Doctoral Dissertation
博士論文

Full Commissioning of Liquid Xenon
Scintillation Detector to Search for µ+ → e+γ
with the Highest Sensitivity in MEG II
Experiment（MEG II 実験における最高感度での µ+ → e+ γ 探索のための液体キセノンシンチレーション検出器のコミッショニング）A Dissertation Submitted for the Degree of Doctor of Philosophy
December 2022
令和 4 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

Satoru Kobayashi
小林 暁

i

Abstract
A charged lepton ﬂavor violating decay of a muon, µ+ → e+ γ, is a promising probe in the
search for physics beyond the Standard Model. The MEG experiment set an upper limit of
the branching ratio of µ+ → e+ γ of 4.2 ×10−13 (90% conﬁdence level). An upgrade experiment of MEG called MEG II is designed to improve the sensitivity by one order of magnitude
using detectors with improved performance. This upgrade is motivated by the fact that theresolutions of the detectors are essential to discriminate the µ+ → e+ γ signal from the accidental background. To improve the resolutions of the liquid xenon scintillation detector for the
gamma-ray measurement, a new photosensor VUV-MPPC was installed. This thesis describes
the commissioning of the upgraded liquid xenon detector for the µ+ → e+ γ search with thehighest sensitivity in the MEG II experiment. Precise calibration measurements for the new
VUV-MPPC are developed to achieve uniform and stable gamma-ray measurements. The systematic uncertainty of the gamma-ray measurement is suppressed to 0.4% and 0.6 mm for energy
and position, respectively, by several calibration measurements. The resolutions for the signal
gamma ray are estimated based on measurements with 17.6 MeV and 54.9 MeV gamma rays.
The best resolutions of 1.7%, 2.5 mm, and 61 ps are achieved for energy, position, and time, respectively. Improvements in the energy and position resolutions for gamma-ray hits close to theentrance face are achieved compared to the MEG liquid xenon detector. By utilizing the pileup
analysis algorithm, a reduction of the rate of accidental background events in the analysis region
by 25% is achieved. The MEG II experiment started a pilot physics data taking in 2021, followedby the ﬁrst long-term data acquisition in 2022. The experimental sensitivity is estimated basedon the measured resolutions and counting rate in 2021. It is (8.1 ± 0.4) × 10−13 with the 2021
dataset, and it evolves down to (2.1 ± 0.1) × 10−13 by adding the 2022 dataset. Another three
years of data acquisition will improve the sensitivity down to (8.1 ± 0.4) × 10−14 , which is six
times better than the sensitivity of 5.3×10−13 in the MEG experiment. The upgraded liquid
xenon detector has been fully commissioned and is ready to search for the µ+ → e+ γ with thehighest sensitivity.

ii

Contents

Chapter 1

Introduction

1

1.1

Physics motivation of µ → e γ search . . . . . . . . . . . . . . . . . . . .

3

1.2µ → e γ search in MEG experiment

6

Chapter 2

+

+

+

+

. . . . . . . . . . . . . . . . . . . .

MEG II Experiment

14

2.1

Beam & Target . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

14

2.2

Positron Spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

17

2.3

Liquid Xenon gamma-ray detector. . . . . . . . . . . . . . . . . . . . . .

23

2.4

Radiative Decay Counter . . . . . . . . . . . . . . . . . . . . . . . . . . . .

43

0

2.5

π measurement setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

43

2.6

17.6 MeV CW-Li gamma-ray . . . . . . . . . . . . . . . . . . . . . . . . .

49

2.7

Data acquisition system . . . . . . . . . . . . . . . . . . . . . . . . . . . .

50

2.8

Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

53

2.9

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

56

Run 2021

60

3.1

Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

60

3.2

Preparation for physics run . . . . . . . . . . . . . . . . . . . . . . . . . .

61

3.3

Physics run . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

62

Chapter 3

3.40

π run . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

66

Calibration and Monitoring of the Liquid Xenon Detector

69

4.1

Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

69

4.2

Noise reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

71

4.3

MPPC gain and ECF calibration . . . . . . . . . . . . . . . . . . . . . . .

75

4.4

PMT gain calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

78

4.5

PDE and QE calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . .

82

4.6

Light yield and energy scale . . . . . . . . . . . . . . . . . . . . . . . . . .

89

4.7

Alignment of MPPC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

93

Radiation Damage to VUV-MPPC

103

Chapter 4

Chapter 5
5.1

Radiation environment for MPPC . . . . . . . . . . . . . . . . . . . . . . . 103

5.2

Decrease in MPPC PDE . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

Contents

iii

5.3

Thermal annealing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

5.4

Impact on the experimental sensitivity . . . . . . . . . . . . . . . . . . . . 115

Chapter 6

Position Resolution

118

6.1

Position Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

6.2

Resolution Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

Chapter 7

Energy Resolution

130

7.1

Reconstruction Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

7.2

Uniformity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

7.3

Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

7.4

Energy scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

7.5

Summary

Chapter 8. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

Time Resolution

142

8.1

Time Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

8.2

Resolution Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

Chapter 9Eﬃciency

149

9.1

Eﬃciency for signal gamma-ray in MC simulation . . . . . . . . . . . . . . 149

9.2

Eﬃciency measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

9.3

Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152

Chapter 10

Background

154

10.1

Pileup analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154

10.2

Cosmic-ray rejection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

10.3

Background rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

Chapter 11

Sensitivity

165

11.1

Maximum Likelihood Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 165

11.22021 dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

11.3

PDF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

11.4

Normalization and single event sensitivity with 2021 dataset . . . . . . . . 173

11.5

Estimated number of background events with 2021 dataset . . . . . . . . . 174

11.6

Sensitivity with 2021 dataset . . . . . . . . . . . . . . . . . . . . . . . . . . 175

11.7

Sensitivities with 2022 run dataset and further . . . . . . . . . . . . . . . . 176

11.8

Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178

Chapter 12Conclusion

181

Appendix A

Summary of commissioning runs

182

A.1

Commissioning run 2017 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182

A.2

Commissioning run 2018 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182

Contents

iv

A.3

Commissioning run 2019 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182

A.4

Commissioning run 2020 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

Appendix B

Optimization of weights for uniform online Eγ reconstruction

185

1

Chapter 1

Introduction
The Standard Model (SM) is a fundamental model that describes physics below the electroweakenergy scale precisely. However, it faces many problems, such as the hierarchy problem and dark
matter, and is considered to be a low-energy approximation of a more general theory. In building
such a theory, it is important to discover phenomena that are suppressed or prohibited in theSM, such as neutrino oscillations. In this context, charged lepton ﬂavor violation (cLFV), ﬂavor
mixing for charged leptons, has attracted much attention. This is because the cLFV is prohibitedin the SM while it is predicted to be detectable based on many promising new theories. Therefore
the discovery of the cLFV would be clear evidence of the physics beyond the SM.
The current upper limit on the branching ratio of the µ+ → e+ γ of 4.2×10−13 (90% C.L.) was
set by the MEG experiment [1]. The sensitivity of MEG was limited by the rate of accidental
backgrounds, and it motivated an upgraded experiment MEG II with detectors with improved
resolutions to achieve a higher sensitivity by one order of magnitude, O(10−14 ). In particular, theupgrade of the gamma-ray detector is important because the number of accidental backgrounds
greatly depends on the gamma-ray energy resolution. The MEG II liquid xenon (LXe) gammaray detector uses a new small photosensor VUV-MPPC to improve the position and energy
resolutions with the granular readout on the entrance face.
The detector performance studies with datasets collected in 2017–2020 with a limited readout
region are summarized in Ref. [2]. The energy resolution is estimated from the continuous
spectrum under a high-intensity muon beam, and the time resolution is estimated based on the
intrinsic time diﬀerence between the time reconstructed by using a diﬀerent set of photosensors.
The observations of unexpected radiation damage of the VUV-MPPC under a high-intensity
muon beam environment are described, and its impact on the detector performance is evaluatedwith simulations. The analysis of the background gamma rays implies that the fraction of
the events with two coincident background gamma rays is twice larger than expected from thesimulation, and it could lead to a worse sensitivity of the µ+ → e+ γ search.
Ref. [3] describes the suppression of accidental background with the LXe detector and a tagging
detector called RDC. A new analysis algorithm is developed to reduce the accidental backgroundusing the waveforms and the light distribution of the LXe detector. It implies that the measured
time resolution might be considerably worse than expected, possibly due to the systematic errorChapter 1 Introductionin the estimation. A measurement to suppress the systematic error to measure the resolution
accurately is proposed.
This thesis describes the full commissioning of the upgraded LXe detector, which can be
categorized into a few works as follows.
• Calibration measurements of the detector with the new VUV-MPPC.
• Performance evaluation of the gamma-ray measurement.
• Study of the rate and distributions of background events.
Calibration measurements for the VUV-MPPC are newly developed to monitor the performance of the VUV-MPPCs and to have stable, uniform, and precise gamma-ray reconstruction.
A novel measurement method of the MPPC positions was developed to measure the positions
with good accuracy and to suppress the systematic uncertainty of the gamma-ray position measurement.
The detector performance for the signal gamma ray with the full scintillation readout isunderstood by this work. Dedicated performance measurement was performed to collect 55 MeV
gamma rays from π 0 → γγ decay. The energy and time resolutions and detection eﬃciency forthe signal gamma ray are estimated by the measured performance for 55 MeV gamma rays. The
position resolution of the detector is estimated based on a measurement with 17.6 MeV gammarays.
The qualitative analysis of background events is essential to estimate the sensitivity of theexperiment. The pileup analysis algorithm is applied to the real dataset to identify pileup gamma
rays and reduce the rate of accidental backgrounds. The measured rate and distributions of the
background are studied, and they agree well with the rate and distributions of background eventsin MC simulation.
At the end of this thesis, the experimental sensitivity with the achieved performance and themeasured background rate in 2021 is estimated. It is proved that the search for the µ+ → e+ γ
decay with the highest sensitivity is achievable with the measured detector performance.
This thesis is organized as follows. In this chapter, the physics motivation of the µ+ → e+ γ
and the previous µ+ → e+ γ search in the MEG experiment are discussed. The experimental
setup of MEG II is introduced in Chap. 2. The situation of the 2021 run is summarized in
Chap. 3. The calibration measurements for the stable and precise gamma-ray reconstruction
are described in Chap. 4. The observation of the unexpected radiation damage of the VUVMPPC and our countermeasure, thermal annealing, are summarized in Chap. 5. The position,energy, and time resolution measurements are described in Chap. 6, Chap. 7, and Chap. 8,
respectively. The evaluation of the detection eﬃciency for the signal gamma-ray is explained in
Chap. 9. The analysis of the rate and distribution of background events is presented in Chap. 10.
The projected sensitivity of the MEG II experiment based on current estimates of the detector
performance will be discussed in Chap. 11. Finally, the conclusion of this thesis is given in
Chap. 12.

2

Chapter 1 Introduction

3

1.1 Physics motivation of µ+ → e+ γ search

Quark

I
u

up

d

Leptondown

𝜈#electronneutrino𝑒electron

Generation
II
c

charm

s

III
t

top

b

strangebottom

𝜈!

𝜈"

muon
neutrino

𝜇

muon

tau
neutrino𝜏

tau

Figure 1.1: Fermions and their mixing in the Standard Model (SM). There are 12 fermionsin three ﬂavors (generations). While the mixing between ﬂavors is observed for quarks andneutrinos, the mixing in the charged lepton sector has never been observed to date.

The Standard Model (SM) is a ﬁeld theory based on the fundamental fermions and the gauge
theory. The electromagnetic and the weak interactions are uniﬁed into a single SU(2)×U(1)electroweak interaction and the strong interaction is described by quantum chromodynamics(QCD, SU(3)) in this model. The SM has been veriﬁed by a wide variety of experiments sofar, and it successfully describes the physics of an energy range from O(1) eV to O(100) GeV.
However, the SM is considered to be only a low-energy approximation of a higher scale theory
beyond the Standard Model (BSM) because it faces both theoretical and experimental problems.
One of the theoretical problems of the SM is the hierarchy problem [4]. The hierarchy problem
is related to the huge diﬀerence between the weak scale (O(100) GeV) and the reduced Planckscale (O(1018 ) GeV). Since the SM Higgs mass parameter m is aﬀected by the presence offermion and boson particles with squared masses m2i + λ2i ϕ2 /2, where mi and λi are the massand the Higgs quartic coupling of the particle i, respectively, the running of the mass parameterfrom the scale µ to the scale Q is calculated as [5]m2 (Q) = m2 (µ) + δm2 ,X
Q2
λ 2 m2δm2 =gi (−1)2Si i 2i log( 2 ),
32π
µ
i

(1.1)
(1.2)

where the sum is over all particles and gi and Si correspond to the number of degrees of freedom
and the spin of the particle i. Particles that couple to the Higgs and have a large squared
mass parameter m2i would induce very large corrections to the Higgs mass parameter. This

Chapter 1 Introduction

4

nature requires a large ﬁne-tuning to keep m2 small. Hence, the mass of the Higgs boson is notprotected in the presence of heavy states at higher energy scales such as grand-uniﬁcation or
Planck scales. The SM also has several other theoretical issues, such as that the electro-weakforce and the strong force are not uniﬁed and that the SM does not account for the existence ofthe three generations of quarks and leptons shown in Fig. 1.1.
The SM is not complete also from the experiment point of view. The discovery of neutrino
oscillation [6, 7] and the existence of dark matter [8] are clear evidence of the incompleteness of
the SM.
In order to construct the theory that describes physics at the high energy scale beyond the SM,
it is important to search for phenomena prohibited in the SM and predicted by BSM theories.
One promising probe is charged lepton ﬂavor violation (cLFV) process, ﬂavor mixing between
charged leptons. As shown in Fig. 1.1, the ﬂavor mixing in the quark sector and in the neutrino
sector has already been observed, whereas the cLFV has never been observed. The discovery ofneutrino oscillation indicates that the lepton ﬂavor is not strictly conserved and implies that the
ﬂavor mixing process may occur in the charged lepton sector as well. In the following sections,the small branching ratio of the µ+ → e+ γ in the extension of the SM with neutrino oscillation
is explained in Sec. 1.1.1 and the detectable branching ratio in the BSM models is discussed inSec. 1.1.2.

1.1.1 µ+ → e+ γ decay through neutrino oscillation
The neutrino oscillation, transition in ﬂight between the diﬀerent ﬂavor neutrinos νe , νµ , ντ , isevidence of the nonzero neutrino masses and the mixing. The unitary transformation between
ﬂavor eigenstates and mass eigenstates of the neutrino can be written as,Xνα =Uαi νi(i = 1, 2, 3)

(1.3)

i

νi =

X

∗
Uαi
να

(α = e, µ, τ )

(1.4)

α

where να = νe , νµ , ντ are ﬂavor eigenstates and νi = ν1 , ν2 , ν3 are mass eigenstates with mass
eigenvalues m1 , m2 , m3 . U is a unitary matrix known as Pontecorvo-Maki-Nakagawa-Sakata(PMNS) matrix. The time evolution of the mass eigenstate of i after a time interval t can begiven by|νi (t)⟩ = e−iEi t |νi (0)⟩,(1.5)

where Ei is the energy of the mass eigenstate i. Thus the time evolution of ﬂavor eigenstate of
α is given by Eq. 1.3 and Eq. 1.5 as|να (t)⟩ =X

Uαi e−iEi t |νi (0)⟩.

(1.6)

i

The probability of ﬁnding ﬂavor νβ in να beam at a distance x from the source is given byPνα →νβ =Xi|Uαi |2 |Uβi |2 +

X
i̸=j

∗
∗
Uαi UβiUαjUβj cos(

2πx
)
Lij

(1.7)

Chapter 1 Introduction

5

where Lij = 2π/(Ei − Ej ) ≃ 4πp/|m2i − m2j | is the oscillation length.
While the cLFV is strictly forbidden in the SM, ﬂavor mixing in the neutrino sector is thesource of the cLFV in a simple extension of the SM with neutrino oscillations. The µ+ → e+ γ
decay occurs in a process through neutrino oscillation as shown in Fig. 1.2. The branching ratioof this process can be calculated as [9]3α X ∗∆m2i1
Uµi UeiB(µ → eγ) =232π i=2,3
MW2≃ 10−54 ,(1.8)

where α is the ﬁne-structure constant, MW is the mass of the W boson, ∆m2i1 is the massdiﬀerence of neutrinos. The branching ratio is very small and far from the experimental reachbecause the neutrino mass diﬀerence is very small compared to the mass of the W boson. Since
the cLFV processes are free from the SM and the neutrino oscillation background, the discoveryof the cLFV processes would be clear evidence of BSM.

W

γ

+

µ+

e+
νµ

νe

Figure 1.2: Feynmann diagram of the µ+ → e+ γ through neutrino oscillation.

1.1.2 µ+ → e+ γ in BSM models
The supersymmetric (SUSY) model is one of promising BSM models. The SUSY transformation is such that fermions are converted to bosons and bosons to fermions, and all particles
have supersymmetric partners. If such partners exist, the quantum corrections to the mass ofthe Higgs boson are canceled between the corrections due to fermions and the corrections due
to bosons, and the mass of the Higgs boson is protected without ﬁne-tuning. A SUSY partner is introduced to each SM particle in the minimal extension of the SM with SUSY called
MSSM. In the context of the SUSY, the SM particles and their superpartners have the same
mass when the SUSY is not broken. However, the superpartners with the same masses havenot been found, and thus the symmetry is broken. In the SUSY models, the source of theChapter 1 Introduction

6

cLFV is oﬀ-diagonal elements in the slepton mass matrix that comes from the misalignment
between particle and superparticle mass eigenstates. Here we present the oﬀ-diagonal elements
expected in two representative SUSY scenarios, SUSY-seesaw and SUSY-GUT, and then discuss
the expected branching ratio in a model incorporating both of them [10].
The seesaw model can naturally explain the extremely light neutrino masses with respect toother fermions by introducing heavy right-handed neutrinos. The SUSY-seesaw model introduces the seesaw mechanism to the SUSY model [11, 12]. In this model, Majorana right-handed
heavy neutrinos are introduced. The Yukawa coupling constant for the neutrinos becomes alarge source of the LFV. In this model, the LFV oﬀ-diagonal components are(me2lL )ij ≃ −1
MX),(3m20 + A20 )(Yν )ik (Yν† )jk ln(
2
8π
MRk

(1.9)

where MX is the scale of the SUSY breaking, m0 is the universal scaler mass, A0 is the trilinear
coupling, MRk is the mass of the right-handed Majorana neutrino, Yν is the Yukawa couplingof the neutrinos.
Another example is the SUSY-GUT model [13, 14]. A Grand Uniﬁed Theory (GUT) is amodel to unify the electroweak and strong interactions into a single force at the GUT scale.
In the SUSY-GUT model, the interactions are integrated with the help of the SUSY particles.
While the model with SU(5) symmetry, which is the simplest Lie group that contains the SM,
is already excluded by the longer lifetime of the proton than the prediction [15], many othermodels, including an extended version of SU(5) with SUSY, predict a longer lifetime and are
therefore not excluded. The oﬀ-diagonal terms of the right-handed slepton mass matrix are
2)i̸=j = −3(mR̃3m20 + A20
MX
Vti Vtk ln(
),
8π 2
MGUT

(1.10)

where V is the CKM matrix, MGUT is the mass scale of the GUT.
Ref. [10] calculates the branching ratio of the µ+ → e+ γ in a SUSY model incorporating
both grand uniﬁcation and see-saw mechanism, by paying attention to Casas–Ibarra parametersthat aﬀect the mixing structure of the neutrino Yukawa matrix. Fig. 1.3 shows the expectedbranching ratio of the µ+ → e+ γ on (m0 , tan β) plane [10]. It indicates that the current limitof the µ+ → e+ γ by MEG already excluded a part of the expected regions, and the extensive
search for the µ+ → e+ γ will explore the parameter space with higher m0 and lower tan β.

1.2 µ+ → e+ γ search in MEG experimentFig. 1.4 shows the progress of cLFV searches of three muonic channels, µ → eγ, µN → eN ,and µ → eee. The sensitivity of the muon cLFV search has been continuously improved withthe evolution of experimental techniques. The current upper limit on the branching ratio ofµ+ → e+ γ of 4.2 × 10−13 (90% C.L.) was set by the MEG experiment [1]. In this section,
the principle, experimental setup, and limitations of the MEG experiment are described. They
will help us to understand the approaches to realize the search for µ+ → e+ γ with the highest
sensitivity of O(10−14 ) in the upgraded experiment MEG II.

Chapter 1 Introduction

7

��

-��

-��

-��

-��

��

-�
-��

-��
-��

�
���

-��

-��

���

���

Figure 1.3: Expected µ → eγ branching ratio (orange) and electron electric dipole moment(green) on (m0 , tan β) plane [10]. The parameters are chosen as follows: the universal right
handed neutrino mass MNR = 1013 GeV, Casas–Ibarra parameters (r, θ, ϕ) = 2.2, π2 , 0 . Blacklines show the Higgs mass MH = 123, 124, 125, 126, 127 GeV from left to right. Orange andgreen dashed lines show the present limit of the µ+ → e+ γ branching ratio and electron electric
dipole moment.

1.2.1 Principle of µ+ → e+ γ search
The MEG experiment used positive muons to avoid the formation of muonic atoms and to
take full advantage of a high-intensity polarized muon beam. Since the µ+ → e+ γ is a two-bodydecay, a positron and a gamma ray are produced in opposite directions and at the same time.
The energies of the positron and gamma ray are well approximated to be half of the muon
mass (mµ c2 /2 = 52.8 MeV). Thus, the signal of µ+ → e+ γ can be searched for by measuring
the following variables and discriminating from backgrounds.
• Ee+ : energy of positron• Eγ : energy of gamma-ray• te+ γ : time diﬀerence between the positron and gamma-ray

Chapter 1 Introduction

Figure 1.4: Experimental upper limits (90% C.L.) on cLFV muon processes as a function of theyear where the µ → eee and µ → e conversion bounds are converted into equivalent µ → eγ
bounds [16].

• Θe+ γ : opening angle between the positron and gamma-ray
The relative angle between the positron and gamma ray is also deﬁned by the relative azimuthal
angle θe+ γ and polar angle ϕe+ γ .
To search for the rare µ+ → e+ γ decay with the highest sensitivity, a large number of muon
decays are necessary. The most intense DC muon beam at Paul Scherrer Institute (PSI) wasused. Since the accidental background is dominant in the search, a DC beam is better thana pulsed beam for collecting a large number of muon decays without increasing instantaneous
intensity. The MEG experiment employed a positron spectrometer and a liquid xenon (LXe)scintillation detector to detect a positron and a gamma ray from a µ+ → e+ γ decay at thetarget in the center of the detectors, as shown in Fig. 1.5.
Tracks of positrons were measured by 16 drift chamber modules [17], and the time of thepositrons was measured by timing counter arrays that consist of two layers of diﬀerent plastic scintillators along the beam axis [18, 19, 20]. Both detectors were placed in a thin-wall
superconducting solenoid magnet called “COBRA” (Constant Bending RAdius).
The gradient magnetic ﬁeld generated by COBRA (1.27 T at the center and 0.49 T at bothends) was designed such that the bending radius of the positron trajectory depends on the
momentum but almost not on the emission polar angle [21]. Only high-momentum positrons,
including the signal positrons, can reach the drift chamber and the timing counter.
The position, energy, and time of the gamma rays were measured by the LXe gamma-ray
detector outside of the COBRA [22].

8µ+ → e+ γ is particularly sensitive to new physics. The
MEG collaboration has searched for µ+ → e+ γ decay at
the Paul Scherrer Institut (PSI) in Switzerland in the period
2008–2013. A detailed report of the experiment motivation,
designcriteria,
goals is available in reference [3,4] andChapter
1 andIntroductionreferences therein. We have previously reported [5–7] results

to the square of the µ+ decay rate, the signal to backgroundratio and data collection efficiency are optimised by using
a direct-current rather than pulsed beam. Hence, the highintensity continuous surface µ+ beam (see Sect. 2.1) at PSI
9
is the ideal facility for such a search.

Fig. 1 A schematic view of the MEG detector showing a simulated event

Figure 1.5: Schematic view of the MEG experiment [23]. The top view (left) and view fromdownstream (right) are shown. The track and time of positrons (red) are measured by the drift
123chamber and timing counter, respectively. Gamma rays (blue) are measured by the liquid xenon
scintillation detector.

Differential Branching Ratio

Differential Branching Ratio

1.2.2 Backgrounds
2
1.5
1
0.5
0
0

0.2 0.4 0.6 0.8
1
Normalized Positron Energy (x)
(a)

1
10−1
10−2
10−3
10−4
10−5
10−6
0

0.2 0.4 0.6 0.8
1
Normalized Photon Energy (y)(b)

Figure 1.6: (a) Simulated energy spectrum of the Michel positron [24]. (b) Simulated energy
spectrum of the RMD gamma ray. Energies on the x-axis are normalized to the half of the muon
mass (52.8 MeV).

There are two kinds of backgrounds that have a similar event signature to the signal. One
is physics background from the radiative muon decay (RMD, µ+ → e+ νe ν̄µ γ), and the other isaccidental background.

Chapter 1 Introduction

1.2.2.1

10

Physics background

When the two neutrinos from the RMD have little energy, a pair of a gamma ray and a positron
is simultaneously emitted nearly in the opposite direction and with signal-like energies. Thus it
imitates the µ+ → e+ γ signal. The diﬀerential branching ratio of this physics background was
calculated within the framework of V−A interactions described in Ref. [25]αdyβdx dΩe dΩγ [F (x, y, d)dBRMD µ+ → e+ νe ν̄µ γ =364πy− β P⃗µ · p̂e G(x, y, d)i−P⃗µ · p̂γ H(x, y, d) ,(1.11)(1.12)(1.13)

where P⃗µ is the muon polarization vector, p̂e and p̂γ are the unit vectors of momenta of thepositron and gamma ray, respectively, β is deﬁned as β ≡ |⃗pe |/Ee+ , d is given by d ≡ 1 − β p̂e · p̂γ ,and x and y are normalized positron and gamma energies, x = 2Ee+ /mµ and y = 2Eγ /mµ . The
formulas of F (x, y, d), G(x, y, d), and H(x, y, d) in the SM are given in Appendix A of Ref. [26].
In addition, we deﬁne here z as z ≡ π − Θeγ . In this notation, an RMD event with x ≈ 1,y ≈ 1, and z ≈ 0 becomes a physics background event. Let us take δx, δy, and δz to be thekinematic range of the signal region for positron energy (1 − δx ≤ x ≤ 1), gamma-ray energy(1 − δy ≤ y ≤ 1), and the opening angle (0 ≤ z ≤ δz), respectively. Then, the partial branchingratio is given as



α 
dB µ+ → e+ νe ν̄µ γ =J1 1 − Pµ+ cos θe+ + J2 1 + Pµ+ cos θe+ d (cos θe+ ) , (1.14)
16π√when the angular resolution is better than the kinematic constraint δz < 2 δxδy. J1 and J2
are given by
2
 4
 8
δz
δz
1 1
δz
2
− 2(δx)+,222
3 (δy)
2
 2
 4
 6
δz
δz
8 δz
2
2
J2 = 8(δx) (δy)− 8(δx)(δy)
+
.
2
2
3 2
8
J1 = (δx)3 (δy)
3(1.15)(1.16)

When we use the detector resolutions (δx ∼ 0.07, δy ∼ 0.02, δz ∼ 17 mrad) and muon polarization (−0.86) in the MEG experiment [1], the eﬀective branching ratio of the physics backgroundis the order of O(10−15 ). Thus, the physics background is not a problem to achieve a sensitivityof O(10−14 ).
1.2.2.2

Accidental backgroundAn uncorrelated pair of a positron and a gamma ray can mimic the signal by an accidental
coincidence when they are emitted nearly in the opposite direction and have signal-like energies
at a close time. The eﬀective branching ratio of the accidental background can be estimated asδωe+ γ00Bacc = Rµ · fe+ · fγ ·· 2δte+ γ ,(1.17)
4π

Chapter 1 Introduction

11

where Rµ is an instant muon intensity, δte+ γ is half width of the signal region for time coincidence, δωe+ γ is that for back-to-back constraint. The terms fe0+ and fγ0 are the fractions of thespectrum within the signal box of positron and gamma ray, respectively. The source of background positrons is Michel decay, µ+ → e+ νe ν̄µ . Michel decay provides high energy positrons
abundantly, as shown in Fig. 1.6a. Since the spectrum is almost ﬂat at x ≈ 1, fe0+ can be
estimated as fe0+ ≈ 2δx.
The background gamma rays can come from RMD, annihilation in ﬂight (AIF) of positrons,
and bremsstrahlung of positrons. The diﬀerential branching ratio of the gamma ray from the
RMD is given by Ref. [25]dB (µ+ → e+ νe ν̄µ γ)
1= [J+ (y) (1 + Pµ cos θγ ) + J− (y) (1 − Pµ cos θγ )] ,dyd cos θγy(1.18)

where θγ is the angle between muon polarization and γ momentum. Terms suppressed by me /mµ
are neglected. J+ (y) and J− (y) are deﬁned by Ref. [25] asα
1 − y 17
J+ (y) = (1 − y) 3 ln
−
6π
r
2


1−y
+ 7 (1 − y)+ −3 lnr
1 − y 132
+ 2 ln−(1 − y)r3
1 − y 93α23 ln−
J− (y) = (1 − y)
6π
r
12


1 − y 29
+ −4 ln+(1 − y)r3
1 − y 55−
(1 − y)2+ 2 lnr
12(1.19)(1.20)

where r = (me /mµ )2 . Fig. 1.6b shows the theoretical energy spectrum of the RMD gammaray. In contrast to the Michel spectrum, the spectrum rapidly decreases with the energy. By
integrating the diﬀerential branching ratio by neglecting the higher order terms of (1 − y), fγ0
purely from RMD gamma ray can be calculated asfγ0 ≈α(δy)2 [ln(δy) + 7.33].
2π(1.21)The source of the AIF gamma ray is the interaction of Michel positrons with the material of
the apparatus, such as the drift chamber and target. The contribution of the AIF gamma ray tothe sensitivity depends on the design of the experiment. In the MEG experiment, contributions
from the two processes (RMD and AIF) were comparable.
The eﬀective branching ratio of accidental background (a Michel positron and an RMD gammaray) can be approximately calculated by the discussions above asαBacc = Rµ · 2δx ·(δy)2 [ln(δy) + 7.33] ·
2π



(δz)2
4




· 2δte+ γ .

(1.22)

Chapter 1 Introduction

12

With the parameters in MEG, the eﬀective branching ratio is O(10−13 ). This calculation indicates that the accidental background must be reduced by an order of magnitude to achieve thesearch for µ+ → e+ γ with a sensitivity of O(10−14 ).

1.2.3 Sensitivity
The expected number of signal events in an experiment Nsig can be formulated as
Nsig = B × Rµ × T × Ω × ϵe+ × ϵγ × ϵsel
= B × k,(1.23)(1.24)

where T is the livetime of the measurement, Ω is the solid angle subtended by the acceptanceof the detector, B is the branching ratio of µ+ → e+ γ, ϵe+ and ϵγ are the detection eﬃciency of
positron and gamma-ray, respectively. ϵsel is the eﬃciency of event selection. k is the inverse of
the single event sensitivity (SES).
The MEG experiment collected physics data from 2008 to 2013. The sensitivity was updated
in steps as shown in Fig. 1.7 [27]. The improvement of the sensitivity slowed down as thestatistics were accumulated because the eﬀective branching ratio of the accidental backgroundwas dominant over the SES. As discussed in Sec. 1.2.2, the number of accidental backgrounds
heavily depends on the detector resolutions. Though a high-rate muon beam up to 1 × 108 /s
can be provided to the experimental setup [28], the beam rate in MEG was limited to 3.3 ×
107 /s to mitigate the rate of the accidental background that increases with the worse detector
performance at a higher intensity. To search for the µ+ → e+ γ with the higher sensitivity ofO(10−14 ), the resolutions for both positron and gamma-ray measurement must be improved toreduce accidental background.

Chapter 1 Introduction

13

Branching ratio

Chapter 10. Conclusion

MEG 2009
Obtained 90% UL

MEGA
90% UL sensitivity

10−11

±1 σ
±2 σ

MEG 2011

10−12

MEG 2013
MEG Final

10−13
0

50

100

150

200
250
300
Accumulated DAQ days

FigureImprovementof search
Figure 1.7: Observed
90%10.1:
upper
limit (pinkcircle)sensitivityof the µof+ MEG→ e+experiment.
γ in the MEG experiment

as a function of the accumulated livetime of the experiment [27]. The black solid line shows the
90% upper limit sensitivity, and 1σ and 2σ bands are shown in green and yellow, respectively.

132

14

Chapter 2

MEG II Experiment
In this chapter, the experimental apparatus of the MEG II experiment is explained. The
detectors are shown in Fig. 2.1. The main upgrades from the MEG experiment are listed asfollows:• Improvement of the detector resolutions.
• Improvement of the positron detection eﬃciency.
• Installation of a radiative decay counter (RDC) to tag RMD gamma rays.
The global coordinate is deﬁned as follows. The z-axis is parallel with the beam axis, they-axis is perpendicular to the ground, the x-axis bisects both y and z axes at right angles. The
origin of the coordinate is the center of the COBRA magnet.

2.1 Beam & Target
2.1.1 Beamline
The MEG II experiment is being carried out at the πE5 beamline at PSI, where the world’s
most intense continuous muon beam is available.
The ring cyclotron at PSI can supply a 590 MeV proton beam of 2.2 mA. The current of the
proton beam was limited to 1.9 mA in the 2021 run because of the limitation of the beam dump.
In the 2022 run, the proton beam current was even lower at 1.76 mA because one of the threecavities for the beam injection was broken. The proton beam is injected into a pion production
target (target E) made of 4 cm-thick graphite, and positive pions are produced through a reaction
such as p + p → p + n + π + .
The muons from pion decays (π + → µ+ +νµ ) around the surface of the target within a few µm
is called surface muons. A surface muon has a low energy loss and a trivial depolarization during
a short path length in a target and has an upper edge of its momenta of 29.8 MeV. The low
momentum of the surface muons (28 MeV) with a good momentum byte of about 7% (FWHM)
enables us to stop the muons by a thin target.
A Wien-ﬁlter (often called Separator) is installed in the πE5 beam line to separate positroncontamination in the muon beam, which comes from the Michel decay of the muon and the π 0Chapter 2 MEG II Experiment15

Liquid xenon photon detector
(LXe)

COBRA
superconducting magnet

Pixelated timing counter(pTC)
Muon stopping target
Radiative decay counter(RDC)

Cylindrical drift chamber(CDCH)

Figure 2.1: Schematic view of the MEG II experiment [29]. A high-intensity µ+ beam is stopped
at the muon stopping target (red) at the center. The track and time of positrons (blue line)
are measured by the cylindrical drift chamber (CDCH) and pixelated timing counter (pTC),
respectively. The energy, position, and time of gamma rays are measured by the liquid xenon
photon detector. The radiative decay counter (RDC) for tagging background is installed in thedownstream.

Figure 2.2: Schematic view of the πE5 beam line and the MEG (II) experimental area [29]. The
production target E and the πE5 area are connected by the πE5 channel shown on the left.
The MEG beam line is composed of a Wien ﬁlter, two sets of quadrupole triplet magnets, anda collimator system to eliminate beam contamination. The ﬁnal momentum adjustment andfocusing are performed by the BTS, before the muons are stopped in an ultra-thin target placedat the center of the COBRA positron spectrometer.

Chapter 2 MEG II Experiment
decay in the target.
A superconducting Beam Transport Solenoid (BTS) is installed to deliver the muon beam to
the MEG II detectors. It applies a magnetic ﬁeld to focus the beam. A degrader made of 300 µm
thick Mylar is placed at the center of the BTS to adjust the muon momentum.
Three systems are used to measure the beam proﬁle and rate. One system is a quasi-noninvasive detector based on scintillation ﬁbers (SciFi) coupled to Silicon Photomultipliers (SiPM),
the second system is a non-destructive system based on a thin CsI(Tl) scintillation foil (luminophore) and a CCD camera, and the third one is a 9×9 matrix of small scintillation counterscalled “MatriX” detector.
The maximum muon beam rate is (1.11 ± 0.01) × 108 /s when the proton current is 2.2 mA.
The stopping rate was adjusted to be 2–5×107 /s during the physics data-taking in the 2021 run.
The lowest beam rate in the 2021 run was 1×106 /s, which was used to investigate the muon
decay events with a low pileup condition. The beam proﬁles were σx ∼ 12 mm and σy ∼ 12 mm
at the muon stopping target.
The beam rate in the physics run is optimized to achieve the best sensitivity based on thedetector performance. The following items must be taken into account.
• Radiation damage of the VUV-MPPC of the LXe detector.
• Performance of positron and gamma-ray measurement.
As later discussed in Chap. 5, the radiation damage of the VUV-MPPC was observed through aseries of commissioning runs. Since the detector resolutions for the signal gamma ray deteriorates
with a degraded PDE (<0.04), the beam rate must be adjusted so that the MPPC PDE stays
higher than 0.04. While this constraint was taken into account in the 2021 run, our experimentis not limited by this constraint from the 2022 run because the annealing procedure for all VUVMPPCs was established at the beginning of 2022, and most MPPCs have a high PDE throughthe beam time by annual annealing. Another point is the performance of positron and gammaray measurements. Though the detectors are designed to measure positrons and gamma rays
with good resolutions under a high-intensity muon beam environment, the actual resolutions
and eﬃciencies, particularly for positrons, are worse at higher beam rates. In particular, theanalysis eﬃciency of positrons gets worse at higher beam rates. In this thesis, it is supposed thatthe physics data will be collected at the beam rate of 5 × 107 /s in the future data acquisition.
This is because a higher beam rate than 5 × 107 /s would not be beneﬁcial in terms of sensitivity.
While the rate of accidental backgrounds increases as the beam rate increases, the rate of theeﬀective number of muons for the µ+ → e+ γ search does not increase because of the beam ratedependence of the positron analysis eﬃciency.

2.1.2 Muon stopping target
The muon-stopping target is placed at the center of the COBRA magnet. There are two tradeoﬀ requirements for the target. One is to maximize the muon-stopping eﬃciency, and the other16

Chapter 2 MEG II Experimentis a small material budget to avoid multiple scattering, annihilation, and bremsstrahlung of theemitted positrons. A 174 µm thick plastic scintillating ﬁlm in Fig. 2.3 is used, and it is tilted
at an angle of 15◦ with respect to the beam axis. This conﬁguration realizes a longer eﬀective
thickness for the muon beam and a shorter thickness for positrons. In the MEG experiment,a distortion of the target during the data-taking was a dominant systematic uncertainty in thereconstructed positron direction. To suppress the systematic uncertainty, the ellipse plasticﬁlm is supported by a rigid carbon-ﬁber frame of 200 µm thick and a system to monitor the
distortion is implemented. Optical markings are printed on the target and are monitored by
CCD cameras [30][31].

Figure 2.3: Muon stopping target for the MEG II experiment [29]. An ellipse plastic ﬁlm of
174 µm thick with holes is supported by a rigid carbon-ﬁber frame of 200 µm thick.

2.2 Positron Spectrometer
The MEG II positron spectrometer is composed of the COBRA magnet, cylindrical drift
chamber (CDCH), and pixelated timing counter (pTC).

2.2.1 COBRA magnet
The MEG II experiment reuses the COBRA magnet used in MEG. The magnetic ﬁeld in
the COBRA magnet ranges from 1.27 T at the center to 0.49 T at the edge (z ∼120 cm). The
concept of the magnetic ﬁeld is shown in Fig. 2.4. Thanks to the gradient magnetic ﬁeld along
the beam axis shown in Fig. 2.5, the positrons with the same momentum have almost constantbending radii independently of their emission angles. This leads to a high detection eﬃciencyof high-energy positrons, while uninteresting low-energy positrons are quickly swept out of thedetector system.
Fig. 2.6 shows the design of the COBRA magnet. A superconducting solenoidal magnet
with a step structure of diﬀerent radii forms the gradient magnetic ﬁeld [21]. A high-strength
superconducting cable of the COBRA magnet consists of a NbTi multi-ﬁlament embedded ina copper matrix and aluminum stabilizer. The operating temperature of the coil is about 5 K.

17

turn repeatedly in the spectrometer. The hit rates of Michel
positrons expected for the gradient and uniform fields arecompared in Fig. 14 and indicate a significant reduction for�����������������
the gradient
field.
Chapter 2 MEG II Experiment
18
The central part of the superconducting magnet is as thin
as 0.197X0 so that only a fraction of the γ -rays from theAt both ends of the
COBRA,a pairof reaching
two large
coils cancel
the stray ﬁeld aroundtargetinteracts
beforetheresistive
LXe detector
placed outthe photomultiplierside
tubes(PMTs)of COBRA
the LXemagnet
detector
lessFig.
than
as shown in Fig. 2.7.
COBRA.
The
(see
15)50
is Gauss
equippeda pairis ofcompensationcoils
to reduce
the stray field
The thickness of thewithmagnetlimitedto 0.197 X
the acceptanceof the LXe detector so
0 withinarounddetector
for the operationof thethe PMTs.
������������
that the gamma rays
fromthetheLXetargetcan
traverse,
thanks tosmall material budget of the
The parameters of COBRA
are listed in Table 2.
�������������
support structure.

��������������
��������������

Fig. 15 Cross-sectional view of the

3.2 Design

3.2.1 Superconducting magne���������������

The gradient magnetic field ran
tre to 0.49 T at either end oferated by a step structure of fi
gure 3.15: Designof the COBRA magnet [26].
Figure 2.4: Positron trajectory in COBRA B-ﬁeld [32]. The MEG detectors areradiidrawn.
(one central coil, two gra(Fig. 16). The field gradient i
radii of the coils and the windi
The coil structure is conductive
refrigerators attached to the e
1.2
d measured here
Gifford–McMahon (GM) refr
power of 1 W at 4.2 K. The
Photon detector(LXe)
1.1
coil is carefully designed in term
and the thermal conductivity. T
1Compensationcoil structure as thin as possi
coil
0.9
conductor on a thin aluminium
Figure 17 shows the layer strucFig. 0.8
13 Concept of the gradient magnetic field of COBRA. The
has the highest current density
positrons follow trajectories at a constant bending radius weakly deEnd coil
is wound in four layers inside
0.7 on the emission angle θ (a) and those transversely emitted
pendent
Gradient coil
Central coilsupport cylinder. Pure alumini
from the target (cos θ ∼ 0) are quickly swept away from the DCH (b)Bz (T)

��

0.6

0.5
0

0.2

0.4

0.6

0.8
1
1.2
Distance along axis (m)Figure 2.5: Magnetic ﬁeld of the COBRA along the beam axis [21]. The magnetic ﬁeld strength
COBRA magnetic
field
Figure3.17: (z=0)
Magnetic(Bzof) thealong
is 1.25 T at the centerof the magnet
and 0.5 T fieldat the end
magnet (z=1.2 m).
beam axis (x = y = 0).

ber

2.2.2 Pixelated Timing Counter (pTC)
The pixelated timing counter (pTC) is designed to measure the time of positrons with a numberof pixel counters, each of which consists of a fast scintillator and SiPMs. The pixel counters areformance arranged so that a single positron track crosses many counters, and a good resolution can beachieved by combining time measurements at each counter. Another important role of the pTCCH) measures a momentum, a decay vertex and an emission angle
is to generate the trigger signal because the CDCH cannot provide a fast enough signal due toproperty of a positron is determined by the timing counter at themain purpose of DCH is to obtain the track of a positron. We
for the MEG positron tracker:

Chapter 2 MEG II Experiment

Figure 2.6: The design of the COBRA magnet in side view (left) and top view (right) [21].
The superconducting solenoid magnet has a step structure of diﬀerent radii. There are twocompensation coils at both ends to cancel the residual magnetic ﬁeld that aﬀects the PMTs of
the LXe detector.

the latency introduced by the drift time.
The pTC has two modules consisting of 256 pixel counters, one each for upstream and downstream. The pixel counters are tilted by 45◦ to the beam axis so that they are nearly perpendicular to the positron tracks, and are cylindrically arranged in 16 lines as shown in Fig. 2.8.
Fig. 2.9 shows a single pixel counter. Each pixel counter is 120 × 40/50 × 5 mm3 fast plastic
scintillator (BC422, Saint-Gobain) coupled to six SiPMs from AdvanSiD (ASD-NUV3S-P HighGain (MEG)) at both sides. The SiPMs at each side are connected in series to realize a fast
response which is essential to achieve a good time resolution.
√
The overall time resolution is σtsingle / Nhit , where σtsingle is the time resolution of a counter(<100 ps). Nhit is the number of hit counters, which is nine on average for signal positrons.
The time resolution of the pTC was measured with Michel positrons in 2017. A resolution of
better than 40 ps was achieved for events with more than 6 hits. The overall resolution for
signal positrons is estimated to be 40 ps, by weighting the number of Nhit distribution obtainedby MC [33].

19Figure 3.15: Design of the COB
20

Bz (T)

Chapter 2 MEG II Experiment

Stray field measured here

26.5mT11.5mT

Photon detector(LXe)

1

1

5mT
Compensationcoil

60.8mT

0

0.14T

0
0.32T
1.7T

End coil
Gradient coil
Central coil000Figure 2.7: Magnetic ﬁeld in- and outside of the COBRA magnet [21]. The magnetic ﬁeld at
the LXe detector is cancelled by the compensation coils at both ends of the COBRA magnet.

Figure 3.16: Map of COBRA magnetic field
Fig
[26].
bea

3.4

Drift chamber

3.4.1

Required performance

The drift chamber (DCH) measures a momentum,
Figure 2.8: Timing counter module assembled with 256 pixel counters. The pixel counters areof a positron. A time property of a positron is det
shielded by black sheets.
end of its track. The main purpose of DCH is torequire following items for the MEG positron trackChapter 2 MEG II Experiment

Figure 2.9: A scintillator tile used for pTC. (left) 40 mm height tile with reﬂector wrapping,(right) 50 mm height tile before wrapping. An optical ﬁber for the calibration using laser isinserted into the tile [29].

2.2.3 Cylindrical Drift Chamber (CDCH)

Figure 2.10: Drift chamber with all wires [29].

The drift chamber of the MEG II experiment is a single volume detector with cylindricalsymmetry along the µ+ beam axis [34],[35]. It is designed to achieve a good tracking performanceby dense stereo wires while positron scattering is suppressed thanks to the low material budget.
Fig. 2.10 shows the drift chamber before the installation. The length is 1.91 m, and the radialwidth ranges from 17 to 29 cm.
Fig. 2.11 shows the drift cell conﬁguration of the CDCH. The readout has nine layers of 192
drift cells, with four times as many hits as MEG per signal-positron track on average. In eachdrift cell, one sense wire is surrounded by ﬁeld wires. The size of the drift cell is 5.8–8.7 mm, andit increases linearly in the radial direction and varies in z. The ratio of the number of ﬁeld wires
to sense wires is ﬁve, and there are ∼12,000 wires in total. Sense (ﬁeld) wires is gold-plated
tungsten (silver-plated aluminum) and their diameter is 20 (40 or 50) µm The sense wire is readout from both ends, which makes it possible to reconstruct the hit position along the wire byboth charge division and the time diﬀerence between the two readouts.

21Chapter 2 MEG II Experiment

Figure 2.11: Drift cell conﬁguration at the center of the CDCH [29]. Red wires and blue wires
are with diﬀerent stereo angles. The ﬁeld wires between the layers form a mesh structure. 40 µm
wire is adopted for the ﬁeld wire. The actual CDCH has nine layers instead of ten.

The sensitive volume is ﬁlled with a low-mass gas mixture. The gas mixture in the 2021 run
was He/iC4 H10 /O2 /2-propanol (88.5%/9.8%/0.5%/1.2%). Isobutane plays an important rolein preventing self-sustained discharge. Small amounts of oxygen and 2-propanol were added to
improve operational stability. The material budget per positron turn is 1.5×10−3 X0 , while itwas 2.0×10−3 X0 in the MEG drift chamber.

22

Chapter 2 MEG II Experiment23

2.3 Liquid Xenon gamma-ray detector
2.3.1 Overview
The MEG II LXe gamma-ray detector uses 900 ℓ of LXe together with 4,092 VUV-MPPCs
and 668 PMTs to achieve good resolutions for the gamma-ray position, energy, and timing withhigheﬃciency.
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
Figure 2.12:
Development view of the MEG II LXe detector [3]. The directions of the axes of
directions of the local coordinate on the detector.

the local coordinates are shown in red. The inner surface of the detector is covered by six faces
called inner, outer, upstream, downstream, bottom, and top faces, respectively.
uniform response than a crystal scintillator.

2.3 Properties of LXe.
Fig. 2.12 illustrates the layout ofTable
MPPCs
and PMTs in the detector. The six faces are called

Value
inner, outer,Item
upstream, downstream, bottom, andtop faces, respectively. The local coordinate
AtomicNumber54 2.1–2.3 and illustrated in Fig. 2.12. R is thesystem of thedetector(u, v, w) is deﬁned as Eq.
in3

Density
2.953ofg/cm[51]
radial distancefrom the beam axis to the surface
the photosensors
on the inner face, which

is 64.84 cm.

Radiation length2.872 cm [51]Moliere radius

5.224 cm

u=z
Scintillation Wavelength (mean)

174.8 ± 0.1(stat.) ± 0.1(syst.) nm [52]v = arctan(−y/x)
× Rin ± 0.2(syst.) nm [52]Scintillation Wavelength (FWHM)
10.2 ± 0.2(stat.)
Decay time (fast)

w=

p

[53]
x2 +4.2y 2 ns−Rin

Decay time (slow)

22 ns [53]The acceptanceof timethe detector
is deﬁned as
Decay(recombination)

45 ns [53]W-value for electron

21.6 eV [54]W-value for alpha

(2.1)
(2.2)
(2.3)

|u| < 23.9 cm(2.4)|v| < 67.9 cm(2.5)

0 cm < w < 38.5 cm(2.6)

17.9 eV [54], 19.6 eV [55]Refractive index (for λ = 175 nm)

1.65

Critical energy

14.5 MeV [56]The ﬁducial volume is 800 ℓ, subtending 11% of the solid angle viewed from the center of theAnotheradvantage is its transparency against its own scintillation light. When a particle
stopping
target.
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

Chapter 2 MEG II Experiment

24
1200

100
80

100

60

80

40

60

20

40

0

20

494

203

84

0

34

-20
14

-40
-60

5

-80
2

-100
-100

0

100

200

300

z

1

(a)
1200

100
80

100

60

80

40

60

20

40

0

20

494

203

84

0

34

-20
14

-40
-60

5

-80
2

-100
-100

0

100

z

200

300
1

(b)

Figure 2.13: Light distribution for the same gamma-ray event in development view in (a) MEG
and (b) MEG II in MC simulation [29].

Compared to the MEG LXe detector that used 216 PMTs for the scintillation readout of theinner face, the MEG II LXe detector has a granular and uniform scintillation readout of theinner face by 4,092 VUV-MPPCs. Fig. 2.13 shows the light distribution of the MEG (II) LXe
detector for the same gamma ray in MC simulation. It indicates that the imaging power of thescintillation is greatly improved with smaller photosensors. This upgrade improved the positionand energy resolutions for gamma-ray hits close to the inner face, as later presented in Chap. 6
and Chap. 7.

2.3.2 Liquid xenon
Table 2.1 summarizes the properties of LXe. LXe has several advantages in detecting the52.8 MeV signal gamma rays. Thanks to the high density, short radiation length, and small
Morielle radius, gamma rays are stopped eﬃciently and the electromagnetic shower is largely
contained in a reasonable size of the LXe volume.
When ionizing radiation is injected into xenon, excited atoms (Xe∗ ) or ions (Xe+ ) are generated. Correspondingly, there are two types of scintillation processes with diﬀerent W-values andtime constants. In the fast scintillation process with time constants of 4.2 ns and 22 ns, excitedChapter 2 MEG II Experiment

25

Table 2.1: Properties of liquid xenon
Atomic number

54

Atomic weight131.293 [36]3Density [g/cm ]2.95 [37]Radiation length[cm]2.77 [36]Critical energy [MeV]

14.5 [38]Morielle radius [cm]

4.2 [38]

W-value for electron [eV]21.6 [39]W-value for α-particle [eV]19.6 [39]

Scintillation Wavelength (mean) [nm]174.8±0.1(stat.)±0.1(syst.) [40]Scintillation Wavelength (FWHM) [nm]10.2±0.2(stat.)± 0.2(syst.) [40]Rayleigh scattering length [cm]

45 [41]

Refractive indices1.69 [42]atoms form excited xenon molecules immediately, and scintillation photons are emitted.
Xe∗ + Xe + Xe → Xe∗2 + Xe

(2.7)

Xe∗2 → 2Xe + hν

(2.8)

The scintillation from the recombination process with the electron and ions has a longer time
constant of 45 ns [43].
Xe+ + Xe → Xe+
2
∗∗
−
+ Xe
Xe+
2 + e → Xe
∗∗
∗

Xe

(2.10)→ Xe + heat

(2.11)+ Xe + Xe → Xe∗2 + Xe
Xe∗2 → 2Xe + hν

(2.12)

Xe

∗

(2.9)

(2.13)

In both processes, a scintillation photon is emitted from the excited state of the Xe molecule
via Xe∗2 → 2Xe + hν. Fig. 2.14 shows scintillation signals by diﬀerent ionization particles [43].
While scintillation processes with a short time constant dominate for alpha particles, rather
slower processes with 45 ns time constants dominate for electrons. One can perform particle
discrimination by scintillation signal waveform. As shown in Fig. 2.15a, pair creation is thedominant process around the energy of the signal gamma ray.
The number of scintillation photons is suﬃcient to achieve a good energy resolution thanks
to the small W-value of 21.6 eV and the absence of self-absorption. A good time resolution isachievable thanks to the fast response.
On the other hand, it also has a few diﬃculties as follows.
• Xenon must be stably cooled down to a low-temperature (165 K) to stay liquid.
• The light yield of LXe is sensitive to impurities.
• The Rayleigh scattering length of LXe is short and inconsistent with the theoretical value.

Chapter 2 MEG II Experiment

26

AKIRA HITACHI et al.

27

10maller than the present values. Kubota
Liq. Xe~Q
Carvalho and Klein also reported smallr a-particle excitation.
for this disagreement is not well unpresent. A possible reason is a differ10
temperature and impurities. The enerstates in argon is relatively large andtates are likely deexcited by collisions
s. According to our experience, nonn showed a shorter lifetime for X~+.
10been reported that a few tens ppm ofor Setupcarbonuch as nitrogen,oxygen, and
32
3. Detector
n lead to a substantial reduction in ininescence originating from low excited
Table 5: Properties of LXe.
tes in condensed argon. 'of the Properties
singlet states
ty ratios Iz/Iz Material
Value & Unit
Ref.
AtomicNumberto be 0.3,
54
are found
triplet states ( X~+)
Atomic Weight131.293[31]
and fissionfor electron, a-particle,
Densityand
at 161.4
2.978 g/cm3[32]
thisK result
citation, respectively,
Boiling point
165.1 K
[31]
formation
ancement of 'XN+Melting
point in higher
161.4 K
[31]
This
shows theergy density.
Tripleresult
point (temperature)
161.3 K[33]
et al. 'point (pressure)0.805 atm
[33]
s results obtained Triple
by Kubota
Radiation
length and a2.77 cm[31]
electronand Klein' under
14.5 MeV[34]
and xenon.
tion for condensedCriticalargonEnergy
Mollier radius
4.2 cm[34]
and the slow (1.6
to the fast (7 nsec)
Scinti. wavelength (peak±FWHM)(17810± 14) nm
[35]
0
50
100
150
an intermediate
component
nents,
Refractive index
at 175 nm
1.57 to 1.72
[36, 37, 40]Time(nsec)
40ph nsec
was observed.
for electron
21.6 eV[38]
decay time of 20 W
α particles
17.9 eV
10 20%%uoof this componentWph isforabout
FIG. 4. Decay[38]curves obtained for the luminescence
Decay time (recombination)
45 ns
[39]
rehas
been
ntensity. This component
from
xenon
excitedFigure2.14:
LXe
scintillation
signalsbyelectrons(circle),rays(k),(triangle), ﬁssion fragments
liquida particles(0),alphaby electrons
Decay time (fast components)
4.2 ns[39]
Kubota et al. ' inDecay
thetimerecombination
andfragments(slow components)
22 fission
ns[39] (8).
(square) [43].
The solid lines
show the double exponential curves ﬁtted to signals.
The origin
under electron excitation.
Absorption length> 100 cm
length29 cm to 50 cm [40, 41, 42, 43]
at present.
nent is not knownScattering
The ratios I~/I~ are found to be 0.45+0.7 and
6+0.
1.
2 under a-particle and fission-fragment exciB. Liquid xenon
tation, respectively, showing an enhancement of 'X~+
curves obtained under a-particle andformation with higher deposited energy density.
nt excitation in liquid xenon showed
Total Attenuation
nential decay forms. Typical decay
d for liquid xenon are shown in Fig. 4.
Liq. Xe
10electron
obtained for 'X~+ under a-particle andnt excitation are 4. 3+0.6 and 4. 3+0.5
ely, and those for X„+ are 22+1 5 andespectively, and agreed within experiPhotoelectric Absorption
The values obtained under a-particle
6oreed with those reported by Kubota
results are listed in Table II.
O
Scattering
Pair
4
Production
ependence of luminescence from liquidby electrons is shown in Figs. 4 and 5,
Photon Energy [MeV]
different from those observed under afission-fragment excitation. Figure
The 3.30:
curve
Photon reaction in liquid xenon.
(b)(a)
vely slow rise and does not follow an
0orm. Kubota et al. ' reported that thisTime
(psec)
eleccomponent disappears
Figure when
2.15:an(a)Photon cross section of xenon as a function of photon energy [44]. The
applied. Therefore, it is clear that the
FIG. 5. Variation ofwhere is the luminescenceof the pair intensity,
production(dottedline)
is dominant
overex-the photoelectric absorpdue to a contribution
component is cross-section
obtainedunder electronof timeas a function
mbination.
citation for liquid xenon. See Ref. 19.

i

CA

'

I

—

I

2

Attenuation Coefficients [cm / g]

—

~

I

I

',

I

tion (dashed dotted line) and Compton scattering (dashed line) at the energy of the signal gamma

ray (52.8 MeV). (b) Phase diagram of xenon [45]. At the nominal detector pressure (1.2 atm),
xenon is liquid at 161–169 K.

Chapter 2 MEG II Experiment• The scintillation light is in the VUV range.
Fig. 2.15b shows the three-phase diagram of xenon. Since the detector is operated at 1.2 atm,
the temperature of xenon must be controlled between 161 K and 169 K. Contaminations suchas oxygen, nitrogen, and water decrease the light yield of scintillation light. Therefore, a xenon
control system that keeps xenon at a low temperature and keeps purifying xenon is necessary.
Furthermore, light yield monitoring is required for stable gamma-ray measurement.
It is known that there is a diﬀerence between experimental and theoretical Rayleigh scattering
lengths [42]. This discrepancy is one reason why it is diﬃcult to reproduce the actual scintillation
light propagation by MC simulations accurately.
The wavelength of the scintillation light is in the vacuum ultraviolet (VUV) region, which
is outside the sensitive region of common photosensors. The MEG II LXe detector has two
types of VUV-sensitive photosensors, PMT and MPPC, and both of them were developed for
the MEG/MEG II experiments.

2.3.3 PMT
The PMT for the LXe detector has to detect the VUV light in a demanding environment, at a
low temperature (165 K), under 50 Gauss magnetic ﬁeld. Furthermore, a low current operation isrequired to suppress the heat inﬂow. A new VUV-sensitive PMT was developed in collaboration
with Hamamatsu Photonics K.K. Bialkali (K-Cs-Sb) is used as a VUV-sensitive photo-cathode.
The basic properties of the PMT are shown in Table 2.2. The PMT window is made of synthetic
quartz glass and is transparent to light with wavelengths from 160 nm to several thousand nm,with a transmittance of about 80% at 178 nm. The bleeder circuit of the PMT is shown in
Fig. 2.17. The last two stages of the 12-stage dynode are equipped with Zener diodes to ensurestable operation even under a high-intensity environment.
A few instabilities are known for our PMTs. One is the degradation of the gain. Undera high-intensity environment, the gain of a PMT decreases by the large photoelectric current
induced by scintillation photons. The decrease is about 2% in one month of the muon beam run.
The gain is adjusted to 8×105 by changing the bias voltage. The measured radiation damage
and gain adjustment are later described in Sec. 4.4.
Another instability is called “gain shift”. The gain of the PMT decreases or increases by
10% at maximum when the beam is turned on or oﬀ. The time variation of the gain due
to the gain shift can be expressed with a few time constants. While the dominant fast time
constant is O(10) s, the slow time constant is O(100 − 1000) s. In the 2021 run, since the datacollection started a few minutes after the beam blocker operation, the impact of the gain shift
was moderate, and it was not corrected, as discussed in Sec. 4.4.
Furthermore, the variation of the quantum eﬃciency (QE) is O(1)%. Because of these instabilities and variations of the sensor performance, the monitoring and correction of gain and QE
are important to reconstruct the number of collected photons at each PMT accurately.

27

Chapter 2 MEG II Experiment28

Figure 2.16: VUV-sensitive PMT for MEG (II) (R9869).

Figure 2.17: Bleeder circuit of the PMT for the MEG (II) LXe detector [46]. The circuit has a
12-stage dynode. Two Zener diodes are installed in the last two dynode stages to ensure stable
operation under a high-intensity environment.

Table 2.2: PMT of the MEG (II) LXe detector
Speciﬁcation

PMT

Number

R9869

Total size

57 mmϕSize of sensitive region

45 mmϕLength32 mmMaterial of cathodeK-Cs-Sb

Type of dynodemetal-channel

Number of dynodes

12

Typical operation voltage

900 V

Typical Gain

8.0×105

Typical QE

0.16

Chapter 2 MEG II Experiment2.3.4 VUV-MPPC
MPPC (Multi-Pixel Photon Counter) is a kind of semiconductor photo-sensor SiPM produced
by Hamamatsu Photonics K.K. In general, an MPPC has several prominent advantages to a
PMT, such as small size, low operation voltage, and insensitivity to the magnetic ﬁeld. Since thecommercially available MPPCs were not sensitive to vacuum ultraviolet (VUV) light, an MPPC
sensitive to VUV light was developed for the MEG II experiment together with Hamamatsu
Photonics K.K [47].
The detection mechanism of VUV light and the installation into the detector will be presented
in Sec. 2.3.4.1. The drawbacks and their impacts on the detector performance will be discussed
in Sec. 2.3.4.2–5.
2.3.4.1

VUV-sensitive MPPC

Fig. 2.18a illustrates the detection mechanism of a typical MPPC pixel. As an ordinary
semiconductor photosensor, it extracts signals from electron-hole pairs generated by photons
incident on the depletion layer. The MPPC is characterized by the operation with a reverse
bias voltage higher than the breakdown voltage, which is called Geiger mode. In the Geiger
mode, the generated electron-hole pairs are accelerated by the electric ﬁeld and collide with thesilicon crystal lattice, generating electron-hole pairs one after another. It is called avalanche
ampliﬁcation.
The avalanche ampliﬁcation is quenched once suﬃcient gain and adequate output signal amplitude have been attained so that the pixel is ready to detect a subsequent photoelectron signal.
Each pixel is quenched by a quenching resistor connected in series, as shown in Fig. 2.18b. The
magnitude of the ampliﬁed signal is determined by the quenching resistance, capacitance, andbias voltage. The electric ﬁeld strength in the ampliﬁcation region is proportional to the difference between the bias voltage and the breakdown voltage, which is called over-voltage. The
number of incident photons on an MPPC is measured by arranging a large number of pixels
and counting the number of ﬁred pixels using the charge or the amplitude of the output signal
waveform.
The standard MPPCs are not sensitive to vacuum ultraviolet (VUV) light because the VUVlight is absorbed by the protective layer and does not produce electron-hole pairs in the Siliconlayer.
A VUV-sensitive MPPC (VUV-MPPC) was developed (S10943-4372, also called VUV3) for
the MEG II LXe detector. The VUV-MPPC is protected with a transparent quartz window
instead of the protective layer. Fig. 2.19 shows the detection mechanism of VUV light by the
VUV-MPPC. VUV light creates electron-hole pairs in the vicinity of the interface between Si
and the passivation layer, and then the electrons are drifted and induce avalanche ampliﬁcation.
The VUV-MPPC is also sensitive to visible light. Visible light reaches a deeper region of the
Si layer than VUV light does. The PDE for the LXe scintillation photon was measured to be29

Chapter 2 MEG II Experiment

(a)

30

(b)

Figure 2.18: (a) Detection mechanism of a typical MPPC [48]. An electron produced in the P−
layer is drifted to the P layer and induces avalanche ampliﬁcation because of the strong electricﬁeld. (b) Simpliﬁed circuit of an MPPC. MPPC pixels are connected with quench resisters inseries [48].

0.18–0.20 at the overvoltage of 7 V [47].

Figure 2.19: Detection mechanism of VUV light by the VUV-MPPC. The VUV light creates
e-h pairs in the vicinity of the interface between the passivation layer and the Silicon layer. The
electrons are drifted to the ampliﬁcation region, and the signal is ampliﬁed by the avalanche
ampliﬁcation.

The area of a typical MPPC is at most 6 mm square. With this small size of an MPPC, morethan 10,000 channels and readout electronics are necessary to cover the entire inner face of the
LXe detector. This is not realistic, considering the cost and the heat inﬂow through the sensor
cables. This problem was solved by connecting four MPPC chips together in what is calleda “hybrid connection” to form a large 12 × 12 mm2 MPPC. Fig. 2.20 shows the circuit of theconnection. The hybrid connection is designed so that the same bias voltage is distributed toeach chip, while the signal is read out in a series connection to keep the signal time constantshort, as shown in Fig. 2.21. Fig. 2.22a and 2.22b show a picture of a single MPPC and its

Chapter 2 MEG II Experiment31

Figure 2.20: Scheme of the series connection of the four MPPC chips on the VUV-MPPC[47].

Voltage [mV]The same bias voltage is distributed to all chips, while the signal is read out in a series connection.

10
5
0
−5

−10

Voltage [mV]

−15

−600

−400

−200

0
Time [nsec]

−600

−400

−200

0
Time [nsec]

10
5
0
−5

−10
−15

Figure 2.21: Typical waveforms of our MPPC with two photoelectrons (primary single photoelectron signal from LED with optical crosstalk). The four chips are connected in (top) paralleland (bottom) series [47].

structure, respectively. The speciﬁcation of our MPPC is summarized in Table 2.3.
After the development of the VUV-MPPC, the mass production of 4,200 MPPCs, including
about 100 spares, was performed by the HPK and completed by Oct 2016. They were delivered
in four batches called production lots A, B, C, and D.
In order to construct a detector with good quality MPPCs, current–voltage (IV) curves were
measured for all 16,800 MPPC chips. Out of them, 16,368 MPPC chips that have normal
behavior were selected to construct 4,092 MPPCs to be installed in the detector. The fraction

Chapter 2 MEG II Experiment

(a)

32

(b)

Figure 2.22: (a) Picture and (b) sketch of the VUV-MPPC developed for the MEG II [47]Table 2.3: Speciﬁcation of MPPC of MEG II LXe detector
Speciﬁcation

MPPC

Number

S10943-4372, VUV3

Total Size

15×15 mm2

Size of sensitive region

12×12 mm2

Pixel pitch

50 µm

The number of pixels

57600

Typical breakdown voltage at room temperature

54 V

Temperature coeﬃcient of breakdown voltage

56 mV/K [29]Typical Gain at overvoltage 7 V

1.5×106

PDE at overvoltage 7 V

0.18–0.20 [47]

Excess charge factor at overvoltage 7 V

1.3–2.5of malfunctioning MPPC chips that have anomalous IV curves was 0.2%, and they were notinstalled in the LXe detector.
Fig. 2.23a shows how the MPPCs are ﬁxed to the detector. Each MPPC is connected to a
printed circuit board (PCB), and the PCBs are supported by carbon-ﬁber-reinforced polymers(CFRP). The gaps between PCB and MPPC, PCB, and CFRP are ﬁlled with spacers to prevent
LXe from entering the gaps. Fig. 2.23b shows the material that makes up the entrance face ofthe detector. In reality, there is a ∼1 mm gap between the CFRP and cryostat because of thediﬀerence between the curvature of the CFRP and that of the inner surface of the cryostat andit is ﬁlled with LXe. The thickness of the LXe volume and its impact on the detection eﬃciency
will be discussed in Sec. 4.7. Each PCB carries 22 MPPCs, and a row consists of two PCBs.
One CFRP carries 23 or 24 PCB rows, and it is ﬁxed to the cryostat with screws at its four
corners. Four CFRPs are used to mount the entire MPPC array that has 93 rows lined up, with
4,092 MPPCs mounted overall. While there was no gap between the CFRPs in the ϕ direction,

Chapter 2 MEG II Experiment

33

their z position can be diﬀerent by O(1) mm.
Fig. 2.24 shows the installation location of the MPPCs in diﬀerent production lot. Most PCB
carries the MPPCs from the same lot, and the PCBs are arranged so that PCBs from the samePrototype
for thespacerproduction lot are not next to each other as much as possible in orderto obtaina uniform
bw/
MPPC
and
PCB
response as a whole as much as possible.

MPPC Support structure

(a)

(b)

Any(a)space
betweenFigure 2.23:
Schematic
view of the MPPC
support structure of the MPPCs. The gap between the•

Cryostatwall
MPPCs andand the
PCB is ﬁlledwith cause
top spacers. The gap between the PCB and the CFRP isdetection
ﬁlled with
PCB spacers.inefficiency
The PCB spacers are ﬁxed to the CFRP by screws. (b) Material of
the entrance face before the LXe volume [2].

•Need to fill the gap withlight material
Top
12

4.00
3.44
2.96
2.48
2.00
1.44
0.96
0.48
0.00

60
40
20
DS 0

US

−20
−40
−60

−20

0

20

40

BottomFigure 2.24: Distribution of the production lot of MPPCs. MPPCs of lot A are shown in blue,
Lot B in green, Lot C in yellow, and Lot D in red.

Chapter 2 MEG II Experiment

Figure 2.25: Dark count rate measured at room temperature (orange), 205 K (green), and
165 K (blue) [29] as a function of the over voltage.

2.3.4.2

Dark current

The MPPC is known to have fake signals without external photons due to thermal excitation,
called dark current. The dark current of the MPPC has a strong temperature dependence. The
dark count rate at 165 K is lower by a factor of 105 than that at room temperature as shownin Fig. 2.25. Therefore, dark current is not a problem as long as the MPPC is used in LXe at
165 K.
2.3.4.3

Correlated noise

A single photon may ﬁre multiple pixels, and it is called correlated noise. Cross-talk andafter-pulsing are known as main correlated noises. Cross-talk is a signal occurring at the sametime as the primary signal because an infrared photon produced in the avalanche ampliﬁcationby the primary photon generates electron-hole pairs in a neighboring pixel. After-pulsing occurs
at a later time than the primary signal. An avalanching carrier trapped by an impurity energy
level is released after a short delay and generates another avalanche. The magnitude of thecorrelated noises of an MPPC was evaluated using excess charge factor (ECF), which stands
for the fake ampliﬁcation of the signal by the correlated noises. The ECF of the VUV-MPPCs
for the LXe detector was measured to be large up to 2.5 at the over-voltage of 7 V based on
calibration measurements with O(1)% precision as described in Sec. 4.3.
A large excess noise factor due to the correlated noises does not deteriorate the energy resolution signiﬁcantly since it is not limited by the photoelectron statistics, as discussed in Sec. 7.3.

34

Chapter 2 MEG II Experiment

Figure 2.26: The maximum number of photoelectrons collected by MPPCs in a detector simulation for the signal gamma-ray [29]. Only 20% of the pixels are ﬁred for a gamma-ray hit in
the shallow region.

2.3.4.4

Non-linearity and saturation

The MPPC is known to exhibit a nonlinear response when a number of photons comparable
to the number of pixels enter the detector. Fig. 2.26 shows the depth dependence of the numberof photoelectrons when a signal gamma-ray is injected into the detector in the simulation, andthe number of photoelectrons at the shallowest part is only about 20 % of the number of pixels.
Therefore, the nonlinearity of the MPPC response is not likely a severe issue in our case.
2.3.4.5

Temperature dependence of breakdown voltage

The temperature coeﬃcient of the breakdown voltage of the MPPC is 56 mV/K. The higher
the temperature is, the higher the breakdown voltage is. Since the characteristics of the MPPC
heavily depend on the overvoltage, the instability of the temperature leads to the instability ofthe performance. The LXe control system is designed to keep the temperature of LXe stable at∼169 K with a precision of 0.1 K, as later described in Sec. 2.3.7.
In the middle of the 2021 run, there was nevertheless an instability in the temperature of thedetector hut where the detectors and electronics are located. Fig. 2.27 shows the time variationof the temperature of the LXe detector and the detector hut. The hut temperature became
unstable around the 5th of November because one pump responsible for the air-conditioning of
the hut became inoperative due to technical issues. Since the increase in the heat inﬂow fromthe detector hut was too fast to keep the LXe temperature stable, the temperature of the LXedetector was also aﬀected. The temperature rise of the LXe by 1 ◦ C increased the breakdown

35

Detector hut temperature[deg]Chapter 2 MEG II Experiment

36

34
32
30
28
26
24

LXe temp[K]

22

170
20

01/08/21

31/08/21

30/09/21

30/10/21

29/11/21

29/12/21
Time

31/08/21

30/09/21

30/10/21

29/11/21

29/12/21
Time

169.8
169.6
169.4
169.2
169
168.8
168.6
168.4
168.2
168
01/08/21

Figure 2.27: Temperature of the detector hut in celsius (top) and the detector in kelvin (bottom)
as a function of time in the 2021 run. While the temperature of the detector hut had been undercontrol until the 4th of November, it became unstable due to an operational issue.

voltage of MPPCs by 0.8% at overvoltage 7 V.
However, the instability of the MPPC response due to the temperature instability was monitored and corrected so that it did not cause a problem, as later discussed in Sec. 4.3.

2.3.5 Signal transmission and readout electronics
The sketch of the signal transmission of the detector is shown in Fig. 2.28. The signals from
MPPCs are transmitted through the coaxial structure in the PCBs as shown in Fig. 2.29. The
signals from the PCBs are transmitted by coaxial cables from the cable connectors on the edge
to the feedthrough of the cryostat. On both sides of custom-made feed-throughs shown in
Fig. 2.30, coaxial cables are directly soldered. The detector has 12 ﬂanges as the feedthroughon the chimney of the detector, and each ﬂange accommodates 432 readout channels.
A patch panel is mounted on the detector for selecting channels to read. After the patch
panel, sixteen cables are bundled and connected to a DAQ module (WaveDREAM board, later
described in Sec. 2.7). Fig. 2.31 shows the grouping scheme of the MPPCs to the modules.

Chapter 2 MEG II Experiment37
feedthroughpatch panel

not to scale

PMT

MPPC
Electronics
COBRA

Figure 2.28: Concept of the signal transmission [2]. The signal cables of the photosensors areconnected to the feedthrough at the top of the detector. The cables from the feedthrough areconnected to the patch panel where they are connected to the cables to the readout electronics.

Figure 2.29: Cross sectional view of a PCB [29]. The signal lines from the MPPCs (grey) aretransmitted in the ground lines (yellow).

A square group of 4×4 MPPCs is read out by a module, and this unit is used for the online
position reconstruction of gamma rays. For this purpose, channels read out by the same module
are designed to have the same cable length.

Chapter 2 MEG II Experiment38

Figure 2.30: Custom-made feedthrough for the signal cables. The signal cables are directly
soldered to both edges of the PCBs attached to the feedthrough.

Inner map
Top

US

DS

BottomFigure 2.31: Grouping scheme of the MPPCs into the readout electronics (WaveDREAM board).
4×4 MPPCs are grouped and connected to a WaveDREAM board except for a few exceptionalgroups. The crate number and the slot number of the WaveDREAM board are written on eachgroup.

Chapter 2 MEG II Experiment39

2.3.6 Calibration sources
LED
Fig. 2.32 shows the positions of the LEDs installed in the detector. In addition to 36 LEDs
used in the MEG experiment (Toyoda Gosei E1L493B1A02 [49]), 48 LEDs (Kingbright KA3021QBS-D [50]) are installed on the outer face and lateral (upstream and downstream) faces
for the calibration of the MPPC. These LEDs are dimmed by Teﬂon as shown in Fig. 2.33 forstable operation.
As described later in Sec. 4.3, a short pulse LED is desirable to measure the magnitude ofafter-pulsing for each MPPC. A function generator Agilent 81150A [51] is used to ﬂash theLEDs. It can provide a short (10 ns width) pulse with an amplitude of 5 V, and it is suﬃcient
to drive two LEDs simultaneously. A system to select a set of two LEDs, one in upstream andanother in downstream, to send a pulse was developed to calibrate all MPPCs with the new
LEDs. Fig. 2.34 shows the circuit to operate the 12 new LEDs on the outer face. A combinationof 12 high-speed relays (G6K-2F-RF-S DC24, Omron [52]) and SCS3000 (Slow Control Systemmodule developed at PSI [53]) is used to distribute the driver signal to an arbitrary set of one
upstream LED and one downstream LED. The high-speed relays are mounted on a board andconnected to the LEDs. A synchronous signal is sent from the function generator to the trigger
system to trigger the LED events. The operation condition of the function generator for thecalibration in the 2021 run is summarized in Table 2.4.
Table 2.4: Conﬁguration of the driver signal for LED calibration.
Oﬀset [V]1.67–1.69

Amplitude [V]1.3

Frequency [Hz]100

Pulse width [ns]10

Am source
The detector is equipped with twenty-ﬁve spots of 241 Am α sources for the PDE calibration ofphotosensors. Each spot source emits alpha rays at 5.485 MeV (84.5%) and 5.443 MeV (13.0%)
at an activity of ∼ 200 Bq, which is low enough not to interfere with other measurements. Eachsource is surrounded by a thin gold foil and wound around a thin gold-plated tungsten wire witha diameter of 100 µm [54], as shown in Fig. 2.35.
Fig. 2.36 shows the position of the sources inside the detector. Five sources are mounted toeach wire with the same spacing of 12 cm. The wires are stretched parallel between the upstream
and downstream faces. Since an 241 Am source produces scintillation light of ﬁxed energy froma ﬁxed position, it is very useful to measure the PDE of photosensors and optical properties of
LXe, such as absorption length and light yield.

Chapter 2 MEG II Experiment

40

Top

Outer
old LED
from MEG
new LED
from MEG II

DS

BottomUSz axisFigure 2.32: Location of the LEDs in the LXe detector. Green and blue points show the LEDs
reused from MEG and ones installed for the MPPC calibration in the MEG II, respectively.

Figure 2.33: A unit of the LED system for MPPC calibration. Three LEDs are mounted to each
PCB and dimmed by Teﬂon.

2.3.7 Xenon control system
The purposes for the xenon control system in the LXe detector are listed below.
• Keep the temperature of the detector at 165 K.
• Keep purifying xenon to have a good light yield and to suppress the absorption in LXe.
• Store xenon when it is not used for the experiment.
Fig. 2.37 shows the xenon control panel of the gaseous and liquid puriﬁcation system. The wholesystem consists of the detector cryostat, refrigerators, storage tanks, and puriﬁers. The control
system was developed for MEG [55], and the cooling capability was upgraded to compensate

Chapter 2 MEG II Experiment

Figure 2.34: Diagram of the circuit to distribute the driver signal from the function generator
to the LEDs for the MPPC calibration. The driver signal is transmitted to the 12-channel relay
board, and then it is distributed to a pair of LEDs: one on the upstream side and the otheron the downstream side of the detector. The function generator and the fast relays on therelay board are controlled by the MIDAS system and an SCS3000 module, respectively. The
amplitude of the driver signal and the LEDs to ﬂash can be changed through the control system.

Figure 2.35: 241 Am source mounted on a gold-plated tungsten wire. The black crosses show thepoints where the wires are ﬁxed to the upstream and downstream faces.

for the heat inﬂow from the increased number of cables. A 200 W pulse-tube refrigerator placedat the top of the detector is reused from MEG, and a new 400 W Giﬀord-McMahon (GM)refrigerator is introduced.
A 1000 ℓ Dewar with a pulse-tube refrigerator is used to safely store LXe when the detector
is not operated. Since it is thermally insulated and is tolerable up to 6 bar, it can store the LXe
for 100 hours even without cooling power.
The xenon control system is equipped with two puriﬁcation systems in the gaseous phaseand in the liquid phase. The gaseous phase puriﬁcation is performed by a metal-heated getter.
The circulation of gaseous xenon (gXe) for the gaseous phase puriﬁcation is continued when thedetector is operating. This is also useful to eﬃciently transfer the cooling power from the GM
refrigerator to the detector. The liquid phase puriﬁcation is performed by molecular sieves in
the liquid puriﬁer module at the back of the detector.

41

Chapter 2 MEG II Experiment

42

Top

Outer
α source
4

3

2

1

0

Wire0
9

8

7

6

5

14 13 12 11 10

19 18 17 16 15

24 23 22 21 20

DS

Bottom

US

Wire1
Wire2
Wire3
Wire4

z axisFigure 2.36: Location of 25 241 Am source spots in the detector. Red circles on the inner andSatorushow
Kobayashi
outer faces
the projected positions of the source spots.

28

Figure 2.37: Xenon control panel in MEG II. The valves with the preﬁx “VL” are the valves in
the liquid circulation line, and those with the preﬁx “VG” are in the gaseous circulation line.
The detector (left), GM refrigerator (top), and 1000 ℓ storage tank (middle) have a heater (blueand black box) at the top of each module to control the temperature.

Chapter 2 MEG II Experiment
The temperature of the MEG II LXe detector is kept stable by a PID control of the xenonpressure with a precision of 0.1 K unless the temperature of the detector hut is changed too
rapidly.

2.4 Radiative Decay CounterIn the MEG II experiment, the Radiative Decay Counter (RDC) is newly introduced to identify
the accidental RMD gamma ray. The typical energy of a positron from the RMD is about
3 MeV when a high-energy gamma ray is emitted. This low-energy positron is swept out witha small radius along the beam axis by the gradient magnetic ﬁeld. The gamma ray from theRMD background can be identiﬁed by detecting this positron as shown in Fig. 2.38. The RDC
consists of time- and energy-measurement parts, as shown in Fig. 2.39 and Fig. 2.40. The timemeasurement part is composed of 12 fast plastic scintillators (BC-418, Saint-Gobain) and 60
SiPMs (S13360-3050PE, Hamamatsu Photonics). Two or three SiPMs are attached to bothsides of scintillators and connected in series. The energy measurement part is composed of 76
cubic LYSO crystals (Shanghai Institute of Ceramics) of 2×2×2 cm3 . Each crystal is read out
with a single SiPM (S12572-25P, Hamamatsu Photonics).

Figure 2.38: Principle of radiative muon decay (RMD) tagging with RDC. A low-energy positronfrom RMD (red) is swept with a small bending radius and detected by RDC downstream. On
the other hand, a high-energy positron (blue) has a large bending radius and detected by thespectrometer.

2.5 π 0 measurement setup
Gamma rays from a π 0 decay, π 0 → γγ, is the most promising calibration source to understandthe response and performance of the LXe detector for a high-energy gamma ray. The MEG II
collaboration has a dedicated setup for the calibration with the π 0 decay. Fig. 2.41 shows theexperimental setup of the π 0 run. The negative pion beam supplied from the PSI accelerator

43

Chapter 2 MEG II Experiment

44

Figure 2.39: Structure of the RDC. The front side is the time measurement part composed ofplastic scintillator bars, and the back side is the energy measurement part composed of LYSO
crystals.

Figure 2.40: Structure of the time-measuring part of the RDC. The scintillation photons generated by an incoming positron in a plastic scintillator are read out by SiPMs connected in series.

is injected into a liquid hydrogen (LH2 ) target placed at the center of the experimental system
instead of the normal target for the muon beam run. A dedicated detector system to measure
the gamma ray from the π 0 → γγ decay is placed at the opposite side of the LXe detector.
It consists of an energy measurement part, a BGO detector, and a time measurement part, apre-shower counter.
When the π − beam is introduced to the target, a part of negative pions are converted to π 0mesons by a charge-exchange reaction π − + p → π 0 + n. The energy of the π 0 meson is
Eπ 0 =(mπ− + mp )2 + m2π0 − m2n= 137.85 MeV
2(mπ− + mp )(2.14)

where the mass of the particles is summarized in Table 2.5. The π 0 meson has a short lifetime (8.5 × 10−17 s [36]), and it immediately decays to two gamma rays with a branching ratioof Br(π 0 → γγ) = 0.988 [36].
The energies of the gamma rays are mπ0 /2 in the center-of-momentum frame. In the laboratory

Chapter 2 MEG II Experiment

45

PMT
LXe

ɶ

MPPC

COBRA
Target insertion tube

ʋ- beamɶ

LH2 cellPre-shower counterz

BGO calorimeteryx

Figure 2.41: Schematic view of the experimental setup of the π 0 run (top view). The negative
pion beam is introduced to the LH2 -target cell and two gamma rays from a π 0 → γγ decay
are emitted in nearly opposite directions. One gamma ray is detected by the LXe detector andthe other gamma ray is detected by the BGO calorimeter and the pre-shower counter on the
opposite side of the LXe detector.

Table 2.5: Mass of the particles
Particle

Mass [MeV]π−

139.570134.97p938.27n939.57πframe, the energies of the two gamma rays are characterized by the opening angle Θ γγ assE 0Eγ = π ±
2

Eπ2 0
m2π0
−
.
4
2(1 − cos Θγγ )(2.15)

In particular, the back-to-back gamma-ray pair has energies of 55 and 83 MeV. The kinematic
topology of the π 0 decay allows measuring the detector response for a high-energy gamma ray
through the measurement of the other gamma ray by the pre-shower counter and BGO detector
at the opposite side of the LXe detector.

Chapter 2 MEG II Experiment46

Figure 2.42: Scheme to hold liquid hydrogen in the LH2 -target cell for the π 0 run [27]. LH2 iscontained in a target cell cooled by the He circuit.

Figure 2.43: Cell of the LH2 target used in the 2021 π 0 run.

In addition to the charge exchange reaction, a radiative capture reaction π − p → γn also
happens in the target. The ratio of the cross-section of the charge exchange reaction to that of
the radiative capture is known as the Panofsky ratio,
P =σ(π − p → π 0 n),σ(π − p → γn)(2.16)

which was measured in the previous measurements to be 1.5 [57, 58]. The radiative captureemits a 129 MeV monochromatic gamma ray and a 9 MeV neutron in opposite directions. The
monochromatic 129 MeV gamma ray is useful to understand the linearity of energy reconstruction and the energy dependence of the energy resolution.

Chapter 2 MEG II Experiment

Figure 2.44: 4 ×4 BGO crystals [27]. The scintillation photons of the BGO crystal are read out
by 16 PMTs on the back.

Figure 2.45: Pre-shower counter module [56]. A fast plastic scintillator is wrapped with reﬂectorsof aluminized mylar and then shielded by a black sheet. The scintillator is read out by 16 MPPCs
at both ends.

Pion beam
The negative pions used in the π 0 run are produced by the reaction p + n → p + p + π −from the proton beam coming from the cyclotron, and their momentum is 70.5 MeV. It has thesame time structure as the proton and has a bunch structure of 50 MHz. The beam intensity is
adjusted by the slits upstream of the detector system to have a suﬃcient π 0 → γγ event rate toaccumulate the statistics in the limited beam time. The pion beam rate in the 2021 π 0 run was
9.5×104 /s.

LH2 target
A schematic of the LH2 target is shown in Fig. 2.42. The LH2 target consists of a cell in
the center of the experimental coordinate, a cooling circuit that circulates liquid helium, anda vacuum tube that prevents heat dissipation from the LH2 cell. The cell that contains LH2

47

Chapter 2 MEG II Experiment48

is a stainless steel cylinder of 0.5 mm thick, 60 mm diameter, and 75 mm length, as shown in
Fig. 2.43. The cooling circuit is connected to a ∼60 ℓ liquid helium dewar. The vacuum level ofthe tube is kept to be O(10−6 ) mbar. The LH2 target was upgraded from the MEG experiment
to reduce the heat dissipation and improve the stability by introducing a new cooling helium
circuit. The material of the LH2 target before and after the upgrade is summarized in Table 2.6.
Table 2.6: LH2 target material
Type

Cell diameter

Cell wall thickness

Tube wall thickness

MEG

50 mm

Stainless, 0.5 mm

Stainless, 1 mm

MEG II

60 mm

Stainless, 0.5 mm

Stainless, 3 mm

BGO detector
The BGO detector is a scintillation detector that consists of 4×4 BGO crystals and 16 PMTs
coupled to each crystal, as shown in Fig. 2.44. The fundamental speciﬁcations of the BGO
detector are summarized in Table 2.7.
Table 2.7: Speciﬁcations of the BGO detector
Density [g/cm3 ]7.13

Radiation length [mm]11.2

Scintillation wavelength [nm]

480

Size

46 × 46 × 200 mm3

Readout

PMT (Hamamatsu H8409-70)

Pre-shower counter
The design of the pre-shower counter is based on that of the pTC. One module of the preshower counter consists of four MPPCs connected in series to a fast plastic scintillator on bothsides. By stacking two of these modules orthogonally, the position and time of gamma rays
can be measured more precisely. A set of two pre-shower counter modules and a lead converterwith 4 mm thickness are placed in front of the BGO detector. About a quarter of incoming
gamma-rays is converted to electrons and positrons by the lead converter, and detected by thetwo pre-shower counter plates.
The BGO detector and the pre-shower counter are moved by rails along the z and ϕ directions
to scan the whole LXe detector with back-to-back gamma-ray pairs.

tChapter 2 MEG II Experiment49
in operation in the, and tuning theinter-bar timing of
2.6 17.6 MeV CW-Li gamma-ray
and LXe detector.
sary on a frequent
The MEG II collaboration has a Cockcroft–Walton (CW) accelerator in the downstream sidee should thereforeof the πE5 area, as shown in Fig. 2.46. By irradiating the Li2 B4 O7 target with 440 keV protons
wing requirements
8
obtained by this accelerator, 17.6 MeV gamma-rays are emitted from the 73 Li(p, γ)4 Be reaction.

The monochromatic gamma rays provided by this system are quite useful for the light yieldea with controlled
monitoring and the uniformity study over the detector volume. The beamline switching between

CW and muon beam can be done relatively quickly (∼ 10 minutes) by pulling down the MEG
rtion bellows sysII target
upstream and installing the CW beamline from downstream with bellows.
Li2B4O7) targetas
am to the centreTheof Li2 B4 O7 target is slanted by 45 ◦ with respect to the beam axis. The position and size ofthe interaction region were measured by a pixel detector at the end of the beam pipe as shown
uum pipes, a set ofin Fig. 2.47. The beam spot size was 6 mm in σ, and it was displaced from the center of the xy
magnets (parallel
2. Axview
Cockcroft–Walton
accelerator.
plane by 5 cm and 1 cmFig.
in theandofy the
directions,
respectively.

BRA stray magnetic
erventions on thein a separate area,s a 1 MeV C–W ofd in Table 2.

in Fig. 2. The C–W
endently radiationand tested. At theccelerator must be
accelerator is in an parallel withFigure
the 2.46: BeamlineFig.
3. Layout of the MEG
and C–W inexperimental
areas. of the MEG II system.
of Cockcroft–Walton
accelerator
the downstreamr, a system of two
ng magnets (paralg an axial injection
properties of the beam. The p-beam has to reach the target undervacuum. The p-beam is introduced into the spectrometer fromet (see Fig. 4.) The
A to reach a target
downstream, in the opposite direction to the normal m-beam. The
present layouts of the downstream-side of the MEG experiment
one of the normal
and of the C–W area are shown in Fig. 3.
so are the optical•

CW proton beam tuning for both Lithium and Boron settings with C•

Initial vacuum acceptable (not optimum)

i.e. Boron Data
Chapter 2 MEG II• Experiment

50

A. Gurgon

Cobra onFigure 2.47: CW proton beam vertex position measured with a pixel detector at the end of
the beam pipe. The x- and y-axis of the plot correspond to the x- and y-position in the pixel
detector in the unit of the pixel size (2 cm).

2.7 Data acquisition system
Given the need for suppression of accidental background events in the µ+ → e+ γ search, it isdesirable to have a fast waveform digitizer that works at a high sampling frequency.
A new DAQ module, WaveDREAM*1 , was developed for MEG II. It is equipped with a fast
waveform digitizer, Domino Ring Sampler (DRS) [60]. As shown in Fig. 2.48, the trigger functions, basic DAQ functions, and HV supplies for SiPMs are integrated into a single WaveDREAMboard. Thanks to this integrated design, the experiment can read out signals from the granularreadouts with a manageable number of cables. The number of readout channels in the MEG II
is three times larger than that in the MEG experiment, as shown in Table 2.8.
Fig. 2.49 shows the principle of the waveform digitization by the DRS. Each capacitor storesvoltage information by means of a sampling signal generated by an inverter delay chain. Whentriggered, this sampling signal stops, and the voltage value at that point is stored in the shift
register. The DRS chip can be operated at sampling frequencies from 0.5 to 5 GHz. In the2021 run, the data were acquired at 1.4 GHz for all readout channels except for the CDCH
readout channels (1.2 GHz). The sampling frequency was determined considering the latency of
the trigger system. It is high enough to achieve a good timing resolution and low enough to*1 Waveform Drs4 REadout Module

Cobra off

Chapter 2 MEG II Experiment

51

PMT
DC

PMT
SiPM
DC

Crate
Chip

Board

PC
HV
DRS

Type 1
Trigger
Board

Type 2
Trigger
Boards

ADC

DRS

FP
GA

ADC

T2

T2

DRS
Board

Inter
face

HV

ADC

FP
GA

TRG
Conc

FP
GA

Inter
face

PC

WaveDREAM
Board

LV

LV

DAQ
Conc

TRG
Conc

TRG
Conc

PC

PC

PC

Figure 2.48: Comparison of the DAQ system in the MEG (left) and MEG II (right). See thelegend at the top for the color of the boxes. A WaveDREAM board has basic trigger functionality
and a slot for an HV card to apply bias voltages to the SiPMs.

Figure 2.49: Working principle of a DRS chip [59].

Chapter 2 MEG II Experiment52

Figure 2.50: WaveDREAM boards in a crate. A WaveDREAM crate has 16 slots for WaveDREAM boards and two slots for a DCB and a TCB.

secure a reasonable margin of 100 ns before the pulse, which is necessary to unfold the pileup
pulse before the main pulse.
Since SiPMs generally have lower gain than PMTs, the readout electronics have ampliﬁers
for compensation. The two stages of switchable ampliﬁers with a gain of 10 and programmableattenuators are implemented for each channel. They allow setting the overall input gain in arange from 0.5 to 100 in eight steps. The high gain of 100 is used to calibrate the photosensors
with small signal waveforms. The low gain of 1–5 is used to collect high-energy gamma-ray
events. In the 2021 run, the ampliﬁer gain was set to 5 for MPPC readout channels and 2.5 for
PMT channels. This is high enough to have a good online timing resolution, while the amplitudeof the waveform is within the dynamic range of the readout electronics for a large fraction of
events. The ampliﬁer gain of 100 was used for MPPC calibration that requires a higher S/Nratio to measure O(1) photoelectrons.
Table 2.8: The number of readout channels of MEG and MEG II detectors.
Detector

MEG

MEG IILXe detector

846

4,760

Positron timing counter

120

1,024

Drift chamber

1,728

3,456

Radiative decay counter

(0)

100

Total

2,690

∼10,000

A single WaveDREAM board can read out 16 channels.
crate (Fig. 2.50) has 16 slots for WaveDREAM boards.

A single WaveDREAM

Since 10,000 channels are used,

36 crates (19 for the LXe detector, 4 for pTC, 10 for CDCH, and 3 for other systems, such as
RDC, BGO, pre-shower, and beam monitoring detectors) are used.
The WaveDREAM crate also has one slot each for Trigger Concentrator Board (TCB) andChapter 2 MEG II Experiment

53

Data Concentrator Board (DCB). The DCB bridges the WaveDREAM boards and the DAQ
system. It is responsible for the conﬁguration of the boards, the distribution of the master clock
and trigger signals, and the readout of waveform data from each board. The upper limit of thedata rate that can be processed by the DCB is 130 MB/s. The TCB is designed for online dataprocessing. The trigger system made up of TCBs reconstructs the physics variables such as
momenta, relative timing, and direction of positrons and gamma-rays. The collected data aretransferred to the online computer and compressed by the pbzip library.
The data acquisition and the slow control of the detectors are controlled by the MIDAS
system [61].

2.8 Trigger
Table 2.9: Trigger logics used for this thesis.
Logic

PurposePedestal trigger

Monitoring of the noise condition.

LED trigger

Calibration with LEDs.

EGamma trigger

Measure the LXe detector response

Alpha trigger

Calibration with 241 Am sources.

MEG trigger

Search for µ+ → e+ γ.

π 0 trigger

π 0 run.

A variety of trigger logics are prepared for the data acquisition as shown in Table 2.9.

2.8.1 Pedestal trigger
The pedestal trigger is ﬁred periodically, and so independently of the detector signals. The
pedestal data is useful to estimate the noise level and the event-by-event ﬂuctuation of thebaseline.

2.8.2 LED trigger
As described in Sec. 2.3.6, two kinds of LEDs are installed in the LXe detector. For both
systems, a trigger signal in synchronous with the driver signal for the LEDs is provided fromthe driver module to the trigger system. The LEDs are ﬂashed by 0.1 Hz with the beam andO(10) Hz in dedicated calibration measurement, and the trigger is ﬁred when the trigger signal
is larger than a given threshold.

Chapter 2 MEG II Experiment54

2.8.3 EGamma trigger
A self-trigger of the LXe detector called “EGamma” trigger is used to take γ-ray eventswith a given threshold. The online γ-ray energy is reconstructed using a weighted sum of thephotosensor waveforms. The trigger is ﬁred when the amplitude of the weighted sum waveform
exceeds the threshold. The weights of each photosensor are calculated from the calibration
parameters such as gain, ECF, and PDE. The scale of the online Eγ was calibrated by 17.6 MeV
gamma-ray from the CW-Li setup.

2.8.4 Alpha trigger
A dedicated trigger is implemented to take α events from the 241 Am sources. The trigger
is ﬁred when the sum of the sensor waveforms of PMTs exceeds a given threshold. A particle
identiﬁcation based on the waveform shape is used to improve the purity of α events by rejecting
gamma rays and cosmic rays.

2.8.5 MEG trigger

1600

1200

MEG TRG

MEG TRG

1400
1000
1200

Wide Angle TRG

Wide Time TRG

800

1000
800

600

600

400

400
200

200
0
−0.1

−6

−0.05

0

0.05

×10
0.1
Teγ [s]

0
0

50

(a)

100

150
Θeγ [deg](b)

Figure 2.51: (a) te+ γ and (b) Θe+ γ distribution of the events collected by the MEG trigger (black)and ancillary trigger with a loose constraint (red). The te+ γ window of the MEG trigger was 25 ns
in the 2021 run. Events with a large opening angle are collected with the direction matching.
The trigger logic for the µ+ → e+ γ search called “MEG trigger” is composed of three independent conditions, as listed below.
• Coincidence trigger of gamma and positron• Back-to-back position selection (Direction matching).
• EGamma trigger

Chapter 2 MEG II Experiment
In addition to the main trigger, three ancillary triggers with a wide time window, a lower Eγ
threshold, and a loose direction match constraint are prepared to evaluate the trigger eﬃciency.
In the 2021 run, the trigger rate was 5–20 Hz depending on the beam rate and the thresholdvalues.
2.8.5.1

Coincidence trigger

A coincidence trigger is designed to select a pair of a positron and a gamma ray produced
at the same time. The trigger is ﬁred when the diﬀerence between the time of a gamma-ray
measured by the LXe detector and the time of a positron measured by the positron timing
counter is smaller than a certain threshold. In the 2021 run, the online gamma-ray time wasdeﬁned as the time when the amplitude of the summed waveform of the MPPCs exceeded acertain threshold. The online tγ resolution was limited by the time walk and was about 3 ns.
The positron timing was reconstructed using the timing of pTC hits.
The center of the coincidence time window was deﬁned by the te+ γ peak of RMD events. In
2021, the width of the window was 25 ns so that the RMD peak was completely included bytaking the online time resolution (∼5 ns) into account, as shown in Fig. 2.51a.
2.8.5.2

Direction matching

As shown in Fig. 2.31, MPPCs are clustered so that 4×4 MPPCs are read out by a single
WaveDREAM board. The direction of gamma-rays is reconstructed by ﬁnding the WDB thathas the largest signal of all boards connected to MPPCs. The online position resolution for
the gamma-ray is ∼3 cm. The direction of positrons is reconstructed by a hit pattern of apositron in the pTC. Fig. 2.51b shows the distribution of the opening angle Θe+ γ . Events with
Θe+ γ ∼ 180 ◦ are collected by the MEG trigger.

2.8.6 π 0 trigger
Four trigger logics were prepared for the π 0 run.
• Coincidence of the LXe detector, pre-shower, and BGO detector.
• Coincidence of the LXe detector and BGO detector with a veto by the pre-shower counter.
• A self trigger of the BGO detector• A self trigger of the pre-shower counter
The ﬁrst two coincident triggers are ﬁred when the following three conditions are met.
• Online gamma-ray position is inside a given region called “patch”.
• The reconstructed timing by the LXe detector and the timing of the hit of the BGO
detector are within the coincidence window.
• The reconstructed timing by the pre-shower counter is inside or outside the coincidence
window, depending on the trigger type.

55

Chapter 2 MEG II Experiment56

The self-trigger of the BGO detector is ﬁred when the amplitude of the summed waveform of the
BGO detector exceeds a given threshold. The dataset with this trigger is useful to calibrate the
BGO detector with CW-Li γ-rays in advance of the π 0 run and to evaluate the detection eﬃciencyof the LXe detector. The self-trigger of the pre-shower counter is ﬁred when a discriminator of
an MPPC readout is ﬁred. It was used for the calibration and performance evaluation of the
pre-shower counter.

2.9 Detector simulation
2.9.1 Overview
Experimental
raw waveform

onlineDAQ

Event reconstruction

Analyzer.mid

Result of analysis

rec

Simulated
raw waveform

raw

gem4
Detector simulation

sev

bartender
Waveform simulation

sim
Simulated MC truth

Figure 2.52: MEG II software framework. The online DAQ system saves the data in .mid ﬁles.
The detector simulation generates .sev ﬁles that contain the time and amplitude of the readout
channels. bartender simulates the waveforms by taking .sev ﬁles as inputs. Then the simulated
waveforms are processed by analyzer so that the variables of gamma rays and positrons arereconstructed.

A detector simulation framework has been developed to understand the detector response
and performance. Fig. 2.52 shows the overview of the simulation framework together with theanalysis ﬂow of the data.
The detector simulation is carried out in a Geant4 [62] based software gem4. Geant4 (Version 4.10.06.p03) is a particle simulation framework with Monte Carlo methods. It generates
an event with a given initial condition, such as the type, momentum, and position of particles,
the geometry of the detectors, and the electromagnetic ﬁeld of the simulation volume. For each
event, the generated particles are propagated based on a list of the particle interactions called“Physics list”. The geometry of the experimental apparatus is reproduced in gem4. The output
of gem4 is stored in “sev” ﬁles and used for the following waveform simulation.
Waveform simulation is performed in software called “bartender”. The main function of thebartender is event mixing and electronics simulation. Multiple events are mixed at a certain
event rate to simulate pileup eﬀects and stored in “sim” ﬁles. The waveform of readout channels
is simulated with the response template and stored in “raw” ﬁles with the same format as theChapter 2 MEG II Experiment

57

y[cm]

1
0.9
−35

0.8
0.7

−36

0.6
−37

0.5
0.4

−38

0.3
0.2

−39

0.1
−40

−73

−72

−71

−70

−69

−68

−67
x[cm]

0

Figure 2.53: Simulation of an electromagnetic shower produced by an impinging gamma ray
from the upper right. Particle tracks are shown as lines (black: γ, red: e+ , green: e− ). Theenergy deposit on each point is overlaid. The scale of the gray bar is in the unit of MeV [2].

real data.
Finally, the “analyzer” analyzes the waveforms with the same algorithm as the data. Bartenderand analyzer are based on the ROME framework [63].

2.9.2 LXe detector simulation
Here we describe the conﬁguration of the detector simulation of the LXe detector and discuss the diﬀerence between the simulation and reality. Table 2.10 summarizes the standard
conﬁguration of the simulation.
In the detector simulation, an electromagnetic shower produced by an incident particle issimulated as shown in Fig. 2.53. VUV scintillation photons are generated at each energy deposit
in LXe with a given scintillation time constant. The number of generated scintillation photons is
calculated from the energy deposit divided by the W-value of LXe, taking the Poisson ﬂuctuation
into account. The reﬂection on the detector material, attenuation by the impurities, and theRayleigh scattering in the LXe are implemented.
The angular dependence of the MPPC PDE is simulated based on that of the reﬂection at thesensor surface, which is calculated from a complex refractive index of Silicon and LXe in gem4.
In the waveform simulation, waveforms are formed in a way that the single photoelectron
response of each photosensor is summed up with the time distribution of the arriving photons

Chapter 2 MEG II Experiment58

amplitude [V]amplitude [V]

1 p.e. Waveform
0

0.004

0.002

0.002

0

0.004

−0.0020.006

rise time:2 ns
fall time: 38 ns

0.008−0.004−0.006
0.01

0

0.05

0.1

0.15

0.2

×10

6

time [sec]

(a)

0

0.05

0.1

0.15

×10
0.2
[sec]

−6

(b)

Figure 2.54: Waveform templates of (a) MPPC and (b) PMT used for waveform simulation [2].
The waveform template of the MPPC is obtained by one photo-electron waveform, and that of
the PMT is obtained by deconvoluting gamma ray waveform by estimated scintillation signal
deﬁned by the scintillation time constant.

simulated in the gem4. Fig. 2.54 shows the single photoelectron response derived from the data.
The single photoelectron response of MPPCs is obtained from the template waveform of single
photoelectron events in data for MPPCs. That of PMTs was obtained by deconvoluting gammaray waveforms by scintillation time distribution since the single photoelectron peak can not be
resolved in the charge distribution.
The MPPC characteristics such as crosstalk, after-pulsing, and saturation are simulated in
the bartender. In the simulation of the crosstalk, each ﬁred pixel in an MPPC can ﬁre anotheradjacent pixel with a given probability. To simulate the afterpulse, a ﬁred pixel can also trigger
another hit on the same pixel with a given probability and time constant. To simulate saturation,
when more than one photon hits the same pixel, the waveform from the second photon is reduced
as a function of the elapsed time from the ﬁrst photon. The individual diﬀerences in the gain,
ECF, PDE, and QE of the MPPCs and PMTs are not taken into account.
The response of readout electronics is applied to reproduce the signal waveforms. A white
noise of a given standard deviation (0.7 mV) is added to the waveform of each readout. The
simulated waveform is digitized by a sampling frequency of 1.4 GHz, and the waveform outside
the dynamic range of the DRS chip (from −950 mV to +50 mV) is cut.
Source of a discrepancy between data and MC
There are several sources of discrepancy between the data and the MC, as listed as follows.
• Reﬂectivity of the inner wall and the surface of the photosensors.
• Attenuation length and Rayleigh scattering length of scintillation light in LXe.
• Liquid level.
• Incident angle dependence of the PDE of the photosensors.

Chapter 2 MEG II Experiment

59

Table 2.10: Standard conﬁguration of simulation for the LXe detector.
gem4
Geant4 version

4.10.06.p03

Physics list

G4EmStandardPhysics

W-value for electron [eV]21.6

W-value for α-particle [eV]19.6

Scintillation Wavelength (mean) [nm]175

Rayleigh scattering length [cm]45

Absorption length [cm]500

Refractive index of LXe

1.69

Reﬂectivity of PMT holder

0.5

PDE (MPPC / PMT)

0.12/0.16

Scintillation time constant [ns]22 (fast) / 45 (slow)

bartender
Sampling frequency [GHz]1.4

Gain (MPPC / PMT)

1.5×106 / 0.8×106

Cross-talk probability

0.15

After-pulsing probability

0.15

After-pulsing time constant [ns]50

The amplitude of white noise [mV]0.7

The reﬂectivities of the detector materials in the MC simulation are deﬁned by the material
properties in literature, and they can be diﬀerent from the real reﬂectivity because of the actual surface conditions of the material. The discrepancy of the reﬂectivity has a large impact
on the light distribution. The Rayleigh scattering length of scintillation light in LXe is set to
45 cm, which is the measured value in Ref. [64], while it is deviated from the theoretical prediction (35 cm) [42]. The discrepancy of the Rayleigh scattering length also can aﬀect the light
distribution. The absorption length was set to 500 cm, which is suﬃciently long with respect tothe detector size. This is because the light yield saturated with the liquid puriﬁcation at the
beginning of the beam time, and because the distance dependence of the number of photons
was consistent with the simulation with 500 cm absorption length as later discussed in Sec. 4.5.
The detector is completely ﬁlled with LXe in the simulation, but it was found that the level isbelow the topmost PMTs in the 2021 run. The light distribution close to the level should havebeen aﬀected by the reﬂection at the interface between LXe and gaseous xenon.

60

Chapter 3

Run 2021
After the LXe detector was installed in 2017, a series of commissioning runs were performed
from 2017 to 2021. The situation of the commissioning runs from 2017 to 2020 is summarized inAppendix A. This chapter focuses on the goal, schedule, and data-taking condition in the 2021
run.

3.1 Overview
Jan

Feb

Installation ofreadout electronics

Mar

Apr

May

Jun

Jul

Aug

Sep

Oct

Nov

Dec

LXe transfer
Cabling
Liquid purification
Signal check
Noise investigation
Detector commissioning run

Physics run
LH2 target preparation
𝝅𝟎 runFigure 3.1: Timeline of the 2021 run. The beam time started at the middle of August aftera series of preparations. After one month of the detector commissioning run, the physics dataacquisition started at the end of September. At the end of year, the π 0 run was performed tomeasure the performance of the LXe detector.

The goal of the 2021 run was to prove that all detectors and hardware were ready for thephysics run and to collect physics data for a short period. To achieve this goal, the following
requirements needed to be fulﬁlled.
• The full system of readout electronics must operate stably and with low noise enough toachieve good detector resolutions.

Chapter 3 Run 2021

61

(a)

(b)

Figure 3.2: Development view with readout region in (top) the 2020 run and (bottom) 2021 run
shown in red. While the number of readout channels was limited to ∼1000 until the 2020 run,the full readout electronics were installed for the 2021 run. Inactive channels are shown in grey.

• All detectors must operate stably in a muon beam environment.
• The trigger for the µ+ → e+ γ search must be established.
• The detector performance and their stability and uniformity are understood to analyze
the dataset.
The timeline of the 2021 run is shown in Fig. 3.1. The detector commissioning run started in
the middle of August after the preparation such as the installation of the readout electronics,
LXe transfer to the detector, and signal check of the photosensors. The physics data acquisition
started in late September and continued until the middle of November. At the end of the year,
the π 0 run was performed to measure the performance of the LXe detector.

3.2 Preparation for physics run
While the number of readout channels was limited to ∼1000 until the 2020 run, as shown in
Fig. 3.2a, the full readout electronics were installed in March 2021 (Fig. 3.2b).
As a result of the signal check, 23 MPPCs and 22 PMTs were found to be unavailable formeasurements, as shown in Fig. 3.2b, with the following reasons.
• The short circuit of the photosensor or the cables connected to the photosensors.

Chapter 3 Run 2021
• The malfunctioning of the HV supply of the PMTs.
• The malfunctioning of the photosensor.
The unavailable channels causes the non-uniformity of the energy reconstruction, which will be
discussed in Sec. 7.2. The noise in the readout electronics was found to be negligible with oﬄine
noise reduction as later described in Sec. 4.2.
The liquid puriﬁcation was performed from 22nd July to 26th July until the light yield reached
the plateau. The light yield of the LXe after the liquid puriﬁcation was 93±5% of the MC
simulation based on the calibration measurements with 241 Am sources. The light yield wasstable within a few % till the end of the 2021 run. The monitoring of the light yield will be
discussed in Sec. 4.6.
The level of LXe in the detector was y =83 cm based on the measurement with the α sources,
later discussed in Sec. 4.5. The reﬂection of the scintillation photons at the interface between
LXe and gXe causes the non-uniformity of the light collection eﬃciency in the detector. Its
impact on the energy reconstruction and the correction will be discussed in Sec. 7.2.
The detector commissioning with the muon beam started in the middle of August. The detector calibration with and without muon beam was established in this preparation period.
Table 3.1 shows the routine of the calibration in the 2021 run. A series of calibration measurements were performed without the beam twice per day. In addition to the dedicated calibration
measurements without the beam, the LED data were mixed with the in-beam data-taking with
0.1 Hz to monitor the photosensor response under a high-intensity environment. Since we had
the plan to carry out the π 0 run at the end of the year, the beam rate was needed to be deﬁned
so that the PDE of the MPPCs did not decrease below 0.04, where the degradation of the resolutions was suggested by the simulation [2]. The beam rate at the beginning of the 2021 run
was set to 3 × 107 /s based on the measured PDE of the MPPCs.
The MEG trigger was developed in parallel with the detector commissioning. The direction
matching and the time coincidence between positrons and gamma rays were developed. The
coincidence window of gamma rays and positrons was aligned with the te+ γ distribution of the
RMD events collected at low intensity (1 × 106 /s).

3.3 Physics run
The physics data-taking started in late September after the MEG trigger was set up. Whenstarting the physics data acquisition, the critical issue was that the data rate with the MEG
trigger was too high to collect all triggered events. The data size of the entire waveform of all
readout channels was 9 MB per event after the compression. Since the trigger rate was 16 Hz
at the beam intensity of 3 × 107 /s, the data rate was 150 MB/s to collect all triggered events.
However, it was not feasible because it exceeded the upper limit of the data rate oﬀered by the
hardware, 130 MB/s. Furthermore, the high data rate was not feasible in terms of the size ofthe data storage. The 1.6 PB data storage of the MEG II collaboration would be shortly used
up if we continue taking the data at such a high data rate.

62

Chapter 3 Run 2021

63

Table 3.1: Calibration routine in the 2021 run. The dedicated calibration measurements were
performed twice per day (morning and afternoon).
Type

Duration [min]Statistics [events]

Random trigger

10

5×103

LED

15

4×103

Alpha

20

1×104

Random trigger

10

5×103

LED

40

2.2×104

Alpha

20

1×104

Neutron generator

12

2.4×104

Cosmic20

9×103

CW Li γ-ray

60

3×104

Morning

Amplitude[mV]

Afternoon

0
− 100
− 200
− 300
− 400
− 500
− 600

Amplitude > 400 mV

Amplitude[mV]

− 700
− 800
20

− 600

− 400

− 600

− 400

− 600

− 400

− 600

− 400

− 200

0
− 20
− 40
− 60
− 80
− 100
− 120
− 140

Amplitude > 50 mV

Amplitude[mV]

− 160
− 180
5

− 200

0
−5
− 10
− 15
− 20

Amplitude < 50 mV

Amplitude[mV]

− 25
− 30

1.5
1
0.5
0
− 0.5
−1
− 1.5
−2
− 2.5

− 200

Amplitude < 10 mV− 200

Time[ns]

Figure 3.3: MPPC waveforms of a gamma-ray event with diﬀerent rebinning conﬁgurations.

Chapter 3 Run 2021

64This issue was solved in two ways. One was data reduction by zero-suppression or rebinningof the waveform. The reduction of the data size from the readout of the LXe detector has a large
impact because the data of the LXe detector readout is 40% of the whole data size due to a large
number of readout channels. Though the rising part of the pulse is important to reconstruct
the timing, the charge integration does not require ﬁne sampling. Furthermore, the waveformwith a small pulse is not used for the timing reconstruction so that the entire waveform can berebinned. Therefore, the rebinning of the waveform was implemented as follows. The reduction
power for each waveform was determined by the peak-to-peak amplitude of the waveform, Apk .
• Apk < 10 mV: fully rebinned by eight.
• 10 mV< Apk < 50 mV: tail part of the waveform is rebinned by 32.
• 50 mV< Apk < 400 mV: tail part of the waveform is rebinned by 16.
• 400 mV< Apk : tail part of the waveform is rebinned by 8.
The rebinned waveforms are shown in Fig. 3.3. The data size of the LXe detector was reduced
to 40% of the original size.
The other solution was the improvement of the uniformity of the online reconstruction ofEγ . In the initial phase of the physics run, there was 10% non-uniformity on the online Eγ
reconstruction, particularly in the v direction. The online Eγ threshold was set to a low value of∼40 MeV at the center of the detector in order to secure ≈100% eﬃciency for >48 MeV gammaray for the whole acceptance of the detector. Since the event rate of accidental backgrounddecreases rapidly with gamma-ray energy, the higher and uniform online Eγ threshold help
reduce the trigger rate without losing the eﬃciency of the µ+ → e+ γ events. The online Eγ
reconstruction was improved by the optimization of the weights used for the EGamma trigger,
as described in Appendix B. Fig. 3.4 shows the v dependence of the EGamma trigger threshold
before and after the optimization. The online Eγ threshold was raised up to 44 MeV without
losing the trigger eﬃciency.
Table 3.2: Beam rate of 2021 run.
PeriodBeam rate [107 /s]

Purpose15 Aug - 15 Oct

3.22

Detector commissioning

25 Sep - 15 Oct

3.22

Physics data acquisition

15 Oct - 28 Oct

1.92

Physics data acquisition

28 Oct - 2 Nov

3.24

Physics data acquisition

2 Nov - 10 Nov

4.01

Physics data acquisition

10 Nov - 18 Nov

4.93

Physics data acquisition

10 Nov - 18 Nov∼0.1

Detector commissioning

These solutions were developed and implemented by late October. They made it possible totake physics data with the MEG trigger at the higher muon beam intensities up to 5 × 107 /s.
The beam rate was increased in steps up to 5 × 107 /s until the end of the muon beam time, in65Ethr [MeV]

Chapter 3 Run 2021

50
Before optimization

49

After optimization

48
47
46
45
44
43
42
41
40

−50

0

50
v [cm]

Figure 3.4: Online Eγ threshold as a function of the v position of the gamma ray. The thresholdNµvalues before (red) and after the optimization (blue) are shown.

×1012
180
160
140
120
100
80
60
40
20
0
01/08/21 31/08/21 30/09/21 30/10/21 29/11/21 29/12/21
Time

Figure 3.5: The time evolution of Nµ in the 2021 run.

order to test the data collection and the stability and to study performance of the detectors at
higher intensities. The beam rate in the 2021 run is summarized in Table 3.2. At the end of
the muon beam time, a dataset was taken to understand the te+ γ distribution with a reduced
beam intensity. Fig. 3.5 shows the time evolution of the number of stopped muons Nµ in the2021 run.
The total live time in the 2021 physics run was 2.9×106 s, which was 63% of the time elapsed
from the beginning to the end of the physics run. The dead time came from the time dedicatedto the calibration measurements, the dead time of the trigger, and the time to transition toa new set of the data-acquisition. The total live time in the 2021 physics run is 8.5% of the
projected total live time in the MEG II experiment, assuming the physics data will be collected
for another three years (2023–2025).

Chapter 3 Run 2021

66

3.4 π 0 run
The goal of the 2021 π 0 run was to investigate the uniformity of the energy and time resolutions
over the detector. As shown in Fig. 3.6, the readout of the inner face was divided into 3 × 8
sections (“patches”). The data were collected for each patch position separately to obtain backto-back two gammas from a π 0 decay. The BGO detector was moved to the opposite directionof each patch position using rails in the z and ϕ direction.

DS

Patch 17

Patch 9Patch 1Patch 18

Patch 10

Patch 2Patch 19

Patch 11

Patch 3Patch 20

Patch 12Patch 4

Patch 21

Patch 13

Patch 5

Patch 22

Patch 14

Patch 6

Patch 23

Patch 15

Patch 7

Patch 24

Patch 16

Patch 8US

Figure 3.6: The 24 patches for the 2021 π 0 run. The size of patches in the middle row (Patch
9–16) is 18×18 cm2 , and that of other patches is 24×18 cm2 . The labels of the x- and y- axis
are the column and row number of the MPPCs, respectively.

The diﬃculty of the 2021 π 0 run was the instability of the new LH2 target because it was not
ﬁlled completely due to a shortage of cooling power. Fig. 3.7 shows the time variation of thetemperature of the LH2 cell and the pressure of gH2 during the run. The plot indicates that thepressure did not fall down to 1.2 bar, which is the pressure when the cell is fully ﬁlled by LH 2 .
It took a long time (a few hours) to have a suﬃcient amount of LH2 in the cell to start dataacquisition after switching to a new liquid helium bottle once per day. The lower LH 2 level thanChapter 3 Run 2021

67

Figure 3.7: Temperature of LH2 cell (top) and pressure of GH2 volume (bottom). The target
was being ﬁlled with LH2 when the pressure of the GH2 volume decreased. The pressure of theGH2 volume jumped when the helium bottle was exchanged.

175770

60556

×10
800

181475

60693

700

30336

157703

60522

600

30325

22775730303

500160520850419360412

18176030300

182421

30336

30337

18205430167

USCenter

DS

3

Top

30263

400
300
200
100

Bottom0

Figure 3.8: The number of events acquired for each patch in the 2021 π 0 run. No data wereacquired for patches 2, 6, and 7 because of the experimental limitation.

Chapter 3 Run 2021
the full coverage of the beam spot caused two diﬃculties on the π 0 run. One is the increase of
the background gamma rays from pions stopped at the back of the target, and the other is thedecrease in the rate of the π 0 → γγ in the target. When this LH2 target became ready for theπ 0 run, there was only one week left until the end of the beamtime.
For the reasons above, the original measurement plan to take suﬃcient data for all patches
was forced to be changed. The π 0 run was performed from 16th December to 22nd December
based on the following priorities. The ﬁrst priority was to measure the detector performancein the central part of the detector to conﬁrm the previous performance evaluation carried out
in 2020 π 0 run. The second priority was to measure the uniformity of the performance in theu and v directions. The middle row in the z-direction (Patches 9–16) was scanned ﬁrst, thenpatches in the downstream side (Patch 17–24) and upstream side (Patch 1, 4–6, 8) were scanned
subsequently. More data were collected for patches 5 and 21 to measure the uniformity of thedetector response in the u direction. The π 0 run ended before completing the scan for patches
2, 3, and 7. Fig. 3.8 shows the number of events obtained for each patch.

68

69

Chapter 4

Calibration and Monitoring of the Liquid
Xenon Detector
4.1 Overview
For a long-term run, it is essential to keep the quality of a gamma-ray measurement bymonitoring and calibrating the detector. The MEG II experiment is planning to take data forﬁve months each year; the stability of the photosensors and the optical properties of LXe must
be monitored throughout the beam time. The response of the photosensors can easily be timevarying due to radiation damage, operating conditions, and the optical properties of LXe, suchas light yield and absorption. The light yield of LXe might change because it depends on thepurity of LXe and must be monitored.
Fig. 4.1 represents the simpliﬁed reconstruction chain from the waveform of 4,760 photosensors
to the position, timing, and energy of the gamma ray. The left-top part shows the analysis foreach photosensor. The raw waveform data is processed to reduce the noise by subtracting noise
templates deﬁned for each readout channel. The corrected waveform is used to calculate thecharge and timing of the pulse.
The number of photo-electrons Nphe and the detected number of photons Npho are calculated
from the integrated charge Q with an integration range of 150 ns as
Q
G × FEC
Nphe
Npho =ϵPD
G = GFE × Gps
Nphe =

(4.1)
(4.2)
(4.3)

where GFE is the gain of the ampliﬁer mounted on the frontend electronics (WaveDREAMboard), Gps is the gain of each photosensor, FEC is the excess charge factor (ECF) that represents
the fake ampliﬁcation factor by correlated noises (crosstalk and after-pulsing) and ϵPD is the
PDE of the MPPCs or the QE of the PMTs.
The left-bottom part of Fig. 4.1 shows the reconstruction phase of the gamma ray. The
position, energy, and timing of the incident gamma ray are reconstructed based on Npho andChapter 4 Calibration and Monitoring of the Liquid Xenon Detector
Nphe , and the timing of the pulse at each photosensor.
The right panel of the ﬁgure summarizes the sensor calibration used for the analysis. In
addition to the noise templates and the conversion factor from Q to Npho and Nphe , the position
and time oﬀset of MPPCs are necessary to reconstruct the position and time, respectively.
The gamma-ray position measurement requires that the positions of MPPCs are aligned witha precision of ∼500 µm to take advantage of the good expected resolution of 2.5 mm. The
alignment will be described in Sec. 4.7. The calibration of the time oﬀset will be later describedin Sec. 8.1.
As summarized in Table 4.1, various methods are prepared to calibrate the detector. Some ofthem are complementary, while others are redundant for backups and crosschecking. CalibrationTmeasurements were frequently carried out in the 2021 run (see Table 3.1).

Calibration

Photosensor
Raw Waveform

Noise template
Corrected Waveform
Timing, 𝑡𝑝𝑚

Integrated charge, 𝑄𝑖𝑛𝑡
Gain & ECF# of photo-electrons, 𝑁𝑝ℎ𝑒

PDE

# of photons, 𝑁𝑝ℎ𝑜
Gamma-ray

MPPC Position

𝛾 - Position

Time offset
𝛾 - Timing

𝛾 - Energy

Energy scale

Figure 4.1: Reconstruction chain of gamma-ray. The left-top part shows the analysis of a photosensor. The raw waveform of a photosensor is corrected by noise templates and the corrected
waveform is analyzed to calculate Nphe , Npho , and tpm . The left-bottom part shows the gammaray reconstruction using the calculated Nphe , Npho , and tpm of the photosensors. The right partshows the calibration parameters necessary for the analysis. The pileup analysis is not includedin this ﬁgure for simplicity.

70

Chapter 4 Calibration and Monitoring of the Liquid Xenon Detector

71

Table 4.1: Calibration measurements
Type

Purpose

SourceEnergyRandom trigger

Noise calibration

-

0

LED

Gain calibration

blue light

460 nm241

Am

PDE calibrationα

5.5 MeV

Cosmic ray

Light-yield monitorµa hundred MeV

CW proton

Light-yield monitorγ17.6 MeV

Thermal neutron captureLight-yield monitor

γ

9 MeV

π0

resolution & eﬃciency measurementγ

54.9–82.9 MeVMPPC Alignmentγ

124 keV57

Co

4.2 Noise reduction
Oﬄine noise reduction for both low- and high-frequency noises is important to calculate thecharge and timing of the pulse for each photosensor. A high-frequency noise can deteriorate
the time resolution. A low-frequency noise whose wavelength is close to the charge integration
time window (150 ns) aﬀects the charge measurement, and it leads to worse energy and position
resolutions. Fig. 4.2 shows the summed waveform of all the MPPC channels with and without
the noise reduction described in this section. The high-frequency noise and the slope of thebaseline as well as the oﬀset are reduced.
For 2021 data, four types of noise reduction are applied. While the ﬁrst three had beendeveloped before the 2021 run, the last one is newly developed for the 2021 run data to suppress
the noise identiﬁed after the installation of the full readout electronics.

Cell pedestal
The voltage response of the DRS cells is calibrated by measuring multiple reference voltages
within the dynamic range of the ADC. This DRS voltage calibration is applied online when the
waveform data is read out and stored on hard disks. However, it is incomplete, and each DRS
cell has a residual voltage oﬀset (cell pedestal). This residual oﬀset generates low-frequency
noise in the DRS waveform. The template of the cell pedestal can be made from a random
trigger dataset by accumulating the waveform as a function of the DRS cell, and it is subtracted
from the data.

High-frequency noise templates
A common clock signal with the same phase is distributed to WaveDREAM boards in order
to align the timing of all boards. However, it generates high-frequency noise synchronously withthe clock phase. This type of noise can be reduced by subtracting a noise template synchronizedChapter 4 Calibration and Monitoring of the Liquid Xenon Detector
to the clock timing. The template can be made from a random trigger dataset by accumulating
the waveform with respect to the clock timing.

Temperature dependent noise
The DRS cells have a small leakage current which depends on the temperature of the DRS
chip. Because the voltage reduction due to the leakage current depends on the hold time until
the readout, the temperature dependence of the leakage current shows up in the DRS waveform
as a slope of the baseline. The relation between the slope and the temperature was measured
and corrected with random trigger datasets collected at diﬀerent temperatures.

Start-cell dependent noise
The coherent noise correlated with the “startcell”, the ﬁrst DRS cell of the waveform, wasfound at the beginning of the 2021 run. Fig. 4.3a shows that the reconstructed energy of thepedestal waveform has a clear dependence on the startcell. The reason for the dependence
remains unknown, but the noise is reduced by making and subtracting a startcell-dependent
waveform template. Fig. 4.3b shows the distribution of reconstructed energy for random trigger
events. While the energy oﬀset and spread are large (O(1) MeV) without any correction, they
are signiﬁcantly reduced down to O(10–100) keV by applying all types of correction. The RMSof the reconstructed energy distribution is 0.26 MeV with all corrections except for the startcell
correction, and it is 0.08 MeV with all corrections. The spread corresponds to 0.16% of thesignal γ-ray energy, and thus it is totally negligible for energy resolution.
Fig. 4.4 shows the stability of the oﬀset and ﬂuctuation of the reconstructed energy for the
random trigger events. The energy spread was 0.15 MeV at maximum through the run, and theenergy oﬀset during the 2021 run had only 0.02 MeV as RMS (Fig. 4.5), which is negligible forthe gamma-ray measurement.

72

Chapter 4 Calibration and Monitoring of the Liquid Xenon Detector

73

Voltage[V]2
w/ Noise Reduction

1

w/o Noise Reduction

0
−1
−2
−3
−4
−600

−400

−200
Time[ns]

Figure 4.2: Summed waveform of MPPC channels with (red) and without (black) noise reduction. The raw waveform has an oﬀset of 3 V, low- and high-frequency noises, but all of them are
reduced by oﬄine noise reduction. The edges of the waveform are noisy and not used for the

1

EventsEped[MeV]

waveform analysis.

0.8

Raw

500

w/o startcell correction

0.6

w/ startcell correction

400

0.4
0.2

300

0
−0.2

200

−0.4

w/o Correction

−0.6

100

−0.8
−1
0

w/ Correction

200

400

600

(a)

800

1000
Start cell

0
−3

−2

−1

0

1

2
3
Eped[MeV](b)

Figure 4.3: (a) Reconstructed energy for random trigger events as a function of the startcell.
(b) The distribution of reconstructed energy for a single random trigger dataset. While theenergy oﬀset and spread are large without correction (black), they are signiﬁcantly reducedwith correction (red).

Eped peak [MeV]

Chapter 4 Calibration and Monitoring of the Liquid Xenon Detector

0.2
0.15
0.1
0.05
0
− 0.05− 0.1

ped

σE [MeV]− 0.15−0.3
0.2

31/08/21

30/09/21

30/10/21

29/11/21

29/12/21
Time

31/08/21

30/09/21

30/10/21

29/11/21

29/12/21

0.25
0.2
0.15
0.1
0.05
0

Time

Figure 4.4: (top) Energy oﬀset and (bottom) the pedestal ﬂuctuation measured with random

Runs

trigger datasets collected in the 2021 run.

30
25
20
15
10
5
0
−0.1

−0.05

0

0.05
0.1
Eped [MeV]

Figure 4.5: Energy oﬀset measured with random trigger datasets collected in the 2021 run.

74

Chapter 4 Calibration and Monitoring of the Liquid Xenon Detector

75

4.3 MPPC gain and ECF calibration
The gain and ECF of the MPPCs were measured by the charge spectrum for low-intensity
LED light (Fig. 4.6). Two LEDs on the outer face at the same vertical position were ﬂashedsimultaneously in a run. The intensity of the LEDs was adjusted so that the MPPCs close to theLEDs detect about one photoelectron on average. This adjustment allows the charge spectrumof MPPCs to have both zero and one photoelectron peaks with a reasonable fraction of events.
The ampliﬁer gain of MPPC readout channels was set to 100 to have the best S/N ratio toseparate the peaks.
The sum of two Gaussian functions was ﬁtted to the zero and one photo-electron peaks,
and the gain was estimated by the distance between the peaks. Since the S/N ratio with an
integration range longer than ∼120 ns was not good enough to separate the two peaks, the total
gain was estimated by the gain values from the analysis of the charge spectra with multiple
short integration ranges. The integration range dependence of the gain values was ﬁtted with
an eﬀective function, G(t) = G × (1 − exp(−(t − t0 )/τfall )), where τfall is the time constant of
the tail of single photo-electron response and t0 is the timing oﬀset, as shown in Fig. 4.7b. The
scale of the function was regarded as the total gain for one photoelectron.
The ECF can be measured from the charge spectrum as,
FEC = Qmeasured /Qexpected(4.4)= Qmeasured /Gλ,(4.5)

where Qmeasured is the average of measured charge. The expected charge without correlated
noises Qexpected is the product of the gain G and the expected number of photo-electrons λ.
If there is no correlated noise, the detected number of photoelectrons from an LED follows a
Poisson distribution with the mean λ. Since the number of zero photoelectron events Npedestal
is not aﬀected by the correlated noise, λ is estimated using the fraction of Npedestal as,
Npedestal /Ntotal = exp(−λ) → λ = − log(Npedestal /Ntotal ),(4.6)

where Ntotal is the total number of events in the charge spectrum. As we did for the gain, λ wasestimated with the measured λ with the multiple short integration ranges as shown in Fig. 4.7a.
Fig. 4.8a shows the MPPC gain and ECF as a function of the serial number. The gainof the photosensor Gps was (1.3–1.7)×106 and had a small production lot dependence. The
precision of the absolute gain measurement was 2.5% from the statistical uncertainty of theﬁtting of the spectrum. On the other hand, the ECF was 1.3–2.5 and had a large dependence
on production lots. Even though a large variation was observed, this is still acceptable as longas we can measure it correctly. The dominant uncertainty of the ECF measurement came fromthe statistical uncertainty of λ, which was 1–5% depending on λ. It should be noted that theuncertainty of the absolute gain and ECF becomes the uncertainty of the PDE measurement,
but they do not aﬀect the conversion factor from the integrated charge to Npho since the PDE
was calibrated with the measured gain and ECF of each photosensor.

Events

Chapter 4 Calibration and Monitoring of the Liquid Xenon Detector

76

80
70
60
50
40
30
20
10
0
−0.1

0

0.1

0.2

0.3
0.4
9
Charge [10 e]

Figure 4.6: Charge spectrum under low-intensity LED light. The red line is the sum of the two
Gaussian functions ﬁtted to the data. The charge integration range is 70 ns.

The time variation of the gain and ECF was monitored by using the charge under stable LED
light. The integrated charge under LED light can be described as
Q = Npho × G × FEC × ϵvis
PD ,

(4.7)

where ϵvis
PD is the detection eﬃciency for visible light. By using this charge, the relative time
variation of the gain and ECF can be traced together with ϵvis
PD with good precision, though
it does not provide an accurate measurement of their absolute values since the number of incoming photons cannot be accurately estimated. A Gaussian function was ﬁtted to the charge
distribution of O(103 ) LED events, and the mean value was used in order to monitor the sensor
response for the visible light.
Fig. 4.9 shows the time variation of the average Q under the LED light in the 2021 run. The
average Q of the MPPCs gradually decreased by 4% during the 2021 run. This decrease wascorrelated with the decrease of the PDE for the VUV light due to the radiation damage later
discussed in Chapter 5. The sharp decrease of ∼1% in early November was due to the temperature instability as explained in Sec. 2.3.4.5. The temperature of LXe increased by 1 K, andthe breakdown voltage increased by 0.8% because of the temperature dependence (56 mV/K).
Since we applied a constant bias voltage to each MPPC, the increase in the breakdown voltage
resulted in a decrease in the overvoltage. The MPPC response decreased by 1.3% since theovervoltage dependence of the ECF is more than linear, while the gain is proportional to theovervoltage.
Another observation was that the charge in the beam was smaller than that without the beam.

λ

1.6

Fit

9

λ

2
1.8

Gain [10 e]

Chapter 4 Calibration and Monitoring of the Liquid Xenon Detector

1.4

0.14

Peak

0.12

Fit

77

0.1

1.2
0.08

1
0.8

0.06

0.6

0.04

0.4
0.02

0.2
0
0

50

100

0
0

150
tint [ns]

50

(a)

100

150
tint [ns](b)

Figure 4.7: (a) λ and (b) gain estimated by the charge spectra with multiple integration ranges.
Red lines show the ﬁtting functions deﬁned by a scale C, the time oﬀset t0 , and a time constant
λ as F (t) = C × {1 − exp (−(tint − t0 )/λ)}.

1800 ×10

ECF

Gain

3

3.5

A
B

1700
3

C
D

1600
2.5

1500
1400

2

1300

A

1.5

B

1200

C
D

1100
0

2000

4000

6000
Serial Number

1
0

2000

(a)

4000

6000
Serial Number(b)Figure 4.8: Measured (a) gain and (b) ECF of MPPCs as a function of the serial number. The
colors of each point show the production lot of the MPPC.

The eﬀect was 0.2% under 3 × 107 /s muon beam and 1.0% during the π 0 run. This is likely
due to the voltage drop by the induced current under a high-intensity environment. Fig. 4.10
shows the current of one MPPC channel in the center of the entrance face. The current value
was 0.5–1.4 µA depending on the beam intensity in the muon beam period and 2–2.5 µA in theπ 0 run. The eﬀect of the induced current on the gain was foreseen in the design phase, and asmall resistance of 2 kΩ in the series connection with the MPPC chip was adopted to reduceit [47]. The measured dependence in the actual detector was 0.2–0.4%/µA, as was expected.
The time variation of Q, as shown in Fig. 4.9, was used to correct the time variation of gain(normalized)

1.02

LED

Chapter 4 Calibration and Monitoring of the Liquid Xenon Detector

0.99

78

w/ Beam

1.01
1Q

w/o Beam

0.98
0.97
0.96
0.95
0.94
31/08/21

30/09/21

30/10/21

29/11/21

29/12/21
Time

Figure 4.9: Average MPPC charge under LED light of a ﬁxed intensity with and without beam
(red and blue, respectively) as a function of time. The average of all MPPCs is shown. The
gradual decrease in charge is due to the decrease in the ϵvis
PD . The sharp drop at the beginningof November is due to the temperature instability.

and ECF of each photosensor. The time variation of Q is normalized with the absolute gain
measured in the middle of the 2021 run. In this method, the time variations of gain and ECF
are corrected together with the ϵvis
PD .
After all the gain calibrations were applied, the peaks of LED events mixed in physics datataking showed good stability. Fig. 4.11a–4.11b show the time variation and distribution of the
LED peak position of Nphe of a single MPPC, and Fig. 4.12a and 4.12b show those of the sum
for all MPPCs. The sigma of the distribution was 0.2% and 0.02% for a single MPPC and all
MPPCs, respectively. This is good enough to achieve <0.5% stability so that the stability does
not limit the energy resolution.

4.4 PMT gain calibration
The PMT gain was calibrated by using the photo-electron statistics of LED light. The averageof the integrated charge can be written as
Q = G · e · N phe ,(4.8)

Current[µA]

Chapter 4 Calibration and Monitoring of the Liquid Xenon Detector

79

4
3.5
3
2.5
2
1.5
1
0.5
0
01/08/21 31/08/21 30/09/21 30/10/21 29/11/21 29/12/21
Time

Figure 4.10: The readout current of an MPPC in the central region of the inner face as afunction of time in the 2021 run. The readout current was 0.5 µA–1.5 µA in the muon beam
period depending on the muon beam rate. The current in the π 0 run was 2.0–2.5%. The current

Nphe

without beam was 0.05 µA.

340

40

25

320
35

300

30

280
260

25

240

20

220

15

200

10

180

20
15
10
5

5

160
04/11

0

07/11

0
250

255

260

Time

(a)

265

270
Nphe

(b)

Figure 4.11: (a) The time variation and (b) distribution of LED peaks of a single MPPC in the2021 physics run.

Chapter 4 Calibration and Monitoring of the Liquid Xenon Detector
15.2 ×10

40

15.15

35

80

Weighted Sum of Nphe (a.u.)

6

15.1
15.05
15

25

14.95

20

14.9

15

25
20
15

14.85

10

10

14.8
14.75
14.7

30

30

04/11

07/11

5

5

0

0

0.996

0.998

1

Time

(a)

1.002
1.004
LED peaks (a.u.), MPPC(b)

Figure 4.12: (a) The time variation of LED peaks mixed in the 2021 physics run. (b) Distributionof LED peaks in the 2021 physics run. A Gaussian ﬁt function with 0.02% sigma is shown in

18

Variance[10 e2]

red line.
PMT 4092

×10−3
0.7
0.6
0.5
0.4
0.3
0.2

Raw

0.1
0
0

Fit, Gain=767697.6

0.1

0.2

0.3
Charge[109e]

Figure 4.13: Measured relation between the variance and mean of the charge spectrum under
LED light with various intensity.

where N phe is the average number of photoelectrons, and e is the elementary charge. The
variance of the charge distribution can be expressed as
2
2
2
2
σQ
= (G2 + σG
) · e2 · (σphe+ σLED) + σ02(4.9)

where σ0 is the noise of the readout electronics, σLED is the ﬂuctuation of the LED pulsar output,and σG is the resolution for a single photo-electron. Assuming that the gain ﬂuctuation is small
with respect to the gain (σG ≪ G), that the LED is suﬃciently stable (σLED ≪ σphe ), and thatthe distribution of the number of detected photo-electrons Nphe follows a Poisson distribution,
2
2
can be described as follows.
σphe= N phe , the variance of the charge distribution σQ
2
2
σQ= G2 · e2 · (σphe) + σ02(4.10)= G2 · e2 · N phe + σ02(4.11)= G · e · Q + σ02(4.12)

Chapter 4 Calibration and Monitoring of the Liquid Xenon Detector
2
Eq. 4.12 means that the variance σQ
can be expressed as a linear expression of the mean of thecharge Q. The charge distribution was measured at several LED intensities, and the mean andvariance are plotted as shown in Fig. 4.13. The absolute PMT gain can be calculated by ﬁtting
this correlation between the mean and variance. This calibration method is called “intensity
scan”.
At the beginning of the 2021 run, the gains were adjusted to 8 × 105 for the following reasons,• Equalize the PMT performance, such as timing response.
• Keep a pulse height within the dynamic range of the readout electronics.
The bias voltage of each PMT was determined by the relation between the voltage and the gain,G ∝ (V − V0 )k , where V0 was 100 V, and k was 9.5. These values were empirically determinedfrom the experience of the commissioning runs. Fig. 4.14a and 4.14b show the distribution of
the PMT gain and the bias voltage after the adjustment, respectively. The gain distribution has
the mean value of 8.4×105 and 3% standard deviation after the adjustment.
Fig. 4.15 shows the time variation of the PMT gain without the beam measured in two
methods, the intensity scan and the charge under stable LED light. The absolute gain fromthe intensity scan decreased by 14% through the beam time, while the charge for LED lightdecreased by 11%. The reason for the discrepancy might be the systematics of the intensity
scan. If σG or σLED has a non-negligible impact on the gain calibration, it could explain thediscrepancy.
The time variation of the gain was corrected by the time variation of charge, and the absolutevalue was normalized by the absolute gain measured by the intensity scan in the middle of the2021 run. Fig. 4.16a shows the time variation of the LED peaks mixed in the physics run after
the gain correction. The ﬂuctuation of the LED peaks was only 0.02%, as shown in Fig. 4.16b.
As mentioned in Sec. 2.3.3, the impact of the gain shift during the data-taking was negligible
in the 2021 run because the data-taking of the physics run started a few minutes after the beam
blocker was opened, while the main time variation of the gain shift has O(10) s time constant.
As shown in Fig. 4.17, the time variation of the number of photons collected by PMTs NPMT
after opening the beam blocker is just 0.03%, which is acceptable. Therefore, no correction isapplied to correct the eﬀect of the gain shift.

81

PMT

PMT

Chapter 4 Calibration and Monitoring of the Liquid Xenon Detector

35

82

50

30
40
25
30

20
15

20

10
10

5
×10
1000
Gain

3

0
700

750

800

850

900

950

0
600

800

(a)

1000

1200
HV[V]

(b)

Figure 4.14: (a) Gain and (b) bias voltage of PMTs at the beginning of the 2021 run. The gain

PMT Response (normalized)of all PMTs is adjusted to be 8.4×105 .

1.1
LED Charge

1.05
Gain

1
0.95
0.9
0.85

31/08/21 30/09/21 30/10/21 29/11/21 29/12/21
Time

Figure 4.15: PMT gain measured with the intensity scan (red) and charge (blue) as a function oftime. The average values of all PMTs are shown. The diﬀerence between the two measurements
is considered to be due to the systematic error of the gain measurement by the intensity scan.

4.5 PDE and QE calibration
The PDE of MPPCs and the QE of PMTs were estimated by using the 241 Am sources. Since
the positions of the installed sources and the energy of the emitted alpha ray are known, thenumber of photoelectrons observed by each photosensor can be calculated by means of MC
simulation. The PDE and QE were extracted from the comparison between the measured
photoelectrons and the calculated ones by the MC. The wavelength of scintillation light fromalpha particles is the same as that from gamma rays. Thus, the estimated PDE and QE from

Weighted Sum of N

phe(a.u.)

Chapter 4 Calibration and Monitoring of the Liquid Xenon Detector

29.3 ×10

6

30

29.2

25

29.1

20

29

15

28.9

10

28.8

5

28.7

04/11

0

07/11

24
22
20
18
16
14
12
10
8
6
4
2
0

0.996

0.998

1

Time

(a)

83

1.002
1.004
LED peaks (a.u.), PMT(b)Figure 4.16: (a) LED signal amplitude of PMTs during the physics run and the time variationof the peak (red) and (b) the distribution of the LED peak.

29.5 ×10

NPMT

6

20

29.4

18

29.3

16

29.2

14

29.1

12

29

10

28.9

8

28.8

6

28.7

4

28.6

2

28.5
0

1000

2000
3000
Time after BB open [s]0Figure 4.17: NPMT of the LED events as a function of the elapsed time after the beam blocker
was open. The mean value of the NPMT distribution in the ﬁnite period is shown in red.

alpha sources can be directly used for the gamma-ray reconstruction.
The main background of the calibration is cosmic-ray events. A particle identiﬁcation was
carried out by pulse shape discrimination. Fig. 4.18 shows the ratio between the charge andamplitude of the summed waveform of all PMTs. The events whose ratio is larger than a given
threshold were rejected as they originated from cosmic-ray.
The source spot that generated the α-ray in each event was identiﬁed with the light distributionof the PMTs. The wire of the source was determined by comparing the total number of detectedEvents

Chapter 4 Calibration and Monitoring of the Liquid Xenon Detector

3500

Cosmic

3000

Alpha

2500
2000
1500
1000
500
0
0

5

10

15
QA ratio

Figure 4.18: Ratio between charge and amplitude of the summed waveform of all PMTs in adataset collected by the alpha trigger. The peak at 5 (red) corresponds to the α-ray events, andEventsthat at 8 (black) corresponds to cosmic-ray events.
120
100
80
60
40

Wire 1

Events

20
120
0−40

−20

0

20

−20

0

20

−20

0

20

−20

0

20

−20

0

20

40
Z [cm]

100
80
60
40

Wire 2

Events

20
120
0−40

40
Z [cm]

100
80
60
40

Wire 3

Events

20
120
0−40

40
Z [cm]

100
80
60
40

Wire 4

Events20

1200−40
100
80
60
40
20
0
−40

40
Z [cm]

Wire 540
Z [cm]

Figure 4.19: Reconstructed z position of ﬁve alpha source spots for wire 1 (top)–5 (bottom).
The distribution of ﬁve source spots is shown in diﬀerent colors.

photons in 32 PMTs in the downstream and upstream faces around each wire. Then, the spot
was identiﬁed with the average z-position of the PMTs weighted by Npho . Fig. 4.19 shows thereconstructed z position for each wire. Five peaks corresponding to the source spots on a wire
were well separated for all the wires, indicating that the spot can be uniquely identiﬁed.
Fig. 4.20 shows the correlation between N phe,Data , the average number of detected photoelectrons in data, and N phe,MC , that in a dedicated MC simulation for each source. The PDE

84

Chapter 4 Calibration and Monitoring of the Liquid Xenon Detector

Nphe

Data

Nphe

MC

vs NpheData

85, PM4759, OUTER, PMMC4759

45
40
35
30
α source

25

Linear Fit

20
15
10

Slope: 1.22

5

χ2/NDF: 1.86

0
0

10

20

30

40
Nphe

MC

Figure 4.20: Correlation of Nphe,Data and Nphe,MC for a PMT. Each data point corresponds toa source spot. The slope of the linear ﬁt function was used for the PDE calibration.

in data ϵData
PD is calculated as,

MC
ϵData
PD = ϵPD × R × FLY ,(4.13)

where R corresponds to the slope of the correlation between N phe,Data and N phe,MC and FLY
is the light yield of liquid xenon. ϵMC
PD was 0.12 for MPPCs and 0.16 for PMTs in the MC
simulation. FLY was adjusted so that the mean of all PMT QEs takes 0.16.
There are several sources of the uncertainties of the PDE (QE) measurement as summarizedin Table. 4.2. The uncertainty of the gain and ECF is a source of the systematic uncertainty
because it becomes the uncertainty of the N phe,Data . The reﬂection at the walls increases Npheof each photosensor. Hence, the diﬀerence in the reﬂectivity of the walls between data and MC
simulation becomes the systematic error of the PDE (QE) and light yield. In particular, the PMT
holder covers a large area of the wall, and its reﬂectivity has a large impact on light distribution.
The reﬂectivity was estimated as 50±10% by comparison of the light distribution between thedata and simulation. The light distribution of several sets of MC simulations with diﬀerent
reﬂectivities was compared with the measured light distribution, and the simulation with 50%
reﬂectivity reproduced the measured distribution best. The uncertainty of the PDE (QE) andthe light yield from the uncertainty of the reﬂectivity was estimated to be 5%.
Another source of systematic uncertainty is the absorption of scintillation photons in LXe.
The absorption induced by impurities decreases Nphe , particularly when a photosensor is distantfrom the source spots. Fig. 4.21 shows the ratio between N phe,Data and N phe,MC as a function

Chapter 4 Calibration and Monitoring of the Liquid Xenon Detector

86of the distance between a 241 Am source spot and a photosensor. The distance dependence
indicates that the absorption in data was not signiﬁcant with respect to MC simulation witha long absorption length (500 cm). The increased R for distant sources (>80 cm) is likely due
to the diﬀerence in the reﬂectivity of the wall between data and MC. The uncertainty of thelight yield from the absorption is <1% and negligible with respect to the uncertainty from thereﬂection.

R = Nphe, Data / Nphe, MC

OUTER

3

25

2.5
20
2
15
1.5
10
1
5

0.5
0
0

20

40

60

80
100
Distance [cm]0

Figure 4.21: Ratio between N phe,Data and N phe,MC as a function of the distance between 241 Am
source and a photosensor. PMTs on the outer face and 25 sources are overlaid. The black points
show the distance dependence of the averaged ratio.

Though the uncertainties of the light yield and the PDE (QE) are large, it does not becomea problem for the gamma-ray measurements, because the energy scale and the non-uniformityof the reconstructed energy will be determined and corrected by using the gamma-ray dataset.
Fig. 4.22 shows the PDE distribution of all channels in the development view, and Fig. 4.23a
and Fig. 4.23b show the distribution of the PDE of MPPCs and PMTs, respectively. The
average PDE of MPPCs at the end of the 2021 run was 0.06. The low PDE with respect tothe reported PDE in the phase of the development (0.18–0.20) [47] is due to the unexpectedradiation damage, and it will be discussed in Chap. 5. The large position dependence comesfrom the systematic errors of the PDE calibration and the position dependence of the radiation
damage. The MPPCs used until the 2020 run are surrounded by red lines in Fig. 4.22 and had
been damaged particularly.
Fig. 4.24 shows the QE of the PMTs as a function of the y position of PMTs. While it isChapter 4 Calibration and Monitoring of the Liquid Xenon Detector

87

Table 4.2: Uncertainties of PDE (QE) measurement.
SourceRelative uncertainty

Gain2.5% (MPPC) / 2% (PMT)ECF

1–5% (MPPC)

Reﬂection at the walls

5%

Absorption

O(1)%Liquid level

O(1)% (y <50 cm) / O(10)% (y >50 cm)

Light yield5%

Total uncertainty

10%

100

0.25

80

100

60

80

40

60

20

40

0

20

0.22

0.19

0.16

0

0.12

−20

0.09

−40
−60

0.06

−80
−100
−100

0.03

0

100

200

z

300
0.00

Figure 4.22: PDE (QE) distribution at the end of the 2021 run in the development view. The
MPPCs surrounded by red lines were used until the 2020 run.

generally uniformly distributed along the y-axis, a lower QE is measured for PMTs at y >83 cm.
Furthermore, the QE of some PMTs slightly below 83 cm was up to twice higher than other
PMTs. This indicates that the liquid surface (the boundary surface with gas xenon) was aroundy=83 cm. The reﬂection at the liquid surface due to a mismatching of the refractive index
between LXe (1.69) and gXe (∼1) reduced the number of photons detected by the PMTs above
the liquid surface. It also explains that the QE of the PMTs slightly below the liquid surface
was high, as the reﬂection increased the number of detected photons. Since the measured QE
for PMTs close to the liquid level had a relatively large systematic error up to 10%, the PMTs
with y >50 cm were excluded from the PMTs for the light yield normalization.
Fig. 4.25a shows the time variation of the average MPPC PDE during the 2021 run. The
average MPPC PDE gradually decreased from 0.082 to 0.060. Considering the monitoring withgamma rays or cosmic rays indicated that the total number of photons detected by the MPPCs
increased during the beam time, the degradation measured with alpha might be overestimated.

300

PMT

MPPC

Chapter 4 Calibration and Monitoring of the Liquid Xenon Detector

88

30

250
25
200

20

150

15

100

10

50

5

0
0

0.05

0.1

0.15

0.2
PDE

0
0

(a)

0.05

0.1

0.15

0.2

0.25 0.3
PDE(b)

Figure 4.23: (a) Distribution of the PDE of the MPPCs and (b) the QE of the PMTs at thePDE

end of the 2021 run.

0.35
0.3
0.25
0.2
0.15
0.1
0.05
0

−100

−50

0

50

100
y [cm]

Figure 4.24: QE as a function of the y position of the PMT. The dashed line shows the estimatedLXe level (83 cm). The QE of the PMTs above this level is obviously lower than that of the
PMTs below.

0.1Light Yield

PDE

Chapter 4 Calibration and Monitoring of the Liquid Xenon Detector

0.095
0.09
0.085
0.08

89

1
0.98
0.96
0.94

0.075

0.92

0.07
0.9

0.065
0.06

0.88

0.055

0.86

0.05

31/08/21 30/09/21 30/10/21 29/11/21 29/12/21
Time

31/08/21(a)

30/09/21

30/10/21

29/11/21
Time(b)

Figure 4.25: (a) Average MPPC PDE and (b) FLY in the 2021 run.

Fig. 4.25b shows the time variation of the light yield, FLY . The absolute light yield value is
93 ± 5% of the MC simulation. The time variation of the light yield will be discussed in the next
section.

4.6 Light yield and energy scale
The energy of the gamma-ray Eγ is calculated by using the weighted sum of the Npho of the
MPPCs NMPPC and that of the PMTs NPMT as
Eγ = C × F (u, v, w) × T (t) × (NMPPC × rMPPC (t) + NPMT )(4.14)

where C is the energy scale to convert the number of photons to the energy, F (u, v, w) is a
uniformity correction function, T (t) is a function to correct the time variation of the energy
scale, and rMPPC (t) is a function to correct the time variation of the NMPPC with respect to
the NPMT . The uniformity correction of the energy scale and the weights for the MPPCs andthe PMTs to calculate the NMPPC and NPMT are summarized in Sec. 7.1. Here we focus on thecorrection functions of the time variation T (t) and rMPPC (t) to discuss the stability of the energy
scale. The time variation of the energy scale comes from the time variation of the properties of
LXe, such as the light yield and the absorption length. Since the NPMT was stable in the MEG,
it was used to monitor the light yield. The rMPPC (t) and T (t) were determined by a procedure
as follows.
1. Determine rMPPC (t) and T (t) based on the monitoring with the 17.6 MeV gamma-ray
from the CW-Li setup and the cosmic-ray .
2. Update T (t) in the physics run based on the energy scale estimated by the energy spectrumof the background gamma-ray collected by the MEG trigger.

Chapter 4 Calibration and Monitoring of the Liquid Xenon Detector

90

EventsEventsCW-Li gamma

450
400

500
400

350
300

300

250
200

200

150
100

100

50
0

15

20

0

25
NMPPC[a.u.]

15

(a)

20

25
NPMT[a.u.](b)

Figure 4.26: The spectrum of the (a) NMPPC and (b) NPMT for 17.6 MeV gamma rays. The redlines are Gaussian ﬁtting functions to estimate the energy peak for the monitoring. The values
are normalized so that the peak comes to around 17.6.

Since the CW-Li gamma-rays are monochromatic (17.6 MeV), the distribution of NMPPC andNPMT has a peak with a simple non-uniformity correction in the w direction. Fig. 4.26 shows
the distribution of NMPPC and NPMT . A Gaussian function was ﬁtted to the distribution tomonitor the NMPPC and NPMT with the mean value of the Gaussian.

450

Raw

400

Position Selection

350

Landau Fit

EventsEventsCosmic-ray

700

MPPC

600

PMT

500

300
400

250

300

200
150

200

100
100

50
0
0

100

200

(a)

300

400
500
Energy[MeV]

0
0

100

200

300

400

500
nsum

(b)

Figure 4.27: (a) The energy spectrum of the cosmic-ray with (blue) and without (black) event
selection. The red line shows a landau function ﬁtted to the spectrum with the selection. (b)The NMPPC (black) and NPMT (red) distribution of the cosmic-ray with the event selection.

Chapter 4 Calibration and Monitoring of the Liquid Xenon Detector

91

The energy deposit by a cosmic ray in the LXe detector depends on the path length in the
LXe volume. By selecting the cosmic rays which passes through the entrance face and makes apeak there in the light distribution with the selection criteria as below, a ∼170 MeV peak was
clearly separated from low-energy events that come from cosmic-ray events with a short path
length in LXe volume, as shown in Fig. 4.27a.
• |u| < 20 cm, |v| <65 cm, w < 10 cm.
• NMPPC /Nouter < 1.6
where Nouter is the weighted number of collected photons by PMTs in the outer face. Fig. 4.27bshows the distribution of NMPPC and NPMT for the cosmic-ray events. A Landau function was
ﬁtted to the peak of the distributions to monitor the relative time variation of the energy scale.
The time variations of the NPMT monitored with alpha, CW-Li gamma-ray, and cosmic-ray
are summarized in Fig. 4.28a. The ﬂuctuation of the NPMT was within a few percent in the 2021
run. The time variation of the NPMT represents the time variation of the light yield of LXe,
considering that the QE of the PMT was stable in the MEG experiment. The time variation of
the NMPPC shown in Fig. 4.28b indicated that the NMPPC gradually increased. The discrepancy
is likely due to the diﬀerence in the distance and the incident angle from the light source to thesensor between the calibration measurements. The reciprocal of the time variation of the NPMT
normalized at the beginning of the π 0 run was used as the T (t), and the rMPPC (t) was calculated
norm
norm
stands for the NPMT at the− NPMT )/NMPPC where NPMT
by interpolating the ratio (NPMT

normalization of the T (t). The data points were interpolated by a smooth line to mitigate thestatistical ﬂuctuation of the individual measurement, and the line was used for correction to

1.05

nMPPC[a.u.]nPMT[a.u.]

keep the energy scale stable during the beam time.

1.04
1.03

1.05
1.04
1.03

1.02

1.02

1.01

1.01

1

1

0.99

0.99

0.98

Cosmic-ray

0.97

CW-Li
Alpha

0.96
0.95

31/08/21 30/09/21 30/10/21 29/11/21 29/12/21
Time

0.98

Cosmic-ray

0.97
0.96
0.95

CW-Li
31/08/21 30/09/21 30/10/21 29/11/21 29/12/21
Time

(a)

(b)

Figure 4.28: (a) NPMT and (b) NMPPC as functions of time. The results with CW-Li gamma-ray(blue), cosmic-ray (red), and alpha (green) are shown.

92

Scale

Scale

Chapter 4 Calibration and Monitoring of the Liquid Xenon Detector

1.004

1.02
After Correction

1.015
1.01

1.002

Before Correction

1.005

1

1
0.995

0.998
0.99
0.985
0.98

0.996
30/09

14/10

28/10

16/12

11/11

17/12

18/12

19/12
Time

Time

(a)

(b)

Figure 4.29: (a) Time variation of the energy scale measured with the BG gamma-ray spectrum.
The energy scale with the T (t) estimated by the cosmic-ray and CW-Li gamma-ray is shown inblue. The energy scale with the updated T (t) by the BG gamma-ray spectrum is shown in red.
(b) Time variation of the energy scale measured with the 55 MeV gamma-ray spectrum in theπ 0 run. The ﬂuctuation of the energy scale was 0.1% for the π 0 run period.

BG gamma-ray spectrum
Fig. 4.29a shows the time variation of the energy scale monitored by the background gammaray in the time sideband*1 of the physics dataset after the correction with rMPPC (t) and T (t)based on the comsic-ray and the CW-Li gamma-ray. The dataset of the time sideband was
divided into subsets based on the periods, and the energy scale in each period was estimatedby ﬁtting an expected Eγ spectrum to the measured Eγ spectrum in the time sideband. The
Eγ spectrum was estimated by smearing the energy spectrum in the MC simulation and adding
the measured cosmic-ray energy spectrum. Fig. 4.29a shows the time variation of the energy
scale with the corrections. The systematic uncertainty of the energy scale that comes from themonitoring was estimated to be 0.36% based on the diﬀerence between the T (t) estimated by
the cosmic-ray and CW-Li gamma-ray (the ﬁrst step) and that by the background gamma-ray
in the second step.

55 MeV gamma-ray from π 0 decay
The time variation of the energy scale during the π 0 run was corrected based only on thecosmic-ray dataset because the CW beamline is not compatible with the LH2 target for theπ 0 run. The correction during the π 0 run was validated with the 55 MeV peak of gamma-rays
from the π 0 → γγ. Fig. 4.29b shows the time variation of the 55 MeV peak during the π 0 run*1 See Sec. 11.1 on the deﬁnition of the time sideband

Chapter 4 Calibration and Monitoring of the Liquid Xenon Detector
after the correction. The time variation of the energy peak was limited to 0.1%, thanks to thecorrection.

4.7 Alignment of MPPC
The position of the MPPCs was measured by two complementary methods. One method is adirect optical alignment at room temperature in the construction phase and the other method
uses a collimated and well-aligned gamma-ray beam after the detector is ﬁlled with LXe.

4.7.1 Alignment at room temperature
The surface of the arrays of the MPPCs was surveyed by a laser scanner (Faro Edge ScanArm [65]) in the construction phase [66] as shown in Fig. 4.30a. The scanner was inserted
from the side of the detector and it measured the surface structure of the MPPC array by triangulation, which measures the position of the object from the reﬂected light of the irradiatedlaser. Fig. 4.30b shows the data points measured with the scanner for several MPPCs. The
colors of the data points show the contour of the surface structure. While the four chips andthe gap between them are clearly visible for the MPPC in the center, data points are missing
from the upper half of the MPPC on the left (white region). The positions of the MPPCs werereconstructed using the gap between the four MPPC chips. A symmetric function was ﬁtted tothe data points in the central part of an MPPC to reconstruct the center position of the MPPC.
All MPPCs were surveyed, and the three-dimensional position of 426 MPPCs was reconstructedwith good quality. While the reconstruction was successful for the MPPCs well within reachof the scanner’s arm, it failed for MPPCs far from the support of the arm due to the diﬀused
reﬂection at the surface.
Since the MPPCs are mounted on the PCBs precisely with the same interval (15.1 mm), theresolution of the measurement was estimated from the distribution of the distance between
adjacent MPPCs, as shown in Fig. 4.31. The resolution was estimated to be 120 µm based on
the sigma of the distribution.
The position of all MPPCs was interpolated by the measured positions of the limited numberof MPPCs by the following procedures separately for all CFRPs.
1. Fit a cylindrical surface to the reconstructed points of the MPPC center with six parameters, ﬁve for the core axis and one for the radius.
2. Project the array of the 3D reconstructed data points to the cylindrical surface.
3. Fit the projected array of reconstructed data points with a lattice assuming equal spacing.
4. Calculate the position of all MPPCs as lattice points.
5. Reconstruct the 3D position of all MPPCs with the parameters of the cylinder and theposition of all MPPCs.
The reconstructed position was consistent with the measured position to an accuracy of 180 µm

93Chapter 4 Calibration and Monitoring of the Liquid Xenon Detector

94yMPPC 224

15
10
5
0
−5
−10
−15

−10

0

10
x

(a)

(b)

Figure 4.30: (a) Survey with a Faro laser scanner. The scanner was inserted from the upstream
or downstream of the detector, and the surface structure of the MPPC array was surveyed. (b)Measured data points around an MPPC with the laser scanner. The color of each data pointshows the contour. The orange and red points show the ceramic package of the MPPCs, andmost of the blue points show the gap between MPPC chips. The white region on left and bottom
show the region where no data are collected by the scanner.

# of MPPC∆ Z=Zi+1-Zi
18
16
14
12
10
8
6
4
2
0
14

14.5

15

15.5

16

∆ Z[mm]Figure 4.31: Distance between adjacent MPPCs. The distribution of the distance between theposition of odd channel − even channel is shown in red and that between even channel − oddchannel in blue.

based on the deviation between them. The interpolated positions by the above procedures wereused to combine the positions measured by the other method, later discussed in Sec. 4.7.3.

4.7.2 Alignment with gamma-ray beam
The positions of the MPPCs are aﬀected by thermal contraction and by cryostat deformations
due to the fact that the detector is ﬁlled with the cold (169 K) and heavy (2.7 t) LXe. SinceChapter 4 Calibration and Monitoring of the Liquid Xenon Detector

95

LXe detector
PMT

Gamma-rayGamma-ray Device

COBRA magnet

y

MPPC

x
z
φ
Satoru Kobayashi

26

Figure 4.32: Schematic side view of the MPPC position measurement with the low-energy
gamma-ray beam. The gamma rays emitted from the collimator in the center of the COBRA
magnet are used for the position measurement of the MPPCs.

Laser Emitter
Rotation Stageφ motion
BubbleBeamCollimatorz motion
Linear Stage
Figure 4.33: Brass collimator where the 57 Co is installed inside and the two stages to control
the gamma-ray beam position at the entrance face.
Satoru Kobayashi

85

neither of the two eﬀects can be precisely modeled, it is diﬃcult to estimate the actual positionof the MPPCs from the measured positions at room temperature. Therefore, the measurements
for the in-situ positions of the MPPCs are necessary.
Fig. 4.32 shows the schematics of the measurement. In order to measure the position of
MPPCs at LXe temperature, a low-energy gamma-ray (∼100 keV) beam is a suitable probe
because it penetrates the material in front of LXe and also interacts at the very shallow region(O(1) mm) in the LXe volume. The source of scintillation photons is so close to the MPPC
surface that the photon distribution is concentrated to a few MPPCs. The rate of the MPPC
signal is quite sensitive to the beam position in the entrance face. By scanning the entrance
face along z and ϕ with the gamma-ray beam, the 2D positions of the MPPCs on the entrance
face can be measured. MPPCs with large |z| cannot be scanned by this technique because theChapter 4 Calibration and Monitoring of the Liquid Xenon Detector

96∆ kx or ∆ ky[rad]∆ kx and ∆ ky
0.002

∆ kx
∆ ky

0.00150.001

0.00050−0.0005−0.001−0.0015−0.002

−300

−200

(a)

−100

0

100

200

300

Zencoder[mm](b)Figure 4.34: (a) Quadrant Photo Diode mounted on the support structure. The spot of theemitted laser from the emission device mounted to the rotation stage is measured to monitor
the rotation of the stage about x and y axis. (b) The rotation angle around x (red) and y (blue)
axes monitored with the QPD as a function of the z position of the collimator. The wavelike
structure comes from the imperfections in the drive screw in the translation stage.
Bubble Level Roll Angle vs Z MEG

0.8

Roll angle (mrad)

0.6
0.4
0.2
0
−0.2
−0.4
−200

(a)

0
Z (mm)

200(b)

Figure 4.35: (a) Bubble level mounted on the rotational stage. A picture of the level is taken
for each measurement position and it is used to monitor the rotation angle about the z axis. (b)Rotation angle about the z axis monitored by the level.

gamma-rays can not penetrate the COBRA magnet outside of the thin window (|z| >120 mm).
Fig. 4.33 shows a picture of the gamma-ray measurement device. A commercial 57 Co dot
source was selected as a probe. The decay of 57 Co has two emission lines at 122 keV (≈80%)
and 136 keV (≈10%). The activity of the source was high enough (3 × 1010 Bq) to performthe measurement within a reasonable time. The source was ﬁxed in a 38×38×116 mm3 brasscollimator with a 0.15×5.0 mm2 slit. The size of the beam spot was 1.5×40 mm2 at the entranceChapter 4 Calibration and Monitoring of the Liquid Xenon Detector
face of the detector. The collimator was mounted on a rotational stage around the z-axis ona linear stage along the z-axis. The linear stage allowed precise and delicate movement witha step of 25 µm in the z direction. The rotational stage allowed rotation with a step of 25 µm
around the z axis. The linear stage was ﬁxed to a rigid support structure that can be mounted
between both ends of the COBRA magnet.
The gamma-ray beam position at the entrance face was aligned with several alignment instruments. An optical survey of the collimator with a laser tracker (Leica Absolute Tracker [67])was performed at multiple positions in z. The precision of the optical survey was 0.1 mm inz and 0.15 mrad in ϕ. The rotation of the stage around the x- and y-axis, which aﬀects the z
position of the beam at the entrance face, was monitored by a Quadrant Photo Diode (QPD,
Fig. 4.34a). The irradiated position of the infrared laser from an emission device mounted on
the rotational stage was detected by a QPD to measure the rotation of the rotational stage.
Fig. 4.34b shows the measured rotation angle around the x and y axis as a function of z positionof the collimator. The wavelike structure comes from the imperfections in the drive screw inthe translation stage because the spacing between the peaks is almost equivalent to one turn ofthe drive screw. The uncertainty of the correction for the z position of the gamma-ray beamin the entrance face was 0.03 mm. A bubble level and a camera are equipped with the back of
the rotational stage to monitor the rotation of the stage around the z-axis (Fig. 4.35), whichaﬀects the ϕ position of the gamma-ray beam. The uncertainty of the ϕ correction from thismonitoring was 0.08 mrad based on the reproducibility during the data-taking period.
The data-taking was performed twice, in 2017 and 2018. Fig. 4.36 shows the measured MPPC
positions in 2017 and 2018. In the ﬁrst data-taking in 2017, 1900 MPPCs were scanned bymeasuring the trigger rate of each MPPC with a certain threshold. The second data-taking in2018 was performed by recording the waveform and reducing the background mainly from thecosmic-ray events. In 2018, 700 MPPCs were scanned. A subset of the MPPCs was scanned
twice to measure the reproducibility of the measurement.
Fig. 4.37 shows the measured gamma-ray event rate as a function of the beam z position. A
symmetric function that has a ﬂat top and Gaussian tail on both sides is ﬁtted to the distribution. The MPPC position is reconstructed as the center of the function. The resolution of themeasurement is estimated to be 0.1 mm by using the spacing between the measured position of
adjacent MPPCs.
The validation of the alignment was performed using 16 lead strips attached to the entrance
face of the cryostat (Fig. 4.38). The lead strips (1 × 1 × 25 mm3 , Fig. 4.38a) were capsulated
by plastic packages and attached to the outer wall of the entrance face of the LXe detector, andaligned by the laser tracker with a precision of ∼100 µm. When an MPPC that is the back of alead strip is scanned by the gamma-ray beam, the measured signal rate is signiﬁcantly reduced
at the position of the strip as shown in Fig. 4.39. The reconstructed positions of the lead strips
with the gamma-ray measurement agree with the optical survey with standard deviations of
σz =0.43 mm and σϕ =0.68 mrad.
Table 4.3 summarizes the uncertainty of the alignment with the gamma-ray beam. The dom-

97

Chapter 4 Calibration and Monitoring of the Liquid Xenon Detector

6 mm

98

240

4.9 mm25.3 mm220

φ [deg]

200

180

0

160

140

120
−100
100

−50

0
50
Z [mm]

100

150

Figure 4.36: Figurez-ϕ positions
MPPCs
measuredbyofthegamma-ray beammeasurementsin
10: Theoffigureshows
the map
photodetectors
scanned
in
DSA
(open
green
circles)andDSB(solidblue
triangles)
X-ray
sur2017 (open green circles) and in 2018 (solid blue triangles).
veys.
beam position with reat three positions in z,
ctions due to increased
inantrate
uncertainty
comes
the consistencyof the lead
strip position
andcalorimethe reproducibility.
shows the average
350
FARO[12]from
coordinate
measuringmachinewhen thecoordinate.
ter was open and at room temperature. This serves as acomplementarymeasurement to that of the X-ray survey
4.7.3 Combinationof two methods
and a benchmark for studying the e↵ects of cooling thens, including results
The 3D positionsof theMPPCs
at thelow temperaturein thecoordinate
system of thestructureandof theweightof the liquid
xenon
on theodetector positions,
MEG II 355
experimentestimated by combining
the twocomplementarymeasurements.
The
relativearephotodetector
positions.
Finally,
the X-ray
meameasurement surementswith the laser
scanner
gives analysed
the 3-D positionsof MPPCs,systematic
but the detector was atwerefurtherto understanduncertainties
duehand,
to manufacturing
room temperature.
On the otherthe measurementand
withinstallation
the low-energye↵ects
gamma-ray beam
andtomeasuresystematic
biases.
gives the (z, ϕ) positions of the MPPC on the incident plane in the coordinate system of theeasuring the Z andMEG II experiment, but the radial position is not known. Assuming that the MPPCs contract
fitting the distribu6.2. Event Selection-ray beam position360
Signal events corresponding to X-ray interactions closerdinate (R) is deterto the surface of an MPPC were first selected by criteria
otodetector spacing
on the same signal and background waveforms as those
otodetectors on theused in the online selection described in section 5.

Rate [Hz]Chapter 4 Calibration and Monitoring of the Liquid Xenon Detector

99

14
12
10
8
6
4
2
0

80

90

100

110

120
z [mm]

Figure 4.37: Gamma-ray event rate measured by an MPPC as a function of z position of thebeam. The rate is signiﬁcantly high where the beam position is pointed to the MPPC.

(a)

(b)

Figure 4.38: (a) Lead strip ﬁxed in a plastic groove. (b) The entrance face of the detector withlead strips mounted.

Table 4.3: Uncertainties of the MPPC position measurement
SourceZ Unc. [mm]ϕ Unc. [mrad]

Beam alignment

0.10

0.21

QPD corrections

0.03

-

Bubble-level corrections

-

0.08

Statistical uncertainty

0.15

0.18

MPPC spacing dispersion

0.25

0.55

Lead strip consistency

0.43

0.68

Reproducibility

0.57

-

Chapter 4 Calibration and Monitoring of the Liquid Xenon Detector

100

EventRate[Hz]Lead Strip @MPPC2398

25
20
15
10
5
0

−10

0

10

20
30
40
Beam Position[mm]Figure 4.39: Gamma-ray event rate of an MPPC with a lead strip as a function of the beam
position (red). A clear dip is observed at the position where a lead strip is mounted. A ﬁtting
function to estimate the position of the lead strip is shown in blue.

uniformly, the 3D in-situ position of an MPPC can be written as follows,⃗xexp = (1 − s)R⃗xFARO + ⃗xoﬀset ,(4.15)

where s is the scaling parameter to correct the thermal contraction, R and ⃗xoﬀset are the rotation
matrix and position oﬀset to align the global rotation and oﬀset of the measured position at room
temperature ⃗xFARO with respect to that at LXe temperature ⃗xexp . The parameters s, R, ⃗xoﬀset
are estimated by minimizing the following χ2 ,X
χ2 (s, R, ⃗xoﬀset ) =[(zγ,i − zexp,i )2 /σz2 + (ϕγ,i − ϕexp,i )2 /σϕ2 ],(4.16)

i

q
σx =

2
σexp
+ σγ2

(x = z, ϕ)(4.17)

where zγ and ϕγ are the measured position in the gamma-ray measurement, and zexp and ϕexp
are the expected position deﬁned by Eq. 4.15. The uncertainty σx (x = z, ϕ) is calculated
by combining the uncertainty of each measurement. The MPPCs that were scanned with the
gamma-ray measurement with good quality are used for the computation of the χ2 . The precisionof the combination of the two measurements is estimated by the distribution of the diﬀerence
between the measured position by the gamma-ray measurement zγ , ϕγ and the expected position
after the ﬁtting zexp , ϕexp . Fig. 4.40 shows the distribution ∆z = zγ − zexp and ∆ϕ = ϕγ − ϕexp .
The sigma of the distribution is 250 µm and 0.38 mrad, respectively. A part of this spread comesfrom the resolution of the gamma-ray beam measurement (150 µm in z and 0.18 mrad in ϕ),Chapter 4 Calibration and Monitoring of the Liquid Xenon Detector

101

which is included in the uncertainties summarized in Table 4.3. The residual (0.20 µm in z and0.33 mrad in ϕ) can be explained by the non-uniformity of the thermal contraction. Therefore,
the total uncertainty of the MPPC position measurement consists of the non-uniformity of thethermal contraction and the uncertainty of the measurement with the gamma-ray beam, and it
is 0.60 mm in z and 0.75 mrad in ϕ. The combined position of the 2018 gamma-ray measurement
and the optical survey is used for the gamma-ray position reconstruction.
To understand the thermal contraction, the thermal expansion coeﬃcient αt is calculatedusing the relations = αt ∆T,(4.18)

where ∆T is the change in temperature, 123±10 K, between the survey performed at room
temperature (293±10 K*2 ) and the gamma-ray survey performed at LXe temperature (170 K).
The calculated αt in 2017 and 2018 measurements are shown in Table 4.4. The calculated αtagrees well with the theoretical value of the coeﬃcient of the thermal contraction of the PCB
material (16±1 ppmK−1 ) used for mounting the photodetectors.
∆ φ= φmeasured

MPPC

MPPC

∆ Z = Zmeasured - Zreconstructed
25
20

- φ

reconstructed

16
14
12
10

15

8
10

6
4

5

2
0
−2

−1

0

1
2
∆ Z [mm]

(a)

0
−2

−1

0

1
2
∆ φ [mrad](b)

Figure 4.40: The distribution of the diﬀerence between the expected position xexp and themeasured position by the gamma-ray measurement xγ in (a) z and (b) ϕ. The sigma of the
distribution was 0.25 mm in z and 0.38 mrad in ϕ.

The position dependence of the signal rate is helpful to estimate the non-uniformity of thematerial budget in the entrance face. The space between the support structure and the cryostat
is ﬁlled with LXe. The signal rate is sensitive to the material budget before the LXe volume.
Fig. 4.41a shows the signal rate for each MPPC. The signal rate is relatively high at the edgesof the CFRP because each CFRP is ﬁxed to the inner wall at the four corners and the thickness*2 The large uncertainty is assigned because the temperature in the measurement was not recorded.

Chapter 4 Calibration and Monitoring of the Liquid Xenon Detector

102

Table 4.4: Thermal expansion coeﬃcient of the MPPC arrayYearsαt [ppmK−1 ]20170.001915.1±1.6

2018

0.002117.1±1.9of the LXe volume is small there. On the other hand, the LXe volume is thick in the middle ofeach CFRP. The thickness of the LXe volume was calculated from the signal rate asdLXe = −λLXe ln(Rγ /Rγ,norm ),(4.19)

where dLXe is the thickness of LXe, λLXe is the attenuation length of LXe for ∼ 120 keV gammaray (2.8 mm), Rγ is the signal rate of each MPPC, Rγ,norm is the signal rate without attenuation
by LXe volume. Rγ,norm is estimated from the signal rate of MPPCs around the boundary
between CFRP 1 and CFRP 2 because the CFRPs are ﬁxed ﬁrmly to the cryostat there according
to the record of the construction. Fig. 4.41b shows dLXe as a function of the v position of the
MPPCs. dLXe is 1.8 mm on average, and the ineﬃciency for the signal gamma-ray due to this

30
25

0.8

dLXe [cm]Rγ [Hz]LXe volume is 1.8%.

CFRP 1
CFRP 2
CFRP 320

CFRP 1

0.7

CFRP 20.6

CFRP 3

CFRP 4

CFRP 4
0.5

15

0.4
0.3

10

0.2
5
0

0.1
−50

0

(a)

50
v [cm]

0

−50

0

50
v [cm](b)

Figure 4.41: (a) The signal rate of gamma-ray measurement as a function of the v position of
the MPPCs. The color of the data points corresponds to the CFRP on which MPPC is ﬁxed.
(b) The measured dLXe as a function of the longitudinal position of the MPPC.

103

Chapter 5

Radiation Damage to VUV-MPPCIn this chapter, the observations of the unexpected radiation damage to the new VUV-MPPCin a series of commissioning runs are discussed. In ﬁve years of the beam time, 4.2 × 1014
muons had been stopped at the target as summarized in Table 5.1. In the meantime, thecalibration measurements revealed that the PDE of MPPC decreased due to radiation damage.
The radiation environment of the MPPC will be described in Sec. 5.1, and the observed radiation
damage to the MPPC will be summarized in Sec. 5.2. In Sec. 5.3, the recovery of PDE byannealing is described. In Sec. 5.4, the impact of radiation damage on the experiment is discussed
based on the previous study [2].
Table 5.1: Muon beam intensity Rµ and the total accumulated number of stopped muons at thetarget, Nµ in the beam time in each year.
YearRµ [107 /s]

Nµ [1012 ]

2017

7

55

2018

7

40

2019

7

60

2020

3

90

2021

2–5

175

5.1 Radiation environment for MPPC
Two types of radiation damage are known for MPPC [68]. One is bulk damage due to NonIonizing Energy Loss (NIEL), and the other is surface damage due to Ionizing Energy Loss (IEL).
The bulk damage is primarily produced by high-energy particles (protons, pions, electrons, andphotons) and neutrons, displacing atoms out of their lattice site and generating crystal defects.
An increase in leakage current and a decrease in the signal are reported as consequences ofthe bulk damage [69, 70, 71, 72]. According to the reports, the damage occurs above 1 ×
108 /cm2 (1 MeV neutron equivalent). Electrons and photons with energies below the thresholdfor bulk defects (∼300 keV) generate only defects in the dielectrics at the interface between

Chapter 5 Radiation Damage to VUV-MPPC

104

the passivation layer (typically SiO2 ) and the silicon layer. This is called surface damage. A
large dark current was reported as a consequence of the surface damage after irradiation ofO(102 ) Gy [73].
Fig. 5.1 illustrates the radiation environment during the muon beamtime. The MPPCs were
irradiated with gamma-rays, neutrons, and VUV photons.
The gamma-ray dose from the beginning of the 2017 run to the end of the 2021 run is estimatedto be 1.2 × 10−4 Gy with a dedicated MC simulation of RMD gamma-rays.
The photon ﬂuence during the beamtime is calculated based on MPPC current and MC
simulation. The MPPC current is expressed as
I = Rpho × G × FEC × ϵPD × celec ,(5.1)

where Rpho is the rate of incident photon for the MPPC, celec is the calibration parameter ofthe readout electronics (≈6.5*1 ). In the 2019 run, the MPPC current was 1 µA on average at
7×107 /s muon beam intensity. The photon rate in data is calculated as Rpho = 4.4×106 /s basedon the sensor parameters given by the calibration measurements (G=1.5×106 , FEC =1.9, ϵPD =0.08). The MC simulation of RMD gamma rays from the target gives the number of detected
photoelectrons for each single RMD decay. By using the branching ratio of the RMD and themuon beam intensity, the average value of the number of photons per event is translated to thephoton rate. The photon rate based on the MC simulation is 3.3 × 106 /s. By a combinationof both results, the ﬂuence to VUV photons by the end of the 2021 run is estimated to be4(1) × 1011 /mm2 at the center of the detector.
Fig. 5.2 shows the position dependence of the estimated exposure for VUV photon and gammaray in the u direction. Since the LXe detector and the COBRA magnet are designed to havea reduced material budget only in the acceptance region (|u| <23.9 cm), the radiation exposure
induced by muon decay at the target is expected to be smaller outside the acceptance.
Neutrons come from the hadronic interaction of the primary proton beam with the pion
production target. The production target is located upstream ∼20 m away from the MEG II
detectors. From a neutron ﬂux measurement in the MEG experimental area [28], the total
neutron ﬂuence by the end of the 2021 run is estimated to be less than 2 × 107 /cm2 .
The estimated neutron ﬂuence and the gamma-ray dose are much smaller than the level where
the NIEL damage has been reported. The radiation damage to SiPMs by the VUV irradiation
has never been reported.

5.2 Decrease in MPPC PDE
Though the absolute scale of the MPPC PDE has 10% systematic uncertainty as discussed
in Sec. 4.5, it is omitted from the discussion below since the relative decrease is important todiscuss the radiation damage. Fig. 5.3 shows the time variation of the MPPC PDE from 2017
*1 This parameter is calculated by taking the ratio of the current readout value of an MPPC by the electronics

to the expected current value based on the measured charge and the frequency to ﬂash the LEDs

Chapter 5 Radiation Damage to VUV-MPPC

105

Figure 5.1: Radiation environment of the detector. MPPCs are exposed to gamma rays, VUVphotons, and neutrons. Gamma rays come from muon decays, VUV photons come from thexenon scintillation induced by incoming gamma rays, and neutrons come from the pion production target in the upstream.

500 ×10VUV photon fluence [× 109/mm 2]-31

Gamma-ray dose [× 10 Gy]

9

400

300

0.5

200
100
0

0

US

CenterDS

Figure 5.2: Estimated radiation exposure of VUV photons (black) and gamma ray (blue) by
MC simulation as a function of u position of MPPCs.

Chapter 5 Radiation Damage to VUV-MPPC

106

PDE

Table 5.2: Exposure to radiation from 2017 to 2021
Particle

Dose / Fluence

Gamma-ray

7 × 10−4 Gy

Neutron2 × 107 cm−2 (1 MeV equivalent)

VUV photon

4 × 1011 mm−2

0.2
0.18
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
0

×1012
100

200

300
400
Stopped muons

Figure 5.3: The degradation of the MPPC PDE on average as a function of the accumulated
number of stopped muons from 2017 to 2021. The red dashed lines show the starting point ofeach year. The calibration data were collected frequently from the 2019 run after the decreaseof the PDE was realized.

to 2021 as a function of Nµ . The time variation of the averaged PDE for the MPPCs read out
through all the beam times is shown. The ﬁgure shows that the MPPC PDE decreased from 0.13
to 0.04 as Nµ evolved up to 4.2×1014 . This damage is categorized as radiation damage because
the decrease during the long shutdown period between the beam time was negligible comparedto the decrease during the beam time. This radiation damage was not expected, consideringthat the level of radiation was small compared to the previous studies of the radiation damage of
SiPMs. Another observation is that the degradation slowed down as the MPPCs were damaged.

Chapter 5 Radiation Damage to VUV-MPPC

107

Relative PDE

Relative PDE

1.05

1

0.95

PDE for VUV light
0.9

Accumulated Exposure[hours at MEG II intensity]

PDE for Visible light
0.85
180

24/10
31/10
Exposure to muon beam

07/11

160
140
120
100
80
60
40
20
0
2019-10-17

2019-10-24

2019-10-30

2019-11-06
Time

Figure 5.4: (top) Average MPPC PDE for visible light (blue) and VUV light in 2019 beam time.
(bottom) Accumulated time of the muon beam usage period.

The PDE decreased from 0.125 to 0.080 at the beginning of a series of the commissioning runs
as Nµ evolves from zero to 1×1014 , while the PDE degradation in the latter half of the 2021 run
was 0.052 to 0.045 as Nµ evolved from 3.2×1014 to 4.2×1014 .
Compared to the decrease in the PDE for VUV light (λ = 175 nm), the decrease of the PDE
for visible light (λ = 430 nm) was one order smaller, as shown in Fig. 5.4. Considering that the
VUV-MPPC detects VUV photons by using avalanche ampliﬁcation of the e-h pairs created in
the vicinity of the interface, the observed damage is likely categorized as surface damage.
Fig. 5.5 shows the measured PDE at the beginning of 2021 as a function of the u positionof the MPPCs. Since the PDE of MPPCs did not have a position dependence right after theconstruction of the detector, the observed position dependence shows the position dependenceof the radiation damage from the installation. The magnitude of radiation damage has a large
u-dependence, which looks correlated to the position dependence of VUV photon and gammaray dose based on MC simulations shown in Fig. 5.2. This implies that this radiation damage iscaused directly or indirectly by radiation coming from the muon-stopping target. Neutrons areunlikely to be the source of the radiation damage because they come from upstream.

Chapter 5 Radiation Damage to VUV-MPPC

108

PDE

0.12
0.1
0.08
0.06
0.04
0.02
0

US

CenterDS

Figure 5.5: Average ϵVUV
as a function of the u position of the MPPCs in the middle of thePD
2021 run. The MPPCs that were not read out in the commissioning runs until the 2021 runwere used to calculate the average PDE at each u position.

VUV light

Ionizing particle

visible light

+
-

Hole
Electron

Passivation layer

- +
+

+ + +
+ -

+

Electric field+ +Si

Recombination

Avalanche
amplification+ Avalanche
amplification

Figure 5.6: Schematic view of surface damage. Ionization makes e-h pairs in the passivation
Satoru Kobayashi

3layer, and a fraction of holes remain in the layer (left). The remaining holes distort the electricﬁeld around the interface and enhance recombination (middle). This eﬀect has little impact on
visible light detection due to the long attenuation length (right).

Chapter 5 Radiation Damage to VUV-MPPC

109

Fig. 5.6 illustrates a suspected mechanism of the PDE degradation by the surface damage.
Injection of the ionizing particles generates e-h pairs in the passivation layer, and a certain
fraction of the holes remain while most electrons leave the passivation layer because of theirhigh mobility and low trapping probability. The electric ﬁeld around the interface is distorted by
the remained holes, and it causes recombination with an electron produced by another incident
photon. Since the VUV light creates e-h pairs in the vicinity of the interface due to its shortattenuation length (∼ 6 nm), recombination around the interface deteriorates the detection
eﬃciency. On the other hand, the recombination probability is smaller for the e-h pairs createdby visible light because of its relatively long attenuation length (∼ 180 nm). If this hypothesis
is correct, thermal annealing has the potential to recover the PDE. As in Ref. [74], the thermal
excitation can de-trap the holes in the interface state and restores the interface states so thatthe electrons from e-h pairs generated in the vicinity of the interface can reach the ampliﬁcation
region again.
Several irradiation tests were performed to reproduce and understand the radiation damage
in a lab [3, 75, 76]. In these tests, neutrons, VUV photons, and gamma-rays were irradiated to
VUV-MPPCs. However, a rapid decrease in the MPPC PDE was not reproduced as observed in
the LXe detector. Therefore, it is not yet identiﬁed which particle induces the radiation damage,and the mechanism of the damage remains unknown.

5.3 Thermal annealing

(a)

(b)

Figure 5.7: Images of (a) MPPC and (b) PCB taken by the thermal camera during the feasibility test of the thermal annealing. The temperature of the MPPC surface increased up to
57.2◦ C when that of the back of the PCB was heated to 36.0◦ C.

The strategy of thermal annealing was to raise the temperature of the MPPCs by using Jouleheat produced by the current ﬂowing through the MPPC. A combination of high reverse bias
voltage and continuous intense LED light can produce high photo-electric current and heat on
the MPPCs by Joule heat.

Chapter 5 Radiation Damage to VUV-MPPC

110

0.35
0.3 Adjacent to annealed MPPC

Annealed MPPC

PDE

0.25
0.2
0.15
0.1
0.05

After Annealing
Before Annealing

0 2673 2717 2762 2805 2806 2674 2675 2716 2718 2719 2763 2804 2807
MPPC
Figure 5.8: PDE of MPPCs before (blue) and after (red) the annealing in 2020. Five MPPCs
on left were adjacent to the annealed MPPCs and moderately heated by the Joule heat of theannealed MPPCs. Eight MPPCs on right were annealed by applying high bias voltage andﬂowing high current.

One concern was the heat damage to the surrounding material. The CFRP that supports
PCBs can be damaged when they are heated over 45◦ C. To avoid this damage, a feasibility
check was carried out in a lab and then annealing tests for several damaged MPPCs in thedetector were performed. In the following sections, the feasibility check including the annealing
tests for damaged MPPCs is presented in Sec. 5.3.1 and the mass annealing for ∼4,000 MPPCs
will be presented in Sec. 5.3.2.

5.3.1 Feasibility test
A spare MPPC was attached to a spare PCB to reproduce the setup in the LXe detector, andit was illuminated by a room light with a bias voltage applied. Its temperature was measured
by a thermal imaging camera (FLIR E50 [77]) as shown in Fig. 5.7a and Fig. 5.7b. It was foundthat the MPPCs can be heated to 62◦ C with the bias voltage of 65 V and the induced currentof 20 mA, while keeping the back side of the PCB to 39◦ C.

Chapter 5 Radiation Damage to VUV-MPPC

111

Recovery of PDE for VUV light

Correlation of PDE recovery

3
2.8
2.6
2.4
2.2
2
1.8
1.6

1st(2019)

1.4

2nd(2020)

1.2
1

1

1.05
1.1
1.15
Recovery of PDE for visible lightvis
Figure 5.9: Correlation between the recovery of ϵVUVPD and ϵPD . The results of the ﬁrst annealing

in 2019 and the second annealing in 2020 are shown in red and blue, respectively.

Table 5.3: Conﬁguration of annealing before the 2020 run.
MPPC ID

current

voltage

time

2763

15–21 mA

67–69 V488 hours

2716

15–21 mA

68 V

215 hours

2807

22 mA

69 V

126 hours

2718

20 mA

67 V

69 hours

2719

22 mA

69 V

84 hours2804

20–22 mA

68–69 V302 hours

2674

20 mA

67 V

61 hours

2675

21 mA

68–69 V

157 hours

Before the beam time in 2019 and 2020, annealing tests were performed for a small numberof damaged MPPCs in the LXe detector. During the test, the LXe was transferred to a storagetank, and the detector was ﬁlled with gXe at room temperature. The bias voltage was applied
to each MPPC by a dedicated HV module that can supply suﬃcient current (> 20 mA), andthe LEDs in the cryostat were used as light sources. Seven MPPCs in 2019 and eight MPPCs
in 2020 were annealed one by one at diﬀerent bias voltages. The annealing condition in 2020 issummarized in Table 5.3. After the detector was ﬁlled with LXe, the PDE for VUV light ϵVUVPD
was measured. It was diﬃcult to measure the PDE with alpha sources at room temperature dueto the large dark current.
A signiﬁcant recovery of the PDE was observed for the annealed MPPCs, as shown in Fig. 5.8.
The amount of the recovery was correlated to the applied current and duration of the annealing.
The PDE after annealing was 0.11–0.18 for annealed MPPCs, while the PDE before the annealingChapter 5 Radiation Damage to VUV-MPPC

112

Qvis (normalized)

Qvis MPPC 2804
1.2

Annealing

1.15

1.1
1.05

1
0.95

23/01

06/02

20/02

05/03

19/03
Time

Figure 5.10: MPPC charge (Qvis ) with stable LED light in the annealing period. The annealing
started on 25th February and ended on 19th March because of the limitation of time. The value
is normalized to one at the beginning of the annealing. Qvis increased by thermal annealing.

was 0.07.
vis
The recovery of the ϵVUVPD was also correlated with the recovery of the ϵPD , as shown in Fig. 5.9.

This correlation can be explained by a hypothesis that the restoration of the surface state gives
more impact on the VUV light detection but less on the visible light detection because a fractionof visible light generates an e-h pair close to the interface between Si and the passivation layer.
VUVThe recovery of ϵvis
PD was about 10% of the recovery of ϵPD . This ratio is comparable with the
VUVunder the muon beam shown in Fig. 5.4. At theratio between the decrease of ϵvis
PD and ϵPDsecond annealing test in 2020, the recovery of the charge under stable LED light was monitored
and used to monitor the progress of the annealing as shown in Fig. 5.10.
Fig. 5.11 shows the time variation of PDE for annealed MPPCs. The PDE degradation of theannealed MPPC was not faster than that of non-annealed MPPCs, considering the PDE of theannealed MPPC decreased from 0.11 down to 0.08 as the Nµ evolved up to 2 × 1014 after theannealing whereas the PDE of the MPPCs decreased from 0.125 to 0.060 as the Nµ evolved tothe same number.

5.3.2 Mass annealing
The 2022 physics run was the ﬁrst long-term run, and in order to take full advantage of the
beamtime to acquire physics data, it was necessary to recover the MPPC PDE signiﬁcantly fromits value at the end of 2021 (0.045) by annealing.
An alternative method of annealing using warm water was tested during the shutdown period
before the 2022 beamtime. This method delivers heat to the MPPCs by circulating warm waterof about 45◦ C through a liquid nitrogen circulation line attached directly to the outer surface

PDE

Chapter 5 Radiation Damage to VUV-MPPC

113

0.14
0.12
0.1
0.08
0.06
0.04
0.02
0

×1012
0

100

200

Nµ

Figure 5.11: Average PDE of annealed MPPCs as a function of the accumulated number ofstopped muons at the target after the annealing. A red dotted line indicates the beginning of
the 2021 run.

1. return the cableannealed ch

2. move to the next channel

Figure 5.12: Cabling scheme of the Joule annealing. Eight MPPC channels that have the samechannel number in WaveDREAM boards are bundled to the same port of the current source
and annealed at once.

of the inner cryostat of the detector. The temperature of the detector was monitored by thethermometers installed in the detector. The potential advantage of this method was that it
might recover the PDE of most MPPCs quickly and at once. The warm water annealing was
carried out from 20th January to 30th March. The temperature of the detector reached fromroom temperature (17◦ C) to 45◦ C in late February. The recovery of the PDE of the MPPC wasestimated indirectly by measuring the time variation of charge under LED light. The average
PDE for the annealed MPPCs recovered from 0.057 to 0.075. However, since the recovery rate
was too slow to reach a suﬃcient level (∼15%) to complete a long-term run in 2022, the warm

Entries

Chapter 5 Radiation Damage to VUV-MPPC

114

140

PDE before annealing (End of 2021 run)120

Estimated PDE after hotwater annealing

100

Estimated PDE after Joule annealing

80
60
40
20
0
0

5

10

15

20

25
30
PDE [%]

Figure 5.13: MPPC PDE before the annealing (grey), after the warm water annealing (red),and after the Joule annealing (black). The PDE was estimated by the charge for the LED light.

water annealing was stopped to start the Joule heat annealing. The slow recovery rate wasprobably because the temperature of the annealing was too low.
A dedicated current source was prepared to anneal many MPPCs at once. The speciﬁcation of
the current source is summarized in Table 5.4. Since the current of 30 mA is required to anneal
a single MPPC, and a single port can provide 250 mA current at maximum, eight channels
connected in parallel can be annealed by the output of a single port at the same time. This
scheme allows us to anneal 240 MPPCs simultaneously. By repeating a set of the annealingfor 240 MPPCs by 16 times, most MPPCs were annealed except for some MPPCs that remain
non-annealed for reference. The scheme of the cabling is shown in Fig. 5.12. An MPPC fromeach WaveDREAM board was annealed in one set of annealing. This scheme was advantageousfrom a safety point of view because it allowed to avoid overheating the MPPCs and their support
structure by selecting MPPCs distant from each other. A set of the annealing process consistsof 26 hours of annealing, 5.5 hours for cabling and cooling for the measurement, and 0.5 hourof data acquisition. In the data acquisition, the charge under a ﬁxed intensity of the LED light
was measured by the standard DAQ system to monitor the recovery of the PDE indirectly.
Table 5.4: Speciﬁcation of the current source for the Joule annealing.
The number of ports

30

Voltage [V]

60–80

Current [mA]

0–250

Manufacturer

Araki Denki inc.

As a result, the PDE recovered from 0.075 to 0.14 on average, as shown in Fig. 5.13. Thanks
to this signiﬁcant recovery, the MPPCs can be operated with PDE > 0.04 at a beam rate of
5 × 107 for ﬁve months based on the degradation rate in 2017–2021 runs shown in Fig. 5.3.

Chapter 5 Radiation Damage to VUV-MPPC

5.4 Impact on the experimental sensitivity
The impact of the low MPPC PDE on the detector performances was already discussed inRef. [2]. Fig. 5.14 shows the position resolution in the simulation at diﬀerent MPPC PDE.
The degradation of the position resolution is expected mainly for deep gamma-ray hits. Thisis because the contribution from the statistical uncertainty becomes larger for the deep events
due to the smaller number of photoelectrons on the inner face, while the contribution from theevent-by-event ﬂuctuation depending on the direction of the shower development is dominant
for the shallow events.
Fig. 5.15 shows the energy resolution as a function of the PDE. Since the measured energy
resolution is limited by an unknown term of 1.5%, it is added to the simulated energy resolution.
The MPPC signal contributes to one-third of the total energy, and the statistical ﬂuctuation is
only 0.2%. Since the statistical contribution to the energy resolution is small compared to theunknown term (1.5%) and the expected resolution (1.0%), the impact of the degradation of theenergy resolution is limited.
With a low PDE, the worse S/N ratio and the larger statistical ﬂuctuation deteriorate thetiming resolution of a single photosensor. The degradation of the S/N ratio can be recovered tosome extent by using the ampliﬁer mounted on the WaveDREAM board. Since the noise on the
input of the ampliﬁer is limited, the noise level is not proportional to the ampliﬁer gain, andthe relative noise level is better with ampliﬁcation. Fig. 5.16a shows the time resolution deﬁned
only by the MPPCs as a function of the MPPC PDE, together with the resolution deﬁned onlyby the PMTs. When the MPPC PDE is lower than 0.10, the timing resolution deﬁned by the
PMTs (55 ps) is better than the resolution deﬁned by the MPPCs and dominates the overall
resolution. As a result, the impact of the PDE degradation on the overall resolution is moderate,
as shown in Fig. 5.16b.
Fig. 5.17 shows the experimental sensitivity evaluated in Ref. [2] as a function of MPPC PDE.
The impact of the PDE degradation on the sensitivity is limited to a few percent as long as
PDE is larger than 0.04. If the MPPC PDE can be recovered up to 0.15 by annual annealing
before the data-taking of each year, the MPPC PDE can stay higher than 0.04 for the wholeyear when the muon beam intensity is lower than 5 × 107 /s. With this beam intensity, thenumber of stopped muons will be increased up to 3.9 ×1014 . In conclusion, the impact of theradiation damage of the MPPC PDE on the physics performance of the MEG II experiment isless than a few percent.

115

PDE 16 %0.9
PDE 8 %
0.8
PDE 4 %

0.7

1
PDE 16 %0.9
PDE 8 %
0.8
0.7

PDE 2 %

0.6

116

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

Chapter 5 Radiation Damage to VUV-MPPC

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)

2

4

6

(b)

8

10
12
depth (cm)(c)

Figure 5.14: Position resolution in the simulation as a function of the conversion depth at various

resolution (%)

PDE for (a) u, (b) v, and (c) w direction [2].

2.4Energy resolution + 1.5%

2.2
2
1.8
1.6
1.4
1.2
1
0

2

4

6

8

10

12

14

16

18

20

22
24
PDE (%)

200

gain 1
gain 2.5
gain 5gain 10

180
160
140

resolution (ps)resolution (ps)Figure 5.15: Energy resolution as a function of the MPPC PDE [2]90absolute
80 MEG II design

intrinsic

70
MEG LXe
60

120
50
100
40
80
30

60 PMT precision

20

40

10

20
0
0

2

4

6

8

10

12

(a)

14

16

18

20

22
24
PDE (%)

0
0

2

4

6

8

10

12

14

16

18

20

22
24
PDE (%)(b)

Figure 5.16: (a) Timing precision with all the MPPCs as a function of the MPPC PDE [2]. (b)Expected timing resolution as a function of the MPPC PDE [2].

Branching ratio sensitivity (a.u.)

Chapter 5 Radiation Damage to VUV-MPPC

117

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 5.17: Experimental sensitivity as a function of the MPPC PDE [2].

118

Chapter 6

Position Resolution
The high-resolution measurement of the opening angle Θe+ γ requires a good position resolutionof the LXe detector. The direction of a gamma ray is determined from the vertex position at thetarget given by the reconstructed positron track and the position of the gamma ray measured by
the LXe detector. The MEG II LXe detector is expected to have a better position resolution thanthe MEG LXe detector thanks to the granular readout of the inner face by the new small VUVMPPCs. This chapter describes the evaluation of the position resolution of the LXe detector
by a combination of an MC simulation and measurement using a collimator with thin slits. In
Sec. 6.1, the position reconstruction method is explained. In Sec. 6.2, the method and resultsof the position resolution measurement using the collimator and the 17.6 MeV CW–Li gamma
rays are explained.

6.1 Position Reconstruction
The position of the ﬁrst conversion point of the gamma ray ⃗x = (uhit , vhit , whit ) in the LXedetector is reconstructed by the light distribution of the MPPCs.
Firstly, the hit position is reconstructed by a method called “projection ﬁtting”. In thismethod, a symmetric function is ﬁtted to the projected Npho distribution in the u and v direction.
It provides a quick reconstruction of the gamma-ray position for the subsequent reconstruction
with a method called “chi-square ﬁtting”.
In the chi-square ﬁtting method, an expected light distribution is ﬁtted to the light distribution
around the peak such that the following χ2pos is minimized.
X(Npho,i − C × Ωi (⃗x))22
σpho,ii∈regionpσpho,i = Npho,i / Nphe,iχ2pos (⃗x) =

(6.1)
(6.2)

where C is the scale of light distribution, Ωi (⃗x) is the solid angle at position ⃗x substended by
the photosensor, σpho,i is the uncertainty of Npho for each photosensor and deﬁned as Eq. 6.2.
Fig. 6.1a shows the distribution of the measured Npho and the expected number of photons
Nexp = C × Ω(⃗x).

Chapter 6 Position Resolution

119

Table 6.1: The criteria of the MPPCs used for the ﬁtting. The MPPCs in a circular region witha radius of the distance threshold around the position reconstructed by the projection ﬁtting
were used for the chi-square ﬁtting.
Reconstructed w

Distance threshold0< w <3 cm

3 cm

3 cm ≤ w <5 cm

5 cm

5 cm ≤ w <7 cm

7 cm

7 cm ≤ w <9 cm

9 cm

9 cm ≤ w <12 cm

12 cm

12 cm ≤ w <38.5 cm

15 cm

The MPPCs in a circular region around the calculated position from the projection ﬁttingwith a certain radius are used for the chi-square ﬁtting as shown in Fig. 6.1b. The radius of
the circular region depends on the reconstructed w as shown in Table 6.1. This is because thewidth of the peak in the light distribution depends on w. Only MPPCs close to the hit are used
for a shallow gamma-ray hit with a narrow peak, while a large number of MPPCs are used fora deep gamma-ray hit with a broad peak.
This ﬁtting is based on the assumption that the number of detected photons by each photosensor is proportional to the solid angle at the interaction point subtended by the photosensor.
In reality, the source of scintillation photons has a ﬁnite size because an electromagnetic shower
is formed in a correlated direction with the direction of the incoming gamma-ray. The position
from the ﬁtting, (uﬁt , vﬁt , wﬁt ) is biased in the direction of the shower development as shownin Fig. 6.2. Two corrections are applied to the position from the ﬁtting to take this eﬀect into
account.
One is called “global correction”, which corrects position-dependent biases. Since the shower
development is correlated to the gamma-ray momentum, the deviation ∆u = uﬁt − uhit iscorrelated with uﬁt as shown in Fig. 6.3a. The relation between the deviation and the ﬁt
position is corrected by the relation in the MC simulation.
The other correction is “shower correction”, which corrects the bias from the event-by-event
ﬂuctuation of shower development. Fig. 6.3b shows the relation between the deviation ∆u =uﬁt − uhit and the ﬁt position with diﬀerent ranges. As with the global correction, the eventby-event shower ﬂuctuation is corrected with the relation in MC.
This reconstruction method provides uniform position resolutions over the detector. Fig. 6.4
shows the position dependence of the position resolution for the signal gamma ray in the MC
simulation. The variation of the position resolutions in all three dimensions was 0.01 cm in RMS
in the acceptance region (|u| <23.9 cm, |v| <67.9 cm), which is small compared to the position
resolution.

Chapter 6 Position Resolution

120

(a)

(b)

Figure 6.1: (a) Measured Npho distribution and the expected (red) distribution from the chisquare ﬁtting. (b) The MPPC region for the chi-square ﬁtting of the Npho distribution for a
gamma-ray event. The MPPCs in the circular region around the reconstructed position fromthe projection ﬁtting (red) are selected.

outer face

LXe
Shower Development

Hit

EM shower

inner face

gamma-ray

Figure 6.2: Shower development in the detector. An electromagnetic shower develops in a
Satoru Kobayashi!46

correlated direction with the momentum of the incoming gamma-ray, and the ﬁt position isbiased to the direction. The distance between the hit position xhit and the position from theﬁtting xﬁt (blue arrow) is calculated with the global correction with xﬁt and the distance between
the positions from diﬀerent ﬁt regions (red arrow).

Chapter 6 Position Resolution

121

(a)

(b)

Figure 6.3: The (a) global and (b) shower correction for u position. The global correction isapplied based on the position from the ﬁtting uﬁt , and the shower correction is based on the

0.5

σ[cm]

σ[cm]

diﬀerence of the position ﬁtted with diﬀerent ranges.

0.45

0.5
0.45

0.4

0.4

0.35

0.35

0.3

0.3

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0.25

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−20

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σv

0.1

σw

0.05

20

40
u[cm]

0

σu
σv
σw

−50

(a)

0

50
v[cm]

(b)

Figure 6.4: The position resolution for the signal gamma ray in u (black), v (red), and w (green)
direciton as a function of (a) u and (b) v in MC simulation.

6.2 Resolution Measurement
6.2.1 Principle
The position resolution was measured using a collimator and the 17.6 MeV gamma ray fromthe CW-Li setup. Fig. 6.5 shows the schematics of the resolution measurement. The position
distribution of incoming gamma rays is shaped with the collimator installed between the detector

Chapter 6 Position Resolution

122

TargetGamma-ray
Event Distribution

collimatorPMT

COBRA magnet

support structure

y

MPPC

x

LXe detectorzφFigure 6.5: Schematic view of the position resolution measurement. The collimator is installed

Satoru Kobayashi

between the detector and the magnet. The position distribution of gamma rays (orange) has apeak structure for each slit.

and the COBRA magnet. Since the observed position distribution F (xrec ) can be expressed as,
F (xrec ) = F (xtrue ) ⊕ σx ,(x = u, v)(6.3)

where xtrue is the hit position distribution estimated from an MC simulation with the measured
geometry of the setup, and σ is the position resolution. The resolution can be extracted byﬁtting the xtrue distribution smeared by a certain resolution σx to the measured distribution
F (xrec ).

6.2.2 Measurement setup
This method was also adopted in the MEG experiment. Fig. 6.6 shows the collimator used in
the MEG experiment. It had wide slits of 1 cm and narrow spacing between slits. The overlap
between the peak structures in the position distribution would prevent the precise measurementof the position resolution.
A new lead collimator was designed as shown in Fig. 6.7 and created as shown in Fig. 6.8. The
new collimator was 240×240×25 mm3 and had eight parallel slits. Each slit was 5 mm wide and
80 mm long, and the slit spacing was 50 mm so that the peak structures at the slits (σ ∼2 mm)
would not interfere with adjacent peaks when the peak is smeared by the detector resolution.
The collimator was designed to measure the local dependence of the position resolution. The

Chapter 6 Position Resolution

123

slit spacing was not an integer multiple of the MPPC size (15 mm), and the two slit rows wereoﬀset from each other by 2.5 mm to locate the slits in the diﬀerent positions with respect tothe MPPC grid. The resolution in both u and v directions can be measured by changing theorientation of the collimator by 90◦ .
The collimator was installed between the COBRA magnet and the detector using a rigid
support structure, as shown in Fig. 6.9. The collimator was ﬁxed by screws and tapes to the
support structure, and the support structure was ﬁxed to the lateral ﬂanges of the detector byscrews. The collimator and the detector were aligned with a laser tracker (Leica, AT960 [67])with a precision of ∼100 µm. Then the detector was moved back by 8 cm from the ordinary
position to avoid a conﬂict between the collimator and the magnet.
The geometry of the gamma-ray production vertex at the target, collimator, and the LXedetector was reproduced in a dedicated MC simulation for position resolution evaluation. The
conﬁguration of the MC simulation is summarized in Table 6.2.
Table 6.2: Conﬁguration of the MC simulation for the resolution evaluation.
Energy of gamma-ray

17.62 MeV (72%) / 14.8 MeV (28%)

Range of emission angle ϕγ

185 ◦ < ϕγ < 205◦

Range of emission angle θγ−0.15 < cos θγ < 0.15

Center position of vertex (x,y,z)[mm](−5, −1, −5)

Spread of vertex [mm]6Total number of simulated events

1×106 (u) / 4×106 (v)Figure 6.6: Collimator for the position resolution measurement in the MEG experiment.

The advantage of using the gamma-ray from the CW-Li setup is that the vertex size is smaller
than those for other gamma-ray sources, as shown in Table 6.3. The peak width of the position
distribution is dominated by the vertex spot size if it is far larger than the slit width of 5 mm.
It would make it diﬃcult to estimate the position resolution since the uncertainty of the vertex
size becomes another source of the uncertainty of the position resolution.
The measurement was performed at the end of the 2018 run. During the measurement, 8 ×104
events were collected with a conﬁguration to measure the resolution in the u direction, and2 × 105 events with the collimator rotated by 90◦ to measure the resolution in the v direction. A
trigger was issued based on the amplitude of the summed waveform of 144 MPPCs back of theChapter 6 Position Resolution

1

2

30

A

3

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4

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50

5

6

7

8

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42.5

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47.5

124

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240

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20

R2.5

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30

C

50

50

50

50

40

D

25

D

E

E

240

Dept.

Technical reference

Created byApproved bySatoru Kobayashi 03.08.18
Document type

Document status

Title

DWG No.

Colli

F

F
Rev.

Date of issue

Sheet

1/1
1

Figure 6.7:

2

3

4

5

6

7

Design of the collimator for the position resolution measurement.

8

The

3

240×240×25 mm lead collimator had eight parallel slits.

Figure 6.8: Collimator for the position resolution measurement. The collimator is ﬁxed to the
support structure by yellow tapes. The red arrows show the sockets for corner cubes to alignthe collimator with a laser tracker.

Chapter 6 Position Resolution

125

Figure 6.9: Installed collimator between the COBRA and the detector. The collimator was ﬁxed
by screws and tapes to the support structure, and the support structure was ﬁxed to the lateralﬂanges of the detector by screws.

Table 6.3: Beam spot size of gamma-ray sources.
Sourceσx,y [cm]σz [cm]

CW-Li

0.6

0.6

π → 2γ

0.6

1

BG γ-ray from muon decay

1

5

0

collimator to collect the gamma rays emitted in the direction of the collimator. Fig. 6.10 shows
the 2D position distribution with the collimator in the horizontal and the vertical direction,
respectively. The readout region covered four peaks formed by the collimator slits.

6.2.3 Resolution
Fig. 6.11a shows 1D-position distribution across a peak. The position resolution is evaluatedby ﬁtting a smeared distribution of the hit position F (xtrue ) in the MC with a resolution σx tothe measured distribution F (xrec ) by a binned-likelihood method.
Fig. 6.11b shows the resolution in the v direction for each slit as a function of the depth w.
The measured resolutions and their depth dependence for the four slits are consistent within thestatistical uncertainties.
Fig. 6.12 shows the depth dependence of the u and v resolutions. The average resolutions for
all four slits are shown. The uncertainty of the resolution consists of the statistical uncertaintyof the ﬁtting and the systematic uncertainty estimated from the variations among the resultswith the four slits. The measured position resolution and expected resolution from the MC
simulation are consistent within the statistical uncertainty for the shallow region (w<4 cm).
The measured resolution in the shallow region is twice better than the resolution with the MEG
LXe detector, which used 2-inch PMTs for the scintillation readout of the inner face. The
granular scintillation readout by the small VUV-MPPCs improves the position resolution for

126

0

14

−5

12

−10

10
8

−15

0

v[cm]

v[cm]

Chapter 6 Position Resolution

45
−5

40
35

−10

30
25

−15

6
−20

4

−25
−30
−15

2
−10

−5

0

5

10
15
u[cm]

0

20
−20

15
10

−25

5
−30
−15

−10

−5

(a)

0

5

10
15
u[cm]

0

(b)

Figure 6.10: Position distribution in UV plane with the collimator with (a) u orientation and(b) v orientation. The readout region covers four or six peaks formed by the collimator slits.

100

σv[cm]

Eventsvrec 2.0 <w< 5.0 cm, Data
Data

90
80

MC(Smeared)70

MC Truth

1
0.9
0.8
0.7

60

0.6

50

0.5

40

0.4

30

0.3

Slit A20

0.2

Slit B

0.1

Slit C

10
0
−24

−23

−22

−21

−20

−19 −18
vrec[cm]

00Slit D

2

(a)

4

6

8

10
12
w[cm]

(b)

Figure 6.11: (a) v distribution at a slit of the collimator. The simulated position distribution (black) was smeared to ﬁt the measured position distribution (red). (b) The position
resolution measured with the peaks at four slits as a function of the conversion depth. The
diﬀerent colors show the diﬀerent slits of the collimator.

Chapter 6 Position Resolution

127v Resolution

σv[cm]

σu[cm]

u Resolution

0.8
0.7

0.8
0.7

0.6

0.6

0.5

0.5

0.4

0.4

0.3

0.3
MEG II Data

0.2

MEG II Data

0.2
MEG II MC

0.1
00

MEG MC

2

4

6

8

10
12
w[cm]

MEG II MC

0.1
0
0

(a)

MEG MC

2

4

6

8

10
12
w[cm]

(b)

Figure 6.12: The position resolution in the (a) u and (b) v direction as a function of w. The
resolutions measured at all four slits are combined. The measured resolution of the MEG II LXe
detector (red) is worse than the expected resolution from the simulation (blue), but signiﬁcantly
better than the resolution in the MEG (black).

the gamma ray as expected. However, the resolution in the deep region (w>4 cm) is worse thanthe expected resolution. Fig. 6.13 shows the squared diﬀerence of the resolution between data
and MC as a function of the conversion depth. The magnitude of the discrepancy is consistent
between the two directions within the statistical uncertainty. The reason for the discrepancy is
not understood. If the following situation is diﬀerent between data and MC simulation, it might
explain the worse resolution.
• Scattering or absorption in LXe.
• Reﬂection at the PMT holder.
• Size of the gamma-ray vertex at the target.
The degraded PDE of the MPPCs does not explain the disagreement of the position resolution.
As shown in Fig. 5.14a–5.14c, the position resolution does not deteriorate with MPPC PDE >0.04. Since the average PDE of MPPCs at the measurement was 0.08 at the measurement in
2018, the impact on the position resolution is too small to explain the disagreement.
Though the resolutions for u and v were measured, the measurement does not give the resolution in the w direction. Considering the depth-dependent discrepancy between MC and data isobserved for both u and v direction, the resolution in w direction is likely to be worse than thesimulated resolution as well. Therefore, the w resolution is estimated by adding the w-dependent
discrepancy of the position resolution in u and v (Fig. 6.13) to the simulated position resolution
in the w direction.
The position resolutions for the signal gamma-ray are estimated by using the resolution forChapter 6 Position Resolution

128

the signal gamma-ray in an MC simulation and the depth-dependent diﬀerence between themeasured and expected resolution (Fig. 6.13). The position resolution for the signal gamma-rayin MC simulation is evaluated by ﬁtting a sum of two Gaussian functions to the distribution of
the position diﬀerence (∆x = xrec − xtrue ), as shown in Fig. 6.14. The estimated resolutions for

σ2Data-σ2MC [cm2]signal gamma-ray in all directions (u, v, w) are summarized in Fig. 6.15.

0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05

U

0

V

−0.05
−0.1
0

5

10

15

20
w [cm]

Figure 6.13: The squared diﬀerence of the position resolutions in the u (red) and v (blue)
between data and MC as a function of the conversion depth w. The red line shows a linear ﬁt

EventsEventsto the dependence.

3000

2500

2500
2000

2000

1500

1500
1000

1000

500

500

0

−4

−2

0

(a)

2

4
Δ u [cm]

0

−4

−2

0

2

4
Δ w [cm](b)

Figure 6.14: The distribution of the (a) ∆u and (b) ∆w for the signal gamma ray in the signal
MC simulation. The red lines show the sum of Gaussian functions ﬁtted to the distributions.

σ [cm]Chapter 6 Position Resolution

129

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3

σu

0.2

σv

0.1
0
0

5

σw
10

15
w [cm]

Figure 6.15: The core resolutions in u (blue), v (red), and w (green) directions as a function of
w.

130

Chapter 7

Energy Resolution
In this chapter, the evaluation of the energy resolution with the datasets collected in 2021
is described. In Sec. 7.1, the energy reconstruction method is presented. In Sec. 7.2, thenon-uniformity correction of the energy is discussed. In Sec. 7.3, the evaluation of the energy
resolution using monochromatic gamma rays is discussed. In Sec. 7.4, the systematic uncertainties of the energy reconstruction is discussed. In Sec. 7.5, the summary of this chapter isgiven.

7.1 Reconstruction Algorithm
The basic idea of the reconstruction of gamma-ray energy Eγ is to sum up the number ofphotons collected by photosensors, correct the non-uniformity and the time variation, and scale
it with an energy scale asEγ = C × T (t) × F (u, v, w) × Nsum

(7.1)

Nsum = (rMPPC (t) × NMPPC + NPMT )XNMPPC,PMT =Ai × Fface,i (u, v, w) × Npho,i ,

(7.2)
(7.3)

i⊂MPPC,PMT

where C is the energy scale from the number of photons to the energy and F (u, v, w) is a function
to correct the position dependence. The weighted sum of the number of photons Nsum is given
with the NMPPC and NPMT by Eq. 7.2. Ai is a constant correction factor of the light collection
eﬃciency deﬁned by the size of the insensitive area around each sensor divided by the size of
its sensitive area. Fface,i (u, v, w) is the weight assigned to each face to improve the uniformity,
called face factor. The correction functions related to the time variation of the energy scale (T (t)and rMPPC (t)) were already discussed in Sec. 4.6.
In practice, the summation in Eq. 7.3 is carried out using a weighted sum waveform. WaveA F

forms of all MPPCs and PMTs are separately summed up with given weights (wi = GFi ECface,iϵPD ),and pulses from oﬀ-timing pileup gamma-rays are identiﬁed and subtracted as later describedin Sec. 10.1. The integrated charge of the weighted summed waveform with pileup subtracted
is regarded as NMPPC and NPMT .
F (u, v, w) and Fface,i (u, v, w) are functions to correct the non-uniformity of energy responseChapter 7 Energy Resolution

131

in the detector. They were optimized using monochromatic gamma-rays as described in thefollowing section.

7.2 Uniformity
18 ×10

18 ×10

16

14

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18 ×10616Energy[a.u.]

6

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Energy[a.u.]

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(a)

50

80

12

4

6

100

14

60
40
20

5

10

v[cm]

(b)

15
w[cm]

0

(c)

Figure 7.1: Position dependence of the reconstructed Nsum in (a) u, (b) v, and (c) w directions
for the CW-Li gamma ray without any corrections.

(a)

(b)

Figure 7.2: (a) The ratio of the reconstructed Nsum with to that without DCR as a function of
the v position of 52.8 MeV gamma rays in an MC simulation. The ratio is enhanced at large
v because the top face has relatively many unavailable PMTs. (b) Reconstructed Nsum peak
as a function of the v position of the signal gamma ray in MC simulation with DCR (red) andwithout DCR (black).

Fig. 7.1 shows the position dependence of the Nsum with active photosensors without any
non-uniformity correction. In other words, F (u, v, w) = 1 and Fface,i (u, v, w) = 1 and npho,i iszero for dead photosensors. There is a large asymmetric non-uniformity, particularly in the v
direction. The reconstructed Nsum close to the top face is lower than that in the central part by∼40%. The non-uniformity of the reconstructed Nsum comes from several reasons, such as theChapter 7 Energy Resolution

Figure 7.3: The position dependence of the face factor of all faces on u-v plane. The CW–Li
dataset is divided into 6×16 sections depending on the (u, v) position of gamma rays and a setof the face factors is optimized so that the spectrum of the weighted sum of the Nsum has a
sharp peak. The face factors of the top and bottom faces are set to zero where the gamma-ray
position is far from the faces (v <0 cm for the top face and v >0 cm for the bottom face).

position dependence of light collection eﬃciency, the systematic bias of sensor calibration, andthe reﬂection at the liquid level.
One of the major causes of the position dependence of the light collection eﬃciency is theexistence of dead channels. As shown in Fig. 3.2b, the detector had ∼1% dead photosensors
in the 2021 run. In particular, the dead channels on the top face are localized in the ﬁrst row,which would detect more photons than other channels in the same face. To mitigate the nonuniformity from the dead channels, the Npho of a dead channel was reconstructed from the Nphoof the surrounding channels in the same face and closer to the dead channel than 20 cm as
P
Npho,iNpho,dead = Ωdead (u, v, w) × P i,(7.4)
i Ωi (u, v, w)
where Ωdead (u, v, w) is the solid angle at the gamma-ray hit position (u, v, w) subtended by adead channel, Ωi (u, v, w) is that by the i-th surrounding channel, and Npho,i is the number of132

Chapter 7 Energy Resolution

133

60

1.9

v[cm]

v[cm]

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US

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0

Figure 7.4: Face factor used for the energy reconstruction. The u and v dependences in Fig. 7.3

Eventsare expressed by a combination of a symmetric function in u and v.

900

w/ Face Factor

800
700

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600
500
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×10

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15
Energy[a.u.]

Figure 7.5: Energy spectrum for the CW-Li gamma-ray with (red) and without (blue) facefactor. Non-uniformity correction with a correction function F (u, v, w) is not applied in bothcases.

Chapter 7 Energy Resolution

134
V correction

Energy[a.u.]

Energy[a.u.]

U correction

1.3
800
1.2

700
600

1.1

W correction

1.3

1.3
1000

1.2

1.2

1.1

1.1

500
1

300

0.9

600

1

400

−20

−10

0

10

20

30
u[cm]

0.9
10

0.8

100

0.7
−30

102

1

400

0.9

200
0.8

103

800

0

0.7

−50

0

(a)

50
v[cm]

200

0.8

0

0.7

10

(b)

20

1

30
w[cm]

(c)

Figure 7.6: The correlation between the reconstructed Nsum and the (a) u, (b) v, and (c) w
positions. Non-uniformity correction functions in Gu (u), Gv (v), and Gw (w) are shown in red
and black.
Seg 8, 11.0 cm < u <33.0 cm, -34.9 cm < v < -17.5 cm

1.08

40

1.06

Normalized energy

v[cm]

1.1
60

1.04
20

1.02

1.5

450

1.4

400

1.3

350

1.2

300

1.1

250

0

1

−20

0.98

0.9

0.96

0.8

150

−40

0.94

0.7

100

−60

0.92

0.6

50

0.9

0.5

−20

0

20

1

200

10

20

30
w[cm]

u[cm]

(a)

0

(b)

1.4

300

1.3
1.2

250

1.1

200

1
150

0.9
0.8

100

0.7
50

0.6
0.5

−20

0

0

20

1.5
500

1.4
1.3

400

1.2
1.1

300

1
0.9

200

1.5
1.4
1.2

0.7

0.5

300

1
0.9
0.8

100

400

1.1

0.7
0.6

500

1.3

0.8

200
100

0.6
−50

0

u[cm]

(a)

Normalized energy

1.5

Normalized energy

Normalized energy

Figure 7.7: Non-uniformity correction function in (a) uv and (b) w directions.

0

50

0.5
0

5

10

v[cm]

(b)

15

20
w[cm]

0

(c)

Figure 7.8: Reconstructed energy of the 55 MeV gamma-ray from π 0 → γγ after the all nonuniformity correction as a function of (a) u, (b) v, and (c) w. The scale of the reconstructedenergy is arbitrarily normalized. Red histograms show the position dependences of the 55 MeV
energy peak.

Chapter 7 Energy Resolution

135

photons detected by the i-th surrounding channel. Let us call this reconstruction dead channel
recovery (DCR).
Fig. 7.2a shows the ratio of the reconstructed energy with the DCR to that without the DCR,
as a function of v. The ratio was large near both ends in v because the top and bottom faces had
many dead channels. Fig. 7.2b shows the reconstructed energy peak with and without the DCR
as a function of the v, indicating that the DCR greatly restored uniformity in the v direction.
The face factor Fface,i (u, v, w) was introduced to mitigate the position dependence of the lightcollection eﬃciency. The factor was calculated with the CW-Li gamma-ray. The whole CW-Li
dataset was divided into 6×16 based on (u, v) position, and a set of the factors that give the
sharpest peak at each subset was calculated. Fig. 7.3 shows the position dependence of the facefactor. The position dependence of face factors shows that they are relatively high when the
gamma-ray hit is close to each face. Fig. 7.4 shows the position dependence of the face factor
actually applied, given by ﬁtting a symmetric function in u and v to the distribution in Fig. 7.3.
Fig. 7.5 shows the Nsum distribution for the CW-Li gamma-rays with and without the face factor
optimization. The position dependence of energy is mitigated by using the face factor, and theenergy spectrum has a relatively sharp peak.
The residual non-uniformity was corrected by optimizing F (u, v, w) with the energy peak of
the 55 MeV gamma-ray from the π 0 → γγ decay. F (u, v, w) is composed of several independent
correction functions as,
F (u, v, w) = Gu (u) × Gv (v) × Gw (w) × Luv (u, v) × Lw (w|u, v),(7.5)

where Gu (u), Gv (v), and Gw (w) are the one-dimensional functions, which correct the global
position dependence in each direction, and Luv (u, v) and Lw (w|u, v) are additional correction
functions which correct the residual non-uniformity.
Fig. 7.6 and Fig. 7.7 show the global correction functions Gu (u), Gv (v), Gw (w) and the
additional correction functions Luv (u, v) and Lw (w|u, v) obtained from the 55 MeV peak of the
gamma-ray. Fig. 7.8 shows the position dependence of the reconstructed energy of the 55 MeV
gamma-ray after all corrections. The distribution of the peaks has 0.1% sigma, and it can be
regarded as the precision of the non-uniformity correction.

7.3 Resolution
In this section, we will ﬁrst discuss the energy resolution and its position dependence for the17.6 MeV gamma-ray from the CW-Li setup and the 55 MeV gamma-ray from the π 0 → γγ
decay. Then, the energy dependence of the resolution will be discussed using the gamma-rays
with higher energies.

17.6 MeV CW-Li gamma-ray
Fig. 7.9 shows the energy spectrum of the gamma-ray from the CW-Li setup in the 2021 run.
The energy resolution is estimated by ﬁtting a Gaussian function to the right side of the energyChapter 7 Energy Resolution

136

spectrum. Fig. 7.10 shows the position dependence of the resolution. The resolution is 2.5%
for w > 2 cm and 3.0% for w < 2 cm. A uniform resolution of 2.5% is achieved for w > 2 cm
events within the acceptance except for the edges (|v| > 60 cm). The reason for the poor energy
resolution at the edge of the detector is likely because of the non-uniformity of the light collection

Eventseﬃciency.

1200
1000
800
600
400
200
0
10

15

20

25
E[MeV]

Figure 7.9: Eγ spectrum for the CW-Li gamma-ray (w >2 cm of the acceptance of the detector)

0.045

0.05

σE/E

0.05

σE/E

σE/E

and a Gaussian ﬁt function in red line.

0.045

0.05

0.045

0.04

0.04

0.04

0.035

0.035

0.035

0.03

0.03

0.03

0.025

0.025

0.025

0.02

0.02

0.02

0.015

0.015

0.015

0.01

0.01

0.01

0.005

0.005

0.005

0

−20

0

0

20

−50

0

u[cm]

(a)

0
0

50

5

10

v[cm]

(b)

15

20
w[cm]

(c)

Figure 7.10: Eγ resolution for the 17.6 MeV CW-Li gamma-ray as a function of (a) u, (b) v,
and (c) w.

2021 π 0 run
The energy resolution for the 55 MeV gamma-ray is estimated with the π 0 run dataset. The
following event selections are applied to select the 55 MeV gamma-ray from the π 0 → γγ decay.
• 65 MeV< EBGO <90 MeV• Eps < 1 MeV• Θγγ > 170◦

Chapter 7 Energy Resolution

137

ELXe[MeV]

100
140

90
80

120

70

100

60
80

50

60

40
30

40

20
20

10
0
150

155

160

165

170

175 180
φ[deg]

0

Figure 7.11: Correlation between the opening angle Θγγ and the reconstructed energy in the

EventsLXe detector. The red line shows the theoretical prediction of the correlation.

1000
800
600
400
200
0
45

50

55

60

65
E[MeV]

Figure 7.12: Energy spectrum for 55 MeV gamma rays. The Θγγ dependence of the energy iscorrected. A ﬁtting function that consists of a Gaussian function and an exponential function
is shown in red.

σE/E

Chapter 7 Energy Resolution

138

0.05

0.045
0.04
0.035
0.03
0.025
0.02
0.015
0.01
0.005
0
0

5

10

15

20
w[cm]

Figure 7.13: Energy resolution at the central part of the detector (|u| < 10 cm, −30 cm < v <

0.05

σE/E

σE/E

−10 cm) for the 55 MeV gamma-ray as a function of the w.

0.045

0.05

0.045

0.04

0.04

0.035

0.035

0.03

0.03

0.025

0.025

0.02

0.02

0.015

0.015

0.01

0.01

0.005

0.005

0

−20

0

0

20

−50

0

u[cm]

(a)

50
v[cm]

(b)

Figure 7.14: Energy resolution for the 55 MeV gamma-ray as a function of (a) u and (b) v
position.

• |∆t| <10 ns• Single pulse in the summed waveform of the BGO detector.
• Convergence of the pileup analysis (see Sec. 10.1).
where EBGO and Eps are the reconstructed energies by the BGO detector and the pre-shower
counter, respectively, and ∆t is the time diﬀerence between the LXe detector and the BGO
detector, Θγγ is the reconstructed opening angle between the two gamma-rays.
Fig. 7.11 shows the correlation between the opening angle and the measured energy by the
LXe detector. The measured correlation follows the expected correlation by the kinematics as

Chapter 7 Energy Resolution

139

σE/E

0.035
Intrinsic
0.03

Absolute

0.025

10.1/Eγ +0.52

0.02

89.4/Eγ +1.22

0.015
0.01
0.005
0
0

50

100

150
Eγ [MeV]Figure 7.15: The energy resolution as a function of the energy. The intrinsic resolution (red)from the even-odd analysis and the absolute resolution (blue) are shown.

in Eq. 2.15. Due to this correlation, the gamma rays are not exactly monochromatic. Theenergy diﬀerence from the 55 MeV is corrected using the reconstructed opening angle Θ γγ . The
ﬂuctuation of the true energy deposit is 0.4% after the correction is applied. This ﬂuctuation
comes from the ﬁnite resolution of the opening angle. Since the vertex position had a O(1) cm
distribution in the LH2 target and the position resolution of the BGO detector is ∼1 cm, theresolution of the opening angle is 1.6◦ .
Fig. 7.12 shows the energy spectrum for the 55 MeV gamma-ray with the Θγγ correction.
The resolution is estimated by ﬁtting a composite function that uses a Gaussian function forthe higher energy part and an exponential function for a tail to the energy spectrum. The
two functions are smoothly connected at a transition point lower than the peak energy. Let us
call this function the “ExpGaus” function. The contribution of the energy spread due to the
opening angle correction (0.4%) is then subtracted in quadrature from the sigma of the Gaussiancomponent.
Fig. 7.13 shows the energy resolution at the central part of the detector (|u| < 10 cm, −30 cm <v < −10 cm) as a function of the depth. The resolution of 1.9/1.8% is achieved for w <2 cm andw >2 cm, respectively. Fig. 7.14 shows the resolution as a function of u and v. The resolution is
distributed between 1.6% and 2.0% within the acceptance except for the edges close to the top
and bottom faces (|v| >60 cm).
Fig. 7.15 shows the energy resolution as a function of the energy. It includes the energy
resolution for the 83 MeV gamma-ray from the π 0 → γγ decay and 129 MeV gamma-ray fromthe radiative capture π − p → γn. The resolution for the 83 MeV gamma-ray is estimated in thesame way as the 55 MeV gamma-ray, by selecting the events with 40 MeV< EBGO <65 MeV.
The resolution for the 129 MeV gamma-ray is estimated by ﬁtting the upper tail of the spectrumwith a Gaussian function. At the central part of the detector (|u| <10 cm, |v| <30 cm, 2 cm<

Chapter 7 Energy Resolution140

w <10 cm), the energy dependence is
σE /E ∼

p89.4/E + 1.22 (%).

(7.6)

To estimate the contribution of the photoelectron statistics to the resolution, the intrinsic
resolution, which is deﬁned by the diﬀerence of the reconstructed energies by diﬀerent partsof the detector, is helpful. The intrinsic resolution σintrinsic is calculated by ﬁtting a Gaussianfunction with the σintrinsic to the distribution of the energy diﬀerence ∆Eintrinsic deﬁned by∆Eintrinsic = (Eeven − Eodd )/2,

(7.7)

where Eeven and Eodd are the reconstructed energies by even channels and odd channels, respectively. The intrinsic resolution is composed of the statistical term and the contribution from theposition dependence and shower development. The absolute energy resolution can be given as
σabsolute = σintrinsic ⊕ σcoherent(7.8)

where σcoherent is the contribution to the energy resolution of the coherent eﬀects such as thenoises, the shower development, and the reﬂection and scattering of scintillation photons. The
good intrinsic resolution with respect to the absolute resolution indicates that the energy resolution is not limited by the photoelectron statistics but by the coherent eﬀects as above.

Ratio

Reconstructed Energy [MeV]

7.4 Energy scale

140

1.01

1.005

120
100

1

80

0.995

60
0.99
40
0.985

20
0
0

50

100
150
Truth Energy [MeV]

(a)

0.98
0

50

100
150
Truth Energy [MeV](b)

Figure 7.16: (a) The energy peak value and (b) the ratio to the gamma-ray energy as a functionof the energy.
The energy scale is determined by the 55 MeV peak in the π 0 run. There are several things
to be considered: the linearity, stability, and uniformity of the energy scale. Fig. 7.16 showsthe energy peak values for diﬀerent gamma-ray sources and their ratios to the true energy
as a function of energy. The nonlinearity of the energy scale of O(1)% is observed. This

Chapter 7 Energy Resolution
might be due to the nonlinearity of the readout electronics or the shower leakage. Since theenergy scale is determined by the 55 MeV peak, the impact of the nonlinearity in the analysis
region (48 MeV< Eγ <58 MeV) is limited. The uncertainty of the energy scale due to thisnon-linearity is estimated as 0.1% by the statistical uncertainty.
The systematical uncertainty of the energy scale from the stability is estimated to be 0.4% by
the monitoring as discussed in Sec. 4.6. The non-uniformity of the energy scale over the detector
volume is 0.1%. The overall uncertainty is 0.4%, dominated by the uncertainty of the precisionof the monitoring of the stability.

7.5 Summary
The energy resolution of the LXe detector for gamma rays is studied with several gamma-ray
sources. The resolution for the 55 MeV gamma ray is 1.9%/1.7% for w < 2 cm/w > 2 cm in theregion where the optimal energy resolution is achieved. The uniformity of the resolution has
been studied using the 17.6 MeV CW-Li gamma-ray and the 55 MeV gamma-ray. The uniform
resolution is achieved for the whole acceptance region except for the very edges close to the top
and bottom faces (|v| >60 cm), where the resolution is limited by the non-uniformity of the lightcollection eﬃciency. The uncertainty of the energy scale is estimated to be 0.4% based on thestudies of linearity, stability, and uniformity.

141

142

Chapter 8Time Resolution
In the 2020 π 0 run, the time resolution of 81(3) ps was measured [3] while the expected
resolution in the design phase was 50–70 ps. The reason for the degraded resolution with respect
to the expected resolution was regarded as a systematic error, and a dedicated measurement tosuppress the systematic error was performed in the 2021 π 0 run.
In this chapter, the evaluation of the time resolution in the 2021 π 0 run is described. First, thetime reconstruction method is explained in Sec. 8.1. Then, the evaluation of the time resolution
using the 55 MeV gamma-ray dataset collected in the 2021 π 0 run is presented in Sec. 8.2.

8.1 Time Reconstruction
The time of a gamma-ray hit is reconstructed by minimization of the following χ2 :

χ2 =

X

χ2i

(8.1)

i⊂MPPC,PMT

χ2i = ∆t2 /σi2

(8.2)

∆t = tpm − tprop − twalk − toﬀset − tγ

(8.3)

where tpm is the detected pulse time of each photosensor, tprop is the time of propagation of
scintillation photons, twalk is the delay in the reconstructed pulse time due to the time-walk eﬀect,
toﬀset is the time oﬀset of the photosensor with respect to the average oﬀset. The photosensors
with large signal (Nphe >50) are used to calculate the χ2 . The sensors whose χ2i is larger than 1.8
are regarded as outliers due to the oﬀ-timing pileup and eliminated from the ﬁtting to minimize
the impact of the pileup. A set of the ﬁtting and the removal of the outliers is repeated until the
reduced chi-square (= χ2 /N DF , N DF is the number of degrees of freedom) gets lower than 1.8.
Fig. 8.1 shows the sensors used for the time reconstruction of an event, and the color of eachsensor indicates its relative time with respect to the reconstructed tγ . For a signal gamma-ray,a few hundred photosensors are used for the reconstruction.
tpm is calculated by a constant fraction method to mitigate the time-walk eﬀect, as shownin Fig. 8.2. In this method, the time of each waveform is obtained from the crossing point of
the threshold deﬁned by a certain fraction of the pulse amplitude. The constant fraction is set

Chapter 8 Time Resolution

143

100

10.00

100
60
80
40
60
20
40
0
20
0
−20
−40
−60
−80
−100
−z 100
80

7.20

4.80

2.40

0.00

-2.80

-5.20

-7.60

0

100

200

300-10.00

Figure 8.1: Photosensors used for the time ﬁtting of an event in the 2021 π 0 run. The reconstructed energy is 56.8 MeV, and the depth is 3.4 cm. The color of each sensor indicates its[mV]relative time with respect to the reconstructed tγ .

0
−50

−100
−150
−200
−250
−300
−350
−400

PM : 1738
Raw data
Mov-Ave 21pnts

−600

−400

−200

[nsec]

Figure 8.2: MPPC waveform (grey) and shaped waveform with moving average (red) of a gammaray event. A green marker shows the amplitude (∼400 mV) and time of the peak, and a blue
marker shows the crossing point of the waveform and the constant fraction threshold (∼40 mV).

to 10% because 5–10% is the best fraction that gives the optimal time resolution in an MC
simulation [2]. To suppress the eﬀect of high-frequency noise, the raw waveform is smoothedwith a 3-point moving average.
The time walk twalk and time oﬀset of each channel were calibrated by using the 55 MeV
gamma-rays in the π 0 run. The time oﬀset was measured by taking the average of the time
diﬀerence tpm − tprop − tγ . The Nphe dependence of tpm − tprop − tγ was calculated and corrected
as shown in Fig. 8.3.

8.2 Resolution Measurement
8.2.1 Principle and setup
The time resolution of the LXe detector σtγ was measured with the pair of two coincident
gamma-rays from the π 0 → γγ decay collected in the 2021 π 0 run. The time diﬀerence between
the measured time by the LXe detector tγ and that by the pre-shower counter tps , and its spreadtime residual (sec)

Chapter 8 Time Resolution
20 ×10

144

9

90
80

15

70
10

60
50

5

40
0

30
20

5
10
10
0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16
0.18
1/sqrt(# of p.e.)0Figure 8.3: tpm − tprop − tγ as a function of the number of photoelectrons (MPPC Lot A) [2].
116 channels × 1000 events are overlaid.

σ∆t can be represented as∆t = tγ − tps − tTOF

(8.4)

σ∆t = σtγ ⊕ σps ⊕ σTOF ,(8.5)

where tTOF is the time of ﬂight correction, σps and σTOF are the spread of tps and tTOF ,respectively.
The resolution of the pre-shower counter was measured to be σps =28.2±0.2 ps from the

Eventsintrinsic time diﬀerence between the two scintillator-plate modules, as shown in Fig. 8.4.

1200
1000
800
600
400
200
0
−0.2

−9

−0.1

0

×10
0.1
0.2
t front -tback [sec]Figure 8.4: Time diﬀerence between two pre-shower counter plates. The red line shows theGaussian ﬁtting function.
The time of ﬂight from the π 0 vertex to the interaction point in the LXe detector and in the
pre-shower counter is corrected using the reconstructed position of each detector. The dominant

145

Events

Chapter 8 Time Resolution

70
60
50
40
30
20
10
0
−0.4

−9

−0.2

(a)

0

×10
0.2
0.4
t ref -tps [sec](b)

Figure 8.5: (a) Setup of the σvertex measurement in 2021. A reference counter with the same
design as the pre-shower counter was placed on the opposite side of the pre-shower counter. (b)∆tvertex distribution in the 2021 π 0 run. A red line shows the Gaussian ﬁt function.

contribution to σTOF comes from the ﬂuctuation of the time diﬀerence due to the transverse
size of the π 0 vertex σvertex . The size is estimated as ∼7 mm in an MC simulation, and thetime spread σvertex corresponds to the 48(2) ps. However, the poor time resolution in 2020 π 0run (81(3) ps [3]) implied that the time resolution was overestimated due to a larger vertex
size in reality. In the 2021 run, the σvertex was measured by a dedicated measurement witha reference timing counter which has the same design as the pre-shower counter. The setupof the measurement is shown in Fig. 8.5a. The reference counter was placed on the opposite
side of the pre-shower counter so that the two counters could measure the time of a pair ofback-to-back gamma rays. The σvertex can be measured by the relation between the spread of
the time diﬀerence ∆tvertex = tref − tps asσ∆tvertex = σvertex ⊕ σref ⊕ σps(8.6)

where σ∆tvertex is the spread of ∆tvertex , σref is the time resolution of the reference counter,
which was measured using the intrinsic time diﬀerence between the two plates as the preshower counter. The uncertainty of the σvertex measurement is dominated by the statisticaluncertainty (6 ps) because of the limited statistics (1600 events) due to the target problem as
described in Sec. 3.4. As a result, σvertex is estimated to be 70±6 ps.

8.2.2 Resolution
Fig. 8.6 shows the measured ∆t distribution in the 2021 π 0 run. The following event selections
were applied to estimate the time resolution.
• 50 MeV< Eγ <58 MeV

Chapter 8 Time Resolution

146

55 MeV
3000

σcore=99.5ps

2500
2000
1500
1000
500
0
−1

−9

−0.5

0

0.5

×10
1
∆ t = tγ - tps [s]Figure 8.6: Distribution of ∆t in the 2021 π 0 run. The ﬁt function composed of two Gaussianfunctions is shown in red.

Table 8.1: Summary of time resolution evaluation
Contribution

Spread [ps]σ∆t (core)

99.5±0.5

σps

28±0.2σvertex

70 ± 6σtγ (core)

65 ± 6• Θγγ >175◦• Convergence of the pileup analysis (See Sec. 10.1)
A composite Gaussian function is ﬁtted to the ∆t distribution. The sigma of the core part
σcore is 99.5±0.5 ps (98.4%), while the tail part σtail is 338±8 ps (1.6%). From these results, theresolution of the LXe detector is calculated to be 65±6 ps. The corrections and their uncertainty
are shown in Table 8.1. The dominant uncertainty is the statistical uncertainty of the σvertex .
The resolution is at the same level as that of the MEG LXe detector (64 ps).
The energy dependence of the time resolution is shown in Fig. 8.7. To discuss the impact of thephotoelectron statistics on the time resolution, the intrinsic resolution is deﬁned as σintrinsic =σ((todd − teven )/2) where teven and todd are the time reconstructed by even and odd channels
respectively. This intrinsic resolution is a part of the absolute resolution and includes a precisionof time estimation at each photosensor and electronics. On the other hand, eﬀects such as theprecision of the propagation time deﬁned by the gamma-ray hit position resolution, per-event
shower development, and the coherent noise over the readout electronics are included only inthe absolute resolution. The discrepancy between the intrinsic and absolute time resolutions
is 55 ps, and it is considered to be coming from such contributions. The energy dependence ofpthe absolute and intrinsic time resolutions can be given by σtγ = 255.82 /Eγ + 54.92 ps and

80

147

×10−12γ

σt [s]

Chapter 8 Time Resolution

70
60
50
40
30
Absolute

20

Intrinsic

10

σt = 281.92/E γ +7.32 [ps]0γσt = 255.82/E γ +54.92 [ps]
γ

0

50

100

150
Eγ [MeV]Figure 8.7: The absolute and intrinsic time resolution as a function of Eγ . Red points and a red
dotted line show the absolute time resolution and the ﬁtting function, respectively. Blue points
and a blue dotted line show the absolute time resolution and the ﬁtting function, respectively.

σtγ =

p
281.92 /Eγ + 7.32 ps with a ﬁt, respectively.

Fig. 8.8 shows the position dependence of the σ∆t . While the resolution is uniform in the u andv direction within the acceptance, the O(10) ps non-uniformity in the w direction is observed.
The depth dependence of the time resolution can be explained by the depth dependence of theposition resolution because the resolution of the tprop is worse with the worse position resolution
for the deep gamma-ray hit. The best time resolution is 61±6 ps in 1 cm< w <5 cm.

Chapter 8 Time Resolution

148

σ∆ t [s]

−9

0.15

×10

0.14
0.13
0.12
0.11
0.1
0.09
0.08
0.07
0.06
0.05
−40

−20

0

20

40
u [cm]

(a)
−9

×10

σ∆ t [s]σ∆ t [s]

−9

0.15
0.14

0.15
0.14

0.13

0.13

0.12

0.12

0.11

0.11

0.1

0.1

0.09

0.09

0.08

0.08

0.07

0.07

0.06

0.06

0.05

−50

0

0.05

50

×10

0

10

20

v [cm](b)30

40
w [cm](c)Figure 8.8: Sigma of the σ∆t distribution as a function of the (a) u, (b) v, and (c) w position of
the 55 MeV gamma ray.

149

Chapter 9Eﬃciency
In this chapter, the detection eﬃciency for the signal gamma ray is estimated. The detection
eﬃciency is deﬁned as the fraction of the detected number of signal gamma-rays Ndetected outof the total number of signal gamma-rays emitted to the acceptance of the detector Nacceptanceasϵγ = Ndetected /Nacceptance ,(9.1)

where Ndetected is the number of events that the Eγ is larger than a given lower energy threshold
Eγthreshold . The analysis eﬃciency deﬁned by the pileup analysis and event selections will be
discussed in Chap. 10.
The LXe detector is thick enough to stop an incoming gamma-ray with 13.9 X0 radiation
length, but when the gamma rays are scattered or absorbed before they reach LXe, or energetic
secondary particles escape from xenon after the gamma rays reach LXe, the energy deposit in
LXe is reduced. The detection eﬃciency was expected to be 69% in the design phase. This value
is better than that of the MEG LXe detector by 9% thanks to the reduced material budget.
The intrinsic detection eﬃciency for the signal gamma-ray without the analysis eﬃciency isestimated as
ϵData
= ϵMC
sig
sig × Rϵ

(9.2)

where ϵMCsig is the eﬃciency for the signal gamma-ray in MC simulation and Rϵ is the ratio of theeﬃciency in data to that in MC simulation. The ratio is estimated by the eﬃciencies of 55 MeV
MCgamma rays from π 0 → γγ in data and MC (ϵData
CEX and ϵCEX , respectively). The evaluation of
Data
MC
ϵMC
sig is described in Sec. 9.1 and that of ϵCEX and ϵCEX is described in Sec. 9.2. The estimationof the ϵData
is discussed in Sec. 9.3.
sig

9.1 Eﬃciency for signal gamma-ray in MC simulation
The ϵMC
sig is evaluated with an MC simulation. In this MC simulation, the signal gamma-rays
were generated from the target in the direction of the LXe detector with the following constraints
loose enough to cover the entire LXe volume,• | cos θγ | < 0.45

Chapter 9 Eﬃciency

150• 110◦ < ϕγ < 250◦
• Eγ = 52.8 MeV
where θγ and ϕγ are the polar and azimuthal emission angles of the gamma ray, respectively.
Fig. 9.1a is the Eγ spectrum when the gamma ray is emitted to the acceptance. Fig. 9.1b is theeﬃciency as a function of the lower energy threshold. The eﬃciency is 0.69 at 48 MeV, which is
the lower energy threshold of the MEG II analysis region.

Efficiency

Events

Efficiency curve, Signal MC

1200

0.8

0.75

1000

0.7

0.65

800

0.6

600

0.55
400
0.5
200
0
0

0.45
10

20

30

40

50
60
Eγ [MeV]

0.4
40

42
44
46
48
50
52
Lower Energy Threshold[MeV]

(a)

(b)

Figure 9.1: (a) Eγ spectrum for the signal gamma-rays emitted to the acceptance of the LXedetector in the MC simulation. (b) The eﬃciency as a function of lower energy threshold. The
eﬃciency at the Eγthreshold =48 MeV is shown in a black star.

9.2 Eﬃciency measurement
9.2.1 Method
The correlated gamma-ray pairs from π 0 → γγ are used to estimate the ratio between theeﬃciency in data and MC. When the BGO detector detects a ∼83 MeV gamma-ray, a ∼55 MeV
gamma-ray must be emitted in the opposite direction. With this kinematics of π 0 decay, thedetection eﬃciency can be deﬁned as ϵCEX = NLXe /NBGO , where NBGO is the number of gammaray events around EBGO ∼ 83 MeV and NLXe is the number of such events with Eγ > Eγthreshold .
The data-taking with the BGO self-trigger that collects events with EBGO > 20 MeV was mixed
with the standard data-taking of the π 0 run at each BGO position.
The background of this measurement comes from the radiative capture of negative pion π − p →γn in the LH2 target. As shown in Fig. 9.2a, a peak of the 129 MeV gamma-ray in the BGO
energy spectrum has a long low-energy tail so that it interferes the signal region of the eﬃciency
analysis (65 MeV< EBGO <90 MeV). In these background events, neutrons are emitted in theChapter 9 Eﬃciency
opposite direction of the 129 MeV gamma-ray.
The analysis ﬂow of the eﬃciency evaluation was as follows.
1. Make a template of the Eγ spectrum of the EBGO > 100 MeV events.
2. Fit an “ExpGaus” function to the 129 MeV peak of the EBGO spectrum.
3. Make the energy spectrum of the LXe detector for the events in the analysis window (65 MeV< EBGO <90 MeV).
4. Scale the template spectrum of the LXe detector from the ﬁrst step using the area underthe “ExpGaus” function in the second step.
5. Subtract the scaled template from the energy spectrum of the LXe detector.
6. Count the number of events with Eγ > Eγthreshold .
Fig. 9.2a shows the energy spectrum of the BGO crystal with the BGO self-trigger. The BGO
and LXe conﬁguration is the nominal conﬁguration with the largest statistics (Patch13). The
low-energy events in the EBGO spectrum are likely from the RMD of the negative muon (π − →µ− νµ , µ− → e− ν̄e νµ γ). In this case, the low-energy background does not aﬀect the evaluationof the eﬃciency because the energy of the RMD gamma-ray has an upper limit of 52.8 MeV.
Fig. 9.2b shows the energy spectrum of the LXe detector with BGO energy cut 65 MeV <EBGO < 90 MeV, together with the scaled template of the radiative capture background. The
peak around Eγ ∼ 0 MeV corresponds to gamma-rays absorbed or scattered before reaching the
LXe volume.

9.2.2 MC simulation
4 0
The ϵMCCEX is calculated with a dedicated MC simulation. In this simulation, 1 × 10 π → γγ

events were generated with a constraint to generate either one of the two gamma-rays in the
direction of the BGO detector. The diﬀerence in the material budget of the LH 2 target between
data and MC would cause systematic uncertainty. The LH2 target is implemented with thematerial budget summarized in Table 2.6.

9.2.3 Result
The dominant uncertainty of the eﬃciency measurement comes from the statistical uncertaintyof the number of radiative capture backgrounds (1%). Fig. 9.3 shows the measured eﬃciency as
a function of the energy lower bound. The ϵData
CEX was 61±1% where the lower bound is 50 MeV,
while the ϵMC
CEX was 64%. A part of the 4.7% disagreement between the data and MC can be
explained by the existence of the LXe volume in the entrance face, as discussed in Sec. 4.7. The
LXe volume between the cryostat and the support structure CFRP was estimated as 1.8 mm
thick on average, and it causes 1.8% ineﬃciency based on the attenuation length of LXe. The
residual disagreement of 2.9% is not understood. This disagreement implies that the material
budget in the measurement is underestimated compared to the MC simulation, but it is not yet
identiﬁed which apparatus has a larger material budget than expected.

151

Chapter 9 Eﬃciency

152

2200
2000
1800
1600
1400
1200
1000
800
600
400
200
0
0

EventsEventsEBGO with BGO self trigger

400

Subtracted

350

Scaled BG

300
250
200
150
100
50
50

100
150
EBGO[MeV]

(a)

0

0

20

40

60
80
EXEC[MeV](b)

Figure 9.2: (a) EBGO spectrum collected by the BGO self trigger. The red line is the ﬁtting
function of the 129 MeV peak from the radiative capture. (b) ELXe spectrum for the events inthe analysis region deﬁned by the EBGO . The ELXe spectrum of the radiative capture (red)is obtained from the events in the 129 MeV peak. It shows the detector response to 9 MeV
neutrons emitted in the opposite direction of 129 MeV gamma rays. The blue spectrum showsthe energy spectrum of gamma rays from the charge exchange reaction.

9.3 Conclusion
MC
It cannot be concluded if the unidentiﬁed disagreement between the ϵdata
CEX and ϵCEX aﬀects theeﬃciency of the signal gamma ray or not. If the disagreement is coming from the misunderstanding of the material budget of the LH2 target, the disagreement is irrelevant to the eﬃciency ofthe signal gamma ray. Otherwise, if the disagreement is coming from the underestimation of thematerial budget of the entrance face of the LXe detector, the disagreement aﬀects the eﬃciencyof the signal gamma ray. The uncertainty of the Rϵ is estimated to be 0.02 by the statisticaluncertainty of the radiative capture background (0.01) and the systematic uncertainty by theMCdisagreement of the ϵdata
CEX and ϵCEX (0.02). Therefore, the Rϵ is estimated as 0.97±0.02. The

intrinsic detection eﬃciency for the signal gamma-ray in data is calculated asϵγ = 0.69 × (0.97 ± 0.02) = 0.67 ± 0.02
The eﬃciency is 0.67 ± 0.02.

(9.3)

Chapter 9 Eﬃciency

153

Efficiency curve

Efficiency

0.75
0.7

0.65
0.6
MEG II

0.55
MEG II MC

0.5
44

46
48
50
52
54
Lower energy threshold [MeV]

Figure 9.3: Eﬃciency curve of the LXe detector in the π 0 run as a function of the lower boundof the energy. The uncertainty of the curve is shown in red, and the curve in the MC simulationis shown in a black dashed line.

154

Chapter 10

Background
There are two methods to reduce the number of background events in the analysis region. One
is to discriminate signal events from background events with good resolutions, and the other isto reject the background events with an event selection. Here we describe two analysis methods
to reduce the background events with event selections. One is the pileup analysis that identiﬁes
and unfolds the on- and oﬀ-time pileup gamma rays and the other is the event selection to rejectcosmic rays. In this chapter, the method and performance of the pileup analysis are discussed
in Sec. 10.1, and the cosmic-ray rejection is discussed in Sec. 10.2. The rates of the backgroundgamma ray in data and MC simulation are discussed in Sec. 10.3.

10.1 Pileup analysis
10.1.1 Source of pileup
Since the LXe detector has a homogeneous LXe volume, when multiple gamma rays impingeon the LXe volume at a close time to a main gamma ray of interest, the measurement of themain gamma ray can be biased.
An oﬀ-time pileup gamma ray comes from an accidental gamma ray, mainly from an RMD.
The rate of the oﬀ-time pileup gamma rays increases with the beam intensity. When the time
diﬀerence between the oﬀ-time pileup gamma ray and the main gamma ray is close, it aﬀects
the energy reconstruction of the main gamma ray depending on the time and amplitude of theoﬀ-time pileup pulse and deteriorates the eﬀective energy resolution.
The source of the on-time pileup gamma-ray pulse is the AIF of Michel positrons. Whenboth of the two gamma rays from the AIF come to the detector, they are spatially distant andcoincident in the detector. This type of event, shown in Fig. 10.1b, is called AIF2γ event. In
contrast, when only one gamma ray is emitted to the LXe detector, it is called AIF1γ (Fig. 10.1a).
The impact on position and time reconstruction is limited, as shown in Fig. 10.2, because only
the photosensors close to the main gamma-ray hit are used for the reconstruction. On the other
hand, the pileup gamma ray has a major impact on energy reconstruction because the energy
is reconstructed by summing up the signal of all photosensors, as presented in Sec. 7.1.

AIF1Gamma

AIF2Gamma

Chapter 10 Background
!"

!"

LXe
COBRA

LXe

"

COBRA

"

CDCH

"

155

CDCH

#$

#$
!#

!#

"

pTC

pTC

MPPC

MPPC

PMT

PMT

(a)

(b)

Figure 10.1: Schematic view of the (a) AIF1γ and (b) AIF2γ event. When both two gamma
rays produced by the annihilation of a positron are detected by the LXe detector, it is an AIF2γ
event. By contrast, only one gamma ray is detected in an AIF1γ event.

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 10.2: Diﬀerence between the true and reconstructed (a) u position and (b) time of signal
gamma rays generated in MC simulation [2]. The diﬀerence without pileup gamma rays (red)and with pileup gamma rays (blue) are shown.

10.1.2 Analysis algorithm
Ref. [3] describes the development of three algorithms to reduce the pileup eﬀect. One isa deep-learning method that uses a deep-learning model trained with an MC simulation todiscriminate signal events from background events by using the light distribution of MPPCs. It
is not used for the analysis of the 2021 dataset because it was diﬃcult to validate the impact of
the systematic diﬀerence in the light distribution between data and MC simulation. The second

Chapter
10 Background
Chapter
5 γ-ray
Background Reduction by Pileup Elimination

156
139
138

Chapter 5 γ-ray Background Reduction by Pileup Elimination
Pileup event identification

without pileup

with pileup
lower threshold

Peak search on inner

Peak search on innertrue peakfake peak

pileup is not foundpileup is found

Clustering

Discarded

5.14 Flow ofof thethe spatial
peak searchalgorithm
light it
distribution
the light
inner distribution
face.
Figure Figure
10.3: Algorithm
pileupsearch in[3].theFirst,
is judged on
if thehas multiple peaks. Then, the peak search on the inner face is performed. A pileup peak with
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.

a higher amplitude than certain threshold proceeds to the clustering phase.

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
timingPeak searchtimingWaveform analysis
timing, energy

Merge pulses

PMT sum waveform

Fitting

Waveform analysis
timing, energy
FittingenergyFigure 5.15 Example timing,of thelight distribution of the event
Mergewithpulsesa pileup γ-ray in thebaseline region. The purple region around the top face reflects the negative value due to
unfolded γ-rays
the pileup.

Figure
5.17Algorithm
Flow of theunfoldingalgorithm
sum waveforms.
It consistsof twoparts:
Figure10.4:of theunfoldingof sum ofwaveforms[3]. First,
MPPC andPMT
summedcluster sum
waveform(leftpart) and total
sum waveform analysis(right part).
Searchinformedtimingwaveforms
bydistribution
theanalysis
clusteredphotosensors
in PileupClustering
are analyzed
to ﬁnd oﬀ-

searchin thetimingperformed
on allthe facesformed
with theχ2 value
timeThepileuppulses.
Then,thedistribution
MPPC andisPMT
summedwaveforms
by timing
all photosensors
2ofﬁttedeach based
channeldefined by
3.13time
becausethe channels
thatanalysis
are affectedby the off-timing
pm,iestimatedareonχthepulse
and amplitudein thefor summed
waveforms

5.2.3pileups
Unfoldingof sum waveform
have large values (Fig. 5.16). The channels with χ2

pm,i > 50 are clustered face by face.
with the clustered photosensors.
To avoid
the noise,channels withthan
50 photons
amplitude thesmallerthanofFinally,
the picking
multipleupγ-rays
are unfoldedusinglesssum
waveforms
to orreconstructenergy5 mVγ-ray.
are ignored.
The centerof the cluster
is defined
the asmeanof sensor
positionsin thethe main
The algorithm
is composedof mainly
twoby
parts
shown
in Fig.
5.17. The
first

cluster, andthepeakclustertimingis definedby the sensor
timingof called
the central
channel.
algorithm
is thesearchof thelight distribution
(Fig.
10.3)
PileupClustering,andpart analyzes the sum waveform of channels in each cluster. The second part analyzes the sum
The oneclusters
merged ﬁt
based
on the distance
betweenclusterin the u, v andTheθ
10.4)
calledcenters
PileupUnfolding.
the last
is theare
templateof summed
waveforms(Fig. thewaveform of all channels. The results are combined, and they are used for fitting of template
directions.were
Thedeveloped
criteria aredefinedthe combinationof the facesof development
the clusters
algorithms
andtesteddepending
with MC on
simulation.
In this thesis,
further
waveforms.
as performancesummarized evaluationin Table 5.3.
Thelatter
thresholds,
dthr andwithθthr ,thearerealset dataset
to 18.6 are
cm described.
and 16.75◦ ,andof thetwo algorithms
respectively,
which aredefinedfor
basedon thedistance
betweenthe sensors.of the inner and outer
PileupClustering
searches
spatialpileupsin thelight distribution
Cluster sum waveform analysis
PLCL
PLCL
faces. Photosensors whose Npho is larger than certain threshold value NInneror NOuterare
The sum waveforms in each cluster are analyzed to extract the timings and energies of theclustered into groups. When a cluster of photosensors is isolated from the cluster of the main
cluster. 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 10 Background

200
0
−200
−400
−600
−800
−1000
−1200
−1400
−1600
−1800

157

×103

Raw
Fit
Main Gamma

0

0.2

0.4

×10−6

Figure 10.5: MPPC sum waveforms of a gamma-ray event with an oﬀ-time pileup pulse. The raw
waveform is shown in black, the ﬁtting waveform given by a linear combination of the template
waveform is shown in blue, and the estimated main gamma-ray waveform by the pileup analysis
is shown in green.

gamma ray, it is recognized as an additional pulse. The position and time of the found pulses
are calculated based on the analysis of individual photosensor waveforms in the cluster.
In PileupUnfolding, a superimposition of the template waveforms is ﬁtted to the summed
waveform of MPPCs and PMTs as shown in Fig. 10.5. Since the MPPCs and PMTs havediﬀerent pulse shapes, the ﬁtting is performed separately for the MPPCs and the PMTs. The
following χ2PLUF (p) is minimized to ﬁnd a set of the amplitude and time of the pulses p = (ti , Ai ).
χ2PLUF (p) =X(hb − fb (p))2 /σh2

(0 ≤ b < Nﬁt ),(10.1)bfb (p) =X

Ai gb (ti )(10.2)i∈pwhere hb represents the b-th amplitude of the measured waveform, fb (p) is that of the expected
waveform by a superimposition of the template waveforms gb (t) as deﬁned in Eq. 10.2, σh is theﬂuctuation of the waveform due to the noise and the correlated noises, and Nﬁt is the numberof bins used for the calculation of the χ2PLUF . The output of the spatial pileup search is used
for the initial ﬁtting parameters. If the ﬁtting does not give a small enough χ2 , the algorithm
attempts to converge the ﬁtting by adding a pulse. The amplitude and time of the additional
pulse are estimated from the diﬀerence between the waveforms (hb and fb (p)) in the ﬁtting.
When the estimated amplitude of the additional pulse is above a certain threshold (AMPPC
and APMT for MPPC and PMT, respectively) and the relative time with respect to the main
pulse is outside a coincidence window (Tcoinc ), the additional pulse is accepted and taken into
account for the next ﬁtting. This selection of the additional pulse is made to avoid introducing

Chapter 10 Background

158

×103

1000.00

60

0
−200
−400
−600
−800
−1000
−1200
−1400
−1600
−1800

380.19165.96
72.44
31.62

40

12.02
5.25
2.29

20

1.00

0

Raw
Fit
Main Gamma

0

0.05

0.1

−20
−40
−6

×10
0.15 −60 −20

(a)

0

20

40

(b)

Figure 10.6: (a) Template ﬁt and (b) light distribution of an identical NotConverged event. The
template ﬁt failed due to pileup pulses with close time to the main gamma-ray pulse. The light
distribution shows the positions of three gamma rays are distant.

a fake pileup gamma-ray pulse, which makes a major error in evaluating the energy of the main
gamma-ray pulse. The ﬁtting is iterated until it converges (i.e. the χ2PLUF (p) is below an upper
limit χ2UL = 20) or the number of iterations reaches a given threshold (3 times).
The parameters of the pileup analysis are summarized in Table 10.2. The threshold values of
the template ﬁt, AMPPC and APMT , should be as low as possible to detect pileup pulses as many
as possible, but should not be too low to misidentify the ﬂuctuation of the waveform as a fakepulse. Therefore, they were adjusted using the low-intensity muon beam dataset (1 × 106 /s)taken at the last period of the muon beam time in the 2021 run. Since the number of oﬀ-time
pileups was limited in this dataset, the threshold values were set so that the oﬀ-time pileup was
PLCL
PLCL
hardly detected. The thresholds of the peak search, NInnerand NOuter, in PileupClustering

were adjusted to avoid detecting a fake on-time pileup peak due to the ﬂuctuation of the light
distribution and the reﬂection at the walls.
Events are categorized according to the results of the pileup analysis into four categories summarized in Table 10.1. While NoPileup and Unfolded events are used for the physics analysis,
Coincidence and NotConverged events are not used for the analysis. A large fraction of Coincidence events comes from AIF2γ. Fig. 10.6 shows the result of the PileupUnfolding and
PileupClustering of a NotConverged event. While the PileupClustering detected two pileup
gamma-ray peaks together with a main gamma-ray peak, the template ﬁt in PileupUnfolding
failed due to the close oﬀ-time pileup pulse. The pileup analysis fails to converge the templateﬁt when the time diﬀerence between the main gamma-ray pulse and an oﬀ-time pileup pulse

Chapter 10 Background159

was smaller than the width of coincidence window Tcoinc = 30 ns and larger than ∼5 ns. In thiscase, the ﬁt failed because the ﬁtting was performed assuming only one pulse in the ﬁt region.
Table 10.1: Event category of the pileup analysis.
Event categorization

Deﬁnition

NoPileup

No gamma-ray pulse is found aside from the main gamma ray.

Unfolded

The template ﬁt is converged with oﬀ-time pileup.

Coincidence

On-time pileup is found by spatial pileup search.

NotConverged

The template ﬁt is not converged.

Table 10.2: Input parameters of the pileup analysis. See the text for the deﬁnition of theparameters.
Parameter

Data

PLCL
NInner250

PLCL
NOuter

250

AMPPC

6×104

APMT

6×104

Tcoinc [ns]

30

χ2UL

20

102

NoPL
Unfolded
Coincident
Not Converged

101Rate [Hz/0.30 MeV]

Rate [Hz/0.30 MeV]

10.1.3 Performance evaluation

102
10
1

10−1

10−1

10−2

10−2

10−3
40

45

50

55

60

65
70
Eγ [MeV]

NoPL
Unfolded
Coincident
Not Converged

10−3
40

45

50

(a)

55

60

65
70
Eγ [MeV](b)

Figure 10.7: Energy spectrum of the accidental gamma ray in (a) data and (b) MC. The spectrums are shown in diﬀerent colors depending on the categorization of events. NoPileup in red,
Unfolded in green, Coincidence in blue, and NotConverged in purple.

Fraction

Chapter 10 Background

160

0.7

MC

0.6

Data

0.5
0.4
0.3
0.2
0.1
0

NoPL

Unfolded

CoincidentDL

Not Converged

Figure 10.8: Fraction of four event categories for gamma-ray events in the analysis Eγ region (48 MeV< Eγ <58 MeV) in data (red) and in MC (black). Category “DL” is not used

Eventsbecause the deep-learning-based analysis algorithm is not used.

105
w/o Pileup Analysis
w/ Pileup Analysis

104

103

102

10

1
45

50

55

60
Eγ [MeV]Figure 10.9: Energy spectrum for accidental background gamma rays with (red) and without (black) pileup analysis. The boundary of the analysis region (48 MeV< Eγ <58 MeV) is
shown in blue dotted lines.

The key parameters of the pileup analysis are the eﬃciency of the signal gamma ray and the
reduction of the background events in the signal Eγ region around 52.8 MeV. The accidental
background gamma-ray events collected with the EGamma trigger were used to compare data
and MC simulation.
Fig. 10.7 shows the energy spectrum for each event status in data and MC. While the energy
spectra for NoPileup events and Unfolded events have sharp falling edges at around the signal
energy (52.8 MeV), that of Coincidence and NotConverged are relatively ﬂat. This is because
the events with a pileup pulse at a very close time (within a few ns with respect to the main
pulse) to the main gamma ray are categorized into Coincidence events. The Coincidence events

Chapter 10 Backgroundconsist of the events with a very close oﬀ-time pileup pulse and the events with an on-time
pileup gamma ray, such as the AIF2γ events.
Fig. 10.8 shows the fractions of event statuses for background gamma-ray events collected by
the EGamma trigger. The fraction of the Coincidence events in data and MC are both 20%
and consistent within the uncertainty (0.5%). This observation indicates that the fraction of theon-time pileup was consistent between in data and MC, contrary to the observation in Ref. [2].
Furthermore, the fraction of NotConverged events is also consistent between data and MC.
Fig. 10.9 shows the Eγ spectrum for background gamma rays in the time sideband*1 of theanalysis region with and without the pileup analyses. The fraction of NoPileup and Unfolded
events is 75% of the events that survive the cosmic-ray cut discussed in the next section, whichmeans that the pileup analysis reduces the number of background events in the analysis region by
25%. When we focus on the energy range around the signal gamma ray, 51.5 MeV< Eγ <54 MeV,
43% of background events are reduced by the pileup analysis. The reduction rate for the background events is 8% worse than the previous study with the MC simulation (51% [3]). Thiscan be explained by the fact that the deep-learning algorithm is not used and that the higher
PLCL
PLCL
threshold values (NInner, NOuter, AMPPC , APMT ) are used in order to cope with the ﬂuctuationof the waveform and the reﬂection at the walls, which are not taken into account in the MC
simulation.
The eﬃciency for the signal gamma ray is estimated with a dedicated MC simulation of
the signal gamma ray with pileup gamma rays. The fraction of Coincidence and NotConverged
events in this dataset is 4.7% and 1.4%, respectively. A part of Coincidence events have two peaksin the MPPC light distribution due to a gamma ray which escapes from the main electromagnetic
shower. Fig. 10.10 shows an energy deposit of such signal gamma-ray event in the MC simulation.
A gamma ray escaping from the main electromagnetic shower is converted in a distant place inthe LXe volume and creates the second peak on the inner face. The systematic uncertainty is
estimated by the deviation of the event categorization between data (time sideband) and theMC simulation. The overall ineﬃciency for the signal gamma ray due to the pileup analysis isestimated to be 6.1±0.5%.

10.2 Cosmic-ray rejection
While the energy spectrum of RMD and AIF events sharply drops with the energy, that ofcosmic-ray events is relatively ﬂat in the analysis region (48 MeV< Eγ <58 MeV). The cosmic
ray has a large impact on the high-energy side of the analysis region. The position and energyof cosmic rays are reconstructed in the same way as for gamma rays. Cosmic-ray datasets taken
without the beam are used to estimate the contribution in the analysis region. Fig. 10.11a shows
the two-dimensional position distribution of cosmic-ray events with 48 MeV< Eγ <58 MeV. The
reconstructed positions of most cosmic rays distribute at the edge of the detector because the*1 See Sec. 11.1 for the deﬁnition of the analysis region and the time sideband.

161

y[cm]

Chapter 10 Background

162

1
60

0.9
0.8

40

0.7
20
0.6
0.5

0

0.4

−20

0.3
−40

0.2
0.1

−60
−90

−80

−70

−60

−50

−40

−30

−20

−10

0

10
x[cm]

0

Figure 10.10: Energy deposit of a signal gamma-ray event in the MC simulation that has two

80

50

60
40

40

Rejected

35

Accepted

30
25

20

30

0
−20

20

−40

20

Gamma

15

Cosmic

10
10

−60
−80
−40

w [cm]

v [cm]

peaks in the inner face [2].

5
−20

0

(a)

20

40
u [cm]

0

0
0

0.5

1

1.5
2
R (NMPPC/N PMT)(b)

Figure 10.11: (a) Two-dimensional distribution of the reconstructed positions u and v in cosmicray events with the signal-like energies (48 MeV < Eγ <58 MeV). The position of most cosmic
rays is at the edge of the readout region because the low-energy cosmic ray has a short path
length in the LXe volume. A red box in the center shows the acceptance of the LXe detector.
(b) The distribution of R = NMPPC /NPMT and w of 55 MeV gamma ray in the π 0 run (red) andcosmic-ray (blue). The black solid line shows the event selection to reduce cosmic-ray eventsdeﬁned in Eq. 10.3.

Chapter 10 Background163

cosmic-ray events reconstructed at low energy have a relatively short path length in LXe.
In order to exclude the cosmic-ray events contained in both the acceptance and analysis Eγ
region, the reconstructed conversion depth (w) and the ratio R = NMPPC /NPMT are used. The
ratio R tends to be smaller for cosmic-ray events because the cosmic rays do not come fromthe target. The depth w is also eﬀective to identify the cosmic rays that scratched the backof the detector. The events that satisfy the following cosmic-ray cut are accepted, as shown in
Fig. 10.11b.
(w < a1 × R + b1 ) ∧ (w > a2 × R + b2 )(10.3)

where (a1 , b1 , a2 , b2 ) are the parameters to deﬁne the cut. The parameters were optimized tobe (a1 , b1 , a2 , b2 ) = (7.9, 22.6, −83.3, 50.0). This cut reduces the number of cosmic-ray events by
46.3% while keeping the eﬃciency for the signal gamma ray to 99.6%.
Since the total analysis eﬃciency is the product of the eﬃciency of the pileup analysis (93.9±0.5%) and the eﬃciency of the cosmic-ray event selection (99.6%), it is 93.5±0.5%.

Rate [Hz/0.30MeV]

10.3 Background rate

102
MC Reconstructed
Data (XEC single)

10
Cosmic

1

10−1

10−2
40

45

50

55

60

65

70
Eγ [MeV]Figure 10.12: Energy spectrum of EGamma trigger events (red). The energy spectrum of
background gamma rays in the MC simulation is shown in black, and that of cosmic-rays isshown in green. The trigger threshold was set to 44 MeV to have ≈100% eﬃciency in theanalysis region (48 MeV).

The absolute rate of the background gamma-ray events is studied with the EGamma trigger
dataset. Fig. 10.12 shows the energy spectrum of the EGamma trigger dataset at 3.24 × 107 /s
muon stopping rate together with the expected Eγ spectrum from MC simulation. The rateof background gamma-ray events in the analysis Eγ region of 48 MeV< Eγ <58 MeV and in
the acceptance of the LXe detector is (1.40± 0.13)×102 Hz. The uncertainty is dominatedby systematic uncertainty in the energy scale. The measured rate agrees well with the expected rate (1.43± 0.01)×102 Hz from the sum of MC ((1.42± 0.01)×102 Hz) and the cosmic-ray

Chapter 10 Backgrounddataset (0.8±0.1 Hz). This good agreement validates the beam rate estimated by other systems,
such as the direct rate measurement by the beam monitoring counter and the hit rate at the
pTC.

164

165

Chapter 11

Sensitivity
In this chapter, the sensitivity of the MEG II experiment is estimated based on the current
estimates of the detector resolutions and counting rate. In particular, the position dependenciesof the gamma-ray energy and position resolutions are taken into account in the sensitivity estimation. The sensitivity calculation method using the maximum likelihood analysis is explainedin Sec. 11.1. The dataset, PDFs, eﬀective number of muons are described in Sec. 11.2–11.5. The
sensitivity of the 2021 dataset is estimated in Sec. 11.6. In Sec. 11.8, the improvement of thesensitivity by the detector upgrade and the possible improvements in the future are discussed.

11.1 Maximum Likelihood Analysis
In the physics analysis of the µ+ → e+ γ search, the expected value of the number of signal
events in a given analysis region Nsig is estimated by the maximum likelihood method. The
analysis region is deﬁned as• 48 MeV < Eγ < 58 MeV• 52.2 MeV < Ee+ < 53.5 MeV• |te+ γ | < 0.5 ns• |θe+ γ | <40 mrad
• |ϕe+ γ | <40 mrad
The likelihood function is described as
(N
−⟨N
⟩)
RMD ⟩)− ACC 2 ACCe−(Nsig +NRMD +NACC ) − (NRMD2σ−⟨N
2
2σ
RMD
ACC
L(Nsig , NRMD , NACC ) :=ee
Nobs !
N
obs
Y×(Nsig S(⃗xi ) + NRMD R(⃗xi ) + NACC A(⃗xi )),2

2(11.1)

i=1

where NRMD and NACC are the expected numbers of RMD and accidental background events inthe analysis region, respectively, and Nobs is the number of observed events. ⟨NRMD ⟩, ⟨NACC ⟩,σRMD , and σACC are the estimated numbers of RMD and accidental background events andtheir uncertainties, based on the sidebands of the analysis region. S(⃗xi ), R(⃗xi ), and A(⃗xi ) are
the probability density functions (PDFs) of signal, RMD, and accidental background events

Chapter 11 Sensitivity

166

as functions of observables ⃗xi = (Eγ , Ee+ , te+ γ , ϕe+ γ , θe+ γ , tRDC , ERDC ) where tRDC and ERDC
are the time and energy of a positron measured by the RDC. The best estimates of a set of(Nsig , NRMD , NACC ) are calculated by maximizing the likelihood function.
The sensitivity that can be achieved in the MEG II experiment is determined by repeating
a number of toy-MC experiments only with the background events and calculating the upper
limits on Nsig at the 90% conﬁdence level. The conﬁdence interval of the Nsig is computed with
the Feldman-Cousins approach with the proﬁle likelihood ratio λp (Nsig ) deﬁned below as a test
statistic.

λp (Nsig ) =ˆˆL(Nsig , N̂RMD , N̂ACC )L(N̂sig , N̂RMD , N̂ACC ),(11.2)

ˆ
where N̂i (i = sig, RMD, ACC) is the best estimated value and the N̂i is the value that maximizes
L for the assumed Nsig . The upper limit of the conﬁdence interval can be calculated either by afull-frequentist method or by an asymptotic method [78]. The full-frequentist method uses toy
MC samples generated with a diﬀerent Nsig to obtain the distribution of λp for a given Nsig . Thismethod requires a large number of toy MC samples (O(104 ) toy experiments for each Nsig ) andis thus time-consuming. The asymptotic method uses the approximation that the distributionof a test statistic −2 ln(λp ) is approximately a chi-square distribution for a large sample [79].
This method is advantageous in terms of computation time because it can estimate the upper
limit without the toy MC experiments. The median of the upper limit of the Nsig divided by
the normalization factor k is deﬁned as the sensitivity.

11.2 2021 dataset
Fig. 11.1 shows the two-dimensional distribution in te+ γ vs Eγ of the 2021 dataset. In order
to avoid possible human biases, the events close to the µ+ → e+ γ signal were blinded so thatthey can not be used for the calibrations and analyses until all necessary parameters become
ready for the likelihood analysis. The blind box is deﬁned by using the Eγ and te+ γ as
• 48 MeV < Eγ <58 MeV,
• |te+ γ | <1 ns.
Fig. 11.2 shows the te+ γ distribution of the energy sideband (45 MeV < Eγ <48 MeV) events.
Though the te+ γ distribution should be ﬂat because a gamma ray and a positron are not correlated in the accidental background events, the te+ γ distribution has a slope slightly down tothe positive time diﬀerence in the 2021 dataset. This is because the trigger eﬃciency depended
on the te+ γ due to the time-walk eﬀect of the MPPC waveform. The slope of the distributionof wγ >10 cm events is steep because the time-walk eﬀect is enhanced for a small waveform.

Eγ [MeV]

Chapter 11 Sensitivity

167

60
58

300

56

250

54

200

52
150
50
100

48

50

46
44

−4

−2

0

2

4

0

t e+γ [ns]Figure 11.1: Two dimensional event distribution in te+ γ and Eγ collected in the 2021 run. The
blank box at the center shows the blind box. The following loose cut is applied for the illustration
purpose; 42 MeV < Ee+ <56 MeV; 44 MeV < Eγ <60 MeV; |te+ γ | <5 ns.

11.3 PDF
11.3.1 Signal PDF
The PDF of signal events is described as
S(Eγ , Ee+ , te+ γ , ϕe+ γ , θe+ γ , tRDC , ERDC |⃗rγ , y⃗i ) = S1 (te+ γ )× S2 (Eγ |⃗rγ )× S3 (ϕe+ γ |wγ , y⃗i )× S4 (θe+ γ |wγ , y⃗i )× S5 (Ee+ |⃗yi )× S6 (tRDC , ERDC |Eγ ),where ⃗rγ is the position of the gamma-ray and ⃗yi is a set of reconstructed positron variables,
the direction, the decay vertex, and the tracking quality.
S1 (te+ γ ) is estimated with the te+ γ distribution of RMD events in the energy sideband (Fig. 11.3).

The sum of two Gaussian functions with a slope is ﬁtted to the te+ γ

distribution, and the core sigma of the function is 85 ps. The average te+ resolution is estimatedto be 50 ps from the intrinsic time diﬀerence between the pTC counters with a method describedin Ref. [33], and the residual 70 ps is dominated by the tγ resolution (65±6 ps).

168

Events

Chapter 11 Sensitivity

2500
2000
1500
1000
500

All events

Events

0 −3
180
160
140
120
100
80
60
40
20
0
−3

−2

−1

0

1

2

3

wγ > 10 cm
−2

−1

0

1

2

3

te+γ [ns]Figure 11.2: te+ γ distribution of the energy sideband events without angular event selection.

Events / ( 0.05 ns )The distributions of (top) all events and (bottom) wγ >10 cm events are shown.

250

200

150
100

50
0
−3

−2

−1

0

1

2

3
te+γ [ns]Figure 11.3: te+ γ distribution in the energy sideband. The opening angle between positrons
and gamma rays is constrained as cos Θe+ γ < −0.995. The blue line shows the ﬁt function thatconsists of two Gaussian functions and a slope (cyan). The line in red and blue in the bottom
shows the function without the slope.

v [cm]Chapter 11 Sensitivity

169

0

60
2 3

4

5

6 7

8

9

1011 12131415 16

17

1819 20212223 24

25

40
20
0
−20
−40
−60
0

10

1
20

30
w [cm]

0.04

0.035
0.03

σE/E

σE/E

Figure 11.4: Division of the gamma-ray acceptance in the w–v plane for the signal Eγ PDF.

0.0 cm < w < 38.5 cm
0.0 cm < w < 2.0 cm
2.0 cm < w < 5.0 cm
5.0 cm < w < 10.0 cm

0.05-67.9 cm < v < -60.0 cm
40.0 cm < v < 60.0 cm

0.04

0.0 cm < v < 20.0 cm

20.0 cm < v < 40.0 cm-20.0 cm < v < 0.0 cm-40.0 cm < v < -20.0 cm

10.0 cm < w < 38.5 cm

0.035

0.025

0.03

0.02

0.025

-60.0 cm < v < -40.0 cm

0.02

0.015

0.015

0.01

0.01

0.005
0

60.0 cm < v < 67.9 cm

0.045

0.005
−50

0

0
0

50

10

20

v [cm](a)30

40
w [cm](b)

Figure 11.5: Core energy resolutions as functions of (a) v and (b) w. The resolutions are
estimated by ﬁtting a sum of two ExpGaus functions to the 55 MeV gamma-ray energy spectrum
collected in the π 0 run. The resolutions are shown in diﬀerent colors depending on the gammaray positions.

Chapter 11 Sensitivity

170

S2 (Eγ |⃗rγ ) is determined by the energy spectrum of the 55 MeV gamma ray from the π 0 → γγ
decay. Since the energy resolution mainly depends on vγ an wγ , the position dependence ofthe detector response was taken into account in the PDF. The acceptance of the LXe detector
is divided into 26 sections, as shown in Fig. 11.4, and the sum of two ExpGaus functions is
ﬁtted to the 55 MeV gamma-ray energy spectrum in each section. Fig. 11.5 shows the position
dependence of the core energy resolution.
S3 (ϕe+ γ ) and S4 (θe+ γ ) are determined by the position resolution for the gamma rays and thepositron tracking performance. The wγ dependences of the uγ , vγ , and wγ resolutions (Fig. 6.15)
are taken into account.
The Ee+ response for signal positrons (S5 (Ee+ |⃗yi )) is estimated by ﬁtting a smeared theoreticalMichel energy spectrum (Fig. 1.6a) to the energy spectrum of Michel positrons in the timesideband. The signal PDF of RDC observables is created by the time and energy distributionof Michel positrons because only accidental hits by Michel positrons are expected in the signal
events.

11.3.2 RMD PDF
The PDF for the RMD event is written as
R(Eγ , Ee+ , te+ γ , ϕe+ γ , θe+ γ , tRDC , ERDC |wγ , y⃗i ) = R1 (te+ γ )× R2 (Eγ , Ee+ , θe+ γ , ϕe+ γ |uγ , y⃗i )× R3 (tRDC , ERDC )R1 (te+ γ ) is the normalized te+ γ distribution for a coincident pair of a positron and a gamma-ray,and thus it is identical to S1 (te+ γ ). R2 (Eγ , Ee+ , θe+ γ , ϕe+ γ |uγ , y⃗i ) is obtained by the convolutionof the theoretical spectrum based on the SM and the detector response. The PDF of RDC
observables R3 is the same as the signal PDF because only accidental hits by Michel positrons
are expected in the RMD events.

11.3.3 Accidental background PDF
The PDF for the accidental background event is written as
A(Eγ , Ee+ , te+ γ , ϕe+ γ , θe+ γ |⃗rγ , y⃗i ) = A1 (te+ γ |Eγ , Ee , y⃗i )× A2 (Eγ |⃗rγ )× A3 (θe+ γ |uγ , y⃗i )× A4 (ϕe+ γ |vγ , y⃗i )× A5 (Ee+ |⃗yi )× A6 (tRDC , ERDC |Eγ )Since positrons and gamma rays are not correlated with each other in accidental background
events, the PDFs can be made based on the time sideband of the analysis region.

171

v [cm]

v [cm]

Chapter 11 Sensitivity

0

60
1

40

2

0

60
3

4

5

6

9

10

11

12

15

16

17

18

40

20

20

0

7

8

0

−20

−20

−40

13

−60
−20

−10

−40

14
19
0

−60
10

−20

20
u [cm]

−10

(a)

19
0

10

20
u [cm](b)

Figure 11.6: Sections to create the accidental background PDF A2 (Eγ |rγ ) for (a) shallow(w <2 cm) and (b) deep (w >2 cm) region.

Data
Fit

103

-1e+20 cm < u < 1e+20 cm, 60 cm < v < 1e+20 cm

Events[/0.20MeV]

Events[/0.20MeV]

0 cm < u < 10 cm, 0 cm < v < 15 cm

104

Cosmic

102

104

Fit

103

10

1

1

0.045

0.05

(a)

0.055

0.06
E [MeV]

Cosmic

102

10

10−1
0.04

Data

10−1
0.04

0.045

0.05

0.055

0.06
E [MeV](b)

Figure 11.7: Background energy spectrum of the time sideband (a) in the central region of thedetector (0 cm< uγ <10 cm, 0 cm< vγ <15 cm, 2 cm< wγ <38.5 cm) and (b) in the edge regionof the detector (-23.9 cm< uγ <23.9 cm, 60 cm< vγ <67.9 cm, 0 cm< wγ <38.5 cm).

Chapter 11 Sensitivity

172
60

90
50

80
40

70
30

60
20

50

-67.9 cm < v < -50.0 cm

10

40
30

0−0.1
120

20

100

-23.9 cm < u < -10.0 cm

10
0
− 0.1

−0.05

0

0.05

0.1
θ e γ [rad]

−0.05

0

0.05

0.1
φ + [rad]
e

γ

80
60

+

40

100

-50.0 cm < v < -25.0 cm

20

80

0−0.1

−0.05

0

0.05

60

0.1
φ + [rad]
e

120

γ

100
80

40
60

20

0
− 0.1
120

-10.0 cm < u < 0.0 cm
−0.05

0

0.05

0.1
θ e γ [rad]+40-25.0 cm < v < 0.0 cm

20
0−0.1

−0.05

0

0.05

0.1
φ + [rad]
e

γ

100
80

100

60

80
40

60

0.0 cm < v < 25.0 cm

20
0−0.1

40

−0.05

0

0.05

0.1
φ + [rad]e

0.0 cm < u < 10.0 cm

20
0
− 0.1

−0.05

0

0.05

0.1
θ e γ [rad]

γ

100
80
60

+

120

40

100

25.0 cm < v < 50.0 cm

20

80

0−0.1
60

−0.05

0

0.05

0.1
φ + [rad]
e

γ

60
50

40

40

10.0 cm < u < 23.9 cm

20

−0.1
0

−0.05

0

0.05

0.1

θe +γ [rad]302050.0 cm < v < 67.9 cm

10

− 0.1
0

− 0.05

(a)

0

0.05

0.1

φe +γ [rad](b)Figure 11.8: θe+ γ and ϕe+ γ distribution in the time sideband. A cubic function was ﬁtted to the
distribution to parameterize the distribution. The red lines show the boundary of the analysis
region (|θe+ γ | <0.04 mrad and |ϕe+ γ | <0.04 mrad).

As discussed in Sec. 11.2, the te+ γ distribution has a slope in the 2021 dataset.

Thesensitivity calculation for this thesis nevertheless uses a ﬂat te+ γ distribution as the PDF
A1 (te+ γ ) assuming the impact of the slope is negligible because the fraction of deep gamma-ray
events (wγ >10 cm) where the te+ γ distribution has a steep slope is small (5%) and because
the shape of the signal te+ γ PDF is diﬀerent from the accidental te+ γ distribution of deep
gamma-ray events (wγ >10 cm).
A2 (Eγ |rγ ) is determined by the time sideband. The acceptance region of the LXe detector
is divided into 20 sections, as shown in Fig. 11.6, and a function to model the accidental background, which consists of the RMD gamma-ray, AIF gamma-ray, and cosmic-ray components,
is ﬁtted to the energy spectrum of each section as shown in Fig. 11.7. This is to improve thesensitivity by taking the position dependence of the background distribution and the detector
resolution into account. In particular, the fraction of the cosmic-ray background is larger in theedge region in the v direction as shown in Fig. 11.7b.
Fig. 11.8 shows the θe+ γ and ϕe+ γ distribution with diﬀerent uγ and vγ requirements in thetime sideband. The position dependence of the θe+ γ and ϕe+ γ distribution reﬂects the position
dependence on the detection eﬃciency and the acceptance of positrons. A cubic function was
ﬁtted to the distributions and used as the angular PDFs (A3 (θe+ γ |uγ , y⃗i ) and A4 (ϕe+ γ |vγ , y⃗i ))after normalization.
A5 (Ee+ ) is determined by ﬁtting a smeared distribution of the theoretical Michel spectrumwith multiple Gaussian functions to the Ee+ spectrum in the time sideband.
The PDF of RDC observables A6 (tRDC , ERDC |Eγ ) is calculated by using the correlation between RDC observables (tRDC , ERDC ) and Eγ in the time sideband.
Table 11.1 summarizes the current estimates of the detector performance in the 2021 run. The

Chapter 11 Sensitivity

173

gamma-ray resolutions are the average values over the acceptance. The position dependenciesof the position and energy resolutions are taken into account for the signal and accidental
background PDFs.
Table 11.1: Summary of the detector performance in 2021. The eﬃciencies and the averagevalues of the resolutions are presented. The w dependence of the position resolution and thev, w dependence of the energy resolution are taken into account for the sensitivity calculation.
Resolution
Eγ resolution (%)

2.0 (w <2 cm) / 1.7 (w >2 cm)

Ee+ resolution (keV)

90 (core, 70%) / 310 (tail, 30%)

θe+ γ resolution (mrad)

8.6

ϕe+ γ resolution (mrad)

6.8

te+ γ resolution (ps)85

Eﬃciency
ϵe+ (%)70

ϵγ (%)

63

ϵsel (%)

87

11.4 Normalization and single event sensitivity with 2021 dataset

stop

Accumulated N µ + (1014)

2.5
Last run: 476386 (2022-11-17 09:17:37)

2

1.52021 Tlive: 2.90e+06 s
2022 Tlive: 7.76e+06 s

1

0.5
0

02/May02/Jul

01/Sep01/Nov

Date
Figure 11.9: The accumulated number of stopped muons at the target Nµ calculated by the
product of the livetime and the muon stopping rate at the target in the 2021 (grey) and 2022
run (black).

Fig. 11.9 shows the evolution of the Nµ in the 2021 run and the 2022 run. In the 2021 run,the Nµ during the physics data-taking evolved up to 8 × 1013 . Based on Eq. 1.23, the following

Chapter 11 Sensitivity

174

relation stands between the Nµ and the eﬀective number of muons for the µ+ → e+ γ search k.
k = Nµ × Ω × ϵγ × ϵe+ × ϵsel

(11.3)The k is estimated by using the number of Michel events triggered by the pTC self trigger
NMichel because the time variations of the beam intensity and the ϵe+ are reﬂected in the time
variation of the number of counted positrons ask=NMichel PMEG ϵMEG
ϵ e+
TRG
·
· Michel· Michel· ϵγ · ϵsel .
BMichel PMichel ϵTRG
ϵ e+(11.4)The deﬁnitions of the variables are listed below.
• BMichel is the branching ratio of Michel decay in the analysis window.
• PMEG and PMichel are the prescaling factors of the MEG trigger and the pTC alone trigger,
respectively.
Michel• ϵMEGTRG and ϵTRG are the eﬃciency of the MEG trigger and the pTC self trigger, respec-tively.
• ϵMichelis the detection eﬃciency of Michel positrons.
e+
The k in the 2021 run is (2.6 ± 0.1) × 1012 .

11.5 Estimated number of background events with 2021 dataset
Table 11.2: The deﬁnition of the analysis region and sidebands for counting the number ofbackgrounds.
Analysis region

Time sideband

Energy sideband

Eγ [MeV][48, 55][48,55][45,48]Ee+ [MeV][52.2, 53.5][52.2, 53.5][42, 56]

te+ γ [ns][-0.5, 0.5][-3.0, -1.0] + [1.0, 3.0][-3.0, 3.0]

cos Θe+ γ--[-1.0, -0.995]

θe+ γ , ϕe+ γ [mrad][-40, 40][-40, 40]-

The number of background events (⟨NACC ⟩ and ⟨NRMD ⟩) is estimated from the time andenergy sidebands deﬁned in Table 11.2, respectively. The ⟨NACC ⟩ can be calculated by counting
the number of background events in the positive and negative time sidebands and scaling it withthe ratio of the te+ γ interval of the analysis region (1 ns) to that of the time sidebands (4 ns).
The impact of the slope of the te+ γ distribution is canceled by using the two sidebands that aresymmetric with respect to the analysis region. Since the number of background events in the
sidebands is 249±16 events, the ⟨NACC ⟩ is 62.3±3.9.
SBThe ⟨NRMD ⟩ is estimated based on the number of RMD events in the energy sideband NRMD.

From the peak in the te+ γ distribution in the energy sideband, shown in Fig. 11.3, the number
SBof RMD events (NRMD) is estimated to be 494 ± 38.

Chapter 11 Sensitivity

175

SB
The ⟨NRMD ⟩ can be expressed using the NRMD
as

SB
⟨NRMD ⟩ = NRMD
×

AR
ϵAR
BRMD
TRG,RMD
×
,
SB
BRMD
ϵSB
TRG,RMD(11.5)

SB
AR
where BRMD
and BRMD
are eﬀective branching ratios of RMD events in the energy sideband

and the analysis region, respectively. The eﬀective branching ratio is calculated by the energy
response measured by the 55 MeV gamma-ray from the π 0 → γγ and the theoretical branchingSBratio (Eq. 1.18). ϵAR
TRG,RMD and ϵTRG,RMD are the trigger eﬃciencies for the RMD events inthe analysis region and energy sideband, respectively. The calculated branching ratios are
SB
AR
BRMD
= 1.2 × 10−10 and BRMD
= 3.2 × 10−13 , respectively. The ratio of the trigger eﬃciency isϵARdetermined as ϵTRG,RMD= 0.78 by the Eγ dependence of the eﬃciency of the EGamma trigger
SB
TRG,RMDand the cos Θe+ γ dependence of the eﬃciency of the direction matching. The ⟨NRMD ⟩ hasSB
a large systematic uncertainty because it has a 60% discrepancy between the NRMD
and theexpectation given by a product of the k and the eﬀective branching ratio (312 ± 12). This
discrepancy should be understood before opening the blinding box, though it will not aﬀect thesensitivity calculation because the accidental background is dominant in the analysis region. For
the sensitivity calculation in this thesis, an average value in the two expected values is used,
and the deviation is assigned as the systematic uncertainty. The ⟨NRMD ⟩ is estimated to be
1.1 ± 0.3.

11.6 Sensitivity with 2021 dataset

50

40

30

20

10

0
0

2

4

6

8

10
12
14
90% C.L. upper limit of Nsig

Figure 11.10: The distribution of the 90% C.L. upper limits on Nsig . The red arrow shows themedian value of the distribution (2.2).

Chapter 11 Sensitivity

176

Table 11.3: Summary of the sensitivity calculation. The values with ∗ are the calculated ones
based on the livetime and the measured values in the 2021 run. See the text for the detail.
Year

2021

2021+2022k(2.7 ± 0.1) × 10

Livetime [s]2.9 × 106

1.1 × 107

3.4 × 107

⟨NACC ⟩

62±4

283±8∗

1360±20∗⟨NRMD ⟩

1.1±0.3

5.2±2.5∗

20.4±9.2∗

The median of 90% U.L. of the Nsig

2.2∗

2.6∗

4.1∗

Sensitivity(8.1 ± 0.3) × 10−13∗(2.1 ± 0.1) × 10−13∗(8.1 ± 0.3) × 10−14∗12(1.3 ± 0.1) × 10

2021–202513(5.0 ± 0.2) × 1013 ∗Table 11.4: Summary of the systematic uncertainties of gamma-ray measurement.
Element

Systematic uncertainty

Alignment of the LXe detector

0.60 mm / 0.75 mrad (z/ϕ)

Center of te+ γ

7 ps

Eγ scale

0.4%

The sensitivity that can be achieved with the 2021 dataset was estimated by 10 4 toy experiments with the parameters summarized in Table 11.3. The conﬁdence interval of the Nsig was
calculated by the full-frequentist method with 4×103 toy MC experiments for 23 Nsig values
between 0 and 15. To take the systematic uncertainties of the gamma-ray measurement into
account, the PDFs are randomized with the estimated uncertainties as summarized in Table 11.4
when the toy MC experiments are generated for the likelihood ratio ordering. Fig. 11.10 shows
the distribution of Nsig upper limit for the toy experiments. The median of the distribution
was 2.2, and the sensitivity was estimated to be (8.1 ± 0.4) × 10−13 . The impact of the systematic uncertainties is <1%, and it is negligible with respect to the systematic uncertaintyof the normalization factor k. This is because the systematic uncertainties of the gamma-ray
direction (0.4 mrad) and time (6 ps) are smaller than the resolutions.

11.7 Sensitivities with 2022 run dataset and further
In this section, we discuss the sensitivity by adding the dataset that was already collectedin the 2022 run and that is to be collected in 2023–2025 run. In the 2022 run, the data werecollected for four months, starting from the middle of July until the middle of November, andthe Nµ evolved up to 2.5 × 1014 as shown in Fig. 11.9. The muon stopping rate was adjusted to
2.8×107 /s in the ﬁrst 3.5 months and then increased to 5.8×107 /s to speed up the accumulationof the statistics. Assuming that the same detection eﬃciency and detector performance as the2021 run were achieved, the normalization factor k in the 2022 run is estimated to be 9.7 × 1012
using the number of Michel decays as described in Sec. 11.4. The ⟨NACC ⟩ and ⟨NRMD ⟩ inthe combined datasets are calculated by using the measured values of the 2021 dataset, theChapter 11 Sensitivity

177

accumulated number of k, and the projected muon stopping rate. The estimated sensitivity will
improve to (2.1 ± 0.1) × 10−13 with the combined dataset collected in 2021 and 2022. This is 2.5
times better than the sensitivity in the MEG experiment, 5.3 × 10−13 . Therefore, the highest
sensitivity for the µ+ → e+ γ can be achieved with the dataset that has already been collected.
Assuming that we will collect the physics data for the same livetime (7.8×106 s) per year
and at the muon stopping rate of 5 × 107 /s from 2023 to 2025, the accumulated k will evolve
up to (5.0 ± 0.2) × 1013 . The sensitivity will further go down to (8.1 ± 0.4) × 10−14 after
another three years of data acquisition up to 2025. The parameters and results of the sensitivity
calculation of the upcoming datasets are summarized in Table 11.3 together with those of the2021 dataset. The sensitivity of the MEG II experiment will be six times higher than that of
the MEG experiment (5.3 × 10−13 ). Fig. 11.11 shows the sensitivity of the MEG II experiment
as a function of the livetime.
However, the estimated sensitivity is worse than the expected sensitivity in the designphase (6 × 10−14 [29]). In the design phase, the estimation of the beam rate dependence ofthe detector performance was optimistic. The analysis eﬃciency of positrons gets lower at ahigher beam rate with the current analysis method, and it is currently preventing the collectionof the physics data at a higher intensity than 5 × 107 /s. The second reason for the degradedsensitivity is the worse Eγ resolution than expected. The impact of the degraded Eγ resolution

Sensitivity

on the sensitivity was estimated to be 15% [2].

10

− 12

2021
MEG sensitivity (90% C.L.)
MEG limit (90% C.L.)
2022
2023

10

2024

− 13

10− 14
0

10

20

30

2025

40
50
60
70
Accumulated DAQ livetime [week]

Figure 11.11: Projected sensitivities with the detector performance achieved in the 2021 run.
The data points show the sensitivity of the dataset collected by the end of the year. The
sensitivity and upper limit of the full dataset of the MEG experiment are shown in blue andred, respectively.

Chapter 11 Sensitivity

178

11.8 Discussion
11.8.1 Impact of the upgrade of the LXe detector from the MEG experiment
Table 11.5: Summary of performances of the LXe detector in MEG [29] and MEG II.
Performance

MEG

MEG II (design)

MEG II (measured)

Position resolution [mm]

5

2.5

2.5

Energy resolution [%] (w <2 cm / w >2 cm)

2.4% / 1.7%

1.1% / 1.0%

2.0% / 1.7%

Time resolution [ps]

62

50–70

65

Detection eﬃciency [%]

63

69

63

Table 11.5 summarizes the measured and expected performance of the LXe detector from the
MEG to the MEG II. While the position resolution improved by a factor of two, as expected, theenergy resolution improved only in the shallow region. To evaluate the impact of the improvement of the gamma-ray measurement, the sensitivity with the performance of the MEG LXedetector is calculated. The signal PDFs (S2 , S3 , and S4 ) and accidental background PDF A2 forthe physics analysis of the MEG dataset collected in the 2012 run are used for the calculation,
while other PDFs are common to the sensitivity calculation for the MEG II. The sensitivity
achieved with the performance of the MEG LXe detector is 1.1 × 10−13 with the dataset to becollected by the end of the 2025 run. Therefore, the impact of the improvement of the detector
performance is 26%.

11.8.2 Possible improvements
We have shown that the highest sensitivity of µ+ → e+ γ can be achieved with the dataset thathas already been collected by the end of the 2022 run and the detector performance achieved in
the 2021 run. In this section, possible improvements of the µ+ → e+ γ sensitivity are shown.
The identiﬁcation of AIF2γ events through a deep-learning technique is one of the possible
improvements. A deep-learning method to discriminate signal events from AIF2γ events was
proposed and developed in Ref. [3]. In this method, a deep learning model to calculate the signal
likelihood from the light distribution is trained using MC simulation to discriminate signal eventsfrom AIF2γ events. However, it is not used because it is diﬃcult to predict how the output of themodel would be aﬀected by the systematic deviation of the light distribution of the data from
the MC. One way to overcome the deviation of the light distribution is the feature extraction.
The momenta of the two gamma rays in an AIF2γ event are correlated with each other, whichappears as a correlation between the distance between the peaks and energy of the gamma rays,
as shown in Fig. 11.12a. On the other hand, when the signal gamma rays have distant peaks,
the correlation of these variables is diﬀerent from the AIF2γ events. The distribution of the
distance between the peaks in the signal events in the MC simulation is shown in Fig. 11.12b. It

179

60
120

50

100

Event fraction

Energy of pileup [MeV]

Chapter 11 Sensitivity

40

0.1

AIF2γ

0.09
0.08

Signal

0.07
0.06

80
30

0.05
60

20

0.04
0.03

40

0.02

10

20

0

0

0

50

100
150
Distance between peak [cm]

0.01
0

0

50

(a)

100
150
Distance between peak [cm](b)

Figure 11.12: (a) Correlation between the distance between peaks in the MPPC light distribution
and the reconstructed energy of the pulse of the AIF2γ events in the MC simulation. (b) Distance
between peaks in the MPPC light distribution for the signal gamma-ray events and AIF2γ eventsin the MC simulation.

is likely that such features were extracted indirectly in the training process of the deep learningmodel. To realize consistent discrimination between data and MC, it would be eﬀective to train
the model with the reconstructed position and peak amplitude of the two peaks as the input
instead of giving the light distribution. By doing this, it would be easier to develop a robustmodel that provides consistent identiﬁcation of the background in data and simulation. The
improvement of the analysis of on-time pileups would recover the analysis eﬃciency of the signal

φγ [deg]

Eventsgamma ray up to 3% and improve the identiﬁcation of AIF2γ events.

∆φ
∆θ

80
70

6

16
14

5

60

12
4

50

10

40

3

8

30

6

2
20

4
1

10
0
−40

−20

0

20

40
∆ [deg]

(a)

0

0

2
2

4
φ

shower

6
[deg]

0

(b)

Figure 11.13: (a) Diﬀerence between the direction of the shower development and the gammaray momentum in θ (blue) and ϕ (red). (b) Correlation of the ϕ direction between the shower
development and gamma-ray momentum.

Another potential improvement is the identiﬁcation of the AIF gamma-ray through the re-Probability of gamma rays per muon decay on target [/0.5 cm]

Chapter 11 Sensitivity
×10

180

6

drift chamber
inner wall

0.16
0.14
0.12

target0.1
0.08

insidedrift chamber

0.06
0.04
0.02
0
0

5

10

15

20

25

30

35
40
radius (cm)SatoruRadial
Kobayashi
5
Figure 11.14:
distribution where the background gamma-rays (Eγ > 48 MeV) are gener-

ated from the Michel positrons in the MC simulation [2] (The title of the y axis is added to theoriginal ﬁgure). The y-axis is normalized to the probability per one muon decay on the target.

construction of gamma-ray direction. Let us deﬁne a vector of the shower development ⃗xshowerin the MC simulation as⃗xshower =X

Ei (⃗xi − ⃗xhit )/Eγ ,(11.6)iwhere Ei is an energy deposit in the shower and ⃗xi is the position of the energy deposit. The
direction of the shower development is correlated with the momentum vector of the incoming
gamma-ray, as shown in Fig. 11.13. If we can reconstruct the direction of the shower developmentfrom the light distribution, the gamma-ray direction can be estimated. The direction of a gamma
ray can be used to identify if the gamma ray comes from a displaced position or from the target.
Fig. 11.14 shows radial positions where high-energy (Eγ >48 MeV) gamma-rays are generated
from the AIF of positrons in the MC simulation [2]. The ∼60% of the high-energy AIF gamma
rays come from positions displaced from the target, such as the CDCH material. Therefore,
the identiﬁcation of AIF gamma rays from the displaced vertex has potential to improve thesensitivity by taking advantage of the granular readout with the MPPCs.

181

Chapter 12Conclusion
The MEG II LXe gamma-ray detector that uses a granular readout with the VUV-MPPCs isfully commissioned to start searching for the µ+ → e+ γ decay with the highest sensitivity.
The performance of the detector was measured with the 55 MeV gamma-ray from the π 0 → γγ
decay and the 17.6 MeV gamma-ray from the CW-Li setup. The resolutions of the position, energy, and time are 2.5 cm (wγ <2 cm), 2.0%/1.7% (wγ <2 cm/wγ >2 cm), and 65 ps, respectively.
The position resolution for gamma-ray hits in the shallow region is improved by a factor of two
from the MEG detector (5 mm). The energy resolution for gamma-ray hits in the shallow regionis also improved from 2.4% to 2.0%. The detection eﬃciency for the 52.8 MeV signal gamma-ray
is estimated to be 67±2% from the measured eﬃciency for the gamma ray from the π 0 → γγ
decay. The total eﬃciency for the signal gamma-ray is 63±2%, considering the analysis eﬃciencyof 93.5±0.5%.
The systematic uncertainties of the gamma-ray measurement are suppressed by several calibration measurements. The systematic uncertainty of the gamma-ray position is limited to
0.6 mm by combining two complementary measurements of the MPPC positions; one was the
optical measurement with a laser scanner in the construction phase, and the other was the insitu measurement with a well-aligned 120 keV gamma-ray beam. The systematic uncertainty of
the gamma-ray energy is 0.4% based on the estimation of the stability, uniformity, and linearityof the energy reconstruction with several gamma-ray sources and cosmic rays.
The rate and distribution of the background events are studied by comparing the data with
the MC simulation. The absolute rate of the background gamma rays and the fraction of theevents that have an on-timing pulse in data are consistent with those in the MC simulation.
The MEG II experiment started a pilot physics data taking in 2021, followed by the ﬁrst longterm data acquisition in 2022. The sensitivity with the measured performance of the detectors
is evaluated by the likelihood analysis. The sensitivity with the dataset collected in the 2021 runis estimated to be (8.1 ± 0.4) × 10−13 . The sensitivity will improve to (2.1 ± 0.1) × 10−13 with the
combined dataset already collected in 2021 and 2022. Furthermore, the sensitivity will improveto (8.1 ± 0.4) × 10−14 by adding datasets to be collected in another three years, assuming thedata will be collected with the same detector performance as in the 2021 run. This sensitivity
is six times better than the sensitivity of 5.3 × 10−13 in the MEG experiment.

182

Appendix A

Summary of commissioning runs
A.1 Commissioning run 2017
The main purpose of the 2017 run was to take some gamma-ray data. After a signal check ofphotosensors, an MPPC alignment measurement with a 60 Co gamma-ray source was performedin July as described in Sec. 4.7. Data acquisition with the muon beam started in late November
at the beam intensity of 3.2 ×107 /s. Gamma-rays close to the signal energy were measured
during the beam time. The PMT gain calibration and the PDE calibration were tested tomeasure the performance of the photosensors. While the PMT gain calibration was successful,the PDE calibration provided limited information about the sensor performance due to thesevere noise condition of the readout electronics and the inappropriate arrangement of readout
channels for PDE calibration.

A.2 Commissioning run 2018
The purpose of the 2018 run was to measure the detector performance with several gamma-ray
sources. The 17.6 MeV gamma-rays from the CW-Li setup were used to measure the positionand energy resolution of the detector. The background gamma-rays were taken at beam intensities of 7×106 /s and 7×107 /s for a study on the background gamma-ray spectrum and thepileup elimination performance. The position resolution measurement described in Sec. 6 was
performed in late December. On the other hand, the π 0 run was canceled due to the delay in the
installation of the drift chamber. While successful data acquisition was achieved, the 2018 run
was not a stable beam time. The major reason was that the beam time was shared by several
MEG II detectors. The beam intensity and DAQ conﬁguration were often switched to reconcile
requests from several detectors. Another reason was instability of the BTS magnet due to an
instability of the liquid helium supply.

A.3 Commissioning run 2019
The major goal of the 2019 run was as follows.

Appendix A Summary of commissioning runs
• Investigate the suspected radiation damage of the MPPCs of the LXe detector.
• Install and test a new drift chamber under a muon beam environment.
The observations that the measured PDE of MPPCs in the 2018 run was signiﬁcantly lower
than expected and that the deterioration of the PDE implied that PDE decreased during thebeam time due to radiation damage. However, it was not conclusive because it was diﬃcult tocorrelate the PDE and the beam usage only with a few times of PDE calibration measurementsin the beam time. Since this degradation can be a crucial issue for the MEG II experiment,
dedicated data acquisition time to conﬁrm the degradation and measure its speed was assigned.
Calibration measurements were performed frequently, twice per day, to measure the detailed
time variation of the PDE. The radiation damage of the PMTs was also studied. Assuming the
speed of radiation damage depends on the gain of PMT, the gain of PMT was halved from thenominal value of 1.6×106 down to 8×105 , and the decrease of gain was measured in a muon
beam environment. Since the decrease was indeed mitigated, the nominal gain of the PMT
is changed to 8×105 from the 2020 run. Another purpose of the 2019 run was to measure thedetector performance by the π 0 run at the end of the beam time. However, it was again canceledby a failure of the BTS magnet. The BTS system could not recover from an unexpected power
cutoﬀ in the experimental area in November because of a breaking of the coil wire.

A.4 Commissioning run 2020
The BTS was successfully repaired during the long shutdown period, and the beam time
started in September. The major goal of 2020 run was as follows.
• Measure the performance of the LXe detector in π 0 run.
• Measure the deterioration of MPPC PDE under muon beam.
• Achieve stable operation of the drift chamber under beam.
The readout electronics was not yet ready. To accomplish the goals, π 0 run was scheduled
in between two muon beam periods. The muon beam rate was adjusted to 3×107 /s so that
the PDE decraese under a moderate beam intensity can be measured. The conditioning andoperation of the drift chamber was performed in parallel to ﬁnd a working point under muon
beam environment.

A.4.1 2020 π 0 run
In the 2020 π 0 run, the LH2 target used in the MEG experiment was reused because a new
LH2 target was not yet ready. Since this target was not compatible with the experimental setupof the MEG II experiment, it was shifted by about 7 cm to the downstream side to avoid conﬂictwith the drift chamber. To collect back-to-back gamma-ray pairs, the MPPCs for the trigger
were shifted by 6 cm downstream, and the BGO detector was shifted 7 cm downstream to matchthe target shift. Table. A.1 summarizes the beam rate and the duration of the data acquisition

183

Appendix A Summary of commissioning runs

184

in 2020 π 0 run. The pion beam rate was reduced from 9.5 × 104 /s to 1.1 × 104 /s by three steps
to mitigate the radiation damage of the SiPMs of the pTC and reduce the pileup γ-rays.
Table A.1: Conﬁguration of the 2020 π 0 run
PeriodBeam rate [104 /s]

Duration [h]20 Nov 22:00 - 21 Nov 22:00

9.5

14

21 Nov 22:00 - 23 Nov 13:00

6.8

30

23 Nov 13:00 - 26 Nov 16:00

2.9

27

26 Nov 16:00 - 27 Nov 8:00

1.1

27

185

Appendix B

Optimization of weights for uniform online
Eγ reconstruction
In the 2021 run, the reconstructed online energy had a large non-uniformity, especially in thev direction, as shown in Fig. 3.4, and the threshold value of EGamma trigger was lowered tosecure a high trigger eﬃciency for gamma-rays in the analysis region (48 MeV< Eγ <55 MeV).
The low online energy threshold led to a high trigger rate and data rate, which was a
obstacle to start the physics run with good eﬃciency at a higher beam rate, as described inSec. 3.3. The primary reason for the non-uniform online energy reconstruction was the biased
weights for the EGamma trigger. The weight of each readout channel was deﬁned by a reciprocalof a product of the gain, ECF, and PDE (QE) of the photosensor as yi = (G×FEC × ϵPD )−1 . An
algorithm to optimize the weights for the online energy reconstruction with the CW-Li dataset
was developed to solve the issue. In this algorithm, the loss function is deﬁned as
X
Loss =(∆E)2 /Nevent
event

∆E =

X

(CAi wi Npho,i − Epeak )/Epeak ,

(B.1)
(B.2)

i∈MPPC,PMT

where C is a factor to convert the number of photons to energy, wi is the weight for eachphotosensor to be optimized, Epeak is the energy peak value of the CW-Li gamma ray (17.6 MeV),
and Nevent is the number of events in the 17.6 MeV peak. See Sec. 7.1 on the deﬁnition of Ai .
The loss function is minimized iteratively by updating the weights as
wi,j+1 = wi,j − λ × ∆E
wi,0 = 1

(B.3)
(B.4)

where j stands for the step in the iteration and λ is the learning rate to update wi (0.1). Fig. B.1
P
shows the spectrum of i∈MPPC,PMT (CAi wi Npho,i ) before and after the weight optimization.
By using the updated weight wi yi instead of the original weight yi , the uniformity of the online
reconstructed energy improved signiﬁcantly, as shown in Fig. 3.4.

Events

Appendix B Optimization of weights for uniform online Eγ reconstruction

Before iteration

120
After iteration

100
80
60
40
20
0

×106
0

2

4

6

8

10

12
14
Energy [a.u.]

Figure B.1: The distribution of reconstructed energy with the weights before the optimization (red) and after the optimization (blue).

186

187

Acknowledgements
I would like to express my appreciation to Prof. Toshinori Mori ﬁrst. He gave me an opportunity to work on the MEG II experiment. Secondly, I am deeply grateful to Prof. Wataru Ootani
for his insightful comments on my research. I would like to express my sincere gratitude to Dr.
Toshiyuki Iwamoto for his support of my research activities. I appreciate Dr. Kei Ieki and Dr.
Shinji Ogawa for enthusiastic discussion. I would like to thank the members of the MEG II LXe
detector group, Dr. Sei Ban, Mr. Atsushi Oya, Ms. Ayaka Matsushita, Dr. Rina Onda, Mr.
Kazuki Toyoda, Mr. Kohei Shimada, Mr. Kensuke Yamamoto, and Mr. Keisuke Yoshida. I
give special gratitude to Dr. Yusuke Uchiyama for many insightful and constructive advice toimprove the research. I also thank the MEG II Japanese colleagues, Dr. Miki Nishimura, Dr.
Mitsutaka Nakao, Dr. Masashi Usami, Mr. Kosuke Yanai, Mr. Taku Yonemoto.
I would like to express many gratitudes to the members of the MEG II collaboration. In
particular, I would like to thank the trigger and DAQ team, Dr. Stefan Ritt, Dr. Luca Galli,
and Dr. Marco Francesconi, for their great eﬀort to take data. I appreciate the beam team,
Dr. Angela Papa, Dr. Patrick Schwendimann, Mr. Giovanni Dal Maso, Mr. Bastiano Vitali.
I am happy that I could work on the development of the MPPC alignment method with thegroup from the University of California, Irvine: Prof. William Molzon, Dr. Terence Libeiro,
Mr. William Kyle, and Mr. Dylan Palo.
I got ﬁnancial support from Advanced Leading Graduate Course for Photon Science (ALPS)
and Japan Society for the Promotion of Science (JSPS). I am deeply grateful to ICEPP secretaries and members. Especially, I appreciate Mori & Ootani laboratory members, Mr. Liu
Linghui, Dr. Naoki Tsuji, Mr. Ryunosuke Masuda, Mr. Tatsuki Murata, Mr. Fumihito Ikeda,
Mr. Yuki Ueda, Mr. Rintaro Yokota, and Mr. Weiyuan Li.
Last but not least, I would like to thank my family for their support.
December 2022,
Tokyo,
Satoru Kobayashi

188

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