8resolution 1.2%

0.7

resolution 1.7%

0.6
0.5
0.4
0.3
0.2
0.1
0

42

44

46

48

50

52

54

56
58
energy (MeV)

Figure 5.5 Expected fraction of the AIF 2γ events with the diﬀerent energy resolutions [62].

Fig. 5.6 shows simulated energy spectra of background γ-rays without accidental pileups andwith full pileups expected at the MEG II intensity. The pileup γ-rays bias the reconstructedenergy to be higher, and the number of events near the signal energy increases from 64 Hz to
178 Hz (51.5 MeV < Eγ < 54 MeV). This greatly deteriorates the sensitivity to signal γ-rays,
and thus they must be eliminated.
Most of this type of pileup γ-rays hit the LXe detector at a diﬀerent timing from the main
γ-ray, and such γ-rays, namely oﬀ-timing pileups, can be found by a temporal search. A searchin space using the light distribution of photosensors is also eﬀective if their hit timings are closeenough to be included in the charge calculation.

event rate (Hz)

Chapter 5 γ-ray Background Reduction by Pileup Elimination

102

10

1

10−1

10−2
45

50

55

60
Eγ (MeV)Figure 5.6 Reconstructed energy spectra of background γ-rays in the simulation without
accidental pileups (black) and pileups from the MEG II beam without pileup elimination(blue).
Pileup event identification
w/ or w/o pileup
Peak search and clusteringin timing distribution

Peak search and clusteringin light distribution

Unfolding of sum waveform
Main γ Reconstruction

Figure 5.7 Flow of the pileup elimination algorithm.

5.2 Elimination algorithm
A pileup elimination algorithm combines methods to search for pileup γ-rays temporally andspatially in order to find both of oﬀ-timing and on-timing pileup γ-rays. Fig. 5.7 shows an
overview of the algorithm flow. There are mainly three steps. The first step judges whether the
event is likely to be a pileup event or not. The second step searches for peaks both in a lightand timing distribution. In the peak search flow in the light distribution, the result from thefirst step is used. The third step unfolds the pileup γ-rays in the sum waveforms of photosensors
using the information from the previous steps. At the end, an event status is assigned combining
the results of the three steps and the main γ-ray energy is reconstructed or the event is discarded
depending on the status. Hereafter, these algorithms are explained in detail.

5.2.1 Identification of pileup events with deep learning
The first step is a pileup event identification. At this step, whether the event is likely toinclude pileup γ-rays or not is judged using a deep learning technique. In this study, the light129

Chapter 5 γ-ray Background Reduction by Pileup Elimination
distribution was used for an input of the deep learning model as the first step to examine
its usefulness though the timing distribution would be also useful to search especially for theoﬀ-timing pileup γ-rays.
Deep learning
The deep learning is a type of machine learning, which consists of a neural network with morethan two layers. These neural networks mimic the behavior of the human brain to learn froma huge amount of data. The network has a layered structure in which dozens of computation
nodes are included. The nodes in one layer are connected to the nodes in the following layers,
and the computational results are transmitted to the connected nodes. The transmitted values
from the previous layers are summed up with given weights and biases which are assigned toeach connection, and the sum is used for the calculation at the node. The final layer outputs
certain values, which is often likenesses with which the input sample belongs to classes for theclassification or expected values for the regression.
Before its use, the deep learning model must be trained how to estimate a correct answer from
data. This is achieved by optimizing the weights to minimize the diﬀerence between the current
output and the correct value using a training dataset which is usually a set of input data andexpected output values.
Model implementation
The deep learning model used for the pileup elimination is based on a two-dimensional convolutional neural network (CNN). The CNN is a type of neural networks which is often used
to treat an image as the input such as image recognition. The input data are convoluted using
a series of filters with trainable weights. In the training stage, the weights are optimized to
extract useful characteristics so that the model can give a correct answer. Since the convolution
is carried out by scanning the whole inputs with the common filter, the CNN has a shift invariance. The extracted features are input to fully connected layers in which a calculation of the
final output is performed using the features.
EﬃcientNet
The model is implemented referring to EﬃcientNet [92], which is a type of the CNNs. The
EﬃcientNet model succeeded in achieving a state-of-the-art performance with a reduced amountof parameters by scaling up its architecture in an optimal way. Fig. 5.8 compares the accuracy of
the EﬀcientNets, which is a family of models developed by scaling up a baseline network obtainedwith neural architecture search, to the accuracies of other famous models. EﬃcientNets achieved
better performance with smaller model sizes.
In general, the performance of the CNN can be improved by being scaled up if more computational resources are available. There are commonly three scalable dimensions in the architecture:depth, width and resolution (Fig. 5.9). The width scaling is a way to increase the image sizes ofintermediate layers. Wider networks tend to be able to capture more fine-grained features and130Mingxing Tan 1 Quoc V. Le 1
Chapter 5 γ-ray Background Reduction by Pileup Elimination

Abstract

EfficientNet-B7

84

AmoebaNet-C

B6

B5

AmoebaNet-A

B4

Imagenet Top-1 Accuracy (%)

Neural Networks (ConvNets) are
loped at a fixed resource budget,
up for better accuracy if morevailable. In this paper, we sysy model scaling and identify thating network depth, width, and resd to better performance. Basedtion, we propose a new scaling
formly scales all dimensions ofolution using a simple yet highly
und coefficient. We demonstrates of this method on scaling up
ResNet.

131

NASNet-A

82

SENet

B3
ResNeXt-101

80

Inception-ResNet-v2
Xception

78

ResNet-152
B0

DenseNet-201

76

ResNet-50
Inception-v2

74

NASNet-A
ResNet-34

0

20

40

ResNet-152 (He et al., 2016)
EfficientNet-B1
ResNeXt-101 (Xie et al., 2017)
EfficientNet-B3
SENet (Hu et al., 2018)
NASNet-A (Zoph et al., 2018)
EfficientNet-B4
GPipe (Huang et al., 2018) †EfficientNet-B7†
Not plotted

Top1 Acc. #Params
77.8%
60M
79.1%
7.8M
80.9%
84M
81.6%
12M
82.7%
146M
82.7%
89M
82.9%
19M
84.3%
556M
84.3%
66M

60
80
100
120
140
Number of Parameters (Millions)

160

180

rther, we use neural architecFigure 1. Model Size vs. ImageNet Accuracy. All numbers aredesign a new baselineFigure
network
5.8 Accuracies
of models
as a function
model sizesignificantly
measured outwith ImageNet [92].
for single-crop,
single-model.
Ourof
EfficientNets
to obtain a family of models,perform other ConvNets. In particular, EfficientNet-B7 achieves
tNets, which achieve muchnew state-of-the-art 84.3% top-1 accuracy but being 8.4x smaller
and efficiency arethaneasierprevious
6.1x faster
thanisGPipe.
EfficientNet-B1
7.6xinsmaller
to train. Theanddepth
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while being 8.4x
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th
Unlike conventional practice that arbitrary scales these facInternational Conference on Machine
California, PMLR Model97, 2019.for pileup identification
tors, our method uniformly scales network width, depth,

The model developed for the pileup identification is based on EﬃcientNet architecture. Table 5.1 summarizes its architecture. It consists of a series of convolution layers for feature
extraction followed by a two-layer prediction part. The convolution part is composed of mobile
inverted bottleneck blocks MBConv [95] [96] with sqeeze-and-excitation optimization.
The smallest model in the EﬃcientNet family, EﬃcientNet-B0, was adopted due to the limited
computation resource. The structure of the convolution part is automatically defined by its
operators and the input resolution while the two fully connected layers were chosen in comparison

Chapter 5 γ-ray Background Reduction by Pileup Elimination

132

EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks

wider#channels

wider
deeperdeeperlayer_ihigherresolution

resolution HxW(a) baseline(b) width scaling(c) depth scaling(d) resolution scaling

higherresolution(e) compound scaling

Figure 2. Model Scaling. (a) is a baseline network example; (b)-(d) are conventional scaling that only increases one dimension of network

FigureSchematicofourmodel(a) baseline
network
example,(b)-(d)width, 5.9
depth, or
resolution. (e) is
proposedscaling:
compound scaling
method that uniformly
scalesall three dimensions
withonea fixeddimenratio.
sional scaling, and (e) compound scaling [92].
and resolution with a set of fixed scaling coefficients. Forof-the-art accuracy on 5 out of 8 widely used datasets, while
example, if we want to use 2N times more computational
reducing parameters by up to 21x than existing ConvNets.
resources, then we can simply increase the network depth byN↵N , widthby the, andsingle
image size
by Nin, where↵, , ofarethe 2.
to the model
with
layer
terms
performance.
Related Work
constant coefficients determined by a small grid search on
the original small model. Figure 2 illustrates the difference
ConvNet Accuracy: Since AlexNet (Krizhevsky et al.,Table
5.1 ourModelarchitecture
for pileup
identification.
The
operator
MBConvnmeanshavethebetweenscaling method
and conventional
methods.
2012) won the
2012
ImageNet competition,
ConvNets
become increasingly more accurate by going bigger: while
Intuitively,
the compound
scaling
method makes
senseofbe-n.
MBConvblockwith anexpansion
factorthe 2014 ImageNet winner GoogleNet (Szegedy et al., 2015)
cause if the input image is bigger, then the network needs
achieves 74.8% top-1 accuracy with about 6.8M parameters,
morelayers to increase the receptive
field and more channels Resolution
Stage
Operator#Channels#Layers
the 2017 ImageNet winner
SENet (Hu et al.,2018) achieves
to capture more fine-grained patterns on the bigger image. In
82.7% top-1 accuracy with 145M parameters. Recently,
fact, previous
theoretical(Raghu
et
al.,
2017;
Lu
et
al.,
2018)
1
Conv3 × 3
93 ×
44 et al., 2018) further
32 pushes the state-of-the-art
1
GPipe(Huangand empirical results (Zagoruyko & Komodakis, 2016) both
ImageNet top-1 validation accuracy to 84.3% using 557M
show 2that there exists certain
relationshipk3
between
MBConv1,
× 3 network parameters:
46 × 21 it is so big that
16it can only be trained
1 with awidth and depth, but to our best knowledge, we are thethefirst to3empirically quantify
the relationship
MBConv6,
k3among× 3 all three specialized
46 × 21pipeline parallelism
24 library by partitioning2
network and spreading each part to a different acceleradimensions of network width, depth, and resolution.
tor. While these models are mainly designed for ImageNet,
4
MBConv6, k3 × 3
23 × 1140
2
We demonstrate that our scaling method work well on existrecent studies have shown better ImageNet models also pering MobileNets(Howardet al., 2017; Sandler
5
MBConv6,
k3 ×et3al., 2018) form
12better× 6 across a variety
80of transfer learning
3 datasets
and ResNet (He et al., 2016). Notably, the effectiveness of(Kornblith et al., 2019), and other computer vision tasks
model6scaling heavily depends
on the baseline
tosuch
MBConv6,
k3 ×network;3
6 as×object
3 detection (He112et al., 2016; Tan et3 al., 2019).
go even further, we use neural architecture search (Zoph
Although higher accuracy is critical for many applications,& Le,72017; Tan et al.,2019) to develop
new3 baseline
we 6
have
hit the hardware
MBConv6,
k3a ×× already3
192 memory limit,
4 and thus
network, and scale it up to obtain a family of models, called
further accuracy gain needs better efficiency.
8× 3 perfor3×2
320
4EfficientNets.
Figure 1MBConv6,
summarizes thek3
ImageNet
mance, where our EfficientNets significantly outperform
ConvNet Efficiency: Deep ConvNets are often over9
Conv1
× 1our&EfficientNet-B7
Pooling &FC
3 × 2 Model compression
1280 (Han et al.,1 2016; Heother ConvNets.
In particular,
surpasses
parameterized.
the best existing GPipe accuracy (Huang et al., 2018), but
et al., 2018; Yang et al., 2018) is a common way to reFC 6.1x faster on in- duce model size by trading256
1 As mousing10
8.4x fewer parameters and running
accuracy for efficiency.
ference. Compared to the widely used ResNet-50 (He et al.,bile phones become ubiquitous, it is also common to hand2016), our EfficientNet-B4 improves the top-1 accuracy
craft efficient mobile-size ConvNets, such as SqueezeNets
from 76.3% to 83.0% (+6.7%) with similar FLOPS. Besides(Iandola et al., 2016; Gholami et al., 2018), MobileNets
ImageNet, EfficientNets also transfer well and achieve state(Howard et al., 2017; Sandler et al., 2018), and ShuffleNets

Model input
The input of the model is a distribution of the number of photons detected with each photosensor on the inner face. Since the MPPCs are aligned in a matrix, the light distribution can
simply be regarded as a two-demential grayscale image of 93 × 44 pixels. The shift invarianceof the CNN is suitable for this application because the pileup γ-rays can be anywhere on theimage.
Although the model adopted for the pileup elimination uses only the light distribution on
the inner face as its input, it is also possible to use the light distributions on the other faces.
Indeed, the model which uses the light distribution on the inner and the outer faces was tried in
expectation of the improvement of the identification performance for the pileup γ-rays with deep
conversion points. However, it could not outperform the model only with the inner face. This

Chapter 5 γ-ray Background Reduction by Pileup Elimination
can be because it fails to benefit from the increased information due to its poor architecture ortraining procedure, and thus there is room for improvement.
Model output
The output of the model denotes how likely the event includes pileup γ-rays. If the event isa single γ-ray event, it should be close to zero while if the event has multiple γ-rays, it should
be close to one.
Training dataset
The model was trained using a dataset generated with MC. It consists of two types of data:
for main γ-rays and for pileup γ-rays. The main γ-ray dataset includes only one γ-ray in each
event, and it was generated from the uniform energy spectrum from 20 MeV to 100 MeV. The
uniformity and the wide energy range make the model independent of deposited energy. Theenergy independence is important since a fraction of pileup events in the background events
depends on the energy. If the model learns to exploit information of the energy, it may justpredict a high energy event as a pileup event, for example. The pileup γ-ray dataset was
resampled from the original pileup γ-ray data from muon decays in order to moderate its energy
dependence of the frequency as shown in Fig. 5.10. Otherwise, the training becomes much morediﬃcult as too many low energy pileup γ-rays appear, which are hardly found. The energy cut of
Eγ > 0.2 MeV was also applied to ignore the pileup γ-rays which do not aﬀect the reconstruction.
Approximately, 1.6 × 105 and 1.2 × 105 events were prepared for two types of the event,respectively. A part of the samples was randomly selected at a fraction of 10% for each event
type. The selected samples were isolated from the others to be used to validate whether themodel is over-fitted to the training dataset.
For the training, events belonging to each class, i.e. single γ-ray events and pileup events, andtheir class labels are required. The former events was simply prepared by sampling from themain γ-ray dataset, which were labeled zero. The latter events were generated by mixing events
sampled both from the main γ-ray and the pileup γ-ray dataset assuming their hit timings are
the same. These events were given labels of one.
To be realistic, the noise data taken with the random trigger without the muon beam wereadded to the simulated waveforms, and the light distribution was extracted by analyzing them.
In addition, the input pixels corresponding to the dead channels observed in the run 2021 weremasked (Fig. 2.68(d)).
Data pre-processing
Data pre-processing was applied to the inputs. Since there are some dead channels in the
LXe detector, the values of pixels corresponding to such channels were estimated by a mean ofsurrounding pixel values. Normalization was applied with the maximum value to suppress anenergy dependent performance. Furthermore, the negative values were cut oﬀ and zero was set
instead to avoid unexpectedly large negative inputs; the number of photons calculated from the133frequency

Chapter 5 γ-ray Background Reduction by Pileup Elimination

134

10−1

10−2

10−3

10−4
0

0.01

0.02

0.03

0.04

0.05
Eγ (GeV)loss

Figure 5.10 Energy spectra of the pileup γ-rays for the original (black) and the resampled(red) dataset.

epoch

Figure 5.11 Transition of the loss for the training (blue) and the validation (red) dataset.

integrated charge can be estimated to be negative if accidental pileup γ-rays are in a baseline
calculation region. These two operations assure the input values range from zero to one.
Training procedure
The model was trained to minimize a loss function of binary cross entropy using a stochastic
gradient decent with an initial learning rate of 0.01. The learning rate was reduced with cosine
annealing scheduler. The batch size was set to 200, and the training was stopped after 500
epochs. It took about 15 hours with Tesla P100-PCIE-16GB. The training successfully converged
and the loss for the validation dataset was reduced to the equivalent level for the training dataset
as shown in Fig. 5.11.

Chapter 5 γ-ray Background Reduction by Pileup Elimination

1

10−1

10−2

10−3
0

0.2

0.4

0.6

0.8
1
probability
outputFigure 5.12 Model outputs for the background events with a single γ-ray (black) andmultiple γ-rays (red).

Prediction
At the prediction stage, the model estimates how likely each event includes pileup γ-rays.
Fig. 5.12 shows distributions of the model outputs for the background events with a single γ-ray
or multiple γ-rays. Almost all single γ-ray events are estimated to be close to zero. On theother hand, the distribution of multiple γ-ray events has two peaks around zero and one anda tail in-between. The peak around zero derives from low energy pileup γ-rays, which are too
diﬃcult to be identified, and the events with moderate energy pileup γ-rays distributes in the
middle. Otherwise, the events are successfully predicted to be near one.
Threshold scan
To decide whether an event has pileup γ-rays, the continuous output value given by the modelneeds to be translated to a binary flag. This can be done by setting a certain threshold for thevalue. A threshold scan was performed to maximize the signal-to-background ratio of the signal
likelihood Rsig defined as

Rsig := log10 (S(xi )),fR R(xi ) + fA A(xi )where fR and fA are fractions of RMD and accidental background, which are set to 0.1 and
0.9, respectively. Fig. 5.13(a) shows the Rsig distributions for signal and background events. A
signal box was defined by setting a lower threshold in these distributions, and the number ofbackground events in the box was counted. Fig. 5.13(b) shows the relation between the signal
eﬃciency and the number of background events with diﬀerent thresholds of the model output,

135Chapter 5 γ-ray Background Reduction by Pileup Elimination

Nbg

102

136

1
10−1

10

10−2
1
10−3
10−1

10−4

10−2
−10

−5

0

5

10−5
0

0.2

0.4

0.6

Rsig

(a)

0.8
1
signal efficiency(b)

Figure 5.13 Threshold scan to decide the threshold for the model output. (a) Rsig distributions for the background (black) and the signal events (red) for the threshold of 0.40.
The number of the backgrounds is normalized by the expected value for three years of datataking, and that of the signals is normalized assuming the branching ratio of 6 × 10−14 . (b)Relation between the number of backgrounds and the signal eﬃciency with the thresholdof 0.10 (black), 0.20 (red), 0.30 (blue), 0.35 (orange), 0.40 (green), 0.45 (magenta), 0.50
(gray), 0.6 (light blue) and 0.7 (violet). The number of backgrounds is normalized by the
maximum value.

and some values are summarized in Table 5.2. The threshold of 0.40 was chosen since the least
number of backgrounds was achieved at most signal eﬃciencies.
Table 5.2 The number of backgrounds at diﬀerent signal eﬃciencies with the diﬀerent
thresholds for the model output. The least value at each signal eﬃciency is written in
boldface.

SignalThe number of backgrounds

eﬃciency

0.10

0.20

0.30

0.35

0.40

0.45

0.50

0.60

0.70

0.3

0.000220.000250.000270.000270.000210.000250.000260.000240.000270.4

0.000460.000470.000500.000500.000450.000500.000490.000500.000520.5

0.00095

0.000920.00098

0.000990.00084

0.000930.000930.000970.00091

0.6

0.00204

0.001860.001920.001780.001710.001770.001820.001820.00173

0.7

0.004880.004270.004110.00392

0.00368

0.00377

0.003780.00360

0.00355

5.2.2 Peak search and clustering of photosensors
The second step consists of peak searches and clusterings of photosensors. The pileup γ-rays
are searched for both in the light distribution and the timing distribution. The searches in thetwo diﬀerent distributions are complementary to each other since the former one mainly focuseson the on-timing pileups while the latter focuses on the oﬀ-timing pileups. The informationfrom the deep learning model is used for the search in the light distribution on the inner face.

Chapter 5 γ-ray Background Reduction by Pileup Elimination
Search in light distribution
The peak search in the light distribution finds local maxima of the number of detected photons
on the inner face and the outer faces separately. It is performed after applying two filters so
as not to pick up fake peaks, which are generated by the shower fluctuation or the noise. One
is re-binning to reduce the granularity of the MPPC readout in which 2 × 2 channel values are
summed up while the re-binning is not applied to the PMTs. The other is a low-pass filter witha moving average of 3 × 3 bins. They are applied both to the MPPC and PMT readout after
the re-binning. The channel whose excess of the number of photons over the expectation fromthe surroundings is larger than a threshold of 200 photons as a nominal value is identified as apeak center. A two-dimensional Gaussian is fitted to the found peak, and the energy is roughlyreconstructed from the integrated volume of the Gaussian.
The information from the deep learning model is used to select the peak search flow on the
inner face as shown in Fig. 5.14 in the belief that the model correctly tells us the existence of thepileup γ-rays. If the model judges the event has only one γ-ray, the peak search is performed
with the nominal threshold. In the case that more than one peak is found by the peak searchagainst with the prediction, only the peaks whose reconstructed energies are larger than 10 MeV
are regarded as true peak; otherwise the found peaks are discarded. This leads to avoiding
picking up fake peaks. If the model judges the event is not a single γ-ray event, the peaksearch is repeated until more than one γ-ray is found lowering the threshold down to 30% of
the nominal one. This treatment helps it to find pileup γ-rays whose conversion positions are
deep, which cannot be found by the nominal threshold since the detected number of photons on
the inner face can be small. There is the case that no additional peak is found even with theminimum threshold. In such a case, the peak search is given up, but the information that the
deep learning model regards the event as a pileup-like event is recorded for the next step.
In addition to the search in the normal light distribution, the search in the “inverted” light
distribution is carried out. This aims to identify the pileup γ-ray entering in the baseline
calculation region of the waveforms. The number of photons calculated from the integrated
charge is biased to be low if the baseline is calculated with the signals, and it can be negativevalue with a large magnitude (Fig. 5.15). Since the magnitude can be larger as the pulse heightin the baseline region becomes higher, there can be a local minimum near the conversion pointof the pileup γ-ray. It is searched for in the light distribution after being multiplied by -1. This
peak search is performed only with the nominal threshold because the deep learning model isinsensitive to such pileup γ-rays, which are not included in the training samples.
The channels around the found peaks are clustered. The clustering starts from the peakchannel, and the neighboring eight channels whose detected number of photons are more than
the greater of either 50% of the peak channel value or 100 photons are added to the cluster. It
is repeated until the update of the members stops. If hit positions of γ-rays are close to eachother, some channels can be assigned to several clusters. Such channels are reassigned to thecluster to which the distance from them is the shortest. The cluster timing and position are
defined by the pulse timing and the position of the peak channel.

137

Chapter 5 γ-ray Background Reduction by Pileup Elimination

138

Pileup event identification

without pileup

with pileup
lower threshold

Peak search on inner
fake peak

Peak search on innertrue peak

pileup is not foundpileup is foundDiscarded

Clustering

Figure 5.14 Flow of the peak search algorithm in the light distribution on the inner face.

Figure 5.15 Example of the light distribution of the event with a pileup γ-ray in thebaseline region. The purple region around the top face reflects the negative value due tothe pileup.

Search in timing distribution
The search in the timing distribution is performed on all the faces with the timing χ2 valueof each channel χ2pm,i defined by 3.13 because the channels that are aﬀected by the oﬀ-timing
pileups have large values (Fig. 5.16). The channels with χ2pm,i > 50 are clustered face by face.
To avoid picking up the noise, channels with less than 50 photons or amplitude smaller than
5 mV are ignored. The center of the cluster is defined by the mean of sensor positions in thecluster, and the cluster timing is defined by the sensor timing of the central channel.
The clusters are merged based on the distance between the cluster centers in the u, v and θ
directions. The criteria are defined depending on the combination of the faces of the clusters
as summarized in Table 5.3. The thresholds, dthr and θthr , are set to 18.6 cm and 16.75◦ ,respectively, which are defined based on the distance between the sensors.

Chapter 5 γ-ray Background Reduction by Pileup Elimination

139

Figure 5.16 Example of the χ2pm,i distribution of the event with an oﬀ-timing pileup γ-ray.
The channels in red have large values.
Cluster Sum Waveform Analysis

Total Sum Waveform Analysis

channel lists in found clusters

MPPC sum waveform

PMT sum waveform

Peak search

Peak searchtimingtimingWaveform analysis

Waveform analysis

MPPC sum waveform

PMT sum waveform

timingPeak searchtimingWaveform analysis

Waveform analysis

timing, energy
Merge pulses

Fitting

Fittingtiming, energy

timing, energy

Merge pulses
unfolded γ-rays

Figure 5.17 Flow of the unfolding algorithm of sum waveforms. It consists of two parts:
cluster sum waveform analysis (left part) and total sum waveform analysis (right part).

5.2.3 Unfolding of sum waveform
Finally, the multiple γ-rays are unfolded using sum waveforms to reconstruct the energy ofthe main γ-ray. The algorithm is composed of mainly two parts as shown in Fig. 5.17. The firstpart analyzes the sum waveform of channels in each cluster. The second part analyzes the sum
waveform of all channels. The results are combined, and they are used for fitting of template
waveforms.
Cluster sum waveform analysis
The sum waveforms in each cluster are analyzed to extract the timings and energies of thecluster. The sum waveform is generated for MPPCs and PMTs separately by summing up
the individual waveforms weighted by the sensor responses used in the energy reconstruction(Eq. (3.17)), which enables the reconstruction of the γ-ray energy directly from the area of theChapter 5 γ-ray Background Reduction by Pileup Elimination
Table 5.3 Criteria to merge clusters found by the timing based clustering. dX is given by
the magnitude of the diﬀerence of X between the two clusters.

Face
Cluster 1

Cluster 2
Inner
Outer

Inner

Upstream
Downstream
Top
BottomOuter
Upstream

Outer

Downstream
Top
BottomUpstream

Upstream

Downstream

Downstream

Top
BottomTop

Top

Bottom

BottomCriterion√

du2 + dv 2 < dthrdθ < θthr ∩ dv < dthr(dθ < θthr × 1.5 ∪ du < dthr × 1.5) ∩ dv < dthr(dθ < θthr ∪ du < dthr ) ∩ dv < dthr × 1.5
dθ < θthr ∩ du < dthr
dv < dthrdθ < θthr
dv < dthr(dθ < θthr ∪ du < dthr ) ∩ dv < dthr(dθ < θthr ∪ du < dthr ) ∩ dv < dthr

sum waveform. The timings of waveforms are shifted by time oﬀsets and propagation times fromthe reconstructed γ-ray hit position of each channel, which are used for the timing reconstruction(Sec. 3.5).
A peak search is applied to two shaped waveforms: a diﬀerential waveform and a movingaveraged waveform. The diﬀerentiation of the waveform is calculated by taking the diﬀerence
between amplitudes of two points given points apart each other. Before taking the diﬀerentiation,a low-pass filter of the moving average is applied to reduce zig-zag structures due to the noise.
The peak search tries to find local minima below a given threshold. The threshold is definedas RMS on the baseline multiplied by a certain factor. The parameters for the shaping and thepeak search are summarized in Table 5.4. The peak search algorithm in the two waveforms is
performed in two steps (Fig. 5.18). First of all, it is applied to the diﬀerential waveform. The
threshold for the diﬀerential waveform becomes too low to find any pulses when the numberof channels used for the sum is small. In such a case, pulses are searched for in the movingaveraged waveform. Note that the pulses which are close to each other can be detected betterin the diﬀerential waveform since they can be separated by the diﬀerentiation while the moving
average smears them.
The pulse timings and energies are extracted from the original sum waveforms based on the

140

0
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−0.4
−0.6

0.5
0
−0.5

amplitude (a.u.)

amplitude (a.u.)

amplitude (a.u.)

Chapter 5 γ-ray Background Reduction by Pileup Elimination

−1

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0

0.2

×10

0.4

0
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−1

−0.8

141

−1

−1.5
−0.2

−1.2
00

0.20.2time (sec)time (sec)

×10−6
0.4
time (sec)

(b)

(a)

Figure 5.18 Two examples of the cluster sum waveforms: the original sum waveforms inblack, the diﬀerential waveforms in orange, the moving-averaged waveforms in light blue.
(a) Peak search is applied to the diﬀerential waveform and (b) to the moving-averaged
waveform. The peak search thresholds are given by the dashed line in violet and green,
respectively.

found peak timings. The pulse timings are defined by the constant fraction method. The energies
are calculated by integrating the waveforms. The pulses found in the diﬀerent clusters whose
extracted timings are within 15 ns are merged. Note that the on-timing pileups are merged tothe main γ-ray here since they cannot be unfolded by the waveform.
Table 5.4 Parameters for the waveform shaping and the peak search.

Waveform

Diﬀerential

Moving-averaged

Parameter

Value

Averaging points

29 points

Diﬀerential points

5 points

Threshold

10× RMS on baseline

Averaging points

21 points

Threshold

15× RMS on baseline

Total sum waveform analysis
The sum waveforms of all MPPCs and PMTs are generated in the same way. The peak search
is applied only to the diﬀerential waveform of the PMTs since a larger statistical fluctuation andnoise fluctuation can be expected when the MPPC PDE gets smaller. The pulse timings andenergies are extracted from the sum waveforms both of the MPPCs and the PMTs referring to
the peak timings in the PMT waveform. For each of the MPPC and the PMT, the pulses in thesum waveforms are merged with the pulses found in the cluster sum waveforms based on thetimings.
Now, we have a list of pulses, each of which corresponds to a temporally separated γ-ray.
The pulses are unfolded by fitting the superposition of Npulse template waveforms to the total
sum waveforms independently, where Npulse is the number of pulses in the list. The template
waveforms are created from the sum waveforms of many single γ-ray events as shown in Fig. 5.19.
A relative event-by-event fluctuation of the pulse shape is also computed from the standard

×10−6

0.2
70
0
60
−0.2

50

−0.4

40

amplitude (a.u.)

amplitude (a.u.)

Chapter 5 γ-ray Background Reduction by Pileup Elimination

0.2

80
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60
40

30

−0.6

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20

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10

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0

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100

200

300

(a)

400
time (s)

100

0

−0.6

−1.2
0

142

20

100

200

300

400
time (s)0(b)

Figure 5.19 Superimposition of sum waveforms of (a) the MPPCs and (b) the PMTs. The
amplitude is normalized and the pulse timing is aligned event by event. The second peakin the PMT waveform at 250 ns is due to a reflection of the signal.

deviation of the amplitude at each timing as shown in Fig. 5.20, which is used to weight thediﬀerence of amplitudes between the raw waveform and the estimated waveform at each timing
in the fitting. The fitting parameters are the timing and amplitude of each pulse, and thebaseline. The extracted pulse timings and energies from the waveform analyses are used as
initial values for them. In the fitting, the deviation of the raw waveform and the sum of thetemplate waveforms is minimized. Fig. 5.21 shows a typical sum waveform with pileups. The
sum waveforms are unfolded to two pulses. The energy of each γ-ray is reconstructed from thefitting results. The pulses in the MPPC waveform and the PMT waveform are merged by thetimings. A pair of pulses whose timings are closest to the trigger timing is regarded as the main
γ-ray.

5.2.4 Event status assignment
At the end, an event status is assigned based on the results of the three steps. There are fivecategories as follows:• NoPileup : No pileup is found, and the fitting in the total sum waveform successfully
converges with a single pulse.
• Unfolded : More than one γ-ray is found, and they are successfully unfolded.
• Coincidence : On-timing pileup γ-rays are found, which cannot be unfolded.
• DLRejected : The deep learning model identifies pileups, but no pileup γ-ray is foundwith the others.
• NotConverged : The fitting in the total sum waveforms fails to converge.
The third status is assigned to the events in which a pileup γ-ray found with the peak searchat the second step are merged to the main as a result of the cluster sum waveform analysis.

0.05

fluctuation (a.u.)

fluctuation (a.u.)

Chapter 5 γ-ray Background Reduction by Pileup Elimination

0.045
0.04
0.035
0.03

0.05
0.045
0.04
0.035
0.03

0.025

0.025

0.02

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0.015

0.015

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0.005

0
0

100

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300

143

0
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400
time (s)

100

200

(a)

300

400
time (s)

(b)

−0.4
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0
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0
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amplitude (V)−0.2

amplitude (V)0amplitude (V)amplitude (V)Figure 5.20 Event-by-event fluctuation of the sum waveform of (a) the MPPCs and (b)the PMTs defined by the standard deviation of amplitudes at each bin in Fig. 5.19. The
local minima at 120 ns (MPPC) and 100 ns (PMT) are due to the normalization at thepeak of the waveform.

0
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Figure 5.21 Sum waveform unfolding for a typical waveform with a pileup γ-ray of (a) thesum waveform and (b) the PMT sum waveform.
The original
waveform is shown
2
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10MPPC102
in black with the diﬀerential waveform (orange) and the moving-averaged waveform (light10
10 The diﬀerence between
blue). The waveform is deconvoluted to two pulses 10(red and green).
the original waveform and the sum of deconvoluted waveforms is shown in gray. The two
11
1 the threshold (dashedpulsesare found by the peak search in the total PMT waveform withline in violet).
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There is the case that the main γ-ray is found in the sum waveform of the pileup cluster in
addition to the pileup pulse when their hit positions are close to each other. The found main
γ-ray pulse is merged to the pulse found in the main γ-ray cluster since they have exactly thesame timings. In order to avoid regarding such a case as the coincidence event, only the pulse
whose extracted timing is the closest to the cluster timing is thought to be an on-timing pileup
γ-ray pulse. Since the cluster timing is defined by the sensor timing of the representative, i.e.
the peak/central channel of the cluster found in the light/timing distribution, the main pulsein the cluster has the closest timing to the cluster timing. The main γ-ray cannot be the main
pulse in the pileup cluster, and thus the misidentification is suppressed.

0.6
time (sec)×10−6Chapter 5 γ-ray Background Reduction by Pileup Elimination
The fourth category corresponds to the case the peak search in the light distribution fails
to find more than one γ-ray even with the lower threshold. This can be caused both by themisidentification of the deep learning model or the incompleteness of the peak search algorithm.
There is also the case the second peak is found in the light distribution, but no pulse is foundwith the waveform analysis when the second peak results from the noise.
The fifth status relies on the fitting result of the total sum waveforms. If there are pileup
γ-rays which are not found by the former analysis, the sum of the fitted waveforms can diﬀer
from the raw waveform. Even if it is not the case, the fitting can fail when the noise is toolarge or too many pulses are in a short time range. The failure is detected by the deviationof the waveforms; the fitting is thought not to converge if the deviation is larger than a given
threshold. The threshold is defined by ten times of the mean of the baseline deviation in order
to consider the noise eﬀect.
The first and the second statuses are the cases that γ-ray energies succeed in being reconstructed while the others are not. Therefore, the events having any of the latter three statuses
are discarded from the analysis.

5.3 Performance evaluation with MC
The expected performance of the series of algorithms was evaluated with the MC for thefull channel readout configuration. The MPPC PDE was set to 13% for all. To make thesimulation realistic, noise data at the amplifier gain of 1 taken in 2021 were added to thesimulated waveforms, and the signals of dead channels were discarded based on the knowledge
in 2021. Hereafter, the performance of each algorithm is explained step by step followed bydiscussions on the contribution from the noise and the dead channels, and the eﬀects of smaller
MPPC PDEs and the precision of the sensor calibration.

5.3.1 Performance of each algorithm
Identification of pileup events with deep learning
In order to show how well the deep-learning-based identification works, the performance ofthe deep learning algorithm is compared to that of the peak search in the light distribution on
the inner face with the nominal threshold, which uses the same distribution as inputs.
Fig. 5.22 compares the fractions of the pileup events correctly identified as a function of theconversion depth of the pileup γ-ray. In the shallow region, the performance of the two methods
is equivalent. In the deep region, however, the fraction of the peak search method decreases
rapidly while the other keeps the high detection eﬃciency. Fig. 5.23 shows an event example inwhich a pileup γ-ray converts in the deep region. Since no clear peak is made on the inner faceby the deep pileup γ-ray hit, the peak search on the inner face cannot identify the second peak.
On the other hand, the deep learning model predicts the event is likely to include pileup γ-rays
with the output of 0.98.
Another event example is shown in Fig. 5.24 which has a single γ-ray. The peak search method

144

Chapter 5 γ-ray Background Reduction by Pileup Elimination
finds the very local peak that derives from the conversion of a γ-ray escaped from the shower
in addition to the main peak. On the other hand, the deep learning model predicts the event
should be a single γ-ray event with output of 0.03.
Fig. 5.25 shows an example of event in which γ-rays enter the edge of the detector. A part ofthe light distribution originating from each γ-ray on the inner face is broken. However, it does
not aﬀect the prediction, and the model successfully outputs the value of 0.99. Fig. 5.26 shows
the fractions of the pileup events correctly identified as a function of the u position of the main
γ-ray. The fraction is kept high even near the edge of the fiducial volume.
Fig. 5.27 shows the relations between the number of backgrounds and the signal eﬃciency of
the two methods. The number of backgrounds is normalized by that after applying the pileup
elimination method in the previous study [62]. The smaller number of background events atthe same signal eﬃciency is achieved by the deep-learning-based rejection because of the higher
detection eﬃciency in the deep region and the tolerance to the fake peaks.
Although the deep learning model succeeds in achieving the high performance, it has a weak
point that its prediction lacks the information of the found pileup γ-rays; it can only give whether
the event is a pileup event or not while the peak search can tell us which peak is identified. The
disadvantage makes it diﬃcult to utilize its result in the following waveform unfolding. On theother hand, the low performance of the peak search in a deep region partly comes from the factthat the peak search threshold is set to a value high enough not to pick up the fake peaks. In
other words, the peak search can find more pileup γ-rays if a lower threshold is used though
this cannot be realized because of the existence of the fake peaks. Therefore, the operation to
select the peak search flow based on the deep learning prediction is adapted to make use of eachstrength as explained in Sec. 5.2.2.
The success of the deep learning model can result from the optimization of the peak search
procedure in the model. As explained in Sec. 5.2.2, the re-binning and the low-pass filter are
explicitly applied in the peak search method to avoid picking up the fake peaks. This kindof process is done automatically in the CNN layers and the strength of the filtering and thethreshold are optimized during the training. In fact, the two strengths of the deep learning
discussed above imply that the deep learning model recognizes the peak-like structure not froma local peak structure but from more global one, which can be accomplished by the optimization.
Peak search and clustering of photosensors
Fig. 5.28 shows the energy spectra of the background γ-rays. The events in which morethan one γ-ray is found with the peak search method are rejected. A pileup identification by
waveform [62] is also applied to reduce the oﬀ-timing pileups, which searches for pileup γ-rays inthe sum waveform by detecting an excess from the template waveform. The algorithms reduce
59% of the background events between 51.5 MeV and 54 MeV in total (red), which is dominatedby the contribution from the peak search in the light distribution on the inner face (blue).
Not only the background events but also the signal events with pileup γ-rays or fake peaks
are rejected, which results in the signal ineﬃciency. If we simply discard all the pileup identified

145fraction

Chapter 5 γ-ray Background Reduction by Pileup Elimination

146

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wγ (cm)Figure 5.22 Detection eﬃciency of the pileup γ-rays for the peak search method (black)and the deep learning model (red) as a function of the conversion depth of the pileup γ-ray.

events, the signal ineﬃciency is estimated to be 27% including 10% rejection of single γ-ray
events.
Unfolding with sum waveform
Fig. 5.29 shows the simulated energy spectrum of the background γ-rays with the sum waveform unfolding (blue). As shown in Fig. 5.30, the signal eﬃciency is recovered by 19% withan increase in the background events of 8% (green) compared to the rejection based on thepeak search result (light blue). This would result in a better branching ratio sensitivity. The
signal ineﬃciency of 7% coming from 4% of Coincidence, 2% of DLRejected and 1% of
NotConverged event statues includes 5% rejection of single γ-ray events.

5.3.2 Eﬀect of noise
The performance described above was evaluated by mixing the noise data to simulated waveforms in order to include non-Gaussian eﬀects such as a correlated noise among channels anda spike. Here, the performance diﬀerence between a simulated Gaussian white noise and a realnoise is discussed. Note that the noise level of the simulated noise is the same as the observation:
0.7 mV RMS.
Fig. 5.31(a) shows the predictions of the deep learning model for a single γ-ray with the realnoise data. The distribution of the model trained with the real noise peaks at zero (black).
On the other hand, that trained with the simulated noise tends to output higher values andforms a peak at one (red) while it correctly predict most of events to be zero for the simulated
noise events (blue). This result implies that the real noise has an eﬀect to create fake peaks,
which deceives the model, and the deterioration can be moderated by training the model withthe real noise. The predictions for multiple γ-ray events with the real noise are also shown inChapter 5 γ-ray Background Reduction by Pileup Elimination(a)pileup γ

inner surface of LXevertexmain γ(b)

Figure 5.23 Example of an event with a pileup γ-ray that converts at a deep position.
(a) The light distribution and (b) the particle track. The deep learning model predicts theevent as a pileup event while the peak search on the inner face does not find the second
peak. The scale of the bar is in the unit of MeV.

Fig. 5.31(b). In this case, no apparent diﬀerence is observed between the outputs of the modeltrained with the simulated noise for the two types of events though the peak at one of the modeltrained with the real noise is higher than the others. This indicates the noise diﬀerence does
not aﬀect the detection of pileup γ-rays so much.
A possible cause of the misidentified peak in the single γ-ray distribution is a correlated noise,
which is not included in the simulated noise. As shown in Fig. 5.32, adjacent channels in the LXedetector are connected to the same WDB. Fig. 5.33 shows the noise distribution of the MPPCs
added to the simulated waveforms. There are noises which coherently arise in the channels of
the same WDB, which results in a cluster of channels whose energies are consistently bias to bepositive or negative, and this cluster can be misidentified as a contribution of a pileup γ-ray.
Fig. 5.34 shows an example of a single γ-ray event with the simulated noise or the real noise.

147

Chapter 5 γ-ray Background Reduction by Pileup Elimination(a)inner surface of LXevertex(b)

Figure 5.24 Example of an event only with a main γ-ray. (a) The light distribution and(b) the particle track. The arrows point to a fake peak generated by a γ-ray escaped fromthe shower. The deep learning model predicts the event as a single γ-ray event correctly
while the peak search on the inner face picks up the fake peak. The scale of the bar is in
the unit of MeV.

The correlated noise forms a peak-like structure resulting in a misidentification of the pileup
event. The deep learning model trained with the simulated noise successfully predicts the event
is not likely a pileup event with the output of 0.0050 for the simulated noise event (Fig. 5.34(a))
while it incorrectly outputs the value of 0.92 for the real noise event (Fig. 5.34(b)). Thismisidentification, however, can be corrected by training the model with the real noise, and theoutput value decreases to 0.0031.
To see the eﬀect of the coherent noise, the noise data are added shuﬄing the channel assignmenton the inner face. This operation simulates with the same noise level, but ignoring the clusterednoise structure (Fig. 5.34(c)). Fig. 5.35(a) shows the predictions of the model trained withthe simulated model for the diﬀerent noise datasets. The shuﬄe reduces the fraction of the148Chapter 5 γ-ray Background Reduction by Pileup Elimination

fraction

Figure 5.25 Example of an event in which γ-rays enter the edge of the detector. The main
and the secondary γ-rays hit at (u, v, w) = (−5.63, −60.24, 3.46), (−27.92, 59.51, 1.61) cm,
respectively. There is another γ-ray hit in the baseline calculation region, i.e. 76.12 ns
before of the main, at (u, v, w) = (10.11, 23.53, 2.40) cm, which is a source of the depression
on the outer face.

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misidentification to some extent (red), but there is still a peak around one, which can comefrom the other eﬀects such as larger noise channels than the simulation. Fig. 5.35(b) shows
the predictions of the models trained with the real noise with and without the shuﬄe for the
shuﬄed noise datasets. The fraction of the model trained without the shuﬄe around one (black)is higher than that with the shuﬄe (red), which also implies the coherent noise contributes toform a peak-like structure. However, the diﬀerence is found to vanish if the models are trainedin the same noise situation with the prediction (Fig. 5.35(c)). These facts tell us the sensitivity
to the noise situation of the model and the importance to tune the model to the noise situations
in order to maximize the model performance.

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Chapter 5 γ-ray Background Reduction by Pileup Elimination

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event rate (Hz)Figure 5.27 Relation between the number of background events and the signal eﬃciency(Eγ = 51.5–54 MeV) for the peak search method (black) and the deep learning model (red)when the events in which more than one γ-ray is found are rejected. The diﬀerent points
for the deep learning model correspond to the diﬀerent thresholds for the rejection. The
optimal point (threshold = 0.40) is in blue.

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56
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Eγ (MeV)Figure 5.28 Energy spectra of the simulated background γ-rays without the peak searchand clustering method (black) and with all the elimination methods (red), the search withthe light distribution on the inner face (blue) and on the outer face (orange), and the searchin timing distribution (green). A pileup identification by waveform [62] is applied to reduce
the oﬀ-timing pileups.

event rate (Hz)

Chapter 5 γ-ray Background Reduction by Pileup Elimination

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Figure 5.29 Energy spectra of the simulated background γ-rays without the peak searchand clustering method (black), with the peak search elimination methods (red) in addition
to the pileup identification by waveform [62], and with the waveform unfolding (blue).

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Figure 5.30 Relation between the number of background events and the signal eﬃciency(Eγ = 51.5–54 MeV) for the unfolding method (green) in addition to those for the peaksearch method (light blue) and the deep learning model (red) when the events in whichmore than one γ-ray is found are rejected. The diﬀerent points for the deep learning model
correspond to the diﬀerent thresholds for the rejection. The optimal point (threshold =0.40) is in blue.

Chapter 5 γ-ray Background Reduction by Pileup Elimination
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Figure 5.31 Predictions of models for (a) single γ-ray events and (b) multiple γ-ray background events to which real noises are added. The models are trained with a real noise(black) and simulated noise (red). The predictions of the model trained with a simulated
noise for simulated noise events are also shown (blue).
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Figure 5.32 Assignment of readout electronics channels in run 2021. The adjacent channels in the same color are connected to the same WDB.

5.3.3 Eﬀect of dead channels
The existence of dead channels can worsen the performance of the pileup elimination by loosing
their information. Its eﬀect was evaluated by comparing the case in which no dead channel isassumed to the case in which the dead channels found in the run 2021 are considered: 30 channels
for the MPPCs and 28 channels for the PMTs.
Fig. 5.36 compares the predictions of the deep learning models trained with and without thedead channels for the background events under the same dead channel assumption with thetraining. No significant diﬀerence is observed in the distribution. The distribution of the modeltrained without dead channels for the background events with dead channels is also shown inthe same plot (blue). There is little diﬀerence compared to the others as well. It is also foundthat the overall elimination power of a series of the algorithms is consistent within 1% precision.

Chapter 5 γ-ray Background Reduction by Pileup Elimination

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Figure 5.33 Noise distribution measured in run 2021 at gain 1. (a) Mean and (b) standard
deviation of the number of photons over O(103 ) events for each channel are shown. Diﬀerent
oﬀsets among the WDB are seen in (a). The striped pattern in (b) is due to the MPPC
lot dependence of the correlated noise.

These observations tell us that the dead channels at the level observed in the run 2021 hardly
aﬀect the performance of the elimination.

5.3.4 Eﬀect of PDE degradation
As discussed in Sec. 3.1.1, the LXe detector will be operated with the annual annealing tokeep the reasonable MPPC PDE from 16% down to 2%. The eﬀect of the reduced PDE can be
partly compensated by increasing the electronics gain, but the lower signal-to-noise ratio canaﬀect the pileup elimination performance. Therefore, the performance was also evaluated atlower PDEs. The amplifier gain was also changed accordingly following Table 3.3.
Fig. 5.37 shows the relations between the number of backgrounds and the signal eﬃciency
when the MPPC PDE is 13% and 2%, where the deep learning model is trained with data at
PDE of 13%. Both of the number of backgrounds and the signal eﬃciency increase due to thelower PDE. Fig. 5.38 compares those for 2% PDE, where the deep learning model is trainedwith data at PDE of 13% and 2%. The number of backgrounds for the model trained at 2%
PDE is less at the optimal point while the signal eﬃciency is equivalent. As a result, that after
being applied all the algorithms is slightly smaller with the similar signal eﬃciency.
Table 5.5 summarizes the number of backgrounds and the signal eﬃciency for the diﬀerent
MPPC PDEs. The number of backgrounds and the signal eﬃciency tend to increase as the PDEgets lower, which results from the gained insensitivity to both of true and fake peaks with small
sizes. The diﬀerence between the models trained assuming the fixed PDE and the correspondingChapter 5 γ-ray Background Reduction by Pileup Elimination

(a)

(b)

(c)

Figure 5.34 Example of an event without a pileup γ-ray when (a) simulated noise or (b)real noise is added. For (c) real noise is added like (b), but the channel assignment of the
MPPCs is randomly shuﬄed.

PDEs is not significant.

5.3.5 Eﬀect of uncertainty from calibration
The reconstructed number of photons can fluctuate and be biased due to the statistical andsystematic errors in the calibration, which can aﬀect the performance. The statistical uncertaintyof the calibration factor was estimated to be 4% both for the MPPCs and the PMTs (Sec. 3.1.1).
The systematic uncertainty was estimated by a half of the diﬀerence between the measured

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Chapter 5 γ-ray Background Reduction by Pileup Elimination
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output(c)Figure 5.35 Predictions of models for single γ-ray background events. (a) The results forthe real noise before (black) and after (red) the shuﬄe, and the simulated noise data (blue).
The models are trained with the simulated noise. (b) The results for the shuﬄed real noise
data. The models are trained with the real noise without (black) and with the shuﬄe (red).
(c) The results for the real noise data without/with the shuﬄe predicted by the models
trained with the real noise without/with the shuﬄe (black/red). The predictions of themodel trained with a simulated noise for simulated noise events are also shown in all (blue).

calibration factors and those after applying the correction to get a uniform sensor response for
CW γ-ray data as shown in Fig. 5.39. The eﬀects of these uncertainties were investigated byartificially changing the calibration factors in the prediction stage while keeping the originalvalues in the training stage. The factors were first systematically changed for the systematic
uncertainty and then randomly fluctuated with 5% or 10% standard deviation. As a result, no
deterioration of the performance was observed.

Chapter 5 γ-ray Background Reduction by Pileup Elimination
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Figure 5.36 Prediction of models for (a) single γ-ray events and (b) multiple γ-ray background events without (black) and with (red, blue) masking dead channels. The models
are trained without (black, blue) and with (red) masking dead channels.

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Figure 5.37 Relation between the number of background events and the signal eﬃciency(Eγ = 51.5–54 MeV) for the unfolding method (violet/green) and the deep learning model(black/red) when the events in which more than one γ-ray is found are rejected when
MPPC PDE is 13%/2%. The model is trained with dataset at MPPC PDE of 13%. The
diﬀerent points for the deep learning model correspond to the diﬀerent thresholds for therejection. The optimal point (threshold = 0.40) is in light blue/blue.

5.3.6 Summary of performance
The performance of the pileup elimination algorithms were evaluated taking the real noise
situation and the dead channels into account. In total, the number of backgrounds was reduced
by 51% keeping the signal eﬃciency of 93% for 51.5–54 MeV. The eﬀects of the PDE degradation and the accuracy of the calibration parameters were also discussed. The lower PDE
was found to increase both of the number of backgrounds and the signal eﬃciency by 9% andNbg

Chapter 5 γ-ray Background Reduction by Pileup Elimination

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Figure 5.38 Relation between the number of background events and the signal eﬃciency(Eγ = 51.5–54 MeV) for the unfolding method (green/violet) and the deep learning model(red/black) when the events in which more than one γ-ray is found are rejected when
MPPC PDE is 2%. The model is trained with dataset at MPPC PDE of 13%/2%.The
diﬀerent points for the deep learning model correspond to the diﬀerent thresholds for therejection. The optimal point (threshold = 0.40) is in blue/light blue.

Table 5.5 Number of backgrounds and signal eﬃciency for diﬀerent MPPC PDEs (Eγ =51.5–54 MeV) when the deep learning model is trained at a fixed PDE of 13% or each PDE.

Trained at PDE 13%

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3% at most, respectively. The increase of the background events was much smaller comparedto the total amount of the reduction power, and thus the algorithms work even at the lower
PDE. The possible error of the calibration turned out to be negligible in terms of the pileup
elimination. Therefore, it is concluded that the pileup elimination algorithms can greatly suppress the background γ-rays with the high signal eﬃciency even under the realistic experimental
condition.

Chapter 5 γ-ray Background Reduction by Pileup Elimination

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Figure 5.39 Systematic uncertainty for calibration (a) in a 2D map and (b) in histogramsfor MPPCs (black) and PMTs (red).

159

Chapter 6

γ-ray Background Reduction with RDC
In the µ+ → e+ γ analysis of the MEG II experiment, the number of signal events is estimatedwith the maximum likelihood analysis, which is discussed in Sec. 2.4. The information from the
RDC can be used to reject background-like events, but this decreases the signal eﬃciency due
to the accidental coincidence of a signal γ-ray hit at the LXe detector and a positron hit at the
RDC. Instead, we use the RDC information in the likelihood function by introducing the PDFs
of the RDC observables. This allows the maximum use of the RDC information in terms of thesensitivity. In this chapter, the implementation of the RDC PDFs and the procedure to makethem are discussed.

6.1 Concept
The likelihood function consists of PDFs of signal, RMD and accidental background.
In the MEG experiment, the likelihood function was defined for the five observables(Eγ , Ee+ , te+ γ , ϕe+ γ , θe+ γ ).

Here, we extend it to include the three RDC observables

ds
ds
(tus
rdc , trdc , Erdc ) to improve the background discriminant power in the MEG II experiment. Notethat the timing measured with the upstream RDC, tus
rdc , is included in the following discussion

for the future application though it is excluded for the sensitivity calculation in Chap. 7.

6.1.1 Correlations between observables
Dependence of relevant variables was investigated to decide how to generate the PDFs because
correct treatment of them is important in order to perform the physics analysis accurately*1 .
From now on, the correlations among the parameters are described.

*1 The eﬀect of the RDC on the branching ratio sensitivity in [2] was overestimated due to the ignorance ofEγ dependence. The detection eﬃciency and the fraction of the RMD events were assumed to be constantin the calculation. In fact, however, they decrease as Eγ gets close to the signal energy as is discussed inthis section, which results in a smaller sensitivity improvement.

Chapter 6 γ-ray Background Reduction with RDC

fraction

102
10

160

1
0.8

1

0.6

10−1

0.4

10−2

0.2

10−3

46

48

50

52

0

54
Eγ (MeV)

46

48

(a)

50

52

54
Eγ (MeV)(b)efficiency

Figure 6.1 (a) Simulated Eγ spectra and fractions of total (black), RMD (blue) and AIF(red) events.

1
0.8
0.6
0.4
0.2
0

44

46

48

50

52

54
Eγ (MeV)Figure 6.2 Simulated detection eﬃciency of the RMD positrons with the downstream
RDC, which is defined by the number of events with a hit at the RDC over the numberof events in which the RMD positrons are emitted toward downstream. The ineﬃciency
mainly comes from the geometrical acceptance.

ds
ds
Eγ vs. (tusrdc , trdc , Erdc )The main sources of accidental background γ-rays are RMD and AIF. Fig. 6.1(a) shows theEγ spectra of each event type. The number of the RMD events decreases rapidly as Eγ getsclose to the signal energy while that of the AIF decreases gently. As a result, the fraction of
RMD events drops in the higher energy region as shown in Fig. 6.1(b), which indicates that thefraction of events detected by the RDC decreases accordingly. Moreover, the detection eﬃciency
of RMD positrons is lower for high energy γ-rays since the energies of positrons accompanied
by such γ-rays are low (Fig. 6.2). Therefore, all the RDC observables depend on Eγ .

Chapter 6 γ-ray Background Reduction with RDC

161

1
10−1
10−2
10−3
10−4
0

5

10

15

20

25

30

Eds
rdc (MeV)

Figure 6.3 Simulated energy spectra of RMD positrons detected by the downstream RDC
with Eγ of 48–49.75 MeV (black), 49.75–51.50 MeV (red) and 51.50–53.25 MeV (blue).

ds
Eγ vs. Erdc
ds
distribution itself has a
In addition to the probability to detect RMD positrons, the Erdc

kinematical correlation with Eγ since the γ-ray detected by the LXe detector and the positrondetected by the RDC originate from the same muon decay. However, the dependence is smallenough to be negligible (Fig. 6.3).
ds
ds
tus
rdc vs. (trdc , Erdc )The positrons from RMD events with high energy γ-rays are swept away either to the upstream
or downstream of the muon stopping target. This means that when an RMD positron is detectedby the downstream RDC, it must not be detected with the upstream RDC, and vice versa.
Therefore, the probabilities of the upstream and downstream RDC to detect the RMD positrons
correlate with each other.
ds
tds
rdc vs. Erdc

The RMD positrons fly along diﬀerent paths depending on their energies. Fig. 6.4 shows thedscorrelation between tds
rdc and Erdc of the RMD positrons under the condition of Eγ > 48 MeV.

Not only the diﬀerence in the width of the first peak but also the existence of the second peak
only for low energy positrons can be seen in the timing distribution. The second peak comesfrom the positrons which rebound from the upstream after hitting some materials.

6.1.2 Format
The PDFs should return the probability density to observe a given observable set, which isusually realized by a function with some parameters. As shown in the previous section, however,the distributions of the RDC observables have too complex forms to be parametrized. Therefore,
we decided to use a non-parametric implementation with four dimensional histograms insteadEdsrdc (MeV)

Chapter 6 γ-ray Background Reduction with RDC

162

30

600

25

500

20

400

15

300
200

10

100
5
0

0

10

20

30

0
×10−9
40
50
tds
rdc (s)Figure 6.4 Correlation between the timing and energy of RMD positrons detected by thedownstream RDC (Eγ > 48 MeV).

of certain functions.
The RDC PDFs are defined for the analysis region of Eγ . The timing PDFs range from −20 ns
to 28 ns. Their last bins contain entries where there is no hit observed in the time range. Theds
Erdc
PDFs are defined in 0–50 MeV. The first bins corresponding to negative energy are filledwith the no hit entries.

6.2 Procedure to make PDFs
Fig. 6.5 shows the projections of the signal and accidental background PDFs. Since the RDC
detects the positrons from the RMD, which is a source of the accidental background γ-rays, there
is a peak deriving from such positrons in the accidental background PDF while only accidental
hits of Michel positrons are in the signal PDF. The procedures to make these PDFs are as
follows.

6.2.1 Signal PDF
In the signal events, the positrons from signal muon decays follow trajectories with large
radii such that they hit the positron spectrometer, and thus they cannot hit the RDC since its
acceptance is small enough. Therefore, only accidental Michel positrons leave hits in the signal
events.
The timing PDFs for the signal events are created assuming a certain hit rate, which is definedfrom the muon beam rate and the hit probability. The hit rate can be calculated directly fromdata by counting the number of events in the timing sideband as demonstrated in Sec. 4.2.2.
ds
The Erdc
distribution, i.e. the Michel positron energy distribution, is also obtained from data inthe timing sideband.
Since there are no upstream-downstream correlation and no dependence on the γ-ray energy,
the signal PDF can be simplified as

Chapter 6 γ-ray Background Reduction with RDC

ds
ds
us
SRDC (tusrdc , trdc , Erdc ) = SRDC (trdc )

163

(6.1)

ds
× SRDC (tdsrdc |Erdc )ds
× SRDC (Erdc).

Note that the timing-energy dependence of the downstream RDC remains since they are dependent on each other in terms of whether there is a hit or not.

6.2.2 RMD PDF
The positrons in the RMD events which are physics backgrounds do not hit the RDC as well,and so the RMD PDF can be created in the same way as the signal PDF.

6.2.3 Accidental background PDF
As described in Sec. 6.1.2, there are correlations among the RDC observables and the energyof γ-ray in the accidental background events. They can be included in the accidental background
RDC PDF as the conditional probability:

ds
ds
ds
ds
us
ARDC (tusrdc , trdc , Erdc |Eγ ) = ARDC (trdc |Eγ , trdc , Erdc )

(6.2)

ds
× ARDC (tdsrdc |Eγ , Erdc )ds
× ARDC (Erdc|Eγ ).

The accidental background RDC PDF can be created from data just by filling the histogramwith the observed parameter sets. It was, however, found to require a huge amount of statistics,
and thus a dedicated approach is taken, which will be discussed in the next section.
For simulation studies using MC, the accidental background PDF is generated by mixing thesimulated distributions of RMD and Michel positrons taking the dependence of the parametersdescribed above into account. Fig. 6.6 depicts the process for the generation. Firstly, an event
type of the γ-ray trigger is selected from RMD or AIF based on their trigger fractions. Then, Eγ
is decided with the energy spectrum of the event type. If RMD is selected, the direction of the
RMD positron and whether it is detected by either RDC are decided. If the positron is detectedby the upstream RDC, the hit timing is chosen from the simulated timing distribution. In thecase the positron is detected by the downstream RDC, the positron energy is chosen from theenergy distribution in addition to the hit timing. Then, contribution from Michel positrons issimulated based on the hit rate and the energy is chosen from the energy distribution of Michel
positrons. If AIF is selected, only accidental hits of Michel positrons should be considered.
Finally, one hit whose timing is the closest to the timing center is chosen from a set of hits forthe upstream and downstream RDC, respectively.

Chapter 6 γ-ray Background Reduction with RDC

1

164

1

1
−1

10

10−1

10−2

10−1

10−3

10−2

10−4

10−2
−9

−20

−10

0

10

20

×10
30
t us
(s)
rdc

−9

−20 −15 −10 −5

(a)

0

5

10

15

20

(b)

×10
25 30
t ds
(s)
rdc

10−5
−0.01

0

0.01

0.02

0.03

0.04
0.05
Eds
rdc (GeV)(c)

Figure 6.5 Projection of RDC PDFs for signal (black) and accidental background (red)dsds
to (a) tus
rdc , (b) trdc and (c) Erdc .

Figure 6.6 Process to create accidental background RDC PDF from MC simulation.

6.3 Statistical limitation and its solution
As mentioned in the previous section, the accidental background RDC PDF can be obtained
directly from data in principle. This implementation requires suﬃcient entries in each bin forstable estimation of the number of signal events. In this section, the problem of statisticallimitation and its solution are explained.

Chapter 6 γ-ray Background Reduction with RDC

165

500
103

400
300

102

200
10
100
1
0
0

10

20

30
40
50
upper limit of Nsig

0

10

(a)

20

30

40

50
∆ UL

(b)

Figure 6.7 (a) Upper limits on the number of signals for 4000 pseudo experiments and(b) deviation of upper limits from those calculated using the accidental background PDF
generated with 1 × 109 events. Each color corresponds to the results using the PDF
generated with 1 × 109 (black), 1 × 108 (red), 1 × 107 (blue) and 1 × 106 (green) events.

6.3.1 Statistical limitation
A lack of entries in each bin can cause an error of the analysis. Assume, for example, thenumber of entries in a certain bin of the accidental background PDF is accidentally much lessthan the expectation. If data is fit with such a PDF, the excess of the entries in the bin will be
regarded as signal-like though it is not true. Fig. 6.7(a) shows the upper limits on the number ofsignals when accidental background PDFs generated with the diﬀerent number of events are used
to analyze the common pseudo experiments. The distribution is deformed when the statistics issmall resulting from an increase of the experiments in which the upper limits are calculated tobe higher as shown in Fig. 6.7(b). Therefore, it should be ensured that the statistical fluctuationis small enough not to aﬀect the result.
The expected number of events which can be used for the accidental background PDF is
calculated to be ∼ 1 × 106 events assuming a DAQ rate of 10 Hz, 120 DAQ days (1 year)*2
and 1% event selection eﬃciency*3 . Apparently, this cannot give suﬃcient entries with the
PDF configuration used for the sensitivity calculation at the design stage such as bin widths ofdsds
0.5 MeV for Eγ , 2 ns for tus
rdc and trdc , and 2 MeV for Erdc : the green case in Fig. 6.7(a).

Note that the statistics for the signal and RMD PDFs is not so severe since only one dimensional histogram of the Michel energy distribution is necessary for their generation, and so thefollowing discussion focuses on the accidental background PDF.

*2 The Eγ PDF for the accidental background events would be prepared year by year since it can be diﬀerent

due to the condition of the LXe detector.
*3 A series of selections is applied to create the Eγ PDF for the accidental background events [44], and its

eﬃciency was a few percent in the MEG.

Chapter 6 γ-ray Background Reduction with RDC

6.3.2 Solution
The problem mainly comes from the sparsity of the four dimensional histogram. To solve this,two methods are developed; one is on the implementation of the histogram, and the other is on
how to generate it.
Optimization of bin widths
The first idea is to optimize bin widths. Originally, the bin widths are set to be narrow
enough not to aﬀect the sensitivity. This is, however, not necessarily required for all bins since
the importance of the bins is diﬀerent depending on their regions; the timing coincidence regionds
is more important than the timing sideband, and the low energy region of Erdc
is more important

than the high energy region for the signal and background identification. Moreover, the sparsity
is striking in such less important regions. Therefore, there is room to improve the setting of thebin widths.
Variable bin widths are adopted for the optimization to increase the entries of the sparse
regions maintaining the information in the important regions. The result of the optimization issummarized in Table 6.1.
Table 6.1 Optimized bin edges of the RDC PDF. The bins for no hit events are not included.

Variables

Bin edges

Eγ

48, 48.5, 49, 49.5, 50, 50.5, 51, 51.5, 52, 52.5, 53, 58 MeV

tus
rdc
tds
rdc
ds
Erdc

−20, −8, −4, 0, 4, 8, 28 ns−20, −8, −4, 0, 4, 8, 28 ns
0, 2, 4, 6, 8, 10, 50 MeVExtraction of distributions in reduced dimension
In the simplest way, the four dimensional histogram is directly filled with obtained events,
but this can waste statistics in the context of the RDC PDF; the Eγ dependences of the timing
and energy distribution of the RMD positrons are not so important, and the energy distributionof the Michel positrons does not depend on Eγ and timing. Therefore, the extraction of those
distributions in reduced dimension and reconstruction of the PDF with them can increase theeﬀective statistics.
Fig. 6.8 summarizes how to extract the distributions. The original four dimensional PDF is
projected to proper dimensions for each purpose. The RMD fraction detected by the upstreamds
or downstream RDC is extracted from the projection to (Eγ , tus
rdc ) or (Eγ , trdc ). The number of

RMD events can be calculated by subtracting the expected number of Michel background eventsfrom the total number of events, and the fraction is given by dividing it with the total number.
This calculation is repeated for all the Eγ bins. The tus
rdc distribution is extracted from theds
projection to tus
rdc by subtracting the expected timing distribution of Michel positrons. The trdc

166

Chapter 6 γ-ray Background Reduction with RDC

Figure 6.8 Overview of the process to extract distributions.

dsand Erdc
distributions are extracted from the two dimensional histogram of them since ignoring

their correlation was found to result in sensitivity deterioration. The extraction can be achievedby subtracting the energy distribution of Michel positrons normalized with the expected numberof Michel events in the timing region.
The extracted distributions are mixed by a similar method to the simulation-based generation;
the RMD and Michel distribution are mixed with the RMD fractions.
Eﬀect of improvements
The eﬀect of the improvements was investigated using MC. Fig. 6.9 shows the median upper
limits and the coverages as a function of the number of events used for the accidental background
PDF. A common set of null signal pseudo-experiments was analyzed with accidental background
PDFs generated with the diﬀerent numbers of events. Thanks to the two methods, both of themedian upper limit and the coverage are kept stable*4 and no deterioration is observed with thestatistics which can be achieved with one year data-taking, i.e. 1 × 106 events.
The test above was performed for the null signal experiments. To test that the analysis
can correctly detect the signal events with the improved RDC PDF, the statistical power andsignificance were also studied under the assumptions of finite branching ratios. Common setsof pseudo-experiments under the assumption of diﬀerent branching ratios were generated andanalyzed with PDFs generated with 1 × 109 and 1 × 106 statistics. The p-value against the null
hypothesis was calculated for each experiment. Fig. 6.10 shows the p-values at 95%-quantile as
a function of the assumed branching ratio. The equivalent signal detection power is achieved
with the improved RDC PDF generated with 1 × 106 statistics. The branching ratio down to
1.4 × 10−13 can be detected at the significance level of 1% with the power of 95%.

6.4 Uncertainty from PDF
The uncertainty from the RDC PDF can be divided into the three components due to thegeneration procedure: the RMD fraction, the RMD timing and energy distribution and the*4 The coverage tends to be 5% higher than the confidence level, which probably comes from the asymptotic

method.

167

8coverage

median upper limit (a.u.)

Chapter 6 γ-ray Background Reduction with RDC

7
6

168

1
0.9
0.8
0.7

5

0.6

4

0.5

3

0.4
0.3

2

0.2

1
0 6
10

0.1
108

107

0 6
10

109
entries

108

107

(a)

109
entries(b)

p-value

Figure 6.9 (a) Median upper limits and (b) coverages as a function of the number of eventsused for the accidental background PDF without (black) and with (red) the improvements.

1

10−1

10−2

10−3

10−4
0.05

0.1

0.15

×10−120.2
0.25
branching ratio

Figure 6.10 P-values at 95% quantile as a function of the assumed branching ratio without(black) and with (red) the improvements.

Michel energy distribution. The uncertainty from them can come from the statistics used togenerate the PDF. Since the Michel energy distribution can be extracted from the oﬀ-timing
region independent of the γ-ray detection, a suﬃcient amount of statistics can be accumulated
for the generation. On the other hand, the others require a γ-ray hit at the LXe detector, andthus the available statistics is limited by the event selection. In particular, the uncertainty fromthe RMD fraction can be the largest as it needs to be extracted for each Eγ region.
The RMD fraction is aﬀected by the statistical fluctuation of the number of events used forthe calculation. The fluctuation is simulated by extracting the fraction from diﬀerent datasets,
and it increases as the energy becomes higher due to the lower statistics as shown in Fig. 6.11.
The RMD timing and energy distribution can fluctuate resulting from the statistics of theoriginal distribution. Fig. 6.12 shows the uncertainty of each bin calculated from diﬀerent PDFs
which are generated using the diﬀerent RMD timing and energy distributions. The fluctuation

fraction

Chapter 6 γ-ray Background Reduction with RDC

169

0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
0.048

0.05

0.052

0.054

0.056
0.058
Eγ (GeV)

10

0.05

(%)

Eds
rdc (GeV)

Figure 6.11 Uncertainty of the RMD fraction defined by the standard deviation (blackbar) and peak-to-peak (red).

0.04
1

0.03
0.02

10−1
0.01
0
−0.01
−20

−10

0

10

20

10−2
×10−9
30
tds
rdc (s)Figure 6.12 Uncertainty of the RMD timing and energy distribution.

is higher in the RMD-like region. Note that only the distribution of the downstream RDC isshown here, but it is obvious that the uncertainty from the timing distribution of the upstream
RDC can be lower since it can be almost the same with the projection of the two-dimensional
distribution.
Fig. 6.13 shows the uncertainty of the median upper limit calculated by analyzing with ten
diﬀerent RDC PDFs generated from diﬀerent datasets. As the statistics for the RDC PDF
generation gets smaller, the uncertainty becomes larger due to the statistical fluctuation. It is,however, limited to 1.2% even with the statistics of one year data-taking, i.e. 1 × 106 events,
which is small enough.

uncertainty (%)

Chapter 6 γ-ray Background Reduction with RDC

170

2.5
2
1.5
1
0.5
0 6
10

107

108
entriesFigure 6.13 Uncertainty of the median upper limit from the RDC PDF as a function of
the number of events used for the generation of the accidental background PDF.

171

Chapter 7

MEG II Projected Sensitivity
In this chapter, the branching ratio sensitivity is evaluated based on the measured performanceof the MEG II detectors through the past pilot runs and the analysis update. As discussed inSec. 2.5, the nominal value for the branching ratio sensitivity without any updates in this thesis
was evaluated to be 7.8 × 10−14 for three years of data-taking. Hereafter, the eﬀects of the
updates in this thesis are described followed by the discussion on the projected sensitivity of the
MEG II experiment.

7.1 Eﬀect of γ-ray pileup elimination
Fig. 7.1 compares the branching ratio sensitivity after applying each algorithm for the pileup
elimination. The event rejection based on the deep learning model improves the sensitivity
by 18% resulting from the reduction of on-timing pileups. The peak search and the waveform
unfolding results in further sensitivity improvement by 4%. In total, the sensitivity improvementfrom the nominal configuration is 22%.
In Fig. 7.1, the sensitivities at the halved intensity are also shown. To see the eﬀect ofthe γ-ray pileups, the variables for positrons which change depending on the beam intensity(Table 2.15) were fixed to those at the nominal intensity. The pileup elimination enables toachieve 15% better sensitivity by doubling the beam intensity. It is also illustrated that thepileup elimination leads to a better sensitivity than that of the previous algorithm even withthe halved statistics thanks to the elimination of the on-timing pileups.
Eﬀect of PDE degradation
As discussed in Sec. 5.3.4, the performance of the pileup elimination depends on the MPPC
PDE: the larger amount of backgrounds and the higher signal eﬃciency at the lower PDE.
Fig. 7.2 shows the branching ratio sensitivity as a function of the PDE. There is no apparent
tendency depending on the PDE, but the variation of the sensitivity fluctuates from −4% to+7%, which depends on the balance between the increase of the backgrounds and the signal
eﬃciency. The diﬀerence between the PDEs at which the models are trained is not significant
as well. Therefore, we can use a single model independent of the actual PDE of data.

branching ratio sensitivity (a.u.)

Chapter 7 MEG II Projected Sensitivity

172

1.3
1.2
1.1
1
0.9
0.8
0.7

nominaldeep learning peak search & unfolding

branching ratio sensitivity (a.u.)

Figure 7.1 Relative size of the branching ratio sensitivity after applying the elimination
algorithms at the beam intensity of 7 × 107 µ+ stops/s (black) and 3.5 × 107 µ+ stops/s(red). It is defined by the branching ratio sensitivity with the corresponding update overthat under the nominal condition. Thus the better sensitivity is, the smaller value in the
plot.

1.3
1.2
1.1
1
0.9
0.8
0.7
0

2

4

6

8

10

12
14
PDE (%)

Figure 7.2 Relative size of the branching ratio sensitivity at the beam intensity of 7 ×
107 µ+ stops/s as a function of MPPC PDE. The deep learning model is trained at a fixed
PDE of 13% (black) and each PDE (red). It is defined by the branching ratio sensitivity
with the corresponding update over that under the nominal condition. Thus the better
sensitivity is, the smaller value in the plot.

Branching ratio sensitivity (a.u.)

Chapter 7 MEG II Projected Sensitivity

173

1.2
1.15
1.1
1.05
1
0.95
0.9
0.85
0.8

7

8

9
10
RDC hit rate (MHz)Figure 7.3 Relative size of the branching ratio sensitivity as a function of RDC background
hit rate. The MC expectation is 7 MHz. It is defined by the branching ratio sensitivity
with the corresponding update over that under the nominal condition. Thus the better
sensitivity is, the smaller value in the plot.

7.2 Eﬀect of RDC
The branching ratio sensitivity was evaluated by introducing the RDC observables to theanalysis. The improvement due to the downstream RDC on the sensitivity was evaluated to be
8%.
Hit rate of Michel positron
The measurements carried out since 2017 suggests the hit rate of the Michel positron at the
RDC is higher than the expectation by up to 40% (Sec. 4.2.2). The eﬀect on the sensitivity wasevaluated by assuming diﬀerent hit rates and a constant beam intensity of 7 × 107 µ+ stops/s for
γ-ray. Fig. 7.3 shows the sensitivity as a function of the background hit rate. The sensitivity
does not change from the MC expectation of 7 MHz up to 42% excess (10 MHz). Therefore, thepossible excess expected from the measurements has no eﬀect on the sensitivity.
Saturation of SiPM for calorimeter
The saturation of the SiPM for the calorimeter was observed, and it deforms the energy
distribution as discussed in Sec. 4.2.2. Fortunately, the most important part in the energy
distribution is the low energy region around a few MeV, which acts as a decisive factor todiscriminate the RMD positrons from the Michel positrons, and thus the deformation in the highenergy region hardly aﬀects the sensitivity. Indeed, the detailed shape ranging from 10 MeV to
50 MeV is decided to be ignored for the physics analysis as discussed in Sec. 6. The eﬀect on
the sensitivity was estimated using the measured energy distribution, and no degradation wasobserved.

Chapter 7 MEG II Projected Sensitivity

7.3 MEG II projected sensitivity
The branching ratio sensitivity of the MEG II experiment was calculated including the eﬀects
from the pileup elimination algorithms and the RDC. As discussed in Sec. 3.1.1, the eﬀect of the
PDE degradation was taken into account assuming the optimistic and the pessimistic cases: thebeam intensity of 7 × 107 µ+ stops/s with the PDE saturation at 2%, and 3.5 × 107 µ+ stops/s
without the saturation.
Fig. 7.4 shows the branching ratio sensitivity as a function of calendar year assuming DAQ
time of 20 weeks per year. The sensitivity with three years of data-taking will be 5.6×10−14 and5.8 × 10−14 with the beam intensity of 7 × 107 µ+ stops/s and 3.5 × 107 µ+ stops/s, respectively.
Thanks to the better performance of the positron reconstruction at the lower beam intensity,
the sensitivity at the halved intensity is equivalent though the total statistics becomes half. The
reduced beam intensity has an advantage in terms of the MPPC PDE degradation of the LXedetector as well; the PDE can be zero or be saturated around 2% after 70–100 DAQ day in thecase of the 7 × 107 µ+ stops/s beam intensity. Other scenarios are also possible, and the beam
intensity will be optimized to maximize the sensitivity considering the accumulated statistics
and the detector performance.
The branching ratio sensitivity of the MEG II experiment is roughly one order of magnitude
better than that of MEG. This is realized by the reduction of the background events and theincrease of statistics. Table 7.1 summarizes the sensitivities and their factors, i.e. the normalizations and the median upper limits, for the MEG and the MEG II experiment*1 . In the caseof the beam intensity of 7 × 107 µ+ stops/s, the statistics is 5.1 times higher that of MEG, whichcomes from the doubled intensity and the improved detection eﬃciency. On the other hand,
the Nsig upper limit is suppressed to 54% of that of MEG thanks to the improved detector
resolutions, the pileup elimination and the background identification with the RDC. Even in thecase of the halved intensity, which is similar to that of MEG, the statistics is 3.0 times higher
while the Nsig upper limit is suppressed to one third of that of MEG.
Thanks to the suppressed background level, the further sensitivity improvement is possible byextending DAQ time; for example, it reaches 4 × 10−14 for five years of data-taking*2 . This alsosuggests that even lower beam intensity enables the achievement of better sensitivity if DAQ
time is extended by extra years.

*1 The nominal values of k in Table 2.15 are reduced taking into account the ineﬃciencies from the pileup

elimination, 6.4% and 4.6% for 48 MeV < Eγ < 58 MeV, for the two cases in MEG II, respectively.
*2 The sensitivity with the halved intensity gets equivalent to the other after five years of data-taking as
shown in Fig. 7.4. This is because the number of backgrounds for the halved intensity is suppressed enoughnot to saturate the sensitivity yet while the other has started to be saturated due to the higher backgroundlevel.

174

branching ratio sensitivity

Chapter 7 MEG II Projected Sensitivity

175

10−12

MEG Final Result

10−13

10−14

0

1

2

3

4

5

year
Figure 7.4 Branching ratio sensitivity as a function of calendar year assuming DAQ time
20 weeks per year at the intensity of 7 × 107 µ+ stops/s (black) and 3.5 × 107 µ+ stops/s(red). The blue point shows that without including any updates in this thesis (Sec. 2.5).

Table 7.1 Sensitivity and its factors for the MEG and MEG II experiment.

Variables

MEG (2009–2013)

MEG II (for three years)

3 × 107 µ+ stops/s

7 × 107 µ+ stops/s

3.5 × 107 µ+ stops/s

k1.71 × 1013

8.78 × 1013

5.09 × 1013

Nsig upper limit (90% C.L.)

9.1

4.9

3.0

sensitivity

5.3 × 10−13

5.6 × 10−14

5.8 × 10−14176

Chapter 8

Conclusions
The MEG II experiment is planned to search for the µ → eγ decay with the higher sensitivity
than the previous MEG experiment by one order of magnitude. Since the sensitivity of the
MEG experiment was limited by the number of accidental backgrounds, a reduction of such
events is mandatory to realize a deeper search for the decay in MEG II. This can be achieved by
improving detector resolutions, reducing pileup events and identifying the backgrounds. This
thesis focuses on the suppression of the γ-ray backgrounds especially from the latter two aspects.
The sources of the γ-ray backgrounds are the RMD and AIF of a positron from the Michel
decay. The γ-ray from the RMD can be tagged by detecting the positron emitted from thesame muon decay. There are two types of AIF γ-ray events in which one or two γ-rays from the
AIF enter the γ-ray detector. In the latter case, the events can be rejected by finding the twocoincident hits. The higher beam intensity significantly increases accidental pileup γ-ray hits,
which increases the number of events in the signal energy region. The contribution from such
γ-rays can be reduced by reconstructing the energy of each hit.
The liquid xenon γ-ray detector has been upgraded by replacing the PMTs with the SiPMs
on the γ-ray entrance face to realize a high granularity and a good uniformity of the scintillation
readout. The performance of the detector was evaluated from the data obtained in the pilot
runs. Improvements of the position and energy resolutions for the shallow events were confirmed
while the energy resolution in the deep events (w > 2 cm) was worse than expected, which isprobably due to the unknown contribution also observed in MEG. The timing resolution was
estimated with two diﬀerent methods. One of them was found to be consistent with the MC
expectation while the other to be much worse than the expected value. This can come from asystematic error of the measurement, and thus a dedicated data-taking was proposed to reduce
it, which is planned to be performed in December 2021.
A series of algorithms to eliminate the pileup γ-rays was developed which utilizes the highgranular readout channels and waveforms digitized at a high sampling frequency. The pileup
γ-rays are searched for spatially and temporally using the information of each channel. For the
spatial search on the inner face, the prediction by a deep learning model is used to increase
the detection eﬃciency of the pileup γ-rays and suppress misidentification of fake peaks. This
spatial search is sensitive to the AIF background with two incident γ-rays, which have a largeChapter 8 Conclusions
contribution near the signal energy. The energies of the found γ-rays are reconstructed separatelyby unfolding waveforms, which allows us to use the pileup events resulting in the high signal
eﬃciency of 93% while the number of the backgrounds around the signal energy is reduced by
51% compared to the previous study.
Although the light distribution was used as the model input in this thesis, the timing distribution would be also useful to identify oﬀ-timing pileups as used for the timing-based search(Sec. 5.2.2). The combination of the light and timing distributions is also possible, which can
improve the performance especially for the pileups whose timings are slightly diﬀerent from themain γ-ray though they are in the charge integration region. In order to correctly train themodel and benefit from the timing information, the model architecture, data pre-processing andtraining procedure must be investigated.
The RDC was newly introduced in the MEG II experiment to tag the RMD γ-ray backgrounds.
The expected performance of the detector was confirmed using the data in the pilot runs. The
RDC identifies 27% of the γ-ray backgrounds in the analysis region. The accidental hit rate of
the Michel positron exceeded the expectation by up to 40%, but it was found not to aﬀect thebranching ratio sensitivity. In addition, a procedure to introduce the observables of the detector
to the µ+ → e+ γ analysis was developed, and the correlations among them and the γ-ray energy
are correctly taken into account in the analysis.
The measured detector performance and the improvement in the analysis lead to the projected
sensitivity of the MEG II experiment of 5.6–5.8 × 10−14 for the branching ratio of µ+ → e+ γwith three years of data-taking, which is 10 times higher than that of the MEG experiment.
This was achieved by the reduction of the γ-ray backgrounds thanks to the development of thepileup elimination algorithms and the introduction of the RDC, which provide a 22–26% and
8% improvement, respectively. The unprecedented sensitivity of the µ+ → e+ γ search of the
MEG II experiment would enable us to test many of the well-motivated BSM theories.
The engineering run with the full detector was successfully completed and a part of physics
data was taken in the run 2021. A full-blown accumulation of the physics data to search for theµ+ → e+ γ decay will start in 2022.

177

178

Appendix A

Lab Test for Downstream RDC
The downstream RDC had been developed toward the installation to the MEG II experiment.
In this chapter, the measurements at the lab during the construction are described.

A.1 Timing counter
The timing resolution of the timing counter was measured with a 90 Sr source. Fig. A.1 shows
the setup for the measurement. A reference counter whose timing resolution was 30 ps wasplaced under the test counters to trigger events. The reference counter was made of a plastic
scintillator with a size of 5 × 5 × 4 mm3 and its scintillation light was read out with a SiPM. The
waveforms of the signals were recorded with a DRS4 evaluation board. The timings of the signals
were extracted using the constant fraction method. The timing resolutions were calculated byσcounter = σ(tleft + tright− tref ),2(A.1)

where tleft and tright are the extracted timings of the left and the right channels of the test
counter, respectively, and tref is the timing of the reference counter. The 90 Sr source was placed
at several positions along the direction of the length and timing resolutions were measured foreach. Fig. A.2 shows results of the measurements. All timing resolutions are better than 90 ps,
which are good enough for the RMD detection.

Figure A.1 Schematic view of the setup for the timing counter [65].

Appendix A Lab Test for Downstream RDC

Figure A.2 Measured timing resolutions [65]. The x-axis corresponds to the position of
the radiative source along the direction of the length where the origin is the center ofscintillators.

A.2 Calorimeter
The LYSO crystals were tested and the energy resolution was evaluated. Fig. A.3 shows the
setup for the measurement. The energy of γ-rays from a 60 Co source was measured with each
LYSO crystal attached to the SiPM using spring pins. The waveform was recorded with a DRS4
evaluation board. The charge was calculated by integrating the waveform. Fig. A.4 shows anexample of the observed energy spectrum. Since the energy tail of the intrinsic radioactivity
overlaps the energy peaks at 1.17 MeV and 1.33 MeV of the 60 Co source, double Gaussian functions with an exponential components were used as a fitting function. The energy resolutions
at each peak energy are defined by σ/Eγ , where Eγ and σ are the mean of sigma of the corresponding Gaussian. Fig. A.5 shows the result for 76 crystals. The energy resolutions of mostcrystals were measured to be ∼6% at 1 MeV.
In a high rate environment, energy resolution can be worsened by the afterglow eﬀect of LYSO.
Afterglow is a delayed light emission of crystals with very long time constant (typically few
hours). When electrons are excited, some of them are trapped in lattice defects such as oxygen
vacancies. Then, these trapped electrons induce scintillation light. Since the high hit rate of
positrons up to 600 kHz at the central crystal is expected, the eﬀect was studied by exposing the
crystals to a 90 Sr source. The increase of the current due to afterglow was measured with the
SiPMs attached to the crystals. The increase of the current in the MEG II beam environment
was estimated to be ∼ 10 µA at maximum, which is small enough; the deterioration of the energy
resolution is less than 1% at 1 MeV.

179

rystal and the SiPM are not glued
in thecalorimeter,
it is necessary
set just
besidethe crystal.
The signaltoofoptimize
the SiPM was transmitted to a w
upling. We investigated the best(DRS4
way ofevaluation
the couplingby comparing
the showslight yieldboard).
Figure 4.2
the observed light yield spect
The detail is summarized in section
4.3.the gamma-ray (1.17, 1.33 MeV) are overlapping with the spectru
peaks ofradioactivity.
Appendix A Lab Test
for Downstream RDC
180-1*charge[0]ss test of the LYSO crystals
1000

ured the light yield and the energy resolution with all the LYSO crystals by using
800
wn in Figure 4.1. The crystals were wrapped with a reflector and tested one by600
M was fixed on the crystal by using spring pins. A gamma-ray source (60 Co) wase the crystal. The signal of the SiPM was transmitted to a waveform digitizer
400
tion board). Figure 4.2 shows the observed light yield spectrum. Two photo200
gamma-ray (1.17, 1.33 MeV) are overlapping with the spectrum of the intrinsic
Figure A.3 Schematic view of the setup to measure the energy resolution [69].
0
0

1

2

3

4

Light yield (a.u.)-1*charge[0]hEntries36053
Mean 2.084
RMS

1.05

Figure 4.1: Schematic view of the setup.

Figure 4.2: Energy spectr

1000

31

800

600

400

32

Chapter 4. Development of LYSO calorimeter
200

0

0
1
2
3
4
6
The light yield and energy
resolution
were
obtainedby5 fitting
the photo-peaks with gausLight yield (a.u.)sians in which beta-decay spectrum was convoluted. The energy resolution R was defined as
60
Schematic
view/EofFigure
setup.
A.4 EObserved
spectrumincluding
Co andintrinsic
radioactivity.
The4.3 shows the
R=
,the
where
and energy
are
the
mean
and
sigma
of theeach
gaussian.
FigureFigure4.2:
Energyspectrum.
two peaks at 1.17 MeV and 1.33 MeV and the background floor are fitted with double
result for the
76 crystals. Thanks to the high light yield of the crystal, good energy resolutions
gaussian functions and an exponential function [69].
were obtained in most of the crystals (⇠6% at 1 MeV).
31

Resolution at 1 MeV (%)

8
7.5
7
6.5
6
5.5
5
4.5
4

6

7

8

9

10

11

Light yield (a.u.)
FigureFigure
A.5 Measured
energy resolutionsof thelight
LYSOyield
crystals
as aenergyfunction resolution.
of the obtained
4.3: Distributionof theandlight yields [69].

4.2

Afterglow

181

Appendix B

Resistive Plate Chamber
A resistive plate chamber (RPC) has been investigated as a candidate of the upstream RDC.
In this chapter, an overview of the RPC as the upstream RDC is given.
Fig. B.1 shows a schematic view of a typical RPC. The RPC consists of parallel plates,
positively-charged anodes and negatively-charged cathodes. They are made of a very highresistivity material. The gap between the plates is filled with a gas and electrons are knocked out
of gas atoms when charged particles pass through the chamber. These electrons are accelerated
with the electric field and hit other atoms causing an avalanche of electrons. The gained signal
is read out with metallic strips.
The high resistive plates realize a stable operation to suppress the electrical discharge. They
are usually made of glass or bakelite. For the upstream RDC, however, the plates made of suchmaterials can be so thick that they cannot avoid aﬀecting the beam. Therefore, a 50 µm thickpolyimid film coated with diamond-like carbon (DLC) is adopted for the resistive plates. DLC
is made of carbon having a combination of sp2 and sp3 bonds. As a result, a DLC coating has a
combination of the properties of both diamond (sp3 bonding) and graphite (sp2 bonding) suchas electric insulation and conductivity. By changing a fraction of the two bonds, the resistivityof DLC can be controlled. Since the high resistivity can be realized with the DLC coat thinnerthan 100 µm, the material budget of DLC is negligible.
A R134a based gas mixture with iso-C4 H10 and SF6 is often used for the RPC. Thanks to
the high electronegativity of R134a and SF6 , a multiplication of electrons can be suppressed
resulting in a stable operation while iso-C4 H10 plays a role of a quencher preventing discharges
by absorbing UV light.
The detection eﬃciency of the RPC can get higher as the gap becomes thicker while the timing
resolution can be worsen due to a longer drift distance. The multiple-layer structure can realize
a high detection eﬃciency keeping the suﬃcient timing resolution. The detection eﬃciency ofthe n-layer RPC can be written by that of the single layer ϵsingle as follows [97]:ϵn = 1 − (1 − ϵsingle )n .

(B.1)

Therefore, the high detection eﬃciency and the good timing resolution can be achieved bystacking thin layers.

Appendix B Resistive Plate Chamber

182

Figure B.1 Schematic view of the RPC [99].

Al readout (100 nm thick)

gap

2 cm

+HV

1 cm
-HV

+HV

Readout

DLC (100 nm thick ) on
Kapton (50 μm thick)

Entry

Concept of the detector design.

Figure2. ofSingle-layer
prototype.
Figure B.2
Overview
the prototype
RPC [98].

2750 V

2700 VA single-layer prototype RPC wastested with a µ beam at the πE5 beamline [98]. Fig. B.22650 V

103

2600 Vshows the overview of the prototype.
It sizes 2 × 2 cm2 with a gap of 384 µm thickness. A

gas mixture of 94% Freon (R134a), 5% iso-C4H10 and 1% SF6 was filled in the gap. The high2

10
voltage
was supplied via conductive tapes attached on the edge of the DLC surface, and thesignal was read out from both ends of the strips. The performance of the RPC was measured
2

with 10positrons and muons at a rate up to 1 MHz/cm . The detection eﬃciency of 60% wasachieved, which implies the aimed eﬃciency of 90% is achievable by stacking four layers. The
timing1 resolution, 170 ps, was much better than the requirement of 1 ns. A voltage drop due to0 hit rate
0.1
0.2 observed,
0.3
0.4
0.5 consistent with the expectation from the design. The
the high
was
which
was

Height [V]results tell us the use of the RPC as the upstream RDC is possible though there still remaintechnical
challenges
such asfor
a suppressionof a voltage
ure 3. Signal someheightdistributions
obtained
MIP positrons
at low drop
rate.and a diﬃculty to control theresistivity.

ance measurement
nt measurements were performed to evaluate the performance for the MIP positron
mentum muon. Firstly, the MIP detection efficiency and timing resolution were
low rate, as described in Sec. 3.1. Secondly, the RPC’s response to a low-momentum
easured at low rate, as described in Sec. 3.2 with discussion on the results. Finally,ance in a high-rate low-momentum muon beam was measured, as described incy and timing resolution for MIP positrons at low ratecy and the timing resolution were measured with positrons from muon decaym2 ). The signal height spectra are shown in Fig. 3 changing the applied voltage

183

Appendix C

Study on Radiation Damage to
VUV-MPPCAs discussed in Sec. 3.1.1, a degradation of MPPC PDE was observed under the muon beam.
Since the degradation is correlated with the beam exposure and its magnitude is larger for VUVlight than visible light, it is likely because of a surface damage by the particle irradiation. This
chapter begins with a summary of radiation damage to the SiPM followed by explanations oflab test results.

C.1 Radiation damage to SiPM
There are two types of radiation damage known for the SiPM: bulk damage due to Non
Ionizing Energy Loss (NIEL), and surface damage due to Ionizing Energy Loss (IEL) [100].
The bulk damage is primarily caused by high energy particles such as protons, pions, electronsand photons, and by neutrons. They can displace atoms out of their lattice site and generatecrystal defects leading to changes in the sensor performance related to the newly introduced
energy levels in the energy gap between the valence and the conduction band, Egap ∼ 1.12. A
typical phenomenon caused by the introduced energy level is an increase of the leakage current;
defects with energy levels close to the middle of the band gap (∼ 0.56 eV) facilitate the thermal
excitation of electrons and holes, increasing the dark current. This is reported to occur above2

1 × 108 /cm (1 MeV neutron equivalent) by many studies [86] [87] [88]. Some studies also
report a decrease of the signal size possibly caused by an increase of pixel occupancy due to theincreased dark signals [88]; if a photon hits a pixel which is not fully recovered from the previous
discharge, the eﬀective gain can be smaller.
The surface damage is primarily produced by photons and charged particles, generating
charges in the oxide (SiO2 ) and at the Si–SiO2 interface, and interface traps at the Si–SiO2
interface. The energy deposit above the energy gap generates electron-hole pairs in the highresistivity passivation layer. Most of the electrons leave the passivation layer due to a relatively
high mobility and low trapping probability. On the other hand, some of the holes, which move
via polaron hopping, are captured by deep traps in the passivation layer or the interface traps

Appendix C Study on Radiation Damage to VUV-MPPC

184

between silicon layers resulting in an accumulation of the stationary charges. A large increase of
the dark current is reported above 200 Gy due to an increase of surface current [89]. If a fractionof the surface current reaches the amplification region, it also increases the dark-count rate.
Fig. C.1 shows the radiation environment of the LXe detector. When the muon beam is used,
γ-rays mainly from the RMDs hit the detector through the MPPCs on the entrance face. The
xenon scintillation light (7.1 (mean) ± 0.1 (FWHM) eV) generated from these γ-rays hit the
MPPCs. Neutrons coming from the accelerator also hit the detector.
The expected irradiation dose in the run 2019 is summarized in Table 3.2. The neutron fluence2

was estimated to be less than 2.9 × 106 /cm (1 MeV neutron equivalent) from the measurement
at the MEG II experimental area [43], which is much smaller than the level where the NIEL
damage is reported. The γ-ray dose was simulated to be 0.01 Gy [43], which is also small
2enough. The VUV fluence was measured to be 4.6 × 1010 /mm from the induced current on
2

the MPPCs in the run 2019 while the estimation from the simulation was 5.8 × 1010 /mm .
A radiation damage to SiPMs by the VUV irradiation was not reported. Thus, a series ofirradiation tests was performed at the lab to understand the observed PDE degradation.

C.2 VUV photon irradiation
VUV-MPPCs were irradiated with the intense VUV light from a xenon lamp to study theeﬀect of the VUV light. The irradiation was performed both at room temperature and at
low temperature since the accumulation of the stationary charges can be enhanced at lower
temperature due to lower mobility.

C.2.1 Irradiation at room temperature
Fig. C.2(a) shows a schematic of the setup for the VUV photon irradiation at room temperature. A VUV-MPPC was irradiated with VUV photons and its response to VUV light was

LXe detector

n
MPPC

VUV

COBRA

γ

μ

not to scale

Figure C.1 Radiation environment of the LXe detector [62].

Appendix C Study on Radiation Damage to VUV-MPPC

185

monitored together with that of another VUV-MPPC without irradiation. All of the irradiationand measurements was performed at 25◦ C.
A VUV-MPPC was irradiated by a xenon lamp (Hamamatsu L9456-03 [101]) placed at a
distance of 5 cm, and the light emitted from the lamp directly entered the irradiation sample
without any filters. The spectrum of the emitted light from the lamp is shown in Fig. C.2(b).
The VUV component of the irradiation light was measured to estimate irradiation flux beforehand. Two bandpass filters (ACTON FB180-B-.5D and Edmund optics #33-026, Fig. C.3)
were used to select VUV light peaked at 190 nm. The amount of light was measured placing
the lamp at diﬀerent distances ranging from 15 cm to 53 cm, and the results were extrapolated
to that at the measurement distance to avoid saturation the MPPC. As a result, the irradiation
2

flux of the VUV light was estimated to be 5 × 1013 photons/mm /hour.
The response to VUV light was monitored by periodically measuring the charge with anotherxenon lamp (Hamamatsu L9455-13 [101]) placed at 35 cm away from the MPPC. The two bandpass filters were used to monitor the response to the VUV light peaked at 190 nm in addition
to one ND filter to avoid saturation. The response of another MPPC without irradiation was
also measured for the comparison. In order to ignore the position dependence of the light distribution from the lamp, the irradiation sample was displaced and the reference sample was puton the same position during the charge measurement. The uncertainty of the measured charge
was estimated to be ∼5% by repeating the measurement including this displacement, which isenough small.
Fig. C.4(a) shows a history of the VUV response for the irradiated and the non-irradiated
MPPCs. The VUV response of the irradiated MPPC was degraded by 65% in total after2

3 × 1016 /mm VUV photon irradiation while that of the non-irradiated sample was stable. The
degradation speed was decreasing and saturated when it reaches 35% of the original value. The
observed degradation is much slower by a factor of O(104 ) than that in the LXe detector: 9%2

degradation at the expected fluence of 4.6 × 1010 /mm VUV photon.
The irradiated MPPC was annealed after the irradiation. It was illuminated with room lightbeing applied bias voltage, and was kept at 70◦ C for 24 hours. The annealing increased thecharge for VUV light from 35% to 105% of that before the irradiation, and thus the degradation
was recovered completely. The recovered MPPC was irradiated again, and the degradation wasobserved at slightly slower speed (Fig. C.4(b)).

C.2.2 Irradiation at low temperature
The PDE degradation was observed, but its speed was found to be much slower than theobservation of the LXe detector. This might be because of the diﬀerence of temperature; morecharges can be accumulated at lower temperature, which results in faster degradation speed.
Therefore, the irradiation at LXe temperature was also tried [102].
Fig. C.5(b) shows the setup for the irradiation. It was covered with a dewar for thermal
insulation, and purged with gaseous nitrogen to avoid condensation. The MPPC was cooledAppendix C Study on Radiation Damage to VUV-MPPC

5 cm

186

Voltage: 600 V
Capacitance: 0.22 uF
Frequency: 126 Hz
Distance: 50 cmn

ND filter
during monitor

or

Xe

la

f
mp

io
iat

d

a
irr

Xe lamp for monitor

ReplaceduringmonitorRadiation Intensity

Irradiated
MPPC
Bandpass
filters
35 cm

Non-irradiatedMPPC

Wavelength (nm)

(a)

(b)

Figure C.2 (a) Setup of VUV photon irradiation and (b) spectral radiation intensity of
the Xe lamp [62]. This lamp can emit VUV light down to λ = 185 nm.

(a)

(b)

relative VUV charge

relative VUV charge

Figure C.3 Spectrum of the bandpass filters.

1.2

1

1.2

1st irradiation set
1st irradiation set
1st irradiation set

1

1st irradiation set
2nd irradiation set
2nd irradiation set

0.8

2nd irradiation set
2nd irradiation set

0.8

0.6
0.6
non-irradiated

0.4

0.4

non-irradiatednon-irradiatednon-irradiated

0.2

0.2

irradiatedirradiatedirradiated00

irradiated

100

200

300

(a)

400

500

600
irradiation time (h)

0
0

100

200

300

400

500
600
irradiation time (h)(b)

Figure C.4 (a) Response to VUV light from a fixed intensity xenon lamp. Diﬀerent data
series with similar colors show four chips on the same MPPC package [62]. The increasearound 390 hours of irradiated samples is due to the annealing at room temperature causedby 12 day intermission. (b) VUV response in the second irradiation after one cycle ofannealing [62].

図 6.24: UV カットフィルタ (EMVL-UV270) の分光曲線。赤いグラフが今回用いたものに該当する。
[39]
第 6. PDE 減少に関するラボ測定

6.7. 低温での VUV 光照射試験

表 6.4: UV 光を用いた 24 時間照射実験の結果

Appendix C Study on Radiation Damage to VUV-MPPC Xe-lamp Room-temp Xe-lamp Low-temp
Total dose level [photon/mm2 ]PDE decrease [%]1.3 × 1015 (UV)
7.5(UV)

1.3 × 1015 (UV)

LXe 2019
5.3 × 1010 (VUV)

14.8(UV)9(VUV)

図 6.26: 実際の写真。ランプの発熱によって窒素ガスが温められないように 5 W モジュールの周りは断熱材で覆われている。

図 6.29: 24 時間の照射による PDE 減少。照射後のシグナルの信号電荷を照射前の積分電荷で割り、さらにレファレンスの値で規格化した。

図 6.25: UV 光を用いて低温と常温の表面損傷を調査する実験における照赤いプロットは可視光、青いプロットは UV 光、黒丸・黒三角形は可視光と UV 光に対するレファレンスの変化率である。低温のほうが減少
射時のセットアップ
が大きいことがわかる。

(a)

(b)

Figure C.5 (a) Setup for the VUV photon irradiation at low temperature and (b) measured
charges after 24 hour irradiation normalized by those before irradiation [102]. The resultsof four chips on a MPPC were shown.52

down to LXe temperature with a pulse tube refrigerator (Aisin TAC 101J), and was irradiatedwith the xenon lamp placed at the distance of 3 cm without any filters. The temperature around
図 6.30: キセノンランプの波形。この図は 20 W モジュールの波形であるが、5 W モジュールと 2 W モジュールも波形の時定数は同程度で∼10 us である。

the MPPC was monitored with a thermometer and kept around 170 K during the irradiation.
54

The irradiation flux was estimated by measuring the charge with the xenon lamp used forthe irradiation. During the measurement, the two bandpass filters and a collimator with aradius of 1 mm was used, and the lamp was placed at the distance of 42 cm to reduce theamount of photons. As a result, the irradiation flux of the VUV light was estimated to be2

5.4 × 1013 photons/mm /hour. The response to VUV light was also measured with the filters
and the collimator.
Fig. C.5(b) shows the relative charges of the irradiated and the non-irradiated samples after2

24 hour irradiation corresponding to the dose level of 1.3 × 1015 photon/mm in total. The
results of the irradiation at room temperature are also shown, which was performed with thesame setup. The charges decreased by 10–20% at low temperature while the decrease was about
10% at room temperature. The charges of the non-irradiated sample also changed up to 7%,
which implies the uncertainty of the measurement.
Although larger degradation at low temperature was observed, it was still too slow comparedto the observation in the LXe detector by a factor of O(104 ). Therefore, it cannot be concluded
that the PDE degradation in the LXe results from the VUV light irradiation.

C.2.3 Dependence on wavelength
If the PDE degradation is caused by the surface damage, there should be wavelength dependence of the magnitude of the degradation; light with a shorter wavelength should be easier tobe aﬀected since it tends to be absorbed near the surface. Indeed, the response for visible light
was not degraded according to the observation in the LXe detector, which supports the surface

187

Appendix C Study on Radiation Damage to VUV-MPPC

188

damage hypothesis. To make the eﬀect of the VUV light irradiation clear, the dependence of
the PDE degradation on the wavelength was also investigated at the lab.
Fig. C.6 shows the setup for the measurement. In this measurement, there are several improvements to gain the amount of VUV light compared to the measurements above. Two xenon
lamps with MgF2 windows (Hamamatsu L13651-01-3 and L12745-01-3 [101]) were used insteadof those used for the previously mentioned lamps with UV glass windows (Fig. C.7). Bandpass
filters which select light with shorter wavelengths (λ ∼ 172 nm) were also used (Fig. C.8). The
whole setup was placed in a thermal chamber, and it was purged with gaseous nitrogen to avoid
the absorption of light with short wavelengths. In order to study the wavelength dependence,
five LEDs with diﬀerent wavelengths raging from 280 nm to 645 nm were also installed.
The irradiation flux was estimated in the similar way; the charge from the 2 W xenon lamp
placed at 45 cm away from a VUV-MPPC was measured using a ND filter and a collimator witha radius of 3 mm, and it was scaled. As a result, the irradiation flux of the VUV light was2estimated to be 2.9 × 1014 –1.2 × 1015 photons/mm /hour depending on the sensor positions.
For the PDE monitoring, the charge for the 20 W xenon lamp was measured with the bandpass
filter, a ND filter and the collimator, which was placed at the distance of 45 cm. The response forwavelength of 150–180 nm was extracted by comparing the charges measured in the atmosphereand gaseous nitrogen. The responses for other wavelengths were measured by illuminating theLEDs.
Fig. C.9 shows histories of the sensor response for diﬀerent wavelengths. The charges for the
VUV light decreased to 10% of the origin and were saturated at the same dose level as theirradiation test at room temperature (Sec. C.2.1). The diﬀerence of the saturation level cancomes from the diﬀerent wavelengths. The decrease was also observed for the wavelengths of
280 nm and 380 nm, and the saturation levels are 15% and 25%, respectively. A large variationof the decreasing speed among the chips was also observed for these wavelengths, which can be
related to the diﬀerence of the irradiation speed. Meanwhile, the responses for longer wavelengths
were almost stable during the irradiation. These results confirmed the eﬀect of the VUV lightirradiation on the PDE depends on the wavelength.
xenon lamp (2 W)
bandpass filter

bandpass filter

LEDs

MPPC
collimator(φ3 mm)ND filter

light shieldxenon lamp (20 W)

3 cm
45 cm

Figure C.6 Setup for the VUV photon irradiation to study on wavelength dependence.

DUV（深紫外線）
アプリケーション

キセノンフラッシュランプは、瞬間的に高い光出力を有しているため、高性能な深紫外光源としても注目されています100

20Wキセノンフラッシュランプ
MgF2（MgF2）
20Wキセノンフラッシュランプ
UV
glass（UVガラス）

放射照度（µW·cm-2·nm-1）

Relative相対光出力
Intensity
(%)
(%)

120

0.14

80
60
40
20
0
100

測定条件
窒素雰囲気下

120

140

160

180

200

220

波長 (nm)(nm)wavelength

240

260

280

0.1

0.08

用途

120

MgF2
UV glass○ 分光光度計
○ 殺菌

0.06
0.04

80
60
40

0.02

20

0

0

300

200 300 400 500 600 700 800 900 1000 1100
200
500
800
1100
波長 (nm)wavelength (nm)

(b)

測定条件

キセノンフラッシュランプ

100○ 光イオン化

窓材質
UVガラス（L13651-01）
MgF（L13651-01-3）
2

(a)
04

0.12

Irradiance (μW･cm2 / nm)

発光スペクトル分布（代表値）

189
発光パルス波形（代相対光出力 (%)

関連製品

にわたり高い性能を維持します。
Appendix
C Study on Radiation Damage to VUV-MPPC
分光放射照度（代表値）

Figure C.7 Spectral radiation intensities of (a) 20
W xenon
主放電電圧：600 V lamp (L12745-01-3) and (b)主放電コンデンサ容量：0.141 µF
2 W xenon lamp (L13651-01-3) (from [101], translatedby theauthor).
(a) was measured
ランプ発光繰り返
し周波数：79 Hz
検出器：光電子増倍管（Cs-Te光電面）（200 nm 〜 320 nm）（280 nm 〜 720 nm）
in gaseous nitrogen while (b) was in the atmosphere. 光電子増倍管（マルチアルカリ光電面）

0.4

0.6

時間

測定条件
アークサイズ：1.0 mm
主放電電圧：600 V
検出器：バイプラナ光電管 R1328U-

キセノンフラッシュランプ(a)Figure C.8 Spectrum of the bandpass filter [103].

C.3 Gamma irradiation
The VUV responses of several VUV-MPPC samples irradiated with γ-rays were measured.
The MPPC were irradiated using a 60 Co source (Eγ = 1.17, 1.33 MeV at the Takasaki Advanced Radiation Research Institute in 2015. The total irradiation dose of each MPPC was
1–4 × 103 Gy [104], which is much higher than the expectation of 0.6 Gy in the whole MEG II experiment.
In 2019, the VUV PDEs were measured with the setup shown in Fig. C.10. The MPPCs wereplaced on a circuit board and the signals from one or two chips on an MPPC were read out
individually. Two blue light LEDs were installed to measure single photoelectron signals forgain calibration. An α source was attached on a tungsten wire and installed in the middle. The
signals were amplified and their waveforms were acquired with the DRS evaluation board. The
PDE was measured by comparing the expected number of photons from the α source and themeasured number of photoelectrons.

0.2

主放電コンデンサ容量
0.141 µF
（L13651-01）
0.047 µF
（L13651-03）

Siフォトダイオード（680 nm 〜 1100 nm）
測定距離：500 mm

060Appendix C Study on Radiation Damage to VUV-MPPC

190

280 (nm)relative charge

relative charge

150-180

1.2

irradiated1

irradiated0.8

irradiatedirradiated

1.2
1
non-irradiatednon-irradiated0.8

non-irradiatednon-irradiated0.6

irradiated0.6

irradiatedirradiated0.4

irradiated

0.4

0.2
0.2

0
0

20

40

60

×1015
80
100
dose (photon/mm2)

0
0

50

(a)

150
dose (photons/mm2)

×1015

(b)
465 (nm)

380 (nm)1

relative charge

1.2

non-irradiatednon-irradiatednon-irradiated0.8

non-irradiated

1.2
1
0.8

irradiatedirradiated

0.6

0.6

irradiatednon-irradiatednon-irradiatedirradiated

0.4

0.4

0.2

0.2

non-irradiatednon-irradiatedirradiated

0
0

50

100

150
dose (photons/mm2)

irradiatedirradiatedirradiated

×1015

0
0

50

(c)

100

150
dose (photons/mm2)(d)569 (nm)relative charge

relative charge

100

1.2
1
0.8
0.6
non-irradiatednon-irradiated0.4

non-irradiatednon-irradiatedirradiated0.2

irradiatedirradiatedirradiated

0
0

50

100

150
dose (photons/mm2)

×1015

(e)

Figure C.9 Response for a fixed intensity of light with wavelengths of (a) 150–180 nm,(b) 280 nm, (c) 380 nm, (d) 465 nm, (e) 569 nm and (f) 645 nm. Diﬀerent data series withsimilar colors show four chips on the same MPPC package. The i-th points of diﬀerent
chips were measured at the same irradiation time, and the variety of the dose levels at thesame time is due to the position dependence of the light distribution. The data points in(a) are normalized by charges measured by the non-irradiated samples to compensate alarge fluctuation due to the instability of the lamp.

×1015Appendix C Study on Radiation Damage to VUV-MPPC

191(not to scale)Alphasource

MPPC

25mm

LED

anti-reflection
tube
9mm

(a)

(b)

Figure C.10 Small chamber setup [62].

Fig. C.11(a) shows the measured PDEs of the γ-ray irradiated samples with that of a nonirradiated MPPC *1 . The PDEs of them were consistent with each other except for one irradiated
MPPC, which may be due to some systematics or mistakes in the measurement. In any case, nosignificant degradation was observed even at the much higher irradiation fluence, and thus the
PDE degradation observed at the LXe detector was not reproduced by this γ-ray irradiation.
It must be, however, noted that the irradiated MPPCs were kept at room temperature for four
years after the irradiation and a possibility of the recovery by an annealing at room temperaturecannot be excluded.

C.4 Neutron irradiation
The VUV responses of several VUV-MPPC samples irradiated with neutrons were also measured. The MPPCs were irradiated at the Tandem electrostatic accelerator at Kobe University
in 2015. Neutrons from 9 Be + d → 10 B + n where deuterons were accelerated to 3 MeV wereused for irradiation. The total fluence of each MPPC was measured by a ELMA diode. It
ranges from 5 × 109 –2 × 1012 n/cm2 (1 MeV neutron equivalent) depending on the irradiation
time and the geometrical distance from the target [104].
The VUV PDEs were measured with the same setup used for the γ-ray irradiated samples
in 2019. As shown in Fig. C.11(b), no eﬀect of irradiation was observed. Therefore, neutrons
were excluded from the candidates though a possibility of recovery due to the annealing at room
temperature still remains.

*1 The VUV PDE was not measured before the irradiation since its degradation was not expected.

0.14
0.12

PDE

PDE

Appendix C Study on Radiation Damage to VUV-MPPC

no irradiation
1.4e3 Gy
4.1e3 Gy
4.1e3 Gy
4.1e3 Gyno irradiation

0.14

7.9e10 n/cm^2
7.9e10 n/cm^2
2.0e12 n/cm^2

0.1

0.08

0.08

0.06

0.06

0.04

0.04

0.02

0.02

1

0.5e10 n/cm^2
0.5e10 n/cm^2

0.12

0.1

0
0

192

2

3

(a)

4

5

6
Vover (V)

0
0

1

2

3

4

5

6
Vover (V)(b)

Figure C.11 VUV PDEs of the irradiated MPPCs as a function of the over voltage in (a)gamma irradiation test, and (b) neutron irradiation test. Diﬀerent colors show diﬀerent
MPPC chips. Black markers in (a) and gray markers in (b) are the MPPCs without
irradiation, and the others are the MPPCs with diﬀerent dose levels [62].

193

Acknowledgements
First of all, I would like to thank Prof. Toshinori Mori and Prof. Wataru Ootani for giving
me a great opportunity to join the MEG II experiment. Especially, I received generous support
from my academic supervisor, Prof. Wataru Ootani. I am grateful to Dr. Toshiyuki Iwamotofor giving me his kind supports not only to my research but also to my daily life in Switzerland.
In addition, I would like to oﬀer my special thanks for Dr. Yusuke Uchiyama, Dr. Kei Ieki and
Dr. Shinji Ogawa for their insightful advices for my study.
Last but not least, I would like to express my appreciation for all the members of the
MEG II collaboration for their generous help and work to progress the experiment. I am particularly grateful to my Japanese colleagues, Dr. Miki Nishimura, Dr. Mitsutaka Nakao, Mr. Masashi
Usami, Mr. Satoru Kobayashi, Mr. Kazuki Toyoda, Mr. Atsushi Oya and Mr. Kosuke Yanai toshare the wonderful time.

194

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