Doctoral Dissertation
博士論文

Liquid xenon detector with highly
granular scintillation readout to searchfor µ+ → e+γ with sensitivity of 5 × 10−14
in MEG II experiment（MEG II 実験における感度 5 × 10−14 での µ+ → e+ γ 探索のための
シンチレーション光を高精細に読み出す液体キセノン検出器）

A Dissertation Submitted for the Degree of Doctor of Philosophy
October 2020
令和２年 10 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

Shinji Ogawa
小川

真治

i

Abstract
A charged lepton flavor violating decay of a muon, µ → eγ, is an interesting probe in the
search of physics beyond the Standard Model. Current upper limit on the branching ratio of
this decay is 4.2 × 10−13 (90% confidence level) given by the MEG experiment. An upgrade
experiment of MEG called MEG II is planned aiming to improve the sensitivity by one order ofmagnitude.
For this purpose, a new liquid xenon detector has been developed to measure γ-rays with agood resolution. It utilises new large area VUV-sensitive Multi-Pixel Photon Counters (MPPC).
A high granularity and a good uniformity of the scintillation readout realized by the MPPCs
enable us to achieve a good position and energy resolution especially for the shallow eventsnear the γ-ray entrance face. Performance of the detector was measured in a series of pilot runs.
Better position and energy resolutions for the shallow events are demonstrated. An improvementon the timing resolution is also achieved by an optimized analysis.
On the other hand, the energy resolution for the deep events is found to be worse than
expected, probably due to an unknown contribution also observed in the previous experiment.
In addition, a degradation was found on the photon detection eﬃciency of the MPPCs for xenon
scintillation light by a radiation damage, while it was neither reported nor expected.
The branching ratio sensitivity of MEG II with this detector is estimated based on the measured detector performances. Even though the worse energy resolution and the degradation of
the photon detection eﬃciency deteriorate the branching ratio sensitivity of MEG II, the planned
sensitivity of 5 × 10−14 is found to be still achievable by a realistic extension of the data-taking
period. Therefore, it is concluded that the liquid xenon detector has a suﬃcient performance tosearch for a µ → eγ decay with a sensitivity of 5 × 10−14 .

iiContents

Abstracti

Preface1

Chapter 1

Introduction to MEG II experiment3

1.1

Physics motivation: Charged lepton flavor violation . . . . . . . . . . . . .

3

1.2

Previous experiment: MEG experiment . . . . . . . . . . . . . . . . . . . .

5

1.3

Concept of MEG II experiment . . . . . . . . . . . . . . . . . . . . . . . .

8

1.4

Beam and target . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9

1.5

Positron spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11

1.6

LXe γ-ray detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

16

1.7

Radiative decay counter . . . . . . . . . . . . . . . . . . . . . . . . . . . .

25

1.8

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

27

1.9

Branching ratio sensitivity expected at design stage . . . . . . . . . . . . .

30

Development of LXe Detector

32

2.1

VUV-sensitive MPPC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

32

2.2

Test of all VUV-MPPCs . . . . . . . . . . . . . . . . . . . . . . . . . . . .

41

2.3

Selection of PMTs

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

42

2.4

Photosensor installation . . . . . . . . . . . . . . . . . . . . . . . . . . . .

44

2.5

Calibration sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

49

2.6

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

52

2.7

Xenon control system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

54

Pilot run56

3.1

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

56

3.2

DAQ system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

57

Detector simulation

62

4.1

Event generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

63

4.2

Waveform simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

64

4.3

Background γ-ray . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

65

Chapter 2

Chapter 3

Chapter 4

Contents
Chapter 5iii
PMT performance

67

5.1

Resoponse to visible light. . . . . . . . . . . . . . . . . . . . . . . . . . .

68

5.2

Resoponse to VUV light . . . . . . . . . . . . . . . . . . . . . . . . . . . .

72

MPPC performance

74

Chapter 6
6.1

Resoponse to visible light. . . . . . . . . . . . . . . . . . . . . . . . . . .

74

6.2

Resoponse to VUV light . . . . . . . . . . . . . . . . . . . . . . . . . . . .

76

6.3

Investigation of VUV PDE degradation . . . . . . . . . . . . . . . . . . . .

81

Position resolution

91

Chapter 7
7.1

Position reconstruction. . . . . . . . . . . . . . . . . . . . . . . . . . . .

91

7.2

Measurement with lead collimator . . . . . . . . . . . . . . . . . . . . . . .

92

7.3

Eﬀect of PDE angular dependence . . . . . . . . . . . . . . . . . . . . . .

94

Timing resolution

97

8.1

Timing reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

97

8.2

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

98

8.3

Single channel performance . . . . . . . . . . . . . . . . . . . . . . . . . .

99

8.4

Detector performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

Chapter 8

Chapter 9

Energy resolution

105

9.1

Energy reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

9.2

Unknown contribution in MEG . . . . . . . . . . . . . . . . . . . . . . . . 106

9.3

Energy measurement performance in MEG II . . . . . . . . . . . . . . . . 107

9.4

Summary and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

Chapter 10

Pileup elimination performance

118

10.1

Sources of pileup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

10.2

Pileup elimination by sum waveform . . . . . . . . . . . . . . . . . . . . . 122

10.3

Pileup rejection by charge distribution . . . . . . . . . . . . . . . . . . . . 125

Chapter 11

Expected branching ratio sensitivity of MEG II

131

11.1

Calculation procedure of branching ratio sensitivity . . . . . . . . . . . . . 131

11.2

Sensitivity imporvement by LXe detector . . . . . . . . . . . . . . . . . . . 134

11.3

Eﬀect of PDE degradation: detector performance . . . . . . . . . . . . . . 136

11.4

Eﬀect of PDE degradation: detector operation . . . . . . . . . . . . . . . . 142

11.5

Eﬀect of pileup rejection by charge distribution . . . . . . . . . . . . . . . 144

11.6

Branching ratio sensitivity of MEG II experiment . . . . . . . . . . . . . . 145

Chapter 12Conclusion

149

Appendix A

Data reduction algorithm

151

Contents

iv

Appendix B

Threshold dependence of timing resolution of a channel

153

Appendix C

List of abbreviations

155

1

Preface
Background
The Standard Model is a fundamental model in the particle physics validated by many experiments up to the electroweak energy scale. Even with its success, it is thought to be a low
energy approximation of more fundamental physics due to the existence of some unexplained
phenomena and some theoretical diﬃculties. Therefore, physics beyond the Standard Model isactively searched.
A charged lepton flavor violating decay of a muon, µ → eγ, is an interesting probe in the searchof the new physics. Experimentally reachable branching ratio of this decay is predicted by manyextensions of the Standard Model, while this decay is prohibited in the Standard Model by the
lepton flavor conservation law. Since this decay emits a coincident pair of monochromatic eand γ in the back-to-back direction, a signal event is eﬃciently distinguishable from many otherbackground events by searching for an event satisfying this criteria. Current upper limit on
the branching ratio of this decay is set to be 4.2 × 10−13 (90% confidence level) by the MEG
experiment [1]. An upgrade of the MEG experiment called MEG II experiment is planned fora further improvement of the branching ratio sensitivity by one order of magnitude. Since thesensitivity in MEG was limited by the number of the accidental backgrounds, an improvementof the detector resolutions is a key to achieve the goal of MEG II.
Structure of this thesis
This thesis focuses on a liquid xenon γ-ray detector developed for this purpose. Chapter 1
gives a basic knowledge on the MEG II experiment needed to understand the discussion infollowing chapters. Chapter 2 explains the developed liquid xenon detector. A new photosensor
developed for this detector is also introduced. A series of pilot runs was performed to evaluate
the detector performance. A details is given in Chapter 3, and a detail of the simulation used
for the analysis is given in Chapter 4. Chapter 5 and 6 summarize measured performances ofthe photosensors in the pilot runs. An unexpected radiation damage is observed on the newphotosensors, and this is also shown in Chapter 6. Each measured detector resolution is shownin Chapter 7, 8, 9, and 10. In Chapter 11, the MEG II branching ratio sensitivity achievablewith the liquid xenon detector is discussed based on the results shown in the previous chapters.
A modification of the MEG II data-taking plan is proposed to deal with the radiation damageof the photosensor. This thesis is concluded in Chapter 12.

Preface
The author’s contribution
The liquid xenon detector has been developed by the liquid xenon group of the MEG II
collaboration. The author participated in the group at the middle of 2014, and contributed
to the finalization of the development of the photosensor whose performance summarized in
Section 2.1. The author joined the construction of the liquid xenon detector on site describedin Section 2.2–2.7.
In the beam test for the demonstration of the detector performance, the author played acentral role both in the data-taking and the analysis of the data. The calibration of the photosensors described in Chapter 5 and 6 was carried out by a few members of the group. The
major contribution of the author is an observation of a radiation damage (Section 6.2.2). The
demonstration of the detector performance (Chapter 7–10) and the discussion of the eﬀect on
the branching ratio sensitivity (Chapter 11) was mainly done by the author except for the position resolution measurement written in Chapter 7. In addition to the performance improvement
expected at the design stage, the oﬄine analysis is also improved by the author for even better
detector performance as described in Section 8.3, 9.3.6, and 10.3.

2

3

Chapter 1

Introduction to MEG II experiment
1.1 Physics motivation: Charged lepton flavor violation
The Standard Model (SM) is a fundamental model in the particle physics. It is validated
by many experiments up to the electroweak energy scale (O(100) GeV). Even with its success,there are several unexplained phenomena such as the existence of the dark matter. It also hassome theoretical problems such as too many parameters and hierarchy problem. The existenceof the generations is also a mystery in the SM. The SM contains three generations for the quarks
and the leptons, while they are not theoretically required. Therefore, the SM is thought to bean approximation of a more fundamental law of nature. Many theoretical extensions of the
SM are proposed, and the physics beyond Standard Model (BSM) is eagerly searched by many
experiments.
Charged lepton flavor violating processes are interesting probes to search for the BSM. In theSM, flavor mixing is allowed for the quark sector, while it is prohibited for the lepton sector by
the lepton flavor conservation law. Since the flavor mixing between neutrinos called neutrino
oscillation is recently found, flavor mixing between charge leptons, namely a charged lepton
flavor violation (CLFV) process, is the only the flavor mixing process which has not yet been
observed.
The purpose of the MEG II experiment is to search for a CLFV decay of a muon, µ → eγ,with a very good branching ratio sensitivity to find a clue for the new physics.
In the SM taking the neutrino oscillation into account, the µ → eγ decay occurs by a Feynman
diagram shown in Fig. 1.1. Its branching ratio is calculated to be as follows [2]:B(µ → eγ) =∆m2i1
3α ∑ ∗∼ 10−55 ,Uµi Uei232π i=2,3MW

where U is the PMNS matrix. Due to the small mass diﬀerence of the neutrinos ∆m2 comparedto the mass of W boson, the branching ratio is largely suppressed, and is too small to be detectedin the experiment.
In contrast, some of the BSM models predict a branching ratio of O(10−13 –10−14 ), which isexperimentally detectable [3]. Supersymmetry (SUSY) is one promising candidate for the BSMs.

Chapter 1 Introduction to MEG II experiment

Figure 1.1 Feynman diagram of µ → eγ in the SM with the neutrino oscillation.

Figure 1.2 Feynman diagram of µ → eγ in the SU(5) SUSY GUT [3].

In the minimal extension of the SM with SUSY called MSSM, a SUSY partner is introduced
to each SM particle. This model is attractive since it can cancel the quadratic divergence inthe radiative corrections of the Higgs mass. In the BSM models with SUSY, if the oﬀ-diagonal
elements on the slepton mass matrix is non-zero in the basis which diagonalize the lepton mass
matrix, it becomes a source of the CLFV.
One example is SU(5) SUSY GUT model [4]. In this model, electromagnetic, weak, and strong
interactions are unified into a single gauge group at the grand unification (GUT) energy scale.
This model is attractive in the sense that coupling constants of three interactions become unified
at the GUT scale thanks to the contribution from the SUSY particles. In this model, when the(SM) lepton mass matrix is diagonalized
VR ye VL† = diagnonal,
the oﬀ-diagonal terms of the right-handed slepton mass matrix is written as follows:(m2ẽR )ij ≃ −MP3(VR )i3 (VR )∗j3 |yu33 |2 m20 (3 + |A0 |2 ) ln
,
8π 2
MG

where ye and yu are the Yukawa coupling constant for leptons and up-type quarks, m0 is theuniversal scaler mass, A0 is the trilinear coupling, MP is the reduce Planck mass, and MG is
the GUT energy scale. This oﬀ-diagonal term leads to the CLFV through Feynman diagrams
shown in Fig. 1.2.
Another example is SUSY seesaw model [5][6]. This model introduces right-handed heavy
neutrinos with a Majorana mass term to explain the observed tiny mass of neutrinos by aseesaw mechanism. By introducing Majorana neutrinos into the SUSY model, a new Yukawa
coupling constant for the neutrinos yν is introduced. Since the Yukawa coupling constant for
the neutrinos and that for the leptons are independent, an oﬀ-diagonal term appears in the4Chapter 1 Introduction to MEG II experiment

(a)

(b)

5

(c)

Figure 1.3 Event signature of (a) Signal, (b) Physics background (RMD), and (c) Accidental background.

left-handed slepton mass matrix as follows, and can be another source of the CLFV:(m2l̃L )ij ≃ −1MP,(yν )∗ki (yν )kj m02 (3 + |A0 |2 ) ln
8π 2MR

where MR is the mass of the right-handed Majorana neutrino.

1.2 Previous experiment: MEG experiment
The current best upper limit to the branching ratio of the µ → eγ decay is set to 4.2×10−13 at
90% confidence level by the MEG experiment [1]. The MEG experiment measured many muon
decays from the world’s most intense continuous muon beam available at Paul Scherrer Institute(PSI) in Switzerland with good detector resolution and eﬃciency. In the search of the µ → eγ
decay, a signal event has to be identified from many other background events by utilizing its
signature. This section describes how the MEG experiment searched for the µ → eγ event, andwhat was a limiting factor of its physics performance. This will be a basis to discuss how to
improve the branching ratio sensitivity in MEG II in the next section.
Principle of µ → eγ search
The signal decay µ → eγ is a two-body decay of a stopped muon to the nearly masslessparticles. Therefore, a signal decay emits a time coincident pair of a positron and a γ-ray
having an energy of the half of the muon mass (mµ /2 = 52.8 MeV) to the back-to-back direction(Fig. 1.3). Their energies Ee and Eγ , opening angle Θeγ , and time diﬀerence teγ were measured
by the positron and γ-ray detectors shown in Fig. 1.4. Signal events which satisfy Ee = Eγ =52.8 MeV, Θeγ = π, teγ = 0 were searched for.
Single event sensitivity
The expected number of signal events Nsig is calculated as follows:
Nsig = B × k,
k := Rµ × T × Ω × ϵe × ϵγ × ϵcut ,Chapter 1 Introduction to MEG II experiment

Figure 1.4 Schematic of the MEG experiment [7].

where B is the branching ratio of the signal decay, and k is the inverse of the single event
sensitivity. Rµ is the muon beam intensity, T is the total data-taking time, Ω is the geometricalacceptance of the detectors, ϵe is the detection eﬃciency for signal positron, ϵγ is the detection
eﬃciency for signal γ-ray, and ϵcut is a product of the trigger eﬃciency and the event selection
eﬃciency in the oﬄine analysis. In the MEG experiment, about Rµ × T = 8 × 1014 muons weredecayed on the target in five years data-taking. These events were measured by the detectors ofΩ = 10.8%, ϵe = 30%, ϵγ = 63%, ϵcut = 91%(from 2009-2010), 96%(from 2011-2013), and thesingle event sensitivity k −1 = 0.58 × 10−13 was achieved.
Background events
Events which satisfy the signal event criteria by chance become background events. There
are two types of background events as shown in Fig. 1.3: physics background and accidental
background.
One is the physics background coming from a radiative muon decay (RMD), µ+ → eνµ νe γ.
A pair of a positron and a γ-ray both of which carry signal-like energies can be emitted nearlyback-to-back direction from the RMD, when two neutrinos carry only a small amount of theenergy. The eﬀective branching ratio of the physics background is calculated to be only about
0.1 × 10−13 from the theoretical spectrum of the RMD folded with the detector resolutions in
MEG. This is smaller than the single event sensitivity, and thus the physics background was
negligible.
The other is an accidental coincidence of a positron and a γ-ray. If a pair of positron and γ-ray
near the signal energy originated from independent muon decays are accidentally emitted backto-back at the same time, it looks like a signal event. Positrons near the signal energy comesfrom the Michel decays. Fig. 1.5(a) shows the spectrum of the Michel positron. Michel positronnear the signal energy can be emitted with a rather high probability. Gamma-rays near thesignal energy come from two types of events. One is the γ-ray from the RMD. Fig. 1.5(b) shows

6

2
1.5
1
0.5
0
0

7

Differential Branching Ratio

Differential Branching Ratio

Chapter 1 Introduction to MEG II experiment

0.2 0.4 0.6 0.8
1
Normalized Positron Energy (x)

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)

(a)

(b)

Figure 1.5 (a) Simulated energy spectrum of the Michel positron [8]. (b) Simulated energy
spectrum of the RMD γ-ray. Energies on the x-axis are normalized to the half of the muon
mass (mµ /2 = 52.8 MeV).

its energy spectrum of γ-ray. Contrary to the Michel positron, its spectrum rapidly decreases at
the high energy. The other is the annihilation of Michel positrons in flight with electrons in thematerials such as target, positron drift chamber, etc. Contributions from both processes werecomparable in MEG. About 55% of background γ-rays in the analysis region (Eγ > 48 MeV)
came from the RMDs, and the others came from the annihilation in flight.
The eﬀective branching ratio of the accidental background was the limiting factor in MEG.
Since the number of the accidental background events depends on the detector resolution as
follows*1 [3]:NBG ∝ Rµ2 × ∆Eγ2 × ∆Ee × ∆teγ × ∆Θ2eγ ,(1.1)

and the MEG II experiment tries to reduce it by improving the detector resolutions.
Branching ratio sensitivity
The branching ratio sensitivity of MEG is determined by a combination of two terms. One
is the single event sensitivity which is an inverse of the accumulated number of muon decaysk. The other is the contribution from the background events, which is inversely proportional to
the square root of k.
In the final result of MEG, the branching ratio sensitivity was 4.2 × 10−13 , while the single
event sensitivity was 0.58 × 10−13 . Therefore, the branching ratio sensitivity was limitted by the
number of the accidental background events. Fig. 1.6 shows the sensitivities of MEG as a functionof the statistics used for each analysis. An improvement in the sensitivity by an increased*1 This assumes that the accidental background γ-rays only come from the RMDs.

Chapter 1 Introduction to MEG II experiment

Figure 1.6 Branching ratio sensitivities (black line) and upper limits (purple markers) of
MEG results as a function of the statistics used in each analysis [9].

statistics was getting smaller since the contribution from the backgrounds only improves by asquare root of the statistics.

1.3 Concept of MEG II experiment
In order to improve the branching ratio sensitivity by one order of magnitude, an upgradeof the MEG experiment, MEG II experiment, is planned. There are two keys to achieve thesensitivity improvement.
One is an upgrade of all detectors to improve the resolutions and to reduce the accidental
background events. As is discussed in the previous section, the sensitivity of MEG was limitedby the number of the accidental backgrounds. Even if we continue data-taking by using MEG
detectors, the sensitivity improves only by a squared root of the DAQ time, and it takes about
100 years to improve it by one order of the magnitude. Therefore, all detectors in MEG are
upgraded or renewed in MEG II aiming to improve the resolutions by a factor of 2 and to reduce
the accidental background events as shown in Equation 1.1.
The other key is an increase of the accumulated statistics. The muon beam rate in MEG waslimited to 3 × 107 mainly due to discharges on the positron drift chamber and an unacceptablebackground level for the MEG detectors. This issue will be fixed by building a new detector, andthe beam rate can be increased to 7 × 107 in MEG II. The detection eﬃciency of the positron
spectrometer is also doubled by the upgrade.

8Chapter 1 Introduction to MEG II experimentFig. 1.7 shows the detectors in the MEG II experiment. Positive muons coming from abeam line are stopped on a target placed at the center of the detectors. Positrons from themuon decays are measured by a spectrometer (Section 1.5) which consists of a constant bending
radius (COBRA) magnet, a cylindrical drift chamber, and a positron timing counter. A liquid
xenon γ-ray detector (Section 1.6) is used for a measurement of γ-rays from the muon decays.
A new detector called radiative decay counter (Section 1.7) is installed to measure low energy
positrons from the RMDs for an active background tagging. A data acquisition (DAQ) system(Section 1.8) to measure signals from the detectors is also upgraded for MEG II.
A global coordinate system (x, y, z) is defined as follows. The origin is defined at the centerof the COBRA magnet where the muon stopping target is located. The z-axis is set parallelwith the muon beam, and the y-axis is set vertical upward. The x-axis is set horizontal, so that(x, y, z) forms a right-handed system. A cylindrical coordinate system (r, θ, ϕ) is also defined√as, r := x2 + y 2 , θ := tan−1 (z/r), ϕ := tan−1 (y/x).
ds
The search of the µ → eγ is performed with a set of observables (Eγ , Ee , teγ , ϕeγ , θeγ , Erdc
, tds
rdc ).

Positron tracks are measured by the spectrometer to reconstruct its energy Ee , direction, anddecay vertex on the target. The γ-ray direction is reconstructed from the hit position in the
γ-ray detector and the decay vertex, and is utilized to calculate the opening angles (ϕeγ , θeγ )of the positron and the γ-ray. The energy of the γ-ray Eγ is measured by the γ-ray detector.
Time diﬀerence of the positron and the γ-ray teγ is calculated from the timing measured by
the positron timing counter, and the γ-ray detector. Their propagation times from the decay
vertex to the detectors are calculated and corrected from their reconstructed track lengths.
ds, tds
Measured positron energy and timing at the radiative decay counter (Erdcrdc ) are also usedin the MEG II analysis.

1.4 Beam and target
The MEG II experiment will be carried out at the πE5 beam line at PSI (Fig. 1.8), where theworld’s most intense continuous muon beam is available. The ring cyclotron at PSI can supply
a 590 MeV proton beam of 2.2–2.4 mA. It is injected into a pion production target (target E)
made of 4 cm-thick graphite. The muon beam is generated by collecting muons from the pion
decays at the surface of the target E. This is called surface muon beam. Since the frequency ofthe cyclotron (50.7 MHz) is higher than the pion lifetime (26 ns), the extracted muon beam canbe regarded as a continuous beam. The small momentum of the surface muons (28 MeV/c) witha good momentum-byte of about 7% (FWHM) enables us to stop the muons by a thin target E.
A Wien-filter (often called “Separator”) is installed in the πE5 beam line to separate positroncontamination in the muon beam, which is derived from the Michel decay of the muon and theπ 0 decay in the target.
A superconducting beam transport solenoid (BTS) is installed to connect the πE5 beam line
to the MEG II detectors. It applies a 0.36 T magnetic field to focus the beam. A degrader madeof 300 µm thick Mylar is placed at the center of the BTS to adjust the muon momentum.

9Chapter 1 Introduction to MEG II experiment

Figure 1.7 Detectors in the MEG II experiment [7]Figure 1.8 Schematic view of the πE5 beam line and the MEG (II) experimental area [7].

The muon beam is injected into the muon stopping target placed at the center of the MEG II
detectors. This target has to be thin enough to avoid a multiple scattering and an annihilationof the emitted positrons. In the pilot run for MEG II, a 174 µm-thick plastic scintillating film
(Fig. 1.9) was used as a target. It was placed 15◦ slanted from the beam axis to achieve a longer
eﬀective thickness for the muon beam and a shorter thickness for the positron. The scintillation
light from the target can be used to measure the intensity and profile of the beam with a CCD
camera.
In the MEG experiment, a distortion of the target during the data-taking was found, which
introduced a systematic uncertainty in the reconstructed positron direction. This was the sourceof the largest systematic uncertainty in MEG. To monitor the stability of the target, opticalmarkings are printed on the target for MEG II, and are monitored by CCD cameras [10].

10Chapter 1 Introduction to MEG II experiment

Figure 1.9 Muon stopping target for MEG II (width:270 mm, height:66 mm) [7].

Figure 1.10 Schematic view of the COBRA magnet [11].

1.5 Positron spectrometer
The positron spectrometer in MEG II consists of the COBRA magnet, the cylindrical drift
chamber, and the positron timing counter.
COBRA magnet
COBRA is a superconducting magnet specially designed for MEG, and is reused in MEG II(Fig. 1.10) [11]. Its gradient magnetic field (1.27 T at z = 0) is designed to have the same
bending radius for the monochromatic positrons emitted from the target independent of theemission angles. It also sweeps low energy positrons quicker from the magnet than a simple
solenoid. These features enable us to measure only the high energy positrons, which we areinterested in. The COBRA magnet is also deigned to allow the signal γ-rays to penetrate it.
It has a thin window at the acceptance region of the γ-ray (| cos θ| < 0.35), whose radiation
thickness is 0.197X0 . It has two compensation coils to suppress the magnetic field at the LXedetector for the PMT operation.
Cylindrical drift chamber
A new single volume wire drift chamber (green one in Fig.1.7) is built for the positron tracking
in MEG II. It has a cylindrical shape whose inner radius is 17 cm, outer radius is 29 cm, andlength is 191 cm. It is designed to have a high transparency to avoid multiple scatterings of thepositrons. A low mass gas mixture of He : C4 H10 = 90 : 10 is used. The total radiation length11Chapter 1 Introduction to MEG II experiment
×10

12

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)Figure 1.11 Simulated position (radius) distribution where the background γ-rays (Eγ >48 MeV) are generated from the Michel positrons. The y-axis is normalized to the probability per one muon decay on the target.

is 1.58 × 10−3 X0 , while it was 2.0 × 10−3 X0 in MEG.
The low material budget can reduce the accidental background γ-rays from the annihilationin flight. Fig. 1.11 shows the position distribution where the background γ-rays are generated
from the Michel positrons. The major contribution comes from the target, and the positron drift
chamber. The number of the accidental background γ-rays above 48 MeV from the annihilationin flight per one muon decay on the target is reduced to 1.35(1) × 10−6 from 2.3 × 10−6 in MEG.
The drift chamber consists of nine drift cell layers as shown in Fig. 1.12(a)*2 . Each drift cellis composed of a 20 µm gold plated tungsten sense wire surrounded by 40/50 µm silver plated
aluminum field wires. The size of the drift cell ranges from 6.6 mm (inner layers) to 9.0 mm (outerlayers). A stereo wire configuration is adopted, in which wire planes are slanted at alternating
signs stereo angles of 6.0◦ –8.5◦ . This allows us to reconstruct z position of the positron track.
The sense wire signals are read out from both sides, so that additional information on z can bereconstructed from a charge division, and from a propagation time diﬀerence.
The positron detection eﬃciency in MEG was limited to 30% by a service material of thedrift chamber on the positron track (Fig. 1.12(b)). They are removed in MEG II, and a 70%
detection eﬃciency is expected.
Positron timing counter
The positron timing counter is renewed for MEG II. For the positron timing measurement in
MEG, 30 BC404 scintillator bars (80 × 4 × 4 cm3 ) read out by fine mesh photomultiplier tubes(PMTs) were used. Though its intrinsic resolution was 40 ps, actual timing resolution in MEG
was 70 ps. This is mainly due to a variation of the optical photon path length from its large
size, and a degradation of the PMT performance in the magnetic field.
To cope with these issues, a new highly segmented positron timing counter has been developed*2 This figure is for the original design where ten layers were planned.

the real detector.

The outer most layer was omitted inChapter 1 Introduction to MEG II experiment

(a)

13

(b)

Figure 1.12 (a) Drift cells configuration at the center of the drift chamber [7]. (b) A crosssection of the positron spectrometer for MEG (top), and MEG II (bottom) [12]. Detection
eﬃciency of the positrons is improved by removing service materials on the positron track.

for MEG II. The counter is composed of an upstream sector and a downstream sector. Fig. 1.13
shows a design of the downstream one. It consists of 256 small plastic scintillator tiles. Each tile
is 120 × 40/50 × 5 mm3 BC422 scintillator coupled to six silicon photo-multipliers (SiPM) from
AdvanSiD (ASD-NUV3S-P High-Gain(MEG)) at each end (Fig. 1.14). The tile is wrapped byan enhanced specular reflector (ESR) from 3M to enhance the light collection. The six SiPMs
on each side are connected in series and read out by a PCB. An optical fiber is inserted to
distribute a synchronous laser signals for the time alignment between tiles.
Thanks to the thin scintillator tile, signal positron can penetrate multiple tiles. Fig. 1.15(a)shows the expected number of hit counters Nhit for a signal positron. On average, nine counters
are hit. Positron timing is reconstructed from a combination of the hit counters. The combined√
resolution will be σtsingle / Nhit , where σtsingle is the timing resolution of a counter, which includes the intrinsic resolution of a counter, the error in time alignment over the counters, andthe electronics jitter. This segmentation scheme also benefits the operation in high pileup environment, and can supply additional information of the positron track. Fig. 1.15(b) shows thetiming resolution measured for Michel positrons in the pilot run. Improvement in the resolution√
proportional to 1/ Nhit is observed, and 31 ps timing resolution is achieved at Nhit = 9.
Expected performance of spectrometer
Combined performance of the spectrometr is simulated by MC. The expected performance issummarized in the Table 1.1.

Chapter 1 Introduction to MEG II experiment

14

Figure 1.13 Design of a module of the positron timing counter [7].

Figure 1.14 A scintillator tile used for positron timing counter. (left) 40 mm height tile
with reflector wrapping, (right) 50 mm height tile before wrapping [7].

100

1
9.281

Resolution (ps)Frequency (a.u.)

Mean

0.5

0
0

5

10
Nhit

(a)

15

20

80

χ2 / ndf

8.537 / 3

single92.62 ± 0.6224

const

0 ± 3.032

60

40
20

2

4

6
N hit

8

10

(b)

Figure 1.15 (a) Expected number of hit counters for a signal positron from the simulation[7]. (b) The total timing resolution measured in the pilot run 2016 [7]. The red curve√shows the best fit by a function of σsingle / Nhit ⊕ σconst .

Chapter 1 Introduction to MEG II experiment

15

Table 1.1 Positron detector performance [7].

MEG (measured)

MEG II (simulated)

Ee resolution (keV)

380

130

θe resolution (mrad)

9.4

5.3

ϕe resolution (mrad)

8.7

3.7

te resolution (ps)

107

37

2.4/1.2

1.6/0.73070vertex resolution (ze /ye , mm)eﬃciency (%)

Chapter 1 Introduction to MEG II experiment

1.6 LXe γ-ray detector
In order to measure the γ-ray from µ → eγ decay with a good resolution and eﬃciency, a liquid
xenon (LXe) detector was used in the MEG experiment. This detector has been upgraded to
MEG II to improve its performance. A review of the MEG LXe detector is given in Section 1.6.1
and 1.6.2, and a concept of the upgrade is given in Section 1.6.3.

1.6.1 LXe as a scintillator
In the LXe γ-ray detector, LXe is used as a scintillator. Table 1.2 summarizes its properties.
The LXe is suitable for the γ-ray detector in MEG (II) experiment in several aspects. The highstopping power of the LXe thanks to its large atomic number and high density makes it possible
to construct a rather compact detector with a reasonable detection eﬃciency. Its suﬃcient lightyield enables us to achieve a good detector resolution. The fast decay time of the scintillation issuitable for an operation in a high pileup environment. Since it is liquid, it is easier to achievea uniform response than a crystal scintillation detector.
Table 1.2 Properties of the LXe

Item

Value

Atomic Number

54

Density

2.953 g/cm3 [13]Radiation length2.872 cm [13]Moliere radius

5.224 cm

Scintillation Wavelength (mean)

174.8 ± 0.1(stat.) ± 0.1(syst.) nm [14]Scintillation Wavelength (FWHM)

10.2 ± 0.2(stat.) ± 0.2(syst.) nm [14]Decay time (fast)

4.2 ns [15]Decay time (slow)

22 ns [15]Decay time (recombination)

45 ns [15]W-value for electron

21.6 eV [16]W-value for alpha17.9 eV [16], 19.6 eV [17]Refractive index (for λ = 175 nm)

1.65

When a particle deposits its energy in the LXe, scintillation light is generated by two processes[18][19]. The first one is from the excited xenon atom Xe∗ .
Xe∗ + Xe + Xe → Xe∗2 + Xe
Xe∗2 → 2Xe + hν

16Chapter 1 Introduction to MEG II experiment
The second process is the recombination of the ionized xenon Xe+ .
Xe+ + Xe → Xe+
2
∗∗
−
Xe+
+ Xe
2 + e → Xe

Xe∗∗ → Xe∗ + heatXe∗ + Xe + Xe → Xe∗2 + Xe
Xe∗2 → 2Xe + hνIn both processes, scintillation light centered at λ = 174.8 nm is emitted from Xe∗2 → 2Xe + hν.
Fig. 1.16(a) shows the scintillation decay time for diﬀerent particles. For the alpha particles,
the recombination occurs very fast, and the decay time constant is determined by the lifetime ofXe∗2 [20]. Two time components of 4.2 ns and 22 ns are observed, which correspond to a singlet
state and a triplet state, respectively. For the electrons or the γ-rays whose energy deposit
densities are lower than the alpha particles, the decay time constant is determined by that of
the recombination and becomes 45 ns. This diﬀerent decay time can be utilized for a particle
identification.
There are three technical diﬃculties in the usage of the LXe. Firstly, its allowed region oftemperature is limited as shown in Fig. 1.16(b). Since our detector is operated at about 1.2 atm,
the liquid phase is only in the range of about 10 K. Secondly, its scintillation light is in thevacuum ultraviolet (VUV) region, and photosensors used for this detector have to be VUVsensitive. Finally, impurities in the LXe have to be removed because an oxygen or a watercontamination can easily absorb scintillation light, and a nitrogen contamination can quench
the xenon scintillation by the following process:Xe∗2 + N2 → 2Xe + N2 .

1.6.2 LXe detector in MEG
Fig. 1.17 shows the LXe detector used in MEG. LXe of 900 ℓ is surrounded by 846 PMTs
placed on the detector wall to detect the scintillation light. The energy, the hit position, andthe hit timing of the incident γ-ray are reconstructed from the observed scintillation light. Thisdetector is designed to subtend 10.8% of the solid angle from the muon stopping target. The
thickness of the LXe is 38.5 cm (= 13.8X0 ) to fully contain the electromagnetic shower of the
52.8 MeV γ-ray from the signal decay. The detector wall consists of six faces (called inner, outer,
upstream, downstream, top, and bottom face). The upstream and the downstream faces arecalled lateral face, and four faces except for the inner and the outer faces are called side face.
A dedicated local coordinate system is defined on this C-shape cryostat as shown in Fig. 1.18.
The horizontal and vertical coordinates on the inner face are defined as u and v, respectively,

17

Chapter 1 Introduction to MEG II experiment

(a)

18

(b)

Figure 1.16 (a) LXe scintillation decay time for each particle [15]. (b) Phase diagram of xenon.

and the depth from the inner face is defined as w*3 :u=zv = tan (−y/x) × Rin√
w = x2 + y 2 − Rin .
The Rin is the radial distance from the beam axis at the photosensor surface placed on the inner
face, which is Rin = 67.85 cm for MEG, and Rin = 64.84 cm for MEG II. The active volume ofthis detector, where γ-ray hits are analyzed, is defined as follows:|u| < 23.9 cm|v| < 67.9 cm
0 < w < 38.5 cm.
The detector cryostat consists of an inner vessel and an outer vessel (Fig. 1.17(a)). The
outer vessel is evacuated to thermally insulate the inner vessel filled with the LXe. Super
insulation layers are installed between these vessels to suppress the heat inflow through thethermal radiation. Since the γ-ray goes into the LXe through an entrance window, the window
has to be as thin as possible to achieve a better eﬃciency. The γ entrance face of the inner
vessel is composed of a honeycomb-structure aluminum window and a carbon fiber plate. Itsradiation thickness is only 0.081X0 .
For the LXe detector in MEG, a new PMT with metal channel dynodes shown in Fig. 1.19(a)was developed in collaboration with Hamamatsu Photonics K.K (HPK). It is equipped with aquartz window to transmit the VUV light, and Bialkali (K-Cs-Sb) is used as a VUV sensitive*3 This equation is true if the LXe detector is placed at the designed position.

Chapter 1 Introduction to MEG II experiment

19

(a)
outer

top

100

downstream

upstream

80
60
40
20

v-axis148.6cm0

w-axis
inner

38
.5

58cm

cm

z

u-axisbottom96cm(b)

Figure 1.17 (a) Overview of the LXe γ-ray detector in MEG [21]. (b) Layout of the PMT
in the LXe detector for MEG [21].

photo-cathode. Zener diodes are put in the last two amplification stages as shown in Fig. 1.19(b),in order to stabilize the gain under a high background condition.
In the MEG data-taking, high voltage applied to each PMT was adjusted to have the samegain (about 1.7 × 106 ) at the beginning of each year. Fig. 1.20(a) shows the time evolution of
the gain averaged over all PMTs in 2013. A gradual decrease of the PMT gain was observed
during the data-taking, probably due to the degradation of the dynode material by the induced
current. The quantum eﬃciency of each PMT was measured from the calibration source insidethe detector. It was measured to be about 22% as shown in Fig. 1.20(b).
The performance of the MEG LXe detector was limited by the granularity and the uniformityChapter 1 Introduction to MEG II experiment

20

u

w

y
v

z
x

Inner face

Figure 1.18 Dedicated coordinate on the LXe detector

(a)

(b)

Figure 1.19 (a) VUV-sensitive PMT for MEG experiment (Hammatsu R9869) [21]. (b)Circuit of the PMT [21].

1800 ×10

PMT Gain

3

90

1750

80
70

1700

60
50

1650

40
30

1600

20
10

1550
05/09

05/23

06/06

06/20

07/04

(a)

07/18

08/01

08/15

08/29
09/12
month/day

0
0

0.05

0.1

0.15

0.2

0.25

0.3

0.35
0.4
PMT QE(b)

Figure 1.20 (a) History of the gain averaged over all PMTs in the run 2013. (b) Quantum
eﬃciency of the PMTs measured in MEG (2013).

Chapter 1 Introduction to MEG II experiment

21

62 mm

57 mm
sensitive area
PMT
46 mm

(a)

(b)

Figure 1.21 (a) Layout of the PMTs on the inner face in MEG. (b) Simulated photon
collection eﬃciency as a function of the photon conversion depth in MEG [7].

450
400
350
300
250
200
150
100
50
0
0

2

4

6

8

10

12

14

16 18 20depth (cm)Figure 1.22 Simulated distribution of the conversion depth for the signal γ-rays [7].

of the scintillation readout. Even though the PMTs were placed with minimum spacing on the
inner face, there was still a large insensitive area between the PMTs as shown in Fig. 1.21(a).
This insensitive area leads to a non-uniformity of the total detected number of photons, fromwhich the γ-ray energy is reconstructed. Fig. 1.21(b) shows a photon collection eﬃciency ofeach event. The collection eﬃciency becomes lower for the events where the γ-ray interacts infront of the insensitive area, and the event-by-event fluctuation becomes larger for shallow event(typically w < 2 cm). This results in a worse energy resolution for the shallow events. Sinceroughly one third of the signal γ-ray converts in the region of w < 2 cm as shown in Fig. 1.22,
this limited the performance of the LXe detector in MEG. The position resolution was also
limited by this insensitive area for the shallow events.

Chapter 1 Introduction to MEG II experiment1.6.3 LXe detector in MEG II
1.6.3.1

Upgrade concept

For the MEG II experiment, an upgrade of the LXe detector is planned to improve theperformance as shown in Fig. 1.23 [7][22]. The major upgrade is a replacement of the 216 PMTs
on the inner face with 4092 multi-pixel photon counters (MPPC). Thanks to the smaller size
and the square shape of the MPPC, the inner face can be covered much more uniformly by thesensitive area than MEG. This leads to a better position and energy resolution of the shallow
event.
The MPPC is a silicon photosensor developed by HPK, and it is a kind of the SiPM. As is in
the normal silicon photosensor, the MPPC is operated by applying a reverse bias voltage to the
p-n junction. By applying the voltage above the breakdown voltage, a photoelectron generated
by an incident photon causes an avalanche in the depletion layer. A MPPC chip consists ofmany pixels connected in parallel as shown in Fig. 1.24. A quenching resistor is connected inseries to each pixel such that avalanche is stopped by the voltage drop of generated charge. By
this mechanism, a single photoelectron always induces the same amount of charge defined by
the capacitance of the pixel and the bias voltage. Sum of the induced charge in all pixels is
measured as a signal, and the number of the arriving photoelectrons can be measured from it.
Compared to the PMT, the MPPC has advantages as follows:• photoelectron counting capability,• insensitive to the magnetic field,• smaller size,• operated at lower voltage (∼ 50 V) with lower power consumption.
On the other hand, it has several drawbacks as follows:• Higher dark signal rate: signal caused by thermal excitation even without external photons.
• Correlated noise: single photon may fire multiple pixels (crosstalk and afterpulse).
• Saturation: when the number of fired pixels is as large as the total number of pixels,
measured number of photoelectrons gets deviated from the true number of photoelectrons.
• Larger temperature coeﬃcient.
These drawbacks of the MPPC are measured in test setups, and the eﬀects on our detector will
be discussed in Section 2.1.3.
The PMTs on the outer face and the side faces are reused from MEG.
As shown in Fig. 1.25, a layout of the lateral PMTs is modified for MEG II. The horizontal
width of the entrance face is extended by 10% to enlarge a fiducial volume of the LXe to suppress
the energy leakage. The geometrical acceptance for the γ-ray is not extended since it is limited by
the size of the thin entrance windows of the COBRA and the LXe detector. In MEG, entrance
face of each lateral PMT is not on the holder surface plane (Fig. 1.25). This is modified in

22

Chapter 1 Introduction to MEG II experiment

Figure 1.23 LXe γ-ray detector in MEG II.

Figure 1.24 Conceptual illustration of the MPPC [23].

MEG II to be on the holder surface in order to minimize the eﬀect of the shower fluctuation for
the events near the lateral wall.
A layout of the top and the bottom PMTs is also modified as presented in Fig. 1.26. A
staggered layout is adopted and more PMTs than MEG are placed with minimum spacing tohave more uniform readout of the scintillation light near the top or the bottom face.
1.6.3.2

Expected performance

Table 1.3 gives the expected performance of the MEG II LXe detector. The position resolution
will be improved especially for shallow events (w < 4 cm) thanks to the better granularity of the23Chapter 1 Introduction to MEG II experiment24

Figure 1.25 Upgrade of lateral PMT layout from MEG (left) to MEG II (right) [7].

115

115

110

110

105

105

100

100

95

95

90

90

85
80

85

r

80

75
70

75

z

70
−40

−20

0

20

40

r
z

−40

−20

(a)

0

20

40

(b)

Figure 1.26 PMT layout in the top and the bottom face (a) in MEG and (b) MEG II.

scintillation readout realized by the MPPCs as shown in Fig. 1.27. This is useful since roughly
half of the the signal γ-rays are converted in this region (Fig. 1.22). The detection eﬃciency isdefined as a ratio of the number of the signal γ-rays which deposit energy above 48 MeV in the
LXe to that of whose initial momentums are in the geometrical acceptance of the LXe detector.
Thanks to the reduced thickness of the MPPC than the PMT, an improvement from 63% to
69% is expected.
Table 1.3 LXe detector performance

MEG (measured)

MEG II (simulated)

position resolution (u/v/w)(mm)

5/5/6

2.6/2.2/5

energy resolution (%)(w < 2 cm/w > 2 cm)

2.4/1.8

0.6/0.5 *timing resolution (ps)6250

eﬃciency (%)

63

69

*

refer to main text for detailThanks to the better uniformity realized by the MPPCs, the energy resolution will get improved especially for the shallow events (w < 2 cm). Though there might be a local nonuniformity of the resolution for the shallow events in MEG which was integrated in the physics
analysis, this kind of non-uniformity should also be fixed in MEG II. Simulated energy resolution becomes 0.5–0.6% independent of the conversion depth. However, this simulated resolution

Chapter 1 Introduction to MEG II experiment

25

MEG I
MEG II2

4

6

Position resolution (vertical)

Position resolution [mm]Position resolution [mm]Position resolution (horizontal)
10
9
8
7
6
5
4
3
2
1
0
0

8

10 12 14 16 18 20
Conversion depth [cm]

10
9
8
7
6
5
4
3
2
1
0
0

(a)

MEG I
MEG II246

8

10 12 14 16 18 20
Conversion depth [cm](b)

Figure 1.27 Simulated hit position resolution as a function of conversion depth. (a) horizontal direction, (b) vertical direction.

may not be reliable. In the MEG LXe detector, the measured energy resolution for the deep
events was 1.8%, while 1.0% was expected in the simulation. The reason for this discrepancyof 1.5% (= 1.8%(meas.) ⊖ 1.0%(M C)) has not been understood yet, and thus this contribution
can remain in MEG II. Therefore, the expected energy resolution of MEG II is 0.5–1.6%.

1.7 Radiative decay counterA radiative decay counter (RDC) is newly introduced for MEG II. As mentioned in Section 1.2,
some of the accidental background events are caused by the γ-rays coming from the RMDs.
The RDC identifies these events by detecting a positron from the RMD. Fig. 1.28(a) showsits concept. Since the positrons from the RMDs emitting a high energy γ-ray tend to be low
energy (typically a few MeV), they are swiped out along the beam axis by the COBRA magnet.
The RDC is placed at the downstream of the beam line to detect them. About half of the
RMD positrons are emitted to the downstream side, and 42% of the positrons from the RMDs
(Eγ > 48 MeV) can be detected by the RDC*4 .
The RDC consists of a timing counter and a calorimeter as shown in Fig. 1.28(b). Twelve
plastic scintillators (BC418) are used for the timing counter, whose signals are read out by
the MPPCs (S13360-3050PE). The timing resolution is estimated to be 90 ps by using a 90 Srsource. Fig. 1.29(a) shows the expected time diﬀerence between the LXe detector and the RDC.
Accidental background events from the RMD γ-rays have a peak in the time distribution, whilea uniform distribution is expected for the signal µ → eγ events due to the accidental Michel
positron hits on the RDC. The achieved timing resolution is suﬃcient to distinguish the RMD
events from the accidental events in this distribution.
The positron energy is measured by the RDC calorimeter made of LYSO crystals placed behind
the RDC timing counter (Fig. 1.28(b)). Fig. 1.29(b) shows the expected energy spectrum on the*4 A study of another counter to detect RMD positron placed at the upstream side (upstream RDC) is also

ongoing. It is more diﬃcult than the (downstream) RDC since the muon beam penetrates it.

Chapter 1 Introduction to MEG II experiment

26

(a)

(b)

Figure 1.28 (a) Concept of the RDC [7]. (b) Design of the RDC. It consists of a timing
counter (plastic scintillators) and a calorimeter (LYSO crystals) [7].

(a)

(b)

Figure 1.29 (a) Expected time diﬀerence between the LXe detector and the RDC. Accidental backgrounds from the RMD γ-rays (red) have a peak, while the signal events (blue)
are uniformly distributed. The uniform components in both distribution is due to the accidental pileups of the Michel positrons on the RDC. Note that some events are not shownin this plot, since they have no RMD hit and pileup hit on the RDC [7]. (b) Expectedenergy spectrum of the RDC [7]. (Blue) The Michel positrons. (Red) The RMD positrons
emitting a γ-ray above 48 MeV.

RDC. Typical energy of Michel positrons is higher than that of the RMD events emitting a highenergy γ-ray. The calorimeter consists of 76 blocks of 2 × 2 × 2 cm3 LYSO crystals each of which
couples to an MPPC (S12572-025). The intrinsic radioactivity of the LYSO is used to calibrate
the response of each LYSO crystal and MPPC. The energy resolution is measured to be 6% for
1 MeV γ-ray by using a 60 Co source. This is suﬃcient to distinguish the RMD positrons from
the Michel positrons.

Chapter 1 Introduction to MEG II experiment

1.8 Data acquisition system
The DAQ system is also upgraded for MEG II. In MEG, detector signals were actively split
for a trigger system and a waveform digitizer. Waveforms of all detectors were recorded at theO(GHz) sampling speed, and utilized in the oﬄine analysis such that we can achieve a good
detector resolution and deal with the high pileup environment. Due to the increased numberof readout channels in MEG II by a factor of three, a simple extension of the MEG’s system is
impossible in the limited space in the experimental area. Therefore, an integrated DAQ systemcalled WaveDREAM is being developed. Fig. 1.30 shows an overview of the WaveDREAMsystem. Signals from each detector are digitized by the WaveDREAM boards (WDB) whose
trigger is generated on the trigger concentrator boards (TCB), and transferred to the online
computer through a Gigabit ethernet from the data concentrator boards (DCB). The whole
DAQ system is controlled by the MIDAS DAQ system [24].
WaveDREAM boards
The signals from each detector are connected to the WDB (Fig. 1.31), on which several
functionalities are implemented. Input waveforms are digitized by DRS4 (Domino Ring Sampling[25]) chips. Fig. 1.32 shows a mechanism of the DRS chip. The amplitudes of the waveforms
are stored on the 1024 capacitors called “DRS cells” as a charge by a logic wave propagating
through the inverter domino chain. The sampling is stopped when the trigger is fired, and thestored charge is read out by an external ADC in the order of the DRS cells by a shift resistor.
Two stage amplifiers and a programable attenuator are implemented on the analog frontendof the WDB, so that we can apply an appropriate size of amplification for each purpose. For
example, in the LXe detector, the maximal amplifier gain (about 100) is used to measure thesingle photoelectron signals of the MPPCs, while no or smaller amplification is used to measureO(104 ) photoelectrons signals from the signal energy γ-ray.
The bias voltages for the SiPMs and the MPPCs can be supplied from the Cockcroft-Walton
voltage multiplier on the WDB. The applied voltage for each channel can be tuned via a 5 V
DAC to deal with the individual diﬀerence of the operating voltage.
To achieve a good timing resolution, a synchronization between channels is important. For thispurpose, a distributed reference clock is digitized on each DRS chip. The precision of the timingalignment is measured to be about 20 ps [12][26], after the timing alignment by the reference
clock.
One WDB can measure the waveforms from sixteen channels, and about 530 WDBs will be
used to read out about 9000 channels in MEG II.
Trigger
The trigger logic of MEG II is based on an online reconstruction of the observables in theµ → eγ search on the FPGA [27]. Since the signals from the drift chamber cannot be used forthe trigger generation due to its slow response, those from the LXe detector and the positron27

Chapter 1 Introduction to MEG II experiment

(a)

(b)

Figure 1.30 (a) Concept of the WaveDREAM system. (b) A prototype WaveDREAM crate.

Figure 1.31 Schematic of WDB [7]28Chapter 1 Introduction to MEG II experiment
Inverter "Domino" Chain

29
Rotating
signalInput

OutputShift Register

Figure 1.32 Mechanism of DRS.

timing counter are used for it.
The γ-ray energy is reconstructed from a sum of the waveforms of the LXe detector. While
the DRS is sampling, the ADC is used for a digitization of the input waveforms at a 80 MHz
sampling frequency. The sum of these digitized waveforms is calculated on the FPGA, whose
peak amplitude corresponds to the online reconstructed energy. In the calculation of the sum
waveform, each waveform can be multiplied by a given weight to compensate an individual
diﬀerence of the photosensor performances such as the gain and the PDE. A diﬀerence of the
waveform shape between the MPPCs and the PMTs is also corrected by this weight. Eventswith an amplitude exceeding a given threshold are triggered to select the events with a signal-likeenergy γ-ray. A veto threshold can also be set to reject high energy background events causedby the cosmic rays which typically have more than 120 MeV energy deposit in the LXe detector.
The timings of the γ-ray and the positron are reconstructed by using a comparator on the
WDBs connected to the signal of each channel.
An event selection on the opening angle is also possible thanks to the detector segmentationin MEG II (MPPC readout in the LXe detector, and scintillator tiles in the positron timing
counter). A correlation between the timing counter hit and the peak position on the inner faceof the LXe detector allows us an angular constraint on the decay kinematics.
By combining these criteria, a trigger rate ≈ 10 Hz is expected for the physics data-taking at
the MEG II beam intensity.
Data size
Obtained data is stored in the 1.2 PB data storage to be analyzed on an oﬄine computing
cluster. In order to store all the MEG II data in the storage, the data size of each event should
be below about 3 MB assuming a trigger rate of 10 Hz *5 . Because the data size of each event will
be about 7.7 MB*6 if we simply store the obtained waveforms with bzip compression, a data size
reduction by a factor of a few is needed. For this purpose, data reduction algorithms are being
studied for each detector waveform to eliminate the information unnecessary or unimportantin the reconstruction. For example, for the LXe detector which occupies more than half of the*5 Total size becomes 930 TB after three years data-taking in this case.
*6 Estimated by scaling a measurement in the run 2019 with a limitted number of readout channels (Chap-

ter 3). The data size was 1.0 MB/event with 1088 channels readout.

Chapter 1 Introduction to MEG II experiment

Figure 1.33 A schematic of the online DAQ system including the software trigger [28].

readout channels and the data size before the reduction, algorithms summarized in Appendix A
are planned.
Another planned solution to reduce the data size is an introduction of a software trigger(Fig. 1.33). By running a fast event reconstruction on a dedicated computer which is moresophisticated than the trigger generation by the FPGA, better resolutions of the observables
than the online resolution should be achievable. A positron track information may also be
utilized. With the software trigger, a more stringent event selection can be applied, and thenumber of stored events is expected to be reduced.

1.9 Branching ratio sensitivity expected at design stage
The branching ratio sensitivity of MEG II was calculated by assuming the expected resolutionsof the upgraded detectors at the design stage [7][22]. The result is shown in Fig. 1.34.
Since there was an uncertainty on the performance improvement in each detector, the sensitivity in an optimistic scenario, and a pessimistic scenario were also calculated. Ambiguity ofthe sensitivity was estimated to be 30%. It is notable that the sensitivity of the nominal scenario
shown in Fig. 1.34 adopted an intermediate energy resolution (1.0%) of the LXe detector, wherea half of the unknown contribution is assumed.

30

BR(µ→ eγ )Chapter 1 Introduction to MEG II experiment

90% C.L. MEG 201131

5σ Discovery
3σ Discovery
90% C.L. Exclusion

10− 12

90% C.L. MEG 2013

− 13

10

MEGII in 3 years
10− 14
0

10

20

30

40

50

60

70

80

90 100weeks

Figure 1.34 Expected branching ratio sensitivity of MEG II experiment at the design
stage as a function of the DAQ time [7].

32

Chapter 2

Development of LXe Detector
Based on the design shown in Section 1.6, the LXe detector has been upgraded to improve
its performance to achieve the physics goal of the MEG II experiment. This chapter describes
the development of the LXe detector. Section 2.1 describes a concept and a performance of a
new MPPC developed for this detector. Section 2.2, and 2.3 explains a quality control of thephotosensors. Support structures and the signal readout chain for the photosensors are shownin Section 2.4. Section 2.6 describes the alignment of the MPPCs, which is required for a good
position resolution of γ-ray. Other subsystems of the detector operation such as a slow control
system and calibration sources are also summarized in this chapter.

2.1 VUV-sensitive MPPC
2.1.1 Concept of VUV-MPPC
There are three major requirements for the MPPCs used in the MEG II LXe detector. First,
it has to be sensitive to the xenon scintillation light in the VUV range (λ = 175 nm). Since
standard MPPCs do not have a sensitivity to the VUV light, a new MPPC has to be developed.
Second, in order to cover the whole inner face by the MPPCs with a reasonable number ofreadout channels, the sensitive area per channel has to be as large as 12 × 12 mm2 . Typicalcommercial MPPCs can read out 3 × 3 mm2 per channel at most, and are not suitable for ouruse. Third, it has to be operational inside the 165 K LXe.
A new MPPC which satisfies these requirements has been developed in collaboration with
HPK (Fig. 2.1, S10943-4372, also called VUV3).
In the standard MPPC, there is a protection layer of epoxy resin at the sensor surface. This
layer is removed in our MPPC since it absorbs VUV photons before entering the sensitive
region. To improve the VUV sensitivity, optical matching between the liquid xenon and thesensor surface is optimized, and the contact layer before the active layer is thinned down. The
dopant concentration in the contact layer is also adjusted to have an non-zero electric field.
Instead of the removed protection layer, a VUV-transparent quartz window is mounted on the
MPPC package. The LXe can go into the gap between the window and the MPPC chips when
the MPPC is immersed in the LXe. Since the refractive index of the quartz is 1.60 and isChapter 2 Development of LXe Detector

(a)

33

(b)

Figure 2.1 VUV sensitive MPPC developed for MEG II (Hamamatsu S10943-4372) [29]suﬃciently close to that of the LXe (1.65), a loss of the VUV photon by the reflection on thequartz window is negligible in the LXe.
The detection mechanism of a VUV photon is diﬀerent from that of the visible light. In thedetection of the visible light in an MPPC, a photon generates an electron-hole pair in the active
layer, which directly triggers an avalanche. Since the attenuation length in silicon for the VUVlight is only 5 nm, and is still shorter than the thickness of the contact layer, a VUV photon isdetected in the way that a part of the charge carriers generated in the contact layer drifts tothe active layer, and triggers an avalanche.
There are two possible issues to have a large sensitive area on the MPPC. One is the dark
signal whose rate is proportional to the size of the MPPC. This is, however, not a problem inour case because the dark signal caused by a thermal excitation is largely suppressed at the
LXe temperature. The other is a longer decay time caused by the larger capacitance of thelarger sensitive area. To reduce the capacitance, our MPPC package is designed to have four
independent 6 × 6 mm2 chips, which can be connected in series when it is read out.
The pixel pitch of this MPPC is 50 µm. The number of pixels per channel is 5.57 × 104 . Thisis suﬃcient for our use in terms of the saturation of the MPPC because the largest signal on
one MPPC is expected to be about 1 × 104 photoelectrons for the 52.8 MeV signal γ-ray.

2.1.2 Apparatus for test measurements
The performance of the VUV-MPPC was measured in test setups to confirm its suﬃcientperformance. This section shows two kinds of setups used for these measurements.
Small chamber
The first setup is a 2 ℓ LXe setup used for the measurement of a small number of MPPC
samples (up to eight). A pulse tube refrigerator (Iwatani PDC08) was used for the xenon

Chapter 2 Development of LXe Detector

34(not to scale)Alphasource

MPPC

25mm

LED

anti-reflection
tube
9mm

(a)

(b)

Figure 2.2 Small chamber setupliquefaction. A heater was attached on the refrigerator to regulate the cooling power based on
the xenon pressure or temperature.
Fig. 2.2 shows the core part of this setup. The MPPCs were placed on a circuit board on which
the signals from four chips on an MPPC package are connected in series. A few blue LEDs were
installed to measure single photoelectron signals from them. An alpha source (241 Am) placedon a tungsten wire was installed for the PDE measurement. Thanks to the short path length(40 µm) of an alpha particle in the LXe, this source can be used as a point source of the xenon
scintillation light. Due to the energy loss in the protection material around the source, theenergy of the emitted alpha particle becomes smaller than the original energy of 5.5 MeV. Itsenergy was measured to be 4.8 MeV on average with a spread of 4% by a silicon surface barrier
detector. In order to suppress the reflection of the scintillation light at the cryostat wall, thewhole setup was placed inside a tube with anti-reflection coating (Acktar black [30]).
The signals from the MPPCs are transmitted to the outside of the cryostat through coaxial
cables and a feedthrough. The signals are amplified by an amplifier developed by PSI shown in
Fig. 2.3, and are recorded by a DRS evaluation board. A pi-pad attenuator is implemented on
this amplifier, whose strength can be adjusted by replacing the resistance in order to keep thesize of the output signals in the dynamic range of the DRS and the amplifier.
Large chamber
Another setup called “large chamber” was used for a mass test of about 600 VUV-MPPCsof a prototype version (called VUV2 [31]). The major diﬀerence between the prototype modeland the final model is that an optical trench around every MPPC pixel to suppress the opticalcrosstalk [23] is not implemented on the prototype version. The main purpose of this test is tocheck the performance of many MPPCs inside the LXe before starting the mass production of
the final model. Another purpose is to test a signal transmission scheme in the LXe detector.
Fig. 2.4 shows a support structure used for this test, which was immersed in the LXe. TwentyChapter 2 Development of LXe Detector

35

Figure 2.3 Amplifier developed by PSI.

αsources241Am
PCBs(12+12)

LED

(a)

(b)

Figure 2.4 Support frame in large chamber test. About 600 MPPCs are arranged.

(not to scale)alpha source
PCB MPPC

124 mm

124 mm62 mm

Figure 2.5 The position of the alpha sources and the MPPCs in the large chamber test.

four MPPCs were placed on a PCB, and twenty four PCBs were fixed on the support structure.
LEDs and alpha sources were installed to measure the MPPC characteristics.
This setup was also used to study the angular dependence of the PDE. Fig. 2.5 shows the
position of the alpha sources. The PDEs at diﬀerent incident angles can be measured from manykinds of geometrical combinations of the alpha sources and the MPPCs.

Chapter 2 Development of LXe Detector

36

2.1.3 Measured performance of VUV-MPPC
Gain and single photoelectron signal
Fig. 2.6 shows two-photoelectrons waveforms obtained from a weak LED light. As is discussed
in Section 2.1.1, our MPPC package consists of four independent chips which can be connected
in series to reduce the decay time of the MPPC signal. The decay time of the MPPC signal bya series connection is found to be shorter than that by a parallel connection.
The gain of the MPPC is estimated by integrating the MPPC waveform in a time windowof 150 ns. A charge distribution shown in Fig. 2.7(a) is obtained, where photoelectron peaks
are clearly resolved. The gain is measured from the diﬀerence between the single photoelectron
peak and the pedestal. Fig. 2.7(b) shows the measured gain with series connection as a functionof the applied voltage, and a linear correlation is obtained as expected.
Correlated noise
In the MPPC, a primary avalanche can trigger another avalanche [23]. This phenomena iscalled correlated noise. One source of the correlated noise is an afterpulse. An avalanching carrier
trapped by a impurity energy level is released after short delays and generates another avalanche.
Another source is a prompt optical crosstalk, where a photon produced by an avalanche generates electron-hole pairs in a neighboring pixel. The probabilities of these correlated noises are
estimated from the weak intensity LED data. If there is no correlated noise, the detected number of photoelectrons from a LED follows a Poisson distribution Pλ (x), where λ is the Poisson

Voltage [mV]mean. Since the number of zero photoelectron events is not aﬀected by the correlated noise, λ

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 2.6 Typical two-photoelectrons waveform of our MPPC (primary single photoelectron signal from LED with a optical crosstalk), connected in parallel (top), and connected
in series (bottom) [29].

Chapter 2 Development of LXe Detector

37

can be obtained from the relation of(A fraction of 0 photoelectron events) = Pλ (0) = e−λ .
The probability of the correlated noise p is derived from the measured fraction of the single
photoelectron events, which reflects the eﬀect of the correlated noise as follows:(A fraction of 1 photoelectron events) = Pλ (1) × (1 − p).
Another variable which represents the size of the correlated noise is an averaged amplification
size of signals, called the excess charge factor (ECF). This is calculated as ECF := µ/λ, whereµ is a mean of the detected number of photoelectrons.
Fig. 2.8(a) shows the correlated noise probability estimated from a charge distribution of ashort integration range (30 ns). This should represent prompt eﬀects like optical crosstalk. The
correlated noise probability with a longer integration range (150 ns) is shown in Fig. 2.8(b), where
the probability in the short range is subtracted. This should represent the delayed contribution
such as afterpulse. Thanks to the suppression technique implemented on the final model of
MPPC, the correlated noise probability is only up to 30%, and operation at higher over voltages
up to 7 V becomes possible.
Dark count rate
The dark count rate at the LXe temperature is measured by counting events above the single
photoelectron charge without external light. Scintillation events caused by environmental radioactivity are subtracted by identifying them from the coincident signals on the several MPPCs.
Since some of the scintillation events observed only on one MPPC may still be left, the measured
rate is an upper limit of the dark count rate. Fig. 2.9(a) shows that the rate is measured to be
only 5 Hz/mm2 , which is suﬃciently small for our use.

1000 ×10

Gain

Number of events

700
pedestal

600

3

900
800

500

700

Npe=1

400

600
500

300

400

200
100
0

300

Npe=2
Npe=3
0

0.2

0.4

(a)

0.6

0.8
1
Charge [a.u.]

200
100
0
0

1

2

3

4

5

6

7
8
Over-voltage [V](b)Figure 2.7 (a) Charge distribution of LED [29]. (b) Gain of MPPC as a function of overvoltage (series connection). Gain of amplifier is corrected.

0.6

38

0.6

Afterpulse probability

Crosstalk probability

Chapter 2 Development of LXe Detector

0.5
0.4

0.5
0.4

0.3

0.3

0.2

0.2

0.1

0.1

0

0

−0.1
0

1

2

3

4

5

6

7
8
Over-voltage [V]

−0.1
0

1

(a)

2

3

4

5

6

7
8
Over-voltage [V](b)Figure 2.8 Measured correlated noise probability of final version MPPC as a function ofover voltage [29]. (a) crosstalk (b) afterpulse. Black data series in (a) is for the prototype
version without crosstalk suppression technology.

PDE for LXe scintillation light
The photon detection eﬃciency (PDE) for the LXe scintillation light is measured by using analpha source, which can be regarded as a point source of the xenon scintillation light by theenergy deposition of Eα = 4.8 MeV. The PDE is calculated as a ratio of the detected numberof photoelectrons Nphe to the arriving number of photons Npho . The Nphe is obtained from amean of the measured charge Q of alpha events, and the Npho is calculated by a solid angleΩ from the alpha source subtended by each MPPC, and the W-value of the LXe W = 19.6 eV(Table 1.2). The amount of indirect light is estimated in the simulation, and included as acorrection factor r. The systematic uncertainty of the measured PDE is mainly coming fromabout 10% uncertainty of the W-value (Table 1.2).
Nphe
,
Npho
Q
Nphe =,
Gain × ECF
EαΩ
Npho =×× r.
W
4π

P DE :=

Fig. 2.9(b) shows the measured PDE, a suﬃcient PDE above 15% is confirmed.
Energy resolution
The energy resolution, namely the precision of the number of photoelectrons measurement,
is checked. In the ideal case, the energy resolution just follows a statistical fluctuation. The
excess noise factor (ENF) is a parameter which stands for a degradation of the resolution fromthis ideal case defined as:
2
2
EN F := σmeas/σideal,

where σmeas is the measured resolution, and σideal is the ideal resolution. Since the energy
reconstruction of the LXe detector is based on the total number of detected photoelectrons, its

39

PDE

Dark count rate [Hz/mm^2]

Chapter 2 Development of LXe Detector

6

0.3
0.25

5

0.2
4

0.15
3

0.1

2

0.05

1
0
0

2

4

6
8
Over-voltage [V]

0
0

2

(a)

4

6

8

10
Vover [V](b)

Figure 2.9 (a) Dark count rate per 1 mm2 at LXe temperature. Diﬀerent colors correspondto diﬀerent MPPCs [29]. (b) PDE for xenon scintillation light as a function of the overvoltage. The PDEs for two MPPCs are shown [29].

energy resolution can deteriorated if the ENF is too large. The statistical fluctuation of the
MPPC signals for the 52.8 MeV γ-ray is expected to be only 0.2%. Therefore, the contribution
to the energy resolution from the ENF of the MPPCs is small enough to achieve the 1% ofenergy resolution if the ENF is smaller than 10.
The correlated noise is one process which can contribute to the ENF. Since the correlated
noise is a stochastic process, it will add some fluctuation to the measured charge. In a modelof the correlated noise often used, distribution of the number of the photoelectrons becomes ageneralized Poisson distribution [32]. In this model, the ENF caused by the correlated noise
becomes 1 + p + 3p2 /2 + O(p3 ), where p is the correlated noise probability. The ENF does not
become as large as 10 under the normal operation condition.
In order to check other unexpected contributions to the ENF, the resolution for the visible
light was measured from the relative spread of the charge distribution from LED light. Thismeasurement was performed at diﬀerent LED intensities. The MPPC was operated at the overvoltage of 1.5 V to suppress the eﬀect of the correlated noise.
Fig. 2.10(a) shows the measured resolution as a function of the total detected number ofphotoelectrons Nphe . It is confirmed that the resolution goes down to 1% according to thestatistical relation that the resolution is inversely proportional to the square root of Nphe . The
smaller ENF observed at larger photoelectrons is probably due to an underestimation of thenumber of photoelectrons by the saturation of the MPPC. The ENF for the visible light ismeasured to be 1.4–1.7 including the contribution from the ECF.
The resolution for VUV light is also measured to study a wavelength dependence. Due to ahigher energy of the VUV photons than the visible light, a single VUV photon may generate
multiple photoelectrons. This process is reported for a VUV-PMT [33], and can also occur
at VUV-MPPC. If a single photon generates multiple photoelectrons, a real bottleneck of theChapter 2 Development of LXe Detector

4×10−1
3×10−1

Energy Resolution

Energy Resolution

3×10− 1
2×10− 1

2×10−110− 1

4×10− 23×10

−2

2×10− 2

−3

3×10

−3

10−1

4×10−2
3×10−2

10− 2

4×10

40

2×10−2

50

102

2×102

10

3

2×10

3

104 2×104
Number of p.e.

10−2
30

102 2×102(a)104
10 2×10
Number of p.e.
3

3

(b)

Figure 2.10 Relative energy resolution for xenon scintillation light as a function of total
number of photoelectron [29]. (a) For visible light. (b) For VUV light. Red line shows the√statistical fluctuation of 1/ Nphe .

statistical fluctuation can become smaller, and the statistical fluctuation can be larger than the
expectation from the apparent photoelectron statistics.
The energy resolution for the VUV light cannot be directly evaluated from a spread of thecharge in alpha events due to the 4% spread of the alpha energy. Instead, an even-odd analysis
is adopted. The same alpha events are measured by MPPCs A and B, and the spread of
NpheA −NpheB is measured as an energy resolution at a photoelectron statistics of NpheA +NpheB .
With this method, a contribution from the event-by-event fluctuation of the alpha energy canbe cancelled out, while a stochastic process on each MPPC remains. This measurement was
performed at over voltage of 1.5 V, which is the same as the measurement for the visible light.
Several geometrical setups were used to change the distance from the alpha source to the MPPCs.
Fig. 2.10(b) shows the resolution as a function of the number of photoelectrons. Similar to thevisible light, the resolution of VUV light also follows the statistical relation. A rather larger
ENF than the visible light may indicate the eﬀect mentioned above.
Mass test of prototype MPPCs
The basic characteristics of the 600 prototype MPPCs were measured in the large chamber.
Except for 24 MPPCs (i.e. 4% of all), normal characteristics are confirmed for all MPPCs. For
most of the bad channels, technical issues on the signal readout chain was found and fixed in
the final detector.
Angular dependence of PDE
The angular dependence of the PDE for LXe scintillation light was measured in the large
chamber test. Fig. 2.11 shows measured PDE as a function of the incident angle. The measured
PDE decreases faster than the theoretical expectation of the reflection calculated from therefractive index. The reason for this dependence is not yet identified, but this may be caused byChapter 2 Development of LXe Detector

41

Normalized PDE

Angular Dependence of PDE
2

1.8

Measured

1.6

Expected

50

40

1.4

1.2

30

1

0.8

20

0.6
0.4

10

0.2
0
0

20

40

60

80

0

Incident Angle[deg]Figure 2.11 VUV PDE measured in the large chamber test as a function of the incident
angle from alpha sources to each MPPC. The red line shows expectation from Fresnel
reflection at the sensor surface [34].

some insensitive layer which can be eﬀectively thicker for photons with larger incident angles.
A crosscheck of this dependence is performed in the LXe detector (Section 6.2), and the eﬀect
on the γ-ray reconstruction will be discussed in Section 7.3.

2.2 Test of all VUV-MPPCs
After the development of the VUV-MPPC, a production of 4200 MPPCs including about 100
spares was performed by HPK, and completed by Oct 2016. They were delivered in four batches
called lot A, B, C, and D in this thesis.
To identify bad MPPCs, I-V curves of all MPPC chips at over voltage of −3 V to +7 V were
measured at room temperature. In total, the I-V curves of 16800 chips were measured.
Fig. 2.12(a) shows a typical I-V curves of four chips on a normal MPPC. The I-V curves are
fitted by a quadratic function smoothly connected to a linear function below the breakdown.
The breakdown voltage Vbd is estimated from the fitted transition point, and compared to theoperation voltage Vhama recommended by HPK. It is found that Vhama corresponds to the overvoltage of 4.9 V as shown in Fig. 2.12(b). The estimation of the breakdown voltage works
correctly for most of the MPPCs except for bad chips mentioned below.
Three types of bad chips are found in this I-V curve measurement. The first one is a “current
oﬀset chip” which has significantly large current below the breakdown. Current of the normal
chips below the breakdown is typically a few tens of nanoampere. Chips whose current is 100 nAlarger than the other three chips on the same MPPC package are identified as bad chips. The
second one is a “strange I-V chip” which has a strange shape of I-V curve. The third one is a“large current chip” whose current is much larger than that measured by HPK. In total, 31 bad
chips (0.2% of all chips) were identified in this measurement, and removed from the detector
construction.
Some of these bad chips were tested in the LXe. Fig. 2.13 shows the measured gain and
PDE. No diﬀerence was found between the normal chips and the bad chips. Therefore, they canChapter 2 Development of LXe Detector

42

chip 0chip 1chip 2
chip 3(a)(b)

Figure 2.12 (a) Typical I-V curves measured for four chips in an MPPC package. (b)Diﬀerence of Vhama and Vbd .

PDE vs. Over Voltage

0.09
0.08
0.07

PDE

Gain (a.u.)

Gain vs. Over Voltage
0.1

Sensor C (normal)
Sensor D (large current)
Sensor F (current oﬀset)
Sensor H (strange I-V)

0.35
0.3
0.25

0.06

0.2

0.05

Sensor A (normal)

0.15

0.04

Sensor C (normal)
0.1

0.03
0.02

Sensor D (large current)
Sensor F (current oﬀset)
Sensor G (strange I-V)

0.05

0.01
0

0

1

2

3

4

5

(a)

6

7
8
Over Voltage (V)

0
0

2

4

6
8
Over Voltage (V)(b)

Figure 2.13 Performance of bad MPPCs in the LXe. (a) Gain, (b) PDE.

probably be used in the detector, but are not used because we have suﬃcient number of normal
MPPCs.
The waveform of each MPPC whose four chips are connected in series for the pulsed LED
light was also measured. Fig. 2.14 shows the pulse decay time of each MPPC. A production lot
dependence probably due to diﬀerent after pulse probabilities is observed. This lot dependence
is also measured in the LXe detector (Section 6.1.1), and is corrected in the reconstruction ofthe γ-rays.

2.3 Selection of PMTs
In the upgrade of the LXe detector, PMTs on the entrance face is replaced with MPPCs, andthe number of PMT is reduced from 846 to 668. These surplus PMTs are utilized to replace
problematic PMTs in MEG, such as dead PMTs or PMTs with strange gain evolution duringPulse decay time (ns)

Chapter 2 Development of LXe Detector

43

70
60
50
40
30
20
10

Lot A

0
0

Lot B
1000

2000

Lot C
3000

Lot D
4000

5000
6000
MPPC serial number

Figure 2.14 Pulse decay time of each MPPC as a function of serial number [29].

the MEG beam time.
The PMTs which cannot keep operating in the whole MEG II experiment are also replaced.
As is mentioned in Section 1.6.2, a gradual degradation of the PMT gain was observed in MEG,
and the applied high voltage was increased from time to time, in order to keep a reasonablegain (> 1 × 106 ) for detector operation. On the other hand, the applied voltage must be lower
than 1400 V since larger voltage will increase a risk of a high voltage trip at the cables andconnectors. This sets a lifetime of PMT. The expected lifetime of each PMT is calculated fromthe gain degradation speed observed in MEG, assuming that the gain degradation is proportional
to the beam intensity. Only the PMTs whose lifetimes are longer than three years are used.
Table 2.1 summarizes types of replaced PMTs. In total, 63 PMTs are replaced.
Table 2.1 List of replaced bad PMTs

Type

number of PMT

Dead

15

Low QE

2

Strange gain evolution

29

Strange QE history

6

Lifetime too short for MEG II

20

Sum (including overlaps)

63Chapter 2 Development of LXe Detector

44

MPPC Support structure

Prototype for the spacer
bw/ MPPC and PCB

(a)

•

(b)

Any space between
MPPC
Figure2.15 MPPC support structure.
and Cryostat wall cause
detection inefficiency

2.4 Photosensor installation• Needto fillthe gap with
MPPC
supportstructure

To light
install material
the MPPCs into the detector, a support structure has been prepared which satisfies

several requirements:
12• The MPPCs have to be aligned within 0.5 mm precision.
• Its material budget has to be minimized since signal γ-ray goes through it.
• It has to be able to be placed inside the LXe, and should not contaminate the LXe.
Fig. 2.15 shows the support structure for MPPC. The MPPCs are aligned on a PCB, which isfixed on a structure made of Carbon Fiber Reinforced Plastic (CFRP). Considering the thermal
contraction at LXe temperature, the temperature coeﬃcient of the CFRP is adjusted to beconsistent with that of the PCB. This CFRP structure is fixed on the cryostat. A spacer madeof FR4 is inserted in the gap between the MPPC and the PCB to prevent the LXe from filling
the gap. Since the CFRP is conductive, another spacer is inserted between the PCB and the
CFRP.
The material budget of photosensors and the support structure is shown in Fig. 2.16 andTable 2.2. The radiation length is reduced from 0.183X0 to 0.029X0 , leading to an improvementin the γ-ray detection eﬃciency by a factor of 1.13.
Twenty two MPPCs are placed on the PCB as shown in Fig. 2.17, and two PCBs are placedin a row. In total, 93 rows (i.e. 93 × 22 × 2 = 4092 MPPCs) are installed in the detector. In
the detector construction, the MPPCs are mounted on the PCBs in lab, and each PCB is fixed
to the CFRP frame which was fixed to the cryostat beforehand.
Signal readout chain
The MPPC signals are read out through this PCB. A coaxial-like structure is implemented
in this PCB as shown in Fig. 2.18(a). Each signal layer is shielded by ground layers, andChapter 2 Development of LXe Detector

45

Material before entrance face(not to scale)
MPPC
package

Filledwith LXe

ceramic

quartzsiliconceramic
spacer (FR4)Assembly PCB (FR4+Cu)
spacer (FR4+Cu)

2.5mm

Support structure (CFRP)

7mm

silicon

1.4mm
1.6mm
1.4mm

Cryostat wall

Figure 2.16 Material of the γ entrance window

Table 2.2 Material budget of the γ entrance window of the LXe detector. (left) MEG,
(right) MEG II.

Radiation

Radiation

thickness X0

thickness X0

Outer cryostat wall

0.040

Outer cryostat wall

0.040

Honeycomb (Section 1.6.2)

0.018

Honeycomb (Section 1.6.2)

0.018

Inner cryostat wall

0.023

Inner cryostat wall

0.023

Peek support or PMT

0.183

CFRP frame

0.003

Total

0.264

PCB & Spacer

0.006

MPPC

0.020

Total

0.110

Figure 2.17 PCB used to align the MPPCs.

the characteristic impedance is adjusted to 50 Ω to avoid a reflection at the interface. The
signal transmission line of each channel is designed to have the same length and thus the same
propagation time.
The four MPPC chips on each sensor are connected in series by a circuit implemented on
the PCB shown in Fig. 2.18(b). Fig. 2.19 shows the schematic of the circuit. In this so-called“hybrid connection”, the four chips are connected in series, but with a decoupling capacitor in
between, in order to connect signals in series with applying bias voltage in parallel. This method
has an advantage that the needed high voltage becomes smaller than that with a simple seriesconnection. This removes a possibility of sparks between adjacent MPPC chips placed with aspacing of 0.5 mm since a common voltage is applied on each MPPC chip.
Fig. 2.20(a) shows a concept of the signal transmission of this detector. The signals from theChapter 2 Development of LXe Detector

46

(a)

(b)

Figure 2.18 (a) Cross section of the PCB [7]. A coaxial like structure is implemented. (b)Circuit implemented on PCB to connect MPPC chips in series.
Coaxial cable (~12m)

2k
22nF

+HV

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

MPPC

PCB

Figure 2.19 Hybrid connection [29].

PCB are transmitted by coaxial cables from the cable connectors implemented on the edge. The
signals are transmitted to outside the cryostat through a custom PCB-based feedthrough shownin Fig. 2.20(b). This feedthrough is made of a DN160CF flange, and six PCBs are glued on it.
The coaxial cables are directly soldered on the PCBs at the both sides. The coaxial structure(Fig. 2.18(a)) is also implemented on this PCB. Each flange accommodates 432 signal channels,
and twelve feedthroughs are installed on the chimney of the detector. The cable length fromthe photosensor to the feedthrough is diﬀerent depending on the sensor position in the detector
as shown in Fig. 2.21, to deal with the limited volume of the inner vessel of the cryostat. A
patch panel is installed on the detector where we can select the channels to be connected to
the readout electronics. After the patch panel, sixteen cables that goes to a WDB are bundled.
Fig. 2.22 shows the grouping scheme. This unit is also used for the online reconstruction for thetrigger generation (Section 1.8). For example, a γ-ray direction and timing are reconstructedfrom the group of the sixteen MPPCs which has the largest signal amplitude. For this purpose,channels read out by the same WDB are designed to have the same cable length.

Chapter 2 Development of LXe Detector
feedthrough47

not to scale

patch panel

PMT

MPPC
Electronics
COBRA

(a)

(b)

Figure 2.20 (a) Concept of signal transmission. (b) Feedthrough for the photosensor signal cables.

100

4.90

80

100

60

80

40

60

20

40

0

20

4.52

4.20

3.87

0

3.55

−20
3.17

−40
−60

2.85

−80
2.52

−100
−100

−50

0

50

100

150

200

250

300

z

2.20

Figure 2.21 Map of signal cable length inside detector.

100
80

100

60

80

40

60

20

40

0

20
0
−20
−40
−60
−80
−100
−100

−50

0

50

100

150

200

250

300

z

Figure 2.22 Assignment of photosensors to the WDBs. Each group of connected sixteen
channels with the same color is read out by the same WDB.

Chapter 2 Development of LXe Detector

Figure 2.23 Lateral PMT holder (top) in MEG, and (bottom) in MEG II.

Figure 2.24 Inside of the constructed LXe detector. View from the upstream face.

PMT support structure
Support structures for the PMTs on the lateral face are modified from MEG as explained in
Section 1.6.3. On the lateral PMT holder in MEG, PMT’s entrance face is not on the holder
surface plane. On the MEG II holder, it is designed to be on the holder surface as shown in
Fig. 2.23. To cope with the reduced thickness and radius of the inner face, position of lateral
PMTs are shifted shallower in radial direction from MEG, to achieve a uniform scintilation
readout for the shallow events. A piece of Teflon is attached at the inner edge of these holders
to fill the gap between the entrance face and to keep the scintillation light inside the detector
wall.

Fig. 2.24 shows the constructed detector.

48

Chapter 2 Development of LXe Detector

49

2.5 Calibration sources
Table 2.3 shows the calibration sources prepared for the MEG II LXe detector. Many ofthem are updated from MEG to calibrate the MPPCs and to measure the improved detector
resolutions.
Table 2.3 Calibration tools of the LXe detector for MEG II experiment. (from [7]. Updated by the author)

Process
Charge exchange by pion beam

Energy−π p→π n055, 83 MeV photons

π 0 → γγLi(p, γ)8 Be

14.8, 17.6 MeV photons

11

B(p, γ)12 C

4.4, 11.6, 16.1 MeV photons

Neutron generator

58

59

Radioactive source

241

Radioactive source

9

Proton accelerator

7

Ni(n, γ) Ni
Am(α, γ)237

9 MeV photons
Np

Be(α241 Am , n)12 C⋆

12⋆5.5 MeV αs
4.4 MeV photons

12

C (γ) CLED

blue-UV region

LED
Blue LEDs are installed for the photosensor calibration. Fig. 2.25 shows a location of the LED
installed in the detector. LEDs on the lateral face (Toyoda Gosei E1L49–3B1A–02. [35]) arereused from MEG, and used for a gain calibration of the PMTs (Fig. 2.26(a)). LEDs (KingbrightKA-3021QBS-D. λ = 460 nm [36]) on the outer face are newly installed for MEG II to illuminate
the MPPCs with a uniform light distribution (Fig. 2.26(b)). These LEDs are covered by a Teflon
sheet to diﬀuse the light. Another purpose of this Teflon cover is to attenuate the light intensity
and to operate LEDs at higher voltage, so that we can suppress an instability of the light intensityfrom the lower applied voltage. LEDs are flashed by a pulse signal. A LED pulser is reused
from MEG for the reused LEDs, and a function generator is used for newly introduced LEDs.
These are controlled by a slow control system integrated to the DAQ system (Section 1.8).
Alpha source
Alpha sources are installed as point sources of the xenon scintillation light for a photosensor
calibration. It is based on the same technology as the one used in MEG [37]. Five 100 µm
tungsten wires are stretched between the upstream and the downstream faces. On each wire fivealpha sources (241 Am) are crimped at 12.4 cm intervals (Fig. 2.27). Since the activity of eachalpha source is 200 Bq at most, these sources do not aﬀect the γ-ray data-taking near the signal
energy. The installed positions are shown in Fig. 2.28.

Chapter 2 Development of LXe Detector

50

Top

Outer
old LED
from MEG
new LED
from MEG II

DS

BottomUSz axisFigure 2.25 Installed position of the LEDs [34]

(a)

(b)

Figure 2.26 LEDs for photosensor calibration [34]. (a) LEDs on the lateral face. (b) LEDs
on the outer face.

Figure 2.27 Alpha source crimped on a wire

17.6 MeV γ excited by proton beam
A dedicated 1 MeV Cockcroft-Walton (CW) proton accelerator is placed at the downstreamside of the πE5 beam line (Fig. 2.29). Accelerated protons are injected into the crystal disk madeof Li2 B4 O7 placed on the center of COBRA [38]. Gamma-rays both from the lithium excitation
7

Li(p, γ)8 Be at Ep = 440 keV, and the boron excitation 11 B(p, γ)12 C at Ep = 163 keV can beutilized.
In this thesis, 17.6 MeV γ from lithium excitation (often called CW-Li) is mainly used, due to
its large cross section. Its energy spread is only 12 keV, and it is also good for energy resolution

Chapter 2 Development of LXe Detector

51

Top

Outer
α source
4

3

2

1

0

Wire0
9

8

7

6

14 13 12 11 10

19 18 17 16 15

24 23 22 21 20

DS

Bottom

US

5

Wire1
Wire2
Wire3
Wire4

z axisFigure 2.28 Installed position of the alpha sources [34]Satoru Kobayashi

28

Figure 2.29 CW proton accelerator at the downstream side of the πE5 beam line [39].

measurement. Another peak of CW-Li at 14.8 MeV is not used due to the large decay width
and the overlap with a lower energy tail of the 17.6 MeV peak.
Coincident γ-rays of 11.7 MeV and 4.4 MeV emitted from the boron excitation can be utilized
for timing alignment of the LXe detector and the positron timing counter in the future.
55 MeV γ from CEX
Another important calibration source is quasi-monochromatic γ-rays from the charge exchange(CEX) reaction of the π − captured in a hydrogen target (Fig. 2.30). A negative pion beam is
injected into the liquid hydrogen target, and two coincident γ-rays are emitted from π − p →π 0 n, π 0 → γγ. Since the energies of two γ-rays are correlated with their opening angle, nearlymonochromatic γ-rays of 55 and 83 MeV can be obtained by selecting two γ-rays emitted backto-back. If the events with opening angle above 175◦ are selected, the energy spread becomes
only 0.2%, which is suﬃcient to measure the energy resolution of 1%. One of the γ-rays ismeasured by a reference counter composed of a timing counter and a calorimeter, and the otherChapter 2 Development of LXe Detector

Figure 2.30 Overview of the CEX measurement [43]. The reference counter of NaI was
upgraded to that of BGO during the MEG experiment.

is used for detector calibration. The calorimeter consists of 4×4 BGO crystals (46×46×200 mm3each). The size of each crystal is small enough to select γ-rays emitted back-to-back.
The timing resolution of the LXe detector can also be measured with the CEX events byusing the reference timing counter which consists of plastic scintillators placed behind a lead
converter. The plastic scintillator counter used as the time reference is upgraded to cope with
the improved timing resolution in MEG II. In MEG, signals from the scintillator were read out
by the PMTs, and its timing resolution was 81 ps. For MEG II, a plastic scintillator read out by
SiPMs is adopted [40][41], which is based on the technology developed for the MEG II positron
timing counter [42]. Two scintillator plates (EJ-230, 80 × 175 × 5 mm3 ) read out by 16 MPPCs(S13360-3050PE) on each side are placed in front of the BGO crystals. The timing resolutionof this counter is measured to be 49 ps.

2.6 Alignment of MPPCs
In order to achieve a hit position resolution of 2 mm, positions of the installed MPPCs haveto be measured at a precision of 0.5 mm. For this purpose, two independent measurements were
performed.
Measurement by laser scanner
The surfaces of all the installed MPPCs were surveyed by a three-dimensional laser scanner(FARO Edge ScanArm) during the detector construction (Fig. 2.31(a)). An example of surveyed
MPPC surface is shown in Fig. 2.31(b). The gap between four chips on each MPPC package
is fitted to reconstruct the position and the normal vector of each MPPC. Due to the limited
space of the cryostat between inner and outer faces, and the available reach of the scanner arm,
suﬃcient data quality like in Fig. 2.31(b) was achieved only for a part of the MPPCs. Positionsof about 10% of MPPCs are reconstructed, and the others are interpolated by the reconstructed
ones.

52

Chapter 2 Development of LXe Detector

53
MPPC Surface
1.5

1

0.5

0

−0.5

−1

(a)

(b)

Figure 2.31 (a) MPPC position measurement by a laser scanner [44]. (b) Example ofmeasured MPPC surface by laser scanner [34]. Color shows the coordinate of perpendicular
direction. The red region corresponds to the ceramic package of each MPPC, and the blue
region corresponds to the gap between four chips on a package (Fig. 2.1).

Measurement by collimated γ-rays
Since the position of MPPCs are aﬀected by the thermal contraction at the LXe temperature,
a complementary measurement was performed after the start of the detector operation. Gammarays of 120 keV from 57 Co were injected into the detector, which interact with the LXe within
3 mm. A compact source with a brass collimator was used for the generation of the γ-ray beam
(Fig. 2.32(a)). The beam size on the MPPC surface is 1.5 × 40 mm2 . To scan the inner face of
the LXe detector, the position and the direction of the γ-ray beam can be changed by motion
stages for the z and ϕ direction. Its movement is monitored by an optical laser attached on thestage projected at a quadrant photodiode, and a bubble level [44]. The accuracy of the beamalignment is 30 µm in z, and 80 µm in ϕ.
Fig. 2.32(b) shows the event rate on an MPPC as a function of beam position. Since thescintillation light is localized thanks to a short attenuation length of low energy γ-ray in LXe,an excess of the event rate is observed when it hits above the MPPC, and the MPPC position
can be reconstructed.
Combined analysis
A three-dimensional position of each MPPC in the LXe is obtained by combining these two
measurements. The laser scanner measurement can give us a three-dimensional position of
MPPCs at room temperature, while it is aﬀected by the thermal contraction. The measurementby the γ-ray gives us the MPPC positions at LXe temperature, while only the two-dimensional(u-v) position can be reconstructed.
The reconstructed position in γ-ray measurement is fitted by the measured position by the laser
scanner ⃗xlaser with a transformation (Euler rotation: R(α, β, γ), oﬀset: ⃗coﬀset ) and a thermal
contraction a defined as follows:x⃗′ laser = (1 − a)R(α, β, γ)⃗xlaser + ⃗coﬀset .

Chapter 2 Development of LXe Detector

54

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

(b)

Satoru Kobayashi

85
Figure 2.32 (a) The collimated γ-ray source used for MPPCalignment [34]. (b) The γ-ray
event rate of an MPPC as a function of z position of the beam [44].

The fitted thermal contraction rate is found to be consistent with that of the detector material(16 ppm/K). The fitted laser positions and the γ-ray positions are in agreement within an
accuracy of 300 µm, which fulfills the requirement of 500 µm.

2.7 Xenon control system
To operate the LXe detector safely and stably, the pressure and the temperature of the liquid
xenon have to be well controlled. For this purpose, the xenon control system is upgradedfrom MEG*1 . It consists of the detector cryostat, refrigerators, storage tanks, and purifiers.
A 200 W pulse-tube refrigerator [45] placed at the top of the detector is reused from MEG. A
new 400 W Giﬀord-McMahon (GM) refrigerator [46] is introduced in MEG II, which is placedon an independent platform to avoid a possible noise. This is to compensate the heat income
from the increased number of cables. A 1000 ℓ Dewar (often called “1000 ℓ storage tank”) with apulse-tube refrigerator is used to safely store the LXe when the detector is not operated. Since
it is thermally-insulated and is tolerate up to 6 bar, it can store the LXe for 100 hours even
without a cooling power. The xenon control system is equipped with two purification systems:
a purification in the gaseous phase by a metal-heated getter, and that in the liquid phase by amolecular sieves. The gaseous circulation for the gaseous phase purification was continued when
the detector is operating. This is also useful to eﬃciently transfer the cooling power from theGM refrigerator to the detector.
The temperature of the MEG II LXe detector is controlled with a precision of 0.1 K by a PID
control of the xenon pressure and temperature. The breakdown voltage of the MPPCs is known
to have a temperature coeﬃcient of 55 mV/K [47]. The fluctuation of the breakdown voltage
due to the temperature instability of 0.1 K is expected to be only 0.1% if operated at 7 V over

*1 see [21][39] for MEG’s system

Chapter 2 Development of LXe Detector

Figure 2.33 Xenon control system in MEG II

voltage. This is suﬃciently smaller than the goal of energy resolution of about 1%.

55

56

Chapter 3

Pilot runThis chapter summarizes a series of pilot runs performed under the high intensity muon beam
to evaluate the performance of the LXe detector.
After the construction of the LXe detector was finished in April 2017, the detector was installedin the MEG experimental area, and the commissioning was started. Fig. 3.1 shows an overview
of the commissioning timeline. We had three beam time periods near the end of each year. To
be ready for each beam time period, detector operation was started from each summer, and thephotosensor calibration and the LXe purification were performed*1 .

3.1 Pilot runs
3.1.1 Pilot run 2017
The purpose of the run 2017 was to try taking some γ-ray data. Similar to the MEG II
physics data-taking, a muon beam was stopped on the target located at the center of the
MEG II detector, and γ-rays near the signal energy from the Standard Model muon decays were
measured. These γ-rays are often called “background γ-rays” since they will be background

2017

2018
μ beamLXeOthersConstruction

Signal check& purification

2019

μ beam+ CW

Purification

CDCH installation& startup

MPPC
mass test

μ beam+ CW

Annealing purification
test

CDCH wire issue
investigation

magnetfailureFigure 3.1 Timeline of LXe detector commissioning.

*1 Since there is an annual power cutoﬀ, and the maintenance of the ground water at PSI at the beginning ofJanuary, we cannot keep LXe inside the detector in that period. This is why we cannot keep the detector
operating.

Chapter 3 Pilot run
events in the search of µ → eγ decay. The muon beam intensity was adjusted to be lower than
MEG II (3.2 × 107 µ/s) to keep the induced current on the RDC in the dynamic range of thereadout. This dynamic range has been extended since the run 2018, and thus this limitation is
only for 2017 data.

3.1.2 Pilot run 2018
In the pilot run 2018, a series of measurements to evaluate the detector resolution was performed. The 17.6 MeV γ-rays from the CW-Li were measured to estimate the energy resolution.
The CW-Li data with placing a lead collimator in front of the detector was also obtained toestimate the position resolution. The background γ-rays were also taken at a reduced beam intensity (0.7 × 107 µ/s) and a MEG II beam intensity (7 × 107 µ/s) for a study on the backgroundγ-ray spectrum and the pileup elimination performance. On the other hand, a data-taking of
55 MeV γ-ray data from the CEX run was cancelled due to the delay of the installation of thedrift chamber.
Even though we were able to take data, the 2018 run was not a stable beam time. The major
reason was that this beam time was shared by several MEG II detectors, and the beam intensity
and DAQ configuration were often switched. Another reason was an instability on the BTS
magnet due to an instability of the liquid helium supply from the PSI.

3.1.3 Pilot run 2019
An unexpected degradation of the MPPC sensitivity to the VUV light by a beam radiation
was suggested from the run 2018 data, but it was diﬃcult to get a conclusive result due to theinstability of the 2018 run. Since this degradation is too rapid and could be a crucial issue
for the MEG II experiment, a dedicated data-taking period to confirm this degradation was
assigned for the LXe detector in 2019. The detector was operated under the MEG II intensity
muon beam, and the photosensor performance was often measured to monitor its degradation.
It is found that the muon beam intensity seems to be 10–20% higher than expected likely due
to a problem on the beam blocker during a beam intensity measurement. This will be discussed
in Section 9.3.5.
Another purpose of the 2019 run was to measure 55 MeV γ from the CEX reaction. However,it was cancelled again because the BTS magnet was broken by an accident.

3.2 DAQ system
3.2.1 Prototype of WaveDREAM system
As mentioned in Section 1.8, a DAQ system called WaveDREAM is being developed for the
MEG II experiment. Since the full DAQ system was not yet available due to the delay of thedevelopment, a prototype system of WaveDREAM was used for the data acquisition in those57

Chapter 3 Pilot run

58

pilot runs [27].
Compared to the full system, there are two major limitations on the prototype system. The
first is the number of readout channels. This prototype system has only 96 WDBs which haveto be shared between several detectors for MEG II in the pilot runs. The second is the DAQ
rate. The DAQ rate of the current system is limitted by the 1 Gbps ethernet connection used forthe data transfer from each WDB to the DAQ computer. The limitation was especially obvious
in the run 2017 and 2018. Thanks to an upgrade of the DAQ computer and an improvementin the frontend software, a reasonable DAQ rate was achieved in the 2019 run. This improved
the statistical precision of the sensor calibration. Table 3.1 summarizes the number of readout
channels and the DAQ rate for each year *2 .
Table 3.1 Number of readout channels, and DAQ rate for each year.

Yearnumber of MPPC channel

number of PMT channel

Typical DAQ rate (γ-ray data)

2017

704

192

∼ 3 Hz

2018

640

378

∼ 3 Hz

2019

640

378

10 − 25 Hz

Due to the limitted number of readout channels, only a quarter of the detector was read out.
Fig. 3.2 shows the channel assignment for run 2017, and 2018/2019. These channel assignments
were decided for the following reasons. To reconstruct the γ hit position, the charge distribution
on the MPPCs near the γ conversion point has to be measured. The information from these
MPPCs is also important for the timing reconstruction, since they have a large signal amplitude.
For this purpose, 640 adjacent MPPCs are read out. Only the events hitting the central part of
the readout area are selected in the oﬄine analysis to be used for the performance estimation.
Additionally, for energy reconstruction based on the total detected number of photons, it isimportant to read out the PMTs which cover the whole detector in order to achieve a reasonableuniformity of reconstructed energy. This is also useful to identify the pileup γ-rays whose hit
position is far from the MPPC readout region, while its tail of the light distribution can still beobserved in the readout MPPC*3 . Therefore, widely distributed PMTs are also read out.
The waveforms of all the readout photosensors are digitized at a given sampling frequency
by the DRS4 chips on each WDB. In the DAQ of the pilot runs, the sampling frequency was
set to 1.2 GHz, instead of 1.4–1.6 GHz planned in the physics data-taking. This is because thetrigger latency is about 680 ns in the prototype system, and 853 ns (= 1024 pnt/1.2GHz) time
window is needed to keep waveform inside the window. In the final system, the trigger latency
is reduced by replacing the ADC with a shorter conversion latency one [27], and a data-taking
at the higher sampling frequency becomes possible.
*2 In reality, the channel configuration was changed during the pilot run for several times in each year to use

the limited readout channels and beam time as eﬃcient as possible. This table shows a major configuration
used in this thesis.
*3 Importance of the PMT information described here was overlooked in the run 2017. This is why the channel
assignment was improved from 2017 to 2018/2019 by increasing the number of the PMT channels.

Chapter 3 Pilot run

59
100
80
60
40
20
0
−20
−40
−60
−80

−100
−100

0

100

200

300

200

300

(a)

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

0

100

(b)

Figure 3.2 Readout channels in (a) 2017 run, (b) 2018/2019 run. Adjacent MPPCs andwidely distributed PMTs around it are read out.

In the pilot run, the PMTs were operated at lower gain than MEG to extend its lifetime(Section 5.1.3), and the MPPC PDEs were found to be smaller than expected (Section 6.2.2).
In order to keep the signal to noise ratio with these small signal amplitudes, an amplification
by 2.5 on the analog frontend of the WDBs was applied, while it was not originally planned.
Fig. 3.3 shows an event display of a typical γ-ray event. The most part of scintillation lightis included in the readout region of the detector.

3.2.2 Trigger
In the WaveDREAM system, many kinds of trigger logics are prepared for the physics datataking and for the detector calibrations. The trigger logics used for this thesis are as follows.
EGamma trigger
In the data-taking of background γ and CW-Li γ, a self trigger called “EGamma trigger”
was used, which is based on the online reconstructed γ energy. As explained in Section 1.8,
the online γ-ray energy is reconstructed from a weighted sum of the photosensor waveforms,

Chapter 3 Pilot run

Figure 3.3 Typical background γ-ray event in the pilot run.

and the trigger is fired when the amplitude of the sum waveform exceeds a given threshold. In
the pilot runs, the diﬀerent weights for the MPPCs and the PMTs were adopted, which were
estimated from the calibrated photosensor performances and validated by the 17.6 MeV peakfrom the CW-Li.
Due to the limited readout area, the purity of this trigger was typically only 10 %. This isbecause γ-ray hitting the outside of the MPPC readout area can also be triggered due to signals
from widely distributed PMTs. In addition, some of the cosmic ray events cannot be vetoed,
since only a part of its energy deposit is read out.
In the prototype system, the online energy resolution was limited by a noise coming from the
DRS*4 [27]. It is measured to be about 4% for 52.8 MeV γ-rays, while it is expected to be 1–2%
in the design. An additional filter for noise reduction will be implemented in the final DAQ
system to solve this issue. In the data-taking of the pilot runs, the energy threshold was set
rather lower (42 MeV) in order not to miss interested events typically above 48 MeV, though thefraction of these interested events gets smaller.
Alpha trigger
A dedicated trigger is implemented to take α events from the calibration source (Section 2.5).
This trigger is based on the sum of the sensor waveforms like the EGamma trigger, but only
the PMTs around each α source wire shown in Fig. 3.4 are included in the sum to have a better
signal to noise ratio. A particle identification based on the waveform shape, namely chargeheight ratio, is also implemented to remove a contamination from the γ-ray and cosmic ray as
shown in Fig. 3.5.
LED trigger
Several kinds of LEDs are installed in the LXe detector, and used for the sensor calibration(Section 2.5). Events from these LEDs are taken by a LED trigger generated from the pulse*4 This was confirmed by checking the noise level with the DRS digitization turned oﬀ.

60

Chapter 3 Pilot run

61

100
80

Wire 060
40Wire 1

20

Wire 20
20

Wire 3

40
60

Wire 4

80
100
100

50

0

50

100

150

200

250

300

Figure 3.4 PMTs used for the alpha trigger. 32 PMTs around each wire are used for thealpha trigger.

eventsOnline pulse shape discrimination

220
200
180
160

QAratio
5341

Mean

3.457

Std Dev

1.046

Alfa norm

153.7 ± 3.8

Alfa mean

2.685 ± 0.010

Alfa sigma 0.4285 ± 0.0071
Gamma norm 136.7 ± 4.2

140
120
100
80
60
40
20
0

EntriesGamma mean4.616 ± 0.009
Gamma sigma
0.3426 ± 0.0077

1

2
3
4
5
6
Alfa Trigger Charge / Alfa Trigger Amplitude

Figure 3.5 Pulse shape discrimination in the alpha trigger. A peak at the lower sidecorresponds the alphas, and the other corresponds to the γ-rays and the cosmic rays [27].

coincident with LEDs.
Random trigger
Data of random trigger are useful to monitor the performance of electronics like noise leveland event-by-event fluctuation of the baseline.

62

Chapter 4

Detector simulation
In addition to the data obtained in the pilot runs, a simulation of the detector is another
tool to understand the performance of the LXe detector. It is used not only for an estimationof the expected detector resolutions, but also for a confirmation whether the detector works as
expected. For example, measured background γ-ray spectrum is compared with a simulated
spectrum including the pileup eﬀect to check their consistency. It is also used to understandhow much the photosensor performance is important to achieve the designed resolutions.
For these purposes, simulation software of the LXe detector is developed to estimate its expected response. It consists of several programs as shown in Fig. 4.1. The software called“gem4” based on the Geant4 (version 10.4 [48][49]) generates an event, and simulates interactions of particles in the detector. The software called “bartender” simulates sensor responses.
The output of the bartender is a set of waveform of each sensor with the same format as thereal data, so that it can be analyzed by the same reconstruction algorithm implemented in thesoftware called “analyzer”. The bartender and the analyzer are based on the ROME framework[50].

Experimental
raw waveform

onlineDAQ

Event reconstruction

Analyzer.mid
Simulated
raw waveform

raw

gem4
Detector simulation

sev

bartender
Waveform simulation

sim
Simulated MC truth

Figure 4.1 MEG II simulation software framework.

Result of analysis

recChapter 4 Detector simulation

63

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 4.2 Simulation of electromagnetic shower. Particle tracks are shown as line (black:γ, red: e+ , green: e− ). Original γ-ray is coming from the right. Energy deposit on eachpoint is overlaid. The scale of the gray bar is in the unit of MeV.

4.1 Event generation
In the gem4 software, an event generation and simulation of particle interactions are carriedout based on the Monte Carlo simulation of Geant4. Users can select a type of the generated
event for each purpose. Event types of signal γ, calibration sources, and Standard Model muon
decay are used in this thesis which are summarized in Table 4.1. All the MEG II detectors andcomponents are implemented in the gem4, and physics interactions of generated particles withmaterials and sensors are simulated in the framework of the Geant4.
Table 4.1 List of event types in gem4

ID

Description

Generated particle(s)21Signal γ

52.8 MeV γ from the signal decay on the target

12

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

22

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

30

Muon beamµ+ injecting into MEG detectors

63

Alpha

5.5 MeV α from 241 Am inside LXe detector

64

CW-Li

17.6 MeV γ from the target

In the simulation of the LXe detector, electromagnetic showers produced by the incident particles are simulated as shown in Fig. 4.2. Based on the energy deposit inside the LXe, scintillation
photons are generated at each energy deposit point of the electromagnetic shower with a given
scintillation time constant. The number of generated scintillation photons is calculated fromthe energy deposit divided by the W-value of LXe. A Poisson fluctuation is added to the number of photons assuming a maximal fluctuation on it. Propagations of scintillation photons areChapter 4 Detector simulation

64

amplitude [V]amplitude [V]

1 p.e. Waveform
0

0.002

0.004

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

time [sec]

6

0

0.05

(a)

0.1

0.15

×10
0.2
[sec]

−6

(b)

Figure 4.3 The waveform template used as the single photoelectron response in the waveform simulation. (a) MPPC, (b) PMT.

simulated where a reflection on the detector material, an attenuation by the impurities, and aRayleigh scattering in the LXe are included. If an scintillation photon enters into a sensitive
volume of a photosensor, the timing, the fired MPPC pixel (i.e. hit position in MPPC), andthe incident angle of the photon are recorded. The LXe properties used in this simulation aresummarized in Table 1.2. A “gaseous xenon mode” can also be selected, in which the W-value,
the scintillation time constant, the density, and the refractive index of xenon are diﬀerent fromthe LXe mode.

4.2 Waveform simulation
The bartender software simulates photosensor waveforms from the gem4 output. It can also
mix diﬀerent events such that pileups can be simulated.
In the waveform simulation, the single photoelectron response of each photosensor is summed
up with the time distribution of the arriving photons simulated in the gem4. Fig. 4.3 shows the
single photoelectron response derived from the data. For the MPPCs, it is obtained from thesingle photoelectron events in the weak LED data. For the PMTs, it is obtained by deconvoluting
γ-ray waveforms by an exponential function of the scintillation time constant since the single
photoelectron peak cannot be resolved in the charge distribution.
The MPPC characteristics are also simulated in the bartender. In the simulation of thecrosstalk, each fired pixel in an MPPC can fire another adjacent pixel with a given probability.
It can also trigger another hit on the same pixel with a given probability and time constant tosimulate the afterpulse. To simulate the saturation, when more than one photons hit the same
pixel, waveform from the second photon is reduced as a function of the elapsed time from thefirst photon.
In the nominal configuration, the angular dependence of the MPPC PDE is based on that of
the reflection at the sensor surface, which is calculated from a complex refractive index in gem4.

Chapter 4 Detector simulation

65
Waveform of max p.e. channel# of p.e. distribution

MC. Eγ = 48 MeV

Figure 4.4 An example of a simulated event.

Additional angular dependence observed for our MPPC (Section 2.1.3) can also be included
from the recorded incident angle of the arriving photons, if needed.
After these simulations, an electronics response is also applied. Two independent methods
are prepared to include a noise contribution. The first method adds a white noise of a given
standard deviation, and the second method adds the measured random trigger waveform. The
simulated waveform is digitized by the sampling frequency of 1.2 GHz, and the waveform outside
the dynamic range of the DRS chip (from −950 to +50 mV) are cut, as is done in the realelectronics.
Fig. 4.4 shows a display of a simulated event.

4.3 Background γ-ray
The simulations can be performed in a reasonable time for most of the event types, except
for the background γ-ray from the muon beam. In this section, a dedicated operation for thisbackground γ simulation is described.
Background γ events from the muon beam are the events mainly taken in the pilot runs from2017 to 2019, and its simulation is needed to evaluate the detector performance. In principle, it
can be simulated by accumulating γ-ray events by generating many muon decays. However, due
to a very small probability of having a high energy γ from a muon decay, the computation time
for the tracking of the muons and the Michel positrons becomes a bottleneck*1 . The probabilityof having a γ-ray above 48 MeV in the readout of 2019 run is O(10−7 ), and thus O(1011 ) events*1

This kind of “full simulation” of background γ was not actually performed in MEG.

Chapter 4 Detector simulation

66

have to be simulated to get comparable statistics with real data. To reduce the computation
time, following operations were carried out.
Background γ-ray events are classified into three groups by their sources as follows*2 , andevents of each group are simulated separately.
• AIF : γ-ray originating from a Michel muon decay stopped on the target. High energy γ
mainly comes from the annihilation in flight of the Michel positrons.
• RMD : γ-ray from a radiative muon decay stopped on the target.
• DIF : γ-ray from a muon decay in flight (i.e. not on the target).
Since we are only interested in the high energy γ above 20 MeV, simulations of particles below
20 MeV is skipped. The phase spaces of the muon decay for the AIF and the RMD are restricted
to Pe > 20 MeV and Eγ > 20 MeV respectively. In the AIF simulation, positrons which reachmore than 16 cm away from the center of the COBRA along beam-axis are killed because they arefound not to produce the high energy γ-rays arriving at the LXe detector. With these reductions,
events roughly corresponding to one day of data-taking in the 2019 run were simulated by using
200 physical cores of the recent CPUs for 50 days.

*2 Definition of RMD event is having photon above 500 keV.

and defined as a Michel decay without radiative photon.

Soft photons below this threshold are ignored,

67

Chapter 5

PMT performance
For a stable detector operation and good resolutions, it is important to calibrate and monitor
photosensor performances correctly. The number of photons Npho , and the number of photoelectrons Nphe on each photosensor are calculated from the observed charge of each waveform q
as follows:q = Gain × Nphe × e= Gain × CE × QE(V U V ) × Npho × e= R(V U V ) × Npho × e,
where a response to a VUV light R(V U V ) is defined as R(V U V ) := Gain × CE × QE(V U V ).
The QE (quantum eﬃciency) is a probability of the photon conversion on the photocathode of the
PMT, and the CE (collection eﬃciency) is the probability where the converted photoelectrons
can reach the first dynode. Similarly, for the observed charge q of visible light, a response to
the visible light R(vis) is defined as follows:
R(vis) := Gain × CE × QE(vis)q = R(vis) × Npho × e.
Since the Npho and Nphe are used in the reconstruction of the γ-rays, an individual diﬀerenceof each photosensor response has to be measured correctly.
From the viewpoint of the detector operation, it is also good for all the MPPCs and PMTs tohave a similar response. Each PMT has a large individual diﬀerence on its gain, and the PMT
high voltage has to be adjusted to have a uniform gain distribution.
In addition, the sensor response has a time variation because of a gain degradation by thebeam usage, a slow recovery of the degradation, a gain dependence on the beam intensity, alight yield of the LXe aﬀected by impurity, an external magnetic field, and a fluctuation of the
LXe temperature. If we fail to monitor these eﬀects correctly, it will lead to a fluctuation of theenergy scale, which becomes a systematic uncertainty in the search of µ → eγ. Even though theenergy scale will be monitored once per week by the 17.6 MeV monochromatic γ-rays from theCW-Li during the physics data-taking, it is still important to monitor and understand the daily
variation of the photosensor performances.

Variance^2 [10^18 e^2]

Chapter 5 PMT performance68

0.00220.002
0.00180.00160.00140.00120.001
0.00080.00060.0004run 353696
PMT 41300.0002
0

0.2

0.4

0.6

0.8

1

1.2
Charge [10^9 e]

Figure 5.1 Charge variance squared σq2 as a function of charge mean ⟨q⟩ in LED data ofa PMT. Diﬀerent points correspond to diﬀerent LED intensities.

5.1 Resoponse to visible light
5.1.1 Measurement of visible light response
The PMT response to visible light R(vis) was measured by using pulsed blue LED light(Section 2.5).
The PMT gain was measured from a relation of the mean and the spread of the LED charge
distribution on the assumption that the LED light follows a Poisson distribution*1 . An observed
charge q from the LED is denoted as q = e × Gain × Nphe + noise, where noise is a noise
contribution whose mean is calibrated to be zero beforehand, while it still has some event-byevent fluctuation. The relation between the mean and the spread of the LED charge is writtenas,⟨q⟩ = e × Gain × ⟨Nphe ⟩22σq2 = (e × Gain)2 × σN
phe + σnoise2= (e × Gain)2 × ⟨Nphe ⟩ + σnoise2= Gain × ⟨q⟩ × e + σnoise.

Fig. 5.1 shows measured σq2 as a function of ⟨q⟩ for a PMT at diﬀerent LED intensities. The
gain is estimated from the slope of this plot, and the contribution of σnoise is extracted as aconstant term*2 . Typically the noise contribution σnoise is about 1 × 101 photoelectron.
Independent of this gain estimation, a relative change of the R(vis) can be monitored by atime variation of the LED charge since the light intensity of our LEDs is known to be suﬃciently*1 Our VUV PMT is known to have a large position dependence of the gain on the photocathode. Therefore,

single photoelectron peak cannot be separated from pedestal.
in the LED data taken during a beam usage, an eﬀect from the accidental pileup γ is not
negligible. If the charge contribution of the pileups is a Gaussian, it is included in the constant σnoise ,and dose not aﬀect the gain calibration. However, the pileup γ-ray spectrum has longer tail for the higher
energy, and its contribution is not a Gaussian. To solve this, pileup charge distribution is measured during
the beam usage by the random trigger beforehand, and is used for a subtraction of the pileup eﬀect.

*2 In reality,

Gain

Chapter 5 PMT performance69
PMT Gain (ch 4347)

×103
3000

3.987e−20 ± 1.284e−20G0V0176.4 ± 5.325

k9.046 ± 0.04512

2500
2000
1500
1000
500
0

750

800

850

900
HV [V]

Figure 5.2 The gain of a PMT as a function of the high voltage fitted by a function:
Gain = G0 × (V − V0 )k [51].
100

1.05

80

100

60

80

40

60

20

40

0

20

1.02

0.99

0.96

0

0.92

−20

0.89

−40
−60

0.86

−80
−100
−100

0.83

0

100

z

200

300
0.80

Figure 5.3 Eﬀect of the magnets on the PMT Gain. “Gain when magnets on” / “Gainwhen magnets oﬀ”.

stable. This variation includes eﬀects of CE and QE for visible light. Thus, we can measure a
relative time variation of CE × QE(vis) by comparing the variation of the LED charge and thatof the PMT gain.

5.1.2 Gain and CE
Fig. 5.2 shows a voltage dependence of a PMT gain. This dependence can be modeled bya equation of Gain = G0 × (V − V0 )k , where k is a parameter proportional to the number ofdynode stages, and V0 is an voltage oﬀset mainly by the two Zener dynodes (Section 1.6.2).
The voltage dependence of the gain was measured for all PMTs, and applied high voltages were
adjusted to have a common gain.
The gain and CE of the PMTs are aﬀected by an activity of the COBRA magnet even though
its magnetic field is suppressed at the LXe calorimeter location by the compensation coils. They
are also aﬀected by an activity of the BTS. Fig. 5.3 and 5.4 show the ratio of the gain and the
CE of each PMT with those magnets on and oﬀ. These eﬀects have some z dependence, due tothe fact that BTS is located on the upstream side.

Chapter 5 PMT performance

70

100

1.05

80

100

60

80

40

60

20

40

0

20

1.02

0.99

0.96

0

0.92

−20

0.89

−40
−60

0.86

−80
−100
−100

0.83

0

100

200

z

300
0.80

Figure 5.4 Eﬀect of the magnets on the PMT CE. “CE when magnets on” / “CE whenmagnets oﬀ”.

5.1.3 Gain degradation by muon beam
The gain of our PMT is known to be decreased by a beam usage in the physics data-taking(Section 1.6.2). To compensate the gain degradation, the applied high voltage will be increased.
If the degradation is too fast, the demand voltage may become too high, and we may not beable to operate the PMTs in the whole MEG II experiment. As explained in Section 2.3, thelifetime of each PMT was calculated from the observed degradation speed in MEG assumingthat the degradation speed is proportional to the beam intensity. Only the PMTs which can be
operated for three years data-taking were installed in the MEG II LXe detector.
To crosscheck the expected lifetime of the PMTs, we measured the gain degradation speed
at the MEG II beam environment in the pilot runs. The PMT gains were adjusted to thenominal value (Gain = 1.6 × 106 , same as MEG) before the beam usage, and the degradation
was monitored. The red markers in Fig. 5.5(a) show the history of the averaged PMT gain in2019 run whose high voltages are kept during the beam time. The degradation speed shown in
Fig. 5.5(b) is calculated from its derivative. It is gradually decreasing and not yet saturated.
Even after six days of operation, the degradation speed is still 1% per day, which is much fasterthan the 0.35% per day expected from MEG.
Even though a further irradiation may reduce the degradation speed in the future, this was
not able to be confirmed in the limited beam time. To test another possible solution, some of
the PMTs were operated at the reduced voltage (Gain = 0.8 × 106 , half of the nominal value)in the latter half of the beam time. Because the PMT gain degradation is expected to be dueto the deterioration of the surface of the last stage dynode, its speed should be suppressed by
reducing induced current on the dynode. Black data markers in Fig. 5.5(a) and 5.5(b) show theresult of these PMTs, and a smaller degradation speed is confirmed.
In order to check whether PMTs can be operated throughout the physics run, an expecteddemand voltage of each PMT after the physics run is simulated. As the best estimation fromthe data so far, the degradation speed measured after the six days of operation is assumed. As
shown in Fig. 5.6, there is a large individual diﬀerence on the gain degradation speed, and this

71

1.02

Gain Degradation (%/day)

PMT Gain [a.u.]

Chapter 5 PMT performance

1

0.98

5
4.5
4
3.5
3
2.5

0.96

2
0.94

1.5
1

0.92

0.5
0.9
0

1

2

3

4

0
0

5
6
7
Days of MEG II beam iradiation

1

2

(a)

3

4

5
6
7
Days of MEG II beam iradiation(b)

Figure 5.5 (a) History of the PMT gain in the 2019 run, and (b) the gain degradation
speed estimated from the derivative of (a). Each color shows the result for each group of the
PMTs. For the PMTs of red markers, the high voltage was kept during the measurement.
For the PMTs of black markers, it was reduced after 4 days of operation to halve the gain.

30

25

20

15

10

5

0
−0.5

0

0.5

1

1.5
2
Gain degradation (%/day)Figure 5.6 Gain degradation speed of each PMT per day in 2019 run after the six days ofoperation. Operated at gain 1.6 × 106 (red), and at gain 0.8 × 106 (blue).

is included in the simulation. The high voltage currently applied, and the voltage dependenceof the gain of each PMT are also included based on the measurement.
The simulated high voltage of each PMT is shown in Fig. 5.7. The operation at the gain of
1.6 × 106 is possible for the three years physics data-taking, while the five years data-taking may
not be a realistic since the demand voltages of one third of the PMTs will exceed the limit of
1400 V. The operation at the gain of 0.8 × 106 looks promising even for five years data-taking,since only 5% of the PMTs will exceed this limit.
In the case of the operation at the reduced gain, the signal to noise ratio can get worse. To
solve it, an additional signal amplification is applied on the frontend of the readout electronics.
Since the dominant noise component comes from the electronics after the amplifiers, the signal tonoise ratio can be kept event if we operate the PMTs at the reduced gain. The noise contribution
to the energy resolution at the reduced gain is measured to be only 0.4% in the run 2019, andthus does not become a limiting factor to achieve the 1.0% energy resolution.

Chapter 5 PMT performance

72

0.18

0.18

operation at gain of 0.8e6
0.16

operation at gain of 0.8e6
0.16

operation at gain of 1.6e6

0.14
0.12

0.12

0.1

0.1

0.08

0.08

0.06

0.06

0.04

0.04

0.02

0.02

0
0

operation at gain of 1.6e6

0.14

200

400

600

800

1000 1200 1400 1600 1800 2000 2200

0
0

200

400

600

800

1000 1200 1400 1600 1800 2000 2200

demand voltage (V)(a)

demand voltage (V)(b)

Figure 5.7 Expected demand high voltage for PMT assuming operation at gain of 0.8×106(blue), and 1.6 × 106 (red). (a) After three years operation. (b) After five years operation.

Another concern is a reduction of the CE, which may lead to a larger statistical fluctuation of
the number of photoelectrons. The reduction of the CE is measured to be only 5% by comparingthat of the gain and the fixed intensity LED charge. Since the photoelectron statistics is not amajor contribution to the resolution in this detector, this reduction does not aﬀect the detector
resolution.
Additionally, the transit time spread (TTS) of the PMTs may also become larger. This should
not be a problem since the timing resolution of the LXe detector is not limited by the TTS. The
timing resolution of the LXe detector is measured by operating the PMTs at the reduced gain,
and the result will be shown in the Chapter 8.

5.2 Resoponse to VUV light
5.2.1 Measurement of VUV light response
The PMT response to the xenon scintillation light R(V U V ) is estimated by using a scintillation
light from the calibration alpha sources (Section 2.5). It is measured from the observed chargeq, which can be written as follows:q = Gain × CE × QE(V U V ) × Npho × e.
The number of arriving photons from the alpha source Npho can be estimated from the simulation. By introducing a parameter LY , which explains a diﬀerent level of the light yield for eachyear, it can be written as
mc
Npho = Npho
× LY,
mc
where Npho
is an expected number of photons calculated in the MC simulation assuming the best

condition achieved in MEG. The direct observable of this measurement is CE ×QE(V U V )×LY ,which can be calculated as follows:mc
CE × QE(V U V ) × LY = q/Gain/Npho.

Chapter 5 PMT performance73

In the oﬄine analysis of data to estimate charge q, a series of event selections is applied. Eventsfrom the cosmic-ray or the environmental radiation are rejected by a particle identification basedon the waveform shape of the PMTs. The vertex of each alpha event is reconstructed from thecharge weighted mean of the sensor position, and the reconstructed position is utilized to identify
an alpha source out of 25 sources installed in the detector. More details on the event selections
are given in [34].

5.2.2 QE and light yieldFig. 5.8(a) shows a history of the xenon light yield during the preparation period of 2017. In
2017, the purification of xenon was conducted both on gaseous circulation and liquid circulation.
A gradual improvement in the light yield was observed, while we could not reach the maximum
light yield achieved in MEG. It shows some degradation once the liquid purification is stopped,
and there should be some source of contamination inside the cryostat or the purification system.
Though the purification was continued also in 2018 and 2019 to improve the situation, the lightyield does not reach the ideal value, due to a time constraint from the schedule and a muchslower improvement by the purification than that in MEG.
Fig. 5.8(b) shows the measured CE ×QE(V U V )×LY of each PMT compared to that in MEG.
On the assumption that the average of the PMT QE is not changed from that in MEG, theachieved light yield for each year’s beam time LY is extracted from the slope of this correlation.

1.4

Gaseous purification

1.2
1

QE in MEG II

sum of # of p.e. [a.u.]

The estimated LY are summarized in Table 5.1.

Liquid purification
MEG's level

0.35

0.3

0.25

0.8
0.2

0.6
0.15

0.4
0.1

0.2
0

0.05

07/23

08/22

09/21
Month/Day

0
0

0.05

(a)

0.1

0.15

0.2

0.25

0.3
0.35
QE in MEG(b)

Figure 5.8 (a) History of the sum of the detected number of photoelectrons on the allread out PMTs in the preparation period of 2017. (b) Measured CE × QE(V U V ) × LY
of each PMT. Result in MEG II (2019) is shown as a function of that in MEG (2013).

Table 5.1 Light yield LY relative to the best condition achieved in MEG, during the beamtime of each year.

Year

2017

2018

2019

LY

89%

78%

86%

74

Chapter 6

MPPC performance
The MPPC response was calibrated and monitored by using LEDs and alpha sources withsimilar methods for the PMTs shown in Section 6.1, and 6.2.1.
Surprisingly, a gradual decrease of the PDE for the xenon scintillation light was observed in therun 2018, which suggests some radiation damage to our MPPC. The absolute value of the PDE
was measured to be lower than the design value, and this also supports the hypothesis of theradiation damage. Therefore, we conducted a precise PDE measurement in 2019 by controllingsystematic uncertainties, and concluded that the VUV PDE degraded during the beam usage.
The results of these measurement are given in Section 6.2.2.
Further investigations of this degradation were performed. It is found that an annealing of
the MPPC can recover this degradation. This is important since the observed degradation is so
fast that we may not be able to operate our detector for the whole MEG II experiment without
any recovery. These results are summarized in Section 6.3.

6.1 Resoponse to visible light
6.1.1 Gain and ECF
The gain of each MPPC was measured by a single photoelectron peak from a weak LED light.
Several LEDs installed in the cryostat were used to achieve a uniform light distribution. Since
the peak amplitude of the single photoelectron signal is roughly only 0.1 mV, the signal was
amplified by a factor of 100 on the frontend of the readout electronics. To suppress the coherent
noises picked up on the 10 m cable between the cryostat and the electronics, an “even-odd”
procedure was adopted. In this procedure, bias voltages are applied only to the even channels,
and the coherent noises are subtracted in oﬄine based on the waveform of the adjacent odd
channel, and vice versa. Fig. 6.1 shows a typical charge distribution, where photoelectron peaks
are clearly resolved. The zero photoelectron peak and the single photoelectron peak in the
charge distribution were fitted by a sum of two Gaussians to evaluate the gain of each MPPC.
All the MPPCs were operated at the over voltage of about 7 V. The operation voltage Vop
for each MPPC was calculated from a voltage provided for each MPPC by HPK called VHama

75

Events

Chapter 6 MPPC performance

300
250
200
150
100
50
0
−0.1

0

0.1

0.2

0.3
0.4
Charge[10 9 e]

Figure 6.1 Single photoelectron charge distribution of an MPPC obtained by the even-odd
procedure.

as follows:
Vop = VHama − 4.9 V + 6.8 V − c × (298 K − 165 K).
Here we used the fact that VHama corresponds to the over voltage of 4.9 V (from the test atroom temperature shown in Section 2.2). The last term is a temperature correction, wherec = 55 mV/K is the temperature coeﬃcient of the breakdown voltage of the MPPCs [47].
Fig. 6.2(a) shows the measured MPPC gains. The power of the amplification on each electronics channel is measured independently and corrected in this plot. Suﬃciently uniform gain
distribution is obtained by applying Vop based on HPK’s information, while a slight production
lot dependence is observed.
The excess charge factor (ECF) of the MPPCs was also measured by using the weak LED lighton the assumption that LED light follows a Poisson distribution. The detail of this method is
described in Section 2.1.3. Fig. 6.2(b) shows the measured ECF. Even though a large production
lot dependence is observed, this is still acceptable as long as we can measure it correctly. Over
voltage of 7 V is adopted in this thesis to improve the S/N ratio to resolve the single photoelectron
peak as much as possible. The rather large ECF and its lot dependence are drawbacks of therather higher over voltage, and operation at smaller over voltage may be an option in the future.

6.1.2 History of visible light response in the beam time
Similarly to the PMT, the visible light response was monitored by the observed charge fromthe fixed intensity LED light. This method cannot give us an absolute size and an individual
diﬀerence of gain and ECF, but can give us a history of the relative response with much better
precision than the single photoelectron measurement. Fig. 6.3 shows the history of the visible
light response during the run 2019. It shows a slight degradation of 1% probably correlated withthe beam activity. A similar but much more prominent degradation is observed for the VUVresponse, which will be discussed in the next section.

1800 ×10

76

3

ECF

Gain

Chapter 6 MPPC performance

2.4
2.2

1700
2
1600
1.8
1500

1.6
1.4

1400
1.2
1300
1
1200
0

1000

2000

3000

4000

0.8
0

5000
6000
MPPC serial number

1000

2000

(a)

3000

4000

5000
6000
MPPC serial number(b)

MPPC Response (a.u.)

Figure 6.2 MPPC characteristics as a function of its serial number at the over voltage
7 V. (a) Gain, (b) ECF.

1.02

MPPC Response under muon beam

1.015

1.01

1.005

1

Accumulated Beam Exposure (hour)

0.995

0.99
200

Response to LED light

19/10

180

26/10
Exposure to muon
beam

02/11

160
140
120
100
80
60
40
20
0

10/19

10/26

11/02

Month/Day

Figure 6.3 History of the visible light response (λ = 470 nm from blue LED) of the MPPCs
during the run 2019. An average of all MPPCs is shown. Lower half is the accumulated
muon beam usage.

6.2 Resoponse to VUV light
6.2.1 MPPC VUV PDE
Similar to the PMT described in Section 5.2, a response to the VUV light R(V U V ) = Gain ×
P DE(V U V ) × LY of each MPPC was measured from the alpha calibration sources.
Fig. 6.4(a) shows the VUV PDEs measured at the beginning of the run 2019, where the lightyield LY is taken from Table 5.1. The average of the PDE is 7%, while 18–22% is obtained in
the measurement at the lab (Section 2.1.3). The possible reason for this inconsistency will be
discussed in the next subsection.
The angular dependence of the PDE was measured to crosscheck the unexpected angular

77

0.18

Normalized PDE

VUV PDE

Chapter 6 MPPC performance

2

1.8

0.16

50

Measured in actual machine
Measured in large prototype

1.6

0.14

40

1.4

0.12

1.2

0.1

30

1

0.8

0.08

20

0.6

0.06

0.4

0.04

10

0.2
0.02
0
0

0
0
1000

2000

3000

4000

20

40

5000
6000
MPPC serial number

(a)

60

80

0

Incident Angle[deg](b)Figure 6.4 (a) PDE of VUV MPPC as a function of serial number at over voltage 7 V.
Smaller LXe light yield (88 % of ideal case in 2019) is corrected. (b) MPPC VUV PDE asa function of the incident angle [34]. The individual diﬀerence of PDE of each MPPC iscorrected by using the data point of the smallest incident angle.

dependence observed in the prototype test (Section 2.1.3). The PDEs of each MPPC were
measured by using many alpha sources located at diﬀerent positions, and Fig. 6.4(b) shows
the VUV PDE as a function of the incident angle from each alpha source to each MPPC. A
consistent result with the prototype test is observed. The eﬀect of this dependence on thedetector performance will be discussed in Section 7.3.

6.2.2 Degradation of MPPC VUV PDE by radiation damage
During the run 2019, the MPPC response to the VUV light was monitored with the alphasources. Fig. 6.5 shows a history of the VUV-response averaged over all the MPPCs. The VUVresponse is found to be decreased by 11%, and its degradation is correlated with the beam
activity. This degradation can be caused by a degradation of the gain, the ECF, the VUVPDE, or the xenon light yield. However, the MPPC response to the visible light decreased only
by 1% in this period (Fig. 6.5), and thus the gain and the ECF should not be a cause of thisdegradation. A slight degradation was found also on the VUV response of the PMTs as shownin Fig. 6.6. This can be due to a degradation of the PMT VUV QE or the xenon light yield.
However, its size is only 4% and cannot explain the observed degradation of the MPPC VUV
response, even if it is totally due to the degradation of the xenon light yield.
Based on these observations, it is concluded that the degradation of the MPPC VUV response
is mainly caused by that of the MPPC VUV PDE. Since the degradation is correlated with thebeam usage, this should be a radiation damage while it is totally unexpected. The degradation
speed is 9 ± 2% in the 160 hours MEG II beam usage, where the possible instability of the lightyield is included as a systematic uncertainty estimated from the PMT response to the VUVlight.
To investigate and crosscheck this degradation, several variables are checked and they are

MPPC Response (a.u.)

Chapter 6 MPPC performance

78

MPPC Response under muon beam

1.06
1.04
1.02
1
0.98
0.96
0.94
0.92
0.9

Response to LED light

0.88

Response to VUV light

Accumulated Beam Exposure (hour)

0.86

200

19/10

180

26/10
Exposure to muon
beam

02/11

160
140
120
100
80
60
40
20
0

10/19

10/26

11/02

Month/Day

PMT Response (a.u.)

Figure 6.5 History of the VUV response of the MPPCs to the alpha source during run
2019 (blue). The average over all MPPCs is shown. The response to the visible light is also
shown for comparison (red, same as Fig. 6.3). Lower half shows the accumulated beam
usage. A much larger degradation correlated with the beam usage is observed for the VUVlight than the visible light.

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

10/26

11/02
Month/Day

Figure 6.6 History of the CE × QE(V U V ) × LY , namely the VUV response except for
the gain degradation, of each PMT in the run 2019. The average over all PMTs is shown.

described in the following subsections.

PDE from 2017 to 2019
Fig. 6.7 shows the measured PDE from 2017 to 2019 as a function of the accumulated muon
beam usage. A gradual decrease of the MPPC PDE is confirmed.
It is also notable that the degradation speed in run 2019 is slower than that in 2017 and 2018.
This implies that the degradation is slowing down, but further irradiation is needed in the future

PDE (%)

Chapter 6 MPPC performance79

run 2017

14

run 2018
run 2019

12
10
8
6
4
2
0
−5

0

5

10

15

20
25
Irradiation Day

Figure 6.7 Averaged VUV PDE of the MPPCs estimated from the alpha sources from2017 to 2019. The x-axis shows the accumulated irradiation days with the MEG II beam
intensity. A period with a reduced intensity muon beam is normalized to the MEG II beam
intensity. The diﬀerent level of the xenon light yield in each year is corrected based on the
Table 5.1.

to understand a full history of the PDE degradation.

VUV charge from γ-rays
In addition to the alpha events, the background γ-rays mainly from the RMDs were continuously measured during the beam time. This can be used as another source of VUV light.
Due to the deterioration of the PDE, the MPPC charge distribution from the RMD γ-ray isshifted smaller as shown in Fig. 6.8(a). Here, only the events with PMT energy above 36 MeV isselected to eliminate the eﬀect of the online energy threshold. The size of the shift is calculated
from the mean of the charge distribution. Fig. 6.8(b) shows a relative history of the MPPCVUV response estimated from the observed shift. A degradation by 9% is observed and this isconsistent with the observation with the alpha source.
Fig. 6.9(a) shows the averaged waveform shapes for the monochromatic γ-rays from the CWLi measured before and after the irradiation. This degradation does not aﬀect the waveform
shapes, and only the signal amplitude deteriorates.

MPPC Current
An induced current on each MPPC from the background γ-rays was also monitored, and its
history is shown in Fig. 6.9(b). Even though the current measurement seems to have someinstability, about 10% degradation, which is consistent with the PDE measurement, is observed
only for the VUV light. The current measurement is independent of the charge measurement

Chapter 6 MPPC performance80

Oct/240.1

1.02

Oct/271

Nov/020.08

Nov/04

0.98

0.06

0.96

0.04

0.94

0.92
0.02
0.9
0
0

5

10

15

20

25
30
Energy from MPPC (MeV)

10/26

(a)

11/02

(b)

0

MPPC current (a.u.)

amplitude (a.u.)

Figure 6.8 (a) Reconstructed γ energy only from the MPPC assuming a constant PDE
in this period (i.e. sum of the MPPC charge). (b) History of the PDE which can explain
the observed shift. The red line is a fitted function assuming a degradation of 0.059(4)%/hour.

−0.05

1.06
1.04

LED light
VUV light (scintilation from BG gamma)

1.02
1
0.98

−0.1

0.96
0.94

Before irradiation

−0.15

0.92

After 57 hours irradiation

0.9

After 121 hours irradiation

−0.2

0

0.05

0.1

0.15

0.2

0.25

0.3

×10
0.35
0.4
time (sec)

0.88
−6

0.86

(a)

10/26

11/02
Month/Day(b)

Figure 6.9 (a) Averaged MPPC waveforms of γ events before and after the irradiation.
The peak amplitude is normalized to compare its shape. (b) The MPPC current during
a run 2019 (blue). An average of all MPPCs except for bad channels is shown. Current
induced by a fixed intensity blue LED is also given for comparison (red).

using the digitized waveforms, so this result rejects a possibility of an instability issue of thereadout electronics only apparent on the VUV signals.

PDE of all MPPCs
The results mentioned above use the data during the beam time with a limited number ofreadout channels. Additionally, at the end of the run 2018, PDEs of all the MPPCs were
measured by subdividing 4092 MPPCs into 12 groups and changing the readout channels fromone group to another. Fig. 6.10 shows a map of the measured PDEs. The PDEs of the MPPCs
located at the edge of the detector along horizontal axis (z-axis) are found to be larger than theChapter 6 MPPC performance

81
0.25

100
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
0.03

100
100

50

0

50

100

150

200

z

250

300
0.00

Figure 6.10 VUV PDE measured after the run 2018. MPPCs used in the run 2018 isindicated by a region surrounded by the black line. PDEs of most of the gray MPPCs were
not measured just due to a technical reason, and not dead channels.

others. This is likely due to a position dependence of the irradiation fluence. For example, if
we assume that this radiation damage is caused by the VUV scintillation light, the dominant
contribution is the scintillation of the γ-rays coming from the muon decays on the target. Since
the LXe detector and the COBRA magnet are designed to have a reduced material budget onlyin the acceptance region, such kind of irradiation is expected to be smaller outside the acceptancelike large |z| region. Fig. 6.11(a) shows the simulated irradiation fluence of the VUV scintillation
light. An anti-correlation of the measured PDE and the expected fluence is observed. It must
be noted that the same discussion is also applicable to the γ-ray irradiation dose.
During the beam irradiation, the bias voltage was applied only to the MPPCs inside thereadout area, and no voltage was applied to the others. Fig. 6.11(b) shows a comparison of
the PDEs with “voltage on” MPPCs and “voltage oﬀ” MPPCs. Only the MPPCs located at|z| < 15 cm are selected, where a uniform irradiation level is expected. Since the original PDE
should be 18–22%, the degradation process also occurs without applying bias voltage. The PDEof “voltage oﬀ” MPPCs is a little higher than that of “voltage on”. It is still not clear that
this is due to an eﬀect of the bias voltage on the PDE degradation or just due to a unknown
systematics in this measurement like v dependence of the PDE measurement.

6.3 Investigation of VUV PDE degradation
6.3.1 Possible cause of PDE degradation
Two types of radiation damage are known for the MPPC and SiPM: a bulk damage and asurface damage [52].
In the bulk damage, an atom in the silicon bulk is displaced by a non ionizing energy loss
(NIEL) by high energy particles. This results in a formation of a defect, which introduces
an additional energy level between the band gap of the silicon. Typical phenomena of thebulk damage are a larger leakage current and dark count rate, which are caused by the increased

82

2.5

0.18

Measured PDE

0.16

Expected fluence

0.14

2

0.12

1.5
0.1
0.08

1
0.06
0.04

0.5

Expected VUV fluence (1e11 / cm^2)

MPPC PDE

Chapter 6 MPPC performance

120

Bias voltage OFF

100

Bias voltage ON

80

60

40

20

0.02
0

−30

−20

−10

0

(a)

10
20
30
Horizontal coordinate z (cm)

0

0
0

0.05

0.1

0.15

0.2

0.25
MPPC PDE(b)

Figure 6.11 (a) The z dependence of the measured MPPC PDE and that of the expected
fluence of the VUV photons from the simulation. (b) Comparison of the PDE just after
the run 2018 between the MPPCs irradiated with bias voltage and those without voltage.
Only the MPPCs located at |z| < 15 cm are shown.

probability of the thermal excitation of electron-hole pairs due to the new energy level. These arereported by many studies typically above 1 × 108 /cm2 (1 MeV neutron equivalent) [53][54][55].
Some studies also report a decrease of the signal size, namely a product of the PDE, the gain,
and the ECF, at 5 × 1013 /cm2 (1 MeV neutron equivalent) [55]. A possible explanation of thisis an increased pixel occupancy by the increased dark signals. If a photon hits a pixel which is
not fully recovered from the previous discharges, the eﬀective gain can be smaller.
The other damage on SiPMs is the surface damage by an ionizing energy loss (IEL) by electromagnetic particles such as X-rays and electrons. By the energy deposit above the band gap,
electron-hole pairs are generated in the high resistivity passivation layer (e.g. SiO2 ). Some ofthe holes are captured by deep traps in the passivation layer or the interface traps between
silicon layer, while most of the electrons leave it by a relatively high mobility and low trapping
probability. This leads to an accumulation of the stationary charges. A large increase of thedark current is reported above 200 Gy [56], which is very likely due to the accumulated andstationary charges at the surface generated by the breakup of SiO2 molecules [57].
Fig. 6.12 shows the radiation environment of the LXe detector. When the muon beam isused, γ-rays mainly from the RMDs on the target hit the detector through the MPPCs on theentrance face. The xenon scintillation light (7.1(mean) ±0.1(FWHM) eV) from these γ-rays hit
the MPPCs. Neutrons from the accelerator also hit the detector in the MEG II experimental
area.
Table 6.1 shows the expected irradiation dose in the run 2019. The neutron fluence is estimatedto be less than 2.9 × 106 /cm2 (1 MeV neutron equivalent) from the measurement at the MEG II
experimental area [22]. This is much smaller than the level where the NIEL damage is reported.
The gamma-ray dose is estimated to be 0.01 Gy by the simulation [22], and should not be a
problem. The VUV fluence is measured to be 4.6 × 1010 /mm2 from the induced current on theChapter 6 MPPC performance

83

MPPC in the run 2019. It is also estimated to be 5.8 × 1010 /mm2 from the simulation, andagrees with a 30% accuracy. A radiation damage on SiPMs by the VUV irradiation was notreported. Therefore, the degradation of the VUV PDE by a radiation damage was unexpected.
One hypothesis to explain the observed PDE degradation is a surface damage by the VUVphoton irradiation. In the surface damage, the accumulated oxide charges near the interface
between the silicon layer and the passivation layer can distort the electric field around it. Dueto the special detection mechanism of the VUV photons (Section 2.1.1), the collection eﬃciency
for the VUV light can be aﬀected by the distortion, while that for the visible light is hardly
aﬀected. It has to be pointed out that the energy of the xenon scintillation light (7.1 eV) issmaller than the band gap of passivation layer (8.9 eV), if it is made of SiO2 . The mechanismof carrier generation in the SiO2 has not been understood in this case, but may be related to
an intermidiate energy level in SiO2 by a defect or a photoemission of the holes from the siliconvalence band to the SiO2 valence band, known for other silicon devices [58][59].
Some studies report that a thermal annealing can recover the radiation damage on the SiPMs[53][54]. In the thermal annealing, SiPM is kept at a high temperature, so that the accumulated
charges are de-trapped by the thermal excitation. We tried it with our damaged MPPCs, andthe results will be given in the next subsection.
Table 6.1 Expected irradiation fluence in run 2019 (i.e. 160 hours MEG II beam)irradiation source

dose/fluenceγ

0.01 GyVUV photon

4.6–5.8 × 1010 /mm2

neutron

2.9 × 106 n/cm2

LXe detector

n
MPPC

VUV

COBRA

γ

μ

not to scale

Figure 6.12 Radiation environment of the LXe detector.

Chapter 6 MPPC performance84

6.3.2 Annealing
As is discussed in the previous subsection, annealing may cure this radiation damage. We
tested it for a small number of MPPCs in the LXe detector after the run 2018. We used an
intense LED light to heat up the MPPCs by the Joule heating of the induced current flowing
through the quench resistors. In order to perform this test, the liquid xenon was transferred tothe storage tank, and the detector was filled with gaseous xenon at room temperature. Annealing
was tested at the several levels of induced current and the duration for the six MPPCs as isshown in Table 6.2. The temperature of the MPPC chips under these conditions were notdirectly measured, but it is expected to be about 70◦ C from a lab test performed under thesame condition.
Table 6.2 Tested annealing conditions.

MPPC ID

current

duration2802

17–19 mA

23 hours

2712

19 mA

23 hours2672

19–20 mA

23 hours2789

19–24 mA

38 hours

2700

20–24 mA

38 hours

2658

21–24 mA

38 hours

The PDEs of the annealed MPPCs were measured before starting the beam usage in 2019. A
significant recovery of the PDE from ∼ 8% to ∼ 17% was observed. The ratios of PDEs after theannealing to those before the annealing are presented in Fig. 6.13(a). A significant recovery of
PDE is observed for the annealed MPPCs, and its size is correlated with the annealing strength.
The response to the visible light is also found to be recovered by the annealing as shown in
Fig. 6.13(b). Similar to the PDE degradation, the recovery for the visible light is much smaller
than that for the VUV light.
One concern was that the recovered PDE by the annealing might rapidly decrease by a small
amount of irradiation. Fig. 6.14 shows the PDE degradation during the run 2019 of the annealed
MPPCs compared with the non-annealed MPPCs. Its degradation speed is found to be the sameor a little slower than the non-annealed MPPCs.

6.3.3 PDE degradation at room temperature
A series of irradiation tests was performed in lab to crosscheck the degradation observed in
the LXe detector. All these irradiations were performed at room temperature.
6.3.3.1

VUV photon irradiation

A VUV-MPPC was irradiated with the intense VUV light from a xenon lamp (Hamamatsu
L9456-03 [60]) to study the eﬀect of the VUV light on the VUV sensitivity. Fig. 6.15(a) shows

85

Vis PDE recovery by annealing.

VUV PDE recovery by annealing.

Chapter 6 MPPC performance

2.2
2
1.8
1.6
1.4

2.2
2
1.8
1.6
1.4

1.2

1.2

1

1

0.8

0.8

Not annealed

2802

2712

2672

2789

2700

2658 MPPC id

Not annealed

2802

(a)

2712

2672

2789

2700

2658 MPPC id(b)

MPPC response (a.u.)

Figure 6.13 Recovery rate of the PDE of the annealed MPPCs (a) for VUV light, (b) forblue LED light. Non-annealed MPPCs are also shown for comparison. The MPPC ids
in the x-axis are in an ascending order of the annealing strength (Table 6.2). The error
bar of the non-annealed MPPCs shows the 1σ spread of the PDE ratio distribution of the
non-annealed MPPCs.

1.06

Non-annealed MPPCs

1.04
Annealed MPPCs

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

10/26

11/02
Month/Day

Figure 6.14 History of the VUV PDE in the run 2019 of the annealed MPPCs. Relative
shift is shown.

schematic of the setup. Light ranges from VUV to blue are emitted from the xenon lamp as
shown in the spectral intensity (Fig. 6.15(b)). The xenon lamp was placed 5 cm away from thesurface of the MPPC without any filters.
The VUV component of the irradiated light was measured to estimate irradiation flux in thistest. Two bandpass filters (ACTON FB180–B–.5D and Edmund optics #33–026, Fig. 6.16)
were placed to select VUV light peaked at 190 nm. Measurement was performed at a larger distance beforehand and the results were extrapolated to that in the measuring point to avoid
a saturation of the MPPC. The irradiation flux of the VUV light is estimated to be 5 ×1013 photons/mm2 /hour.
In order to monitor the VUV response, the charge from another xenon lamp (Hamamatsu
L9455-13 [60]) placed 35 cm away from the MPPC was measured periodically during the irradiation. The two bandpass filters and one ND filter were placed to monitor the response to theChapter 6 MPPC performance

86

5 cm
ND filter
during monitor

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

n

or

Xe

la

f
mp

io
iat

d

a
irr

Replaceduringmonitor

Bandpass
filters
35 cm

Non-irradiatedMPPC

Radiation Intensity

Xe lamp for monitor
IrradiatedMPPC

Wavelength (nm)

(a)

(b)

Figure 6.15 (a) Setup of VUV photon irradiation. (b) Spectral radiation intensity of theXe lamp (from [60], translated by the author). This lamp can emit VUV light down to
λ = 185 nm.

(a)

(b)

Figure 6.16 Spectrum of the bandpass filters.

VUV light peaked at 190 nm and to suppress the signal to avoid saturation.
A VUV response of another MPPC without irradiation was also monitored for the comparison.
These measurements were carried out in a thermal chamber kept at 25◦ C.
Fig. 6.17(a) shows VUV charge history for the irradiated and the non-irradiated MPPCs.
A degradation of the VUV response is observed only for the irradiated MPPC. The observed
degradation is 65% in total after 3 × 1016 /mm2 VUV photons irradiation. It is 9% after 1 ×
1015 /mm2 irradiation. Since the degradation in the LXe detector is 9% at the expected fluenceof 4.6 × 1010 /mm2 VUV photon, this is much slower than the observation in the detector by afactor of O(104 ). It is notable that the degradation of PDE is saturated when it reaches 35% of
the original value.
The annealing of the irradiated MPPC was also tried. The irradiated MPPC was kept at
70◦ C for 24 hours. With this annealing, VUV charge is increased from 35% to 105% of that
before any irradiation. Thus, the degradation is fully recovered. It is also notable that a jumpof VUV response was observed when we suspended the irradiation for twelve days (at 400 hours

87

relative VUV charge

relative VUV charge

Chapter 6 MPPC performance

1.2

1

1.2

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

1

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

0.8

2nd irradiation set
2nd irradiation set

0.8

0.6
0.6
non-irradiated

0.4

0.4

non-irradiatednon-irradiatednon-irradiated

0.2

0.2

irradiatedirradiatedirradiated00

irradiated

100

200

300

400

500

600
irradiation time (h)

0
0

100

200

(a)

300

400

500
600
irradiation time (h)(b)

Figure 6.17 (a) Response to VUV light from a fixed intensity Xenon lamp. Diﬀerent data
series with similar colors show four chips on the same MPPC package. (b) VUV responsein the second irradiation after one cycle of annealing.

of irradiation of Fig. 6.17(a)), which can be due to a slow annealing at 25◦ C.
Another irradiation is performed for the annealed MPPC. The degradation is slower than thefirst irradiation as shown in Fig. 6.17(b).
6.3.3.2

Gamma irradiation

Several MPPCs are irradiated with γ-rays from a 60 Co source (Eγ = 1.17, 1.33 MeV). The
irradiation was carried at the Takasaki Advanced Radiation Research Institute in 2015. The total
irradiation dose of each MPPC is 1–4 × 103 Gy [61], which is much higher than the expectationof 0.6 Gy in the whole MEG II experiment.
We measured the VUV PDEs in 2019 using the small test setup (Section 2.1.2). Fig. 6.18(a)shows the result*1 . Three irradiated MPPCs show consistent PDE with a non-irradiated MPPC.
The other one irradiated MPPC shows inconsistent PDE with others, which may be due to somesystematics or mistake in the measurement. In any case, no significant damage was observed
even at the much higher irradiation fluence, and the PDE degradation observed at the LXedetector was not reproduced by this γ irradiation. It must be, however, noted that the irradiated
MPPCs were kept at room temperature for four years after the irradiation and a possibility of
the recovery by an annealing at room temperature cannot be excluded.
6.3.3.3

Neutron irradiation

An irradiation damage with neutrons is also tested. The irradiation was performed at theTandem electrostatic accelerator at Kobe University in 2015. Deuterons are accelerated to
3 MeV and neutron from 9 Be + d → 10 B + n was used for irradiation. The total fluence of each
MPPC, which was measured by a ELMA diode, ranges from 5 × 109 –2 × 1012 n/cm2 (1 MeV
neutron equivalent), depending on the irradiation time and the geometrical distance from the*1 Though the I-V curve of the MPPC was checked just after the irradiation as reported in [61], VUV PDE

was not measured at that time since its degradation was not expected.

88

PDE

PDE

Chapter 6 MPPC performanceno irradiation
1.4e3 Gy
4.1e3 Gy
4.1e3 Gy
4.1e3 Gy

0.14
0.12

no irradiation

0.14

0.5e10 n/cm^2

0.12
0.1

0.08

0.08

0.06

0.06

0.04

0.04

0.02

0.02

1

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

0.1

0
0

0.5e10 n/cm^2

2

3

4

5

6
Vover (V)

(a)

0
0

1

2

3

4

5

6
Vover (V)(b)

Figure 6.18 VUV PDE of the irradiated MPPCs as a function of the over voltage in (a)gamma irradiation test, and (b) neutron irradiation test. Diﬀerent colors show diﬀerent
MPPCs. Black markers in (a) and gray markers in (b) are the MPPCs without any
irradiation, and the others are the MPPCs with diﬀerent dose levels.

target [61].
The VUV PDE measured in the small test setup in 2019 is shown in Fig. 6.18(b). No eﬀectof irradiation is observed.

6.3.4 Discussion
Possible cause of PDE degradation
The degradation of the VUV response is observed by the VUV irradiation at room temperature, while its speed is much slower than that at LXe temperature. This suggests that theradiation damage in the detector is caused by a surface damage by the VUV irradiation, andits physics process is enhanced by a factor of O(104 ) at the LXe temperature. Another possible
reason of this inconsistency is a wavelength dependence of the damage. Since the light only
above 185 nm is guaranteed in the specification of the xenon lamp [60], the wavelength of theirradiated light can be diﬀerent from the xenon scintillation light peaked at 175 nm. This may
aﬀect the speed of the charge accumulation in the passivation layer. The MPPC response to
the 190 nm was monitored by using the bandpass filters, and this can also be diﬀerent from thatto the xenon scintillation light, due to a wavelength dependence of the attenuation length insilicon.
In contrast, PDE degradation was not observed by the irradiation of γ-ray and neutrons.
It is notable that the degradation observed in the detector could still be explained by these
irradiations, if we assume even larger enhancement at LXe temperature (> O(105 ) for γ, >O(106 ) for neutron) is needed.
In any case, temperature dependence of these processes needs to be studied for a further
understanding. Therefore, an irradiation test at low temperature is planned.

Chapter 6 MPPC performance

Figure 6.19 Measured PDE history (same as Fig. 6.7) and its extrapolation. The x-axis is
the usage time of the MEG II beam. Blue band shows a linear extrapolation of the 9 ± 2%
degradation observed in the run 2019.

Original PDE without irradiation damage
The original PDE of the MPPCs without any radiation damage is not yet fully understood.
The PDE of 18–22% was expected from the measurement in the lab test (Section 2.1.3), but it
was measured to be 12% just before the beam usage in 2017. The PDE after the annealing in
the detector is measured to be 17%, which is slightly lower than the PDE in lab. On the other
hand, a full recovery of the PDE by the annealing was observed for the VUV irradiated MPPCat room temperature.
There are several possibilities which may explain these diﬀerences, but we cannot reach theconclusion on this point.
• The lower PDE just before the run 2017 may be due to some damage accumulated during
the installation to the detector or a beam tuning conducted at the upstream of the πE5beam line before the run 2017.
• The annealing performed in the detector may still not get saturated. The annealing in thelab test was performed at higher temperature than that performed in the LXe detector.

Detector operation with PDE degradation
From the viewpoint of the detector operation, it is important for the MPPCs to have asuﬃcient PDE for a suﬃcient resolution during the data-taking. Fig. 6.19 shows the history of
the measured PDE and its extrapolation to the future. It is notable that an extrapolation of
the PDE with a good precision is rather diﬃcult since the degradation speed seems graduallyslowing down. Thus, only the most optimistic case and the most pessimistic case are discussed.
In the most optimistic scenario, the PDE degradation will get saturated at about 6%, as is

89

Chapter 6 MPPC performanceobserved in the VUV irradiation at room temperature (Section 6.3.3.1). In the VUV irradiation
test, the PDE was saturated at 35% of the original value, namely, PDE of 18–22%, whichcorresponds to the PDE of 6%. The gradual decrease of the degradation speed also supports
this possibility.
In the most pessimistic scenario, the PDE will continue decreasing linearly, and become zeroafter 70–100 days operation in MEG II beam. The original MEG II DAQ plan assumes acontinuous 120 days of data-taking per year, which is not possible in this scenario.
It is notable that the x-axis of Fig. 6.19 is calculated in a conservative way, and the maximaldays of continuous operation in the pessimistic scenario may be biased for the following reasons.
Firstly, the beam intensity in the run 2019 seems to be about 10–20% higher than the MEG II
beam intensity (Section 3.1.3), but this excess is not reflected. Secondly, the smaller LXe lightyield of each year (roughly 85%) is corrected in the calculation of x-axis assuming that the VUVphotons are the cause of this damage. This leads to an overestimation of the degradation speed
if the γ-rays are the cause of this damage. Thirdly, this scenario assumes that the PDE starts
from 12% as observed in the run 2017. It implicitly assumes that the PDE is reduced from 17%
after the annealing to 12% with little amount of irradiation. These assumption are adopted tobe conservative since the PDE without damage is not yet fully understood, though it obviously
contradicts the observed PDE history for the annealed MPPCs (Fig. 6.14).
If the degradation does not get saturated at a reasonable PDE, it is needed to anneal all the
MPPCs in each year. This can be performed in the annual accelerator shutdown period fromJanuary to May. From the experience of the annealing in the detector, the annealing of one
MPPC can be finished in two days. If we perform the annealing of 200 MPPCs in parallel *2 , itwill take 40 days to anneal all the MPPCs, and can be completed in the shutdown period.
The eﬀect of the PDE degradation on the MEG II branching ratio sensitivity in these scenarios
will be discussed in detail in Chapter 11, combined with the expected detector resolutions at
the reduced PDE of the MPPCs.

*2 For this purpose, a voltage supply which can supply suﬃcient power for 200 channel is needed, and it isalready ordered.

90

91

Chapter 7

Position resolution
Good resolutions of the LXe detector are important to reduce the accidental background eventsas shown in Equation 1.1 and to achieve the goal of the MEG II experiment. The resolutions
were measured from the data in the pilot run. From this chapter, each measured resolution will
be presented.

7.1 Position reconstruction
The hit position of the γ-ray ⃗x is reconstructed from the light distribution on the MPPCs.
The detected number of photons of each MPPC Npho is fitted by a function proportional to
the solid angle Ω from the γ hit position subtended by each MPPC. The fit is performed by aminimization of the χ2 defined as2χ :=∑ ( Npho − C × Ω(⃗x) )2MPPC

σ(Npho ).

C is a normalization of the light distribution and a nuisance parameter in the fitting. The
uncertainty of the Npho of each channel σ(Npho ) is calculated from the statistical fluctuation of
the number of photoelectrons as,√σ(Npho ) := Npho / Nphe .
This fit function assumes that all the scintillation light comes from a point, but in reality it
is emitted from each point of the electromagnetic shower. Therefore, the fitted position does
not correspond to the true hit position, and is biased to the shower development direction. To
reduce this bias, the MPPCs used in the position fitting are limited to those around the hit
position.
Additionally, a series of corrections is applied. The first type of correction is called “global
correction”. The direction of the shower development tends to be similar to that of the incident
γ-ray. Events with larger |u| tends to be reconstructed larger as is shown in Fig. 7.1. Thisdependence is corrected as a function of the u. Another correction called “shower correction” isalso applied. Even for the events hitting the same position, the shower direction can fluctuate
event-by-event. The position fit is performed for several sizes of the fit regions, and the showerChapter 7 Position resolution

92

outer faceHit
position

U_fit - U_mc (cm)Fittedposition

Residual of U vs. U

inner face

5

45

4

40

3

35

2

30

1

25

0

20

1

15

2

γ

u

w

3

10

4

5

5
40

30

(a)

20

10

0

10

20

30
40
U_fit (cm)0(b)

Figure 7.1 (a) Schematic of the global correction. A bias in the reconstruction (red arrow)is corrected by the γ hit position (blue arrow). (b) Correlation between red arrow vs. blue
arrow in (a) (in MC).

outer face

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

U_fit - U_mc (cm)1

FittedpositionHit
position

inner face

50

0.8
0.6

40

0.4
0.2

30

0
0.2

20

0.4

γ

0.6
u

w

10

0.8
1
0.2

0.15

(a)

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

Figure 7.2 (a) Schematic of the shower correction. A bias in the reconstruction (redarrow) is corrected by the diﬀerence of the position using diﬀerent size of the fit regions(blue arrow). (b) Correlation between red arrow vs. blue arrow in (a) (in MC).

direction is reconstructed from the fact that the bias by the shower direction is clearer for
wider fit region (Fig. 7.2). The reconstructed direction is utilized to correct the event-by-event
fluctuation of the bias.

7.2 Measurement with lead collimatorThanks to the improved granularity realized by the MPPCs, a better position resolution is
expected for the shallow events. To verify this improvement, γ-ray data were taken by placing
a collimator in front of the detector as shown in Fig. 7.3(a), so that the resolution can beChapter 7 Position resolution

93
TargetGamma-ray
Event Distribution

collimator

PMT

support structure

COBRA magnet

y

MPPC

x

LXe detectorzφSatoru Kobayashi

(a)

(b)

27

Figure 7.3 (a) Principle of position resolution measurement [34]. (b) Lead collimator(240 × 240 × 25 mm3 ) with slits of 5 mm width used for the resolution measurement. [34].

evaluated from the width of the reconstructed position distribution of the slits. Fig. 7.3(b)shows a collimator used in this measurement. It is a 25 mm-thick lead on which several slits of
5 mm width are implemented with a 50 mm spacing. The collimator can be rotated in 90◦ tomeasure the resolutions of both horizontal and vertical directions. In the pilot runs, the verticalresolution was mainly measured, and horizontal resolution was also measured for a cross check.
In this measurement, a spread of the generation vertex of the γ-rays has to be suﬃciently
small. As shown in Fig. 7.4, a spread of the γ generation vertex leads to a smearing of thereconstructed edge in the position distribution and an overestimation of the resolution. Since
the ratio of the distance between the target and the collimator to that between the collimatorand the LXe detector is about 5 : 1, the size of the smearing is about 20% of the spread of
the generation vertex. From this point of view, the γ-rays from the RMDs are not suitable forthis measurement because the spot size of the muon beam on the stopping target is 1.2 cm forvertical direction, and 4 cm for horizontal direction, and the size of the smearing is comparable orlarger than the a few millimeter resolution to be measured. Instead, the γ-rays of 17.6 MeV fromthe CW-Li were used for this measurement. The spot size of the proton beam for the lithium
excitation is measured to be 0.6 mm for vertical direction, and 0.8 mm for horizontal direction.
Thus, the size of the smearing are less than 0.2 mm for both directions, and are negligible. Even
though the energy of the CW-Li γ-ray is lower than the signal γ-ray, almost the same position
resolution as the signal energy should be obtained because the resolution is not dominated by
the statistical fluctuation and does not depend on the γ-ray energy so much.
Fig. 7.5(a) shows a distribution of the reconstructed hit position. An excess of the event rate
corresponding to each slit is successfully observed. The peak of each slit is fitted by a simulated
hit position distribution smeared by a Gaussian as shown in Fig. 7.5(b), and the sigma of theGaussian is regarded as the position resolution.
Fig. 7.6 shows the estimated resolution as a function of the reconstructed conversion depth forhorizontal direction and vertical direction, respectively. Improvements of the resolutions from

Chapter 7 Position resolutions

94
targetcollimator
inner face

LXe
!79

Satoru Kobayashi

vrec[cm]urec vs vrec
−5

slit3

25

slit2

−10

20

−15

15

−20

10

slit0

slit1

−25

−30
−10

EventsFigure 7.4 Smearing of the reconstructed edge due to the spread of the γ generation vertex [34].

−8

−6

−4

−2

0

2

4

6

5

8

10
urec[cm]0(a)histo_Data_rec_1_us

100

Data
Entries4229
Mean−21.14
Std
Dev
1.469
MC(Smeared)

80
60
40
20
0
−24

−23

−22

−21

−20

−19
−18
vrec[cm](b)

Figure 7.5 (a) Hit position distribution of the γ-rays in the collimator run on the uv plane.
(b) Projected position distribution of a slit fitted by the simualted distribution to evaluate
the resolution.

those in MEG are confirmed for the shallow events.
The resolution is measured to be slightly worse than expected for the deep events (Fig. 7.6).
This kind of degradation only for deep events can be qualitatively due to a statistical fluctuationof the number of photoelectron distribution or a contribution of the noise, but it has not yet been
understood quantitatively. Fig. 7.7 shows the measured degradation of the position resolution.
Because many of the signal γ-rays hit in the shallow region, the degradation of the position
resolution for the deep events does not aﬀect the MEG II branching ratio sensitivity so much.
A qualitative discussion of this eﬀect on the sensitivity will be given in Section 11.2.

7.3 Eﬀect of PDE angular dependence
As mentioned in Section 2.1.3 and 6.2, an angular dependence of the MPPC PDE which cannot
be explained by that of the Fresnel reflection was found. The PDE for the larger incident angle
decreases faster than expected. The light distribution on the MPPCs becomes sharper with this

95

0.9

resolution (cm)resolution (cm)

Chapter 7 Position resolution

MEG II. Data
0.8
0.7

MEG II. MC
MEG . MC

0.6

0.9
MEG II. Data
0.8

0.5

0.4

0.4

0.3

0.3

0.2

0.2

0.1

0.1
2

4

6

8

MEG . MC

0.6

0.5

0
0

MEG II. MC

0.7

0
0

10
12
depth (cm)

2

4

6

(a)

8

10
12
depth (cm)(b)

excess in resolution^2 (cm^2)

Figure 7.6 Position resolution for 17.6 MeV γ-ray as a function of the conversion depthfor (a) horizontal u-direction, and (b) vertical v-direction. The resolutions in MEG are
also shown for comparison.

0.3
0.25
0.2
0.15
0.1
0.05
0

−0.05
0

2

4

6

8

10

12

depth (cm)22
Figure 7.7 Degradation of the vertical position resolution (σmeas.
− σexp.
) as a function of
the conversion depth.

dependence, and the conversion depth reconstructed from its width is biased to be shallower.
This bias can be corrected if we know the angular dependence of the PDE correctly. Since
the dependence measured in the large chamber and that in the LXe detector are found to beconsistent with each other, we can use them for the correction. Nonetheless, an uncertainty ofthis angular dependence may have to be included as a systematics in the physics analysis.
Here we discuss the eﬀect on the physics analysis in the most pessimistic case, assuming that
this unexpected dependence is fully included as systematics. Fig. 7.8 shows the bias in thereconstructed depth when the angular dependence is fully ignored in the reconstruction. The
relative size of this bias is constant at the leading order because the shape of the light distribution
on the inner face and its change by the angular dependence are independent of the depth, in theassumption that the scintillation light comes from a point light source. The conversion depth isreconstructed to be about 10% shallower in this case.
The bias in the conversion depth leads to that in the reconstructed propagation time of the
γ-ray from the decay vertex to the hit position, and that in the reconstructed opening angle

Shift of w (cm)

Chapter 7 Position resolution

96

1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

2

4

6

8

10

12

14

16
w(cm)

Figure 7.8 Expected bias in the reconstructed conversion depth if we fully ignore theangular dependence of PDE (MC).

zγ reconγ truestructedθeγe

Shift of Theta / Sigma of Theta

x
0.8

180

0.6

160
140

0.4

120

0.2

100
0
80
− 0.2
60
− 0.4

40

− 0.6
− 0.8

(a)

20
− 20

− 10

0

10

0

20
u (cm)(b)

Figure 7.9 (a) Reconstruction of opening angle with a bias in depth. (b) Expected shiftof θeγ for the signal events divided by resolution of θeγ as a function of z (MC).

of the positron and the γ-ray. The bias in the propagation time is not an issue since it can bemeasured and corrected by using the CEX data and the RMD events in the energy-sideband of
the physics data. On the other hand, the bias in the opening angle cannot be measured. In the
search of µ → eγ, the opening angle of the positron and the γ-ray θeγ is used to distinguish thesignal event from background events. For the signal event θeγ should be back-to-back, while it
is randomly distributed for the accidental background. As shown in Fig. 7.9(a), the bias in thereconstructed depth leads to a misestimation of the γ emission direction for large |z| and w, andthe reconstructed opening angle of the signal event is deviated from back-to-back. Fig. 7.9(b)shows the shift of θeγ for the signal events. Even if we ignore the dependence on z and w of thisshift, the θeγ resolution will relatively increase only by 1.2%. The degradation of the branchingratio sensitivity will be only about 0.6%, and thus the uncertainty of the angular dependence
will not be crucial for the physics analysis. The degradataion can be even smaller by taking thez and w dependence of the shift into account.

97

Chapter 8

Timing resolution
8.1 Timing reconstruction
In the LXe detector of MEG, the hit timing of a γ-ray was reconstructed from a weighted
average of the timing of each PMT’s waveform. The same algorithm is used in MEG II withmodifications to match with MPPC signals. The timing of a γ-ray at the hit position tγ isreconstructed from a minimization of the χ2 defined as follows:∑χ2 :=χ2pm ,
pm(tpm − tcorr − tγ )2,σ2
tcorr := tprop + twalk + toﬀset .
χ2pm :=

Here, tpm is the timing of each photosensor’s waveform, where pm stands for both the MPPCs
and the PMTs. tprop is the propagation time from the reconstructed γ hit position to eachphotosensor, twalk is the time walk eﬀect, toﬀset is the time oﬀset of each channel due to theindividual diﬀerence of the cable length and electronics, and σ is the precision of the timing
information of this channel. These parameters are estimated beforehand, including its dependence on the number of photoelectrons. The γ-ray timing at the µ → eγ decay vertex, which
is used for the MEG II analysis, is calculated by subtracting γ-ray propagation time from thereconstructed decay vertex to the reconstructed γ hit position. To eliminate the pileup eﬀect,
timing information of the photosensors whose chi-square χ2pm is above a threshold of 10 are
removed from the reconstruction.
Even though the timing information of all photosensors can contribute to the timing resolution,
only a part of them has a suﬃcient signal amplitude to have a non-negligible timing resolution.
Typically, contributions from channels below 100 photoelectrons are negligible. The timing
resolution achievable with the limited channel readout in the 2019 run is good enough to evaluate
the resolution achievable with the full channel readout, if the γ-ray events hitting the central
region of the readout area are selected.

98

Before noise reduction

35
After noise reduction

30
25
20

amplitude [V]Amplitude (a.u.)

Chapter 8 Timing resolution

×10−3
0.3
0.2
0.1
0

15

−0.1

10

−0.2
−0.3

5
0
0

−0.4

100

200

300

400
500
600
Frequency (MHz)

(a)

0

10

20

30

40
time [sec]

×10−9

(b)

Figure 8.1 (a) Frequency spectrum of a summed waveform of all MPPC channels in arandom trigger event. Calculated by a Fourier transformation. (b) A typical waveform
template of the noise synchronous to the system clock.

8.2 Waveform analysis
Noise reduction
Since the timing extraction from a sensor waveform is sensitive to high frequency noises, it
is useful to reduce the noise as much as possible. As is described in Section 1.8, a dedicated
DAQ system is being developed for MEG II, and several new functionalities are integrated on
one readout board in that system. As a drawback of this integration, high frequency noise levelis increased from MEG.
To improve this situation, noise reduction algorithm have been implemented in the oﬄine
analysis. Since the development of DAQ was ongoing, and the noise situation was diﬀerent foreach year, diﬀerent algorithms were applied. A reduction algorithm used for 2019 data is given
as an example. Fig. 8.1(a) shows a frequency spectrum of a random trigger waveform. Peaks
at 40, 120, 160, 240, etc. MHz are clearly seen, and they are coming from the readout electronics
whose system clock is 80 MHz. Since these components should be synchronized to the phase of
the system clock, they can be reduced if the phase of the system clock to the obtained waveform
is known. Since this phase fluctuates event-by-event, one channel on each DRS chip is assigned
to measure the sine-wave generated by the system clock and to extract its phase. A templateof the synchronous noise to the system clock (Fig. 8.1(b)) is generated for each channel bytaking an average of the waveforms in O(1000) random trigger events. The noise in each eventis reduced by subtracting this template.
The noise spectrum after the subtraction is shown in Fig. 8.1(a). The peaks from the system
clock are removed. Table 8.1 summarizes the noise level. The size of the reduction is the mostobvious in 2017 data because part of the noise reduction is implemented in the hardware from2018 based on the successful reduction of this thesis. Even after the reduction, the noise level isstill worse than 0.35 mV observed in MEG.
To further reduce the noise, a digital low-pass filter (moving average filter of adjacent threeChapter 8 Timing resolution

99

Table 8.1 Noise level of each channel. Average of all the readout channels is shown. The
noise level is defined as a standard deviation of the random trigger waveform by the 1.2 GHz
sampling.

Yearnoise level (without reduction)

noise level (with reduction)

2017

1.7 mV

0.8 mV

2018-190.8 mV

0.7 mVnzoom iamplitude

thresholdextracted
timingFigure 8.2 Timing extraction from the waveform. The threshold is defined as “amplitude×
r + baseline”.

points, a cutoﬀ frequency of 177 MHz) is also applied for the MPPC waveforms. The applicationof the digital lowpass filter is a trade-oﬀ between a reduction of the high frequency noise and asmearing of the sensor waveforms. The strength of this filter is decided to get the best timing
resolution.
Timing extraction
The timing from each waveform is extracted by using the constant fraction method in theoﬄine analysis shown in Fig. 8.2. In this method, a threshold is defined to be proportional to
the signal amplitude as “amplitude × r + baseline”. The timing of each waveform is obtained
from the crossing point of this threshold. This method has an advantage that the time walk issuppressed. The timing resolution is dependent on the constant fraction r, and the fraction is
optimized to get the best resolution as discussed in the next section.

8.3 Single channel performance
Calculation of calibration parameters
Since the γ-ray hit timing tγ is reconstructed from a combination of all channels information,
its resolution is much better than the resolution of each channel. Thus the timing resolution ofeach channel σ can be estimated from the spread of the distribution of tpm − tprop − tγ , if thetγ is known. The time walk twalk can also be estimated from the mean of the distribution.

time residual (sec)

Chapter 8 Timing resolution

20 ×10

100

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.)0timing resolution (ns)time walk (ns)Figure 8.3 tpm − tprop − tγ as a function of the number of photoelectron (MPPC LotA,
5% threshold). 116 channels × 1000 events are overlaid.

1.4
1.2
1
0.8

2
1.8
1.6
1.4
1.2

0.6
1
0.4
0.8
0.2
0.6
0
0.4
0.2
0.2
0.4
0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16
0.18
1/sqrt(# of p.e.)

0
0

(a)

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16
0.18
1/sqrt(# of p.e.)(b)

Figure 8.4 Measured (a) time walk twalk , and (b) timing resolution σ of an MPPC as a√function of 1/ number of p.e..

The σ and twalk are estimated from the background γ events above 47 MeV in the 2019 run,by reconstructing tγ from the obtained parameters iteratively. Fig. 8.3 shows tpm − tprop − tγ asa function of the number of photoelectrons, where tprop is calculated from the distance from thereconstructed hit position to each photosensors divided by the eﬀective velocity of light in theLXe (11.5 cm/ns). Fig. 8.4(a) and Fig. 8.4(b) show the mean and the standard deviation of theslice along y-axis of Fig. 8.3, which are interpreted as twalk and σ respectively. For the MPPCs,
these parameters are calculated for each production lot since they can have a diﬀerent waveform
shape due to the diﬀerent afterpulse probabilities. The outer PMTs and the side PMTs aretreated separately, since their resolutions are found to be diﬀerent. The mean of tpm − tprop − tγ
on the limit of infinite number of photoelectrons has a channel-by-channel diﬀerence, and thisis interpreted as a time oﬀset of each channel toﬀset .

101

2

Timing resolution (ns)Timing resolution (ns)

Chapter 8 Timing resolution

1.8
1.6
1.4
1.2

1
0.9
0.8
0.7
0.6

1

0.5

0.8

0.4

0.6

0.3

0.4

0.2

0.2

0.1

0
0

0.05

0.1

0.15

0.2

0.25

0.3
0.35
constant fraction

0
0

0.05

0.1

(a)

0.15

0.2

0.25

0.3
0.35
constant fraction(b)

Figure 8.5 The timing resolution σ of a sensor, as a function of the constant fraction r
used in timing extraction. Resolution of 200 photoelectron signals is shown. (a) MPPC
Lot A, (b) Side PMT.

Timing resolution of each channel
Fig. 8.5 shows the timing resolution of an MPPC and a PMT as a function of the constantfraction r. Lower thresholds gives us better resolutions thanks to the smaller statistical fluctuation for the first arriving photon timing. Due to the eﬀects of the noise and the transit
time spread which become dominant at the lower threshold, there is an optimal threshold which
gives best timing resolution. Further details on the dependence on the threshold are given in
Appendix B. From these plots, the constant fractions are set to 5% for MPPC, and 10% for
PMT. Because this dependence on the fraction was not considered in MEG and MEG II design
and the fraction was set to 30% in their studies, the optimized threshold leads to a better tγ
resolution and hence a better MEG II branching ratio sensitivity.
Time oﬀset of each channel
Fig. 8.6(a) shows the toﬀset distribution obtained for the PMT and the MPPC channels. The
distribution of the measured time oﬀset of the PMTs is wider than that of the MPPCs. Thisis likely due to the individual diﬀerence of the cable length, since the PMT signal cables arereused from MEG and the treatment at both ends are modified for MEG II. The time oﬀsets of
the MPPCs are shown in Fig. 8.6(b), and some dependence on the readout electronics channel
is observed.
The time oﬀset of each MPPC channel is also estimated by another independent method [40].
The MPPCs are illuminated by an intense LED light, and the time oﬀset is extracted from thetime diﬀerence of each channel’s waveform. Dependences on the incident angle and the distancefrom each LED to each MPPC, and an eﬀect of the time walk are corrected. Fig. 8.7 shows
a comparison of the time oﬀsets estimated from the two methods, and a clear correlation isobserved.

102

Time offset (ns)

Chapter 8 Timing resolution

MPPC

35

PMT
30
25

1
0.8
0.6
0.4
0.2

20

0
−0.2

15

−0.4

10

−0.6
5
0
−2

−0.8
−1.5

−1

−0.5

0

0.5

1

−1
0

1.5
2
time offset (ns)

100

200

300

(a)

400

500

600
700
800
electronics channel number(b)time offset by gamma (ns)Figure 8.6 (a) Measured time oﬀset of each channel. (b) Time oﬀset of the MPPCs as afunction of the electronics channel number.

1
0.8
0.6
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
−1
−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4
0.6
0.8
1
time offset by LED (ns)Figure 8.7 Time oﬀset estimated from gamma (in this thesis) vs. time oﬀset estimatedfrom LED (in [40])8.4 Detector performance
There are three variables which describe the detector timing resolution. One is the absolutetiming resolution which is a spread of the diﬀerence between the reconstructed timing and itstrue value. This is the resolution directly related to the analysis of the µ → eγ search. In
the MEG LXe detector, the absolute resolution was directly measured in the CEX run. In a
CEX event, two coincident γ-rays are emitted. The timing of one γ-ray measured by plastic
scintillators was used as a time reference. However, the data-taking of the CEX has not yet
been performed for MEG II (Section 3.1), and its direct measurement is still not possible. In
this thesis, instead of the direct measurement, the absolute resolution is estimated from thesimulation which is validated by the other two resolutions measured with data.
The second resolution is the intrinsic timing resolution estimated from an even-odd analysis.
In the even-odd analysis, photosensors are subdivided into two groups (e.g. sensors with evenchannel numbers, and odd channel numbers), and the timing reconstruction is performed independently for both groups. The intrinsic resolution is estimated from the diﬀerence of the103

resolution (sec)

Chapter 8 Timing resolution

140
120

60 ×10

−12

50

40

100
80

30

60
20
40
10
20
0

−0.2

−0.15

−0.1

−0.05

0

0.05

×10
0.1
0.15
0.2
time (Even - Odd)/2. [sec]

−9

0
0

2

(a)

4

6

8

10

12
depth (cm)(b)

Figure 8.8 (a) Distribution of tγ (even)/2 − tγ (odd)/2 of the background γ-ray data. Intrinsic timing resolution is estimated to be 40(1) ps from this plot. (b) Intrinsic resolution(blue) and combined resolution of all photosensors (red) as a function of the conversion
depth of γ.

reconstructed timings. This intrinsic resolution is a part of the absolute resolution. For example,
a precision of the propagation time decided by the hit position resolution is included only inthe absolute resolution. An eﬀect from a coherent noise is also included only in the absolute
resolution.
The third one is the combined precision σtotal of all photosensors, defined as follows:22
2
1/σtotal:= 1/σMPPC+ 1/σPMT∑
2
1/σMPPC
:=
1/σ 2

(8.1)
(8.2)

MPPC

2
1/σPMT:=∑1/σ 2 ,

(8.3)

PMT

where σ is the timing resolution of each channel estimated by the method mentioned above.
This combined precision should be consistent with the intrinsic resolution.
The intrinsic resolution and the combined precision are estimated from the background γ
events above 47 MeV in the 2019 run. Fig. 8.8(a) shows the distribution of the diﬀerence
between γ timing reconstructed from the even channels and that from the odd channels. Intrinsic
resolution of 40(1) ps is achieved. The intrinsic resolution with MEG’s threshold (r = 30%) in
this data set is estimated to be 56(2) ps. Thus 30% improvement is achieved by the threshold
optimization. As shown in Fig. 8.8(b), the combined precision is found to be consistent with
the intrinsic resolution including its dependence on the conversion depth.
These results are compared with the simulation. To correctly introduce the real noise situation
into the simulation including its coherence between channels, the measured random trigger
waveforms are added to the simulated waveforms. The estimation of the calibration parameters
and the reconstruction of the timing are applied to the simulated waveforms in the same way
as data. Table 8.2 compares obtained detector resolutions with diﬀerent conditions. MC anddata are consistent with each other with a few picosecond precision. Absolute timing resolution

Chapter 8 Timing resolution

104

is estimated to be 53 ps by this simulation, which is better than the 62 ps resolution achieved in
MEG.
Table 8.2 Comparison of the detector timing resolution between MC and data.

VariableMC

data

Combined precision (MPPC only)

71 ps

71 ps

Combined precision (PMT only)

57 ps

55 ps

Combined precision (MPPC and PMT)

44 ps

43 ps

Intrinsic resolution (MPPC and PMT)

43 ps

40 ps

105

Chapter 9

Energy resolution
In this chapter, the performance of the energy measurement by the LXe detector is discussed.
In terms of the upgrade from MEG, there are two aspects to be checked in MEG II.
One is a conversion depth dependence of the energy resolution. In MEG, due to the nonuniformity of the scintillation readout, the energy resolution for the shallow events was worse
than that for the deep events. This depth dependence is expected to disappear, and the resolution for the shallow events is expected to improve, thanks to the improved uniformity realized
by the MPPCs as explained in Section 1.6.3.2.
The second one is a consistency with the simualted energy resolution. The measured energy
resolution was worse than expected in MEG, and there was an unknown contribution in the
resolution as large as 1.5% (Section 1.6.3.2). The reason of this unknown contribution has notbeen understood yet, and it can also remain in MEG II. Since the energy resolution in MEG II
expected from the simulation is only about 0.7%, this unknown contribution can become adominant contribution. In an optimistic scenario, this contribution is related to the behaviorof the PMTs, and gets smaller in MEG II. In a pessimistic scenario, this contribution is due tosome intrinsic property of the LXe or that of our LXe detector, and remains unchanged.
In the Section 9.1, the energy reconstruction algorithm, which is common both in MEG and
MEG II, is summarized. A study on the unknown contribution obsereved in MEG is given
in Section 9.2. The measured energy resolution in MEG II from the pilot runs is shown in
Section 9.3.

9.1 Energy reconstruction
The energy of the γ-ray Eγ is reconstructed from the weighted sum of the detected numberof photons on each photosensor.
Eγ = C ×∑

Npho,i × wipm

Npho,i = Qi /Gaini /ECFi /QEi

(9.1)

The number of photons Npho,i on each sensor is calculated from the integrated charge Qi ofeach sensor waveform. This is a sum with a set of weights wi defined for each sensor to achieveChapter 9 Energy resolution
uniform response in the whole detector. This weight is calculated from the size of the insensitive
area around each sensor divided by the size of its sensitive area. A factor C is used to convert thesum of the number of photons to the energy. In MEG, this is calculated from the monochromatic
γ-ray sources of diﬀerent energies. In the analysis of the MEG II pilot runs, it is defined fromthe 17.6 MeV peak in the CW-Li data, which is the only available monochromatic data for thepresent. An oﬀset of the reconstructed energy is monitored independently from the random
trigger data.
A hit position dependence of the reconstructed energy is evaluated from the monochromatic
γ-ray data, and is used for a further correction of the non-uniformity. This is to correct possible
errors in the calibrated photosensor responses, and to correct a position dependent photon
collection eﬃciency especially in the partial readout of the detector in the pilot runs. A correction
by the solid angle from the hit position subtended by the PMTs applied in MEG is no longer
adopted in MEG II.
It is often useful to define the energy reconstructed from a part of the photosensors. For
example, “energy from MPPC” stands for the energy reconstructed from a weighted sum of the
MPPC signals. Energies from the MPPCs, the PMTs, the even channels, the odd channels, etc.
are used in this chapter.

9.2 Unknown contribution in MEG
As is mentioned in the previous section, the unknown contribution observed in MEG can be
crucial in the energy resolution in MEG II. However, its cause has been poorly discussed in theprevious studies, and we review it in this section.
Fig. 9.1(a) shows the measured energy resolution in MEG as a function of the energy. The√
resolution follows a combination of a constant term and a 1/ Eγ term. However, the energy√
dependent term in data is larger than that in MC by a factor of about 2.5 (= 108/17). This
discrepancy of the energy dependent term is 1.3% for the signal γ-ray, and will explain the mostof the observed 1.5% unknown contribution.

√
The simplest hypothesis to explain the discrepancy proportional to the 1/ Eγ is to assume alarger statistical fluctuation of the detected number of photoelectrons on the PMTs. In the ideal
case, energy resolution of this detector is not aﬀected by the statistical fluctuation. By using
the PMTs with a 22% QE, the total detected number of photoelectrons becomes about 3.9 × 104
for the 52.8 MeV γ-ray, and the statistical contribution in the energy resolution is expected to√
be 14/Eγ (MeV)%. Thus, most of the energy dependence in the simulated resolution is dueto this statistical fluctuation eﬀect. There are two possibilities which can enlarge this statisticalcontribution in data. The first is that the ENF of the PMTs is as large as 6.4. As is discussed in
Section 2.1.3, a double photoelectron emission from a single VUV photon is reported for someof the VUV-PMT, which can increase the ENF of the PMTs. The second is the smaller QEof the PMT. If the real QE of the PMTs is 3.5%, while it is measured to be 22%, statisticalcontribution can become larger by a factor of 2.5. It is notable that this assumption is not

106Chapter 9 Energy resolution
consistent with independent QE measurements by HPK.
In this thesis, these hypotheses are tested by directly evaluating the statistical contribution
from the PMTs by an even-odd analysis. The energies of the γ-ray from the even channels
and the odd channels are reconstructed independently, and the resolution is estimated from an
event-by-event fluctuation of their diﬀerence. In the case of the large ENF or the low QE of thePMTs, its statistical eﬀect surely appears in the even-odd resolution because it is an independent
stochastic process on each PMTs. Since other fluctuations can also contribute to the even-odd
resolution, the even-odd resolution gives us an upper limit on the statistical fluctuation. For
example, if the hit position of the γ-ray is too close to the PMTs, detected number of photons
on an even channel and that on an odd channel can be diﬀerent. This diﬀerence fluctuates
depending on the hit position and shower direction, and contributes to the even-odd resolution.
Fig. 9.1(b) shows the measured diﬀerence of the energy from even channels and odd channels
for CW-Li γ-ray. Here the PMTs located on the outer face or the third–sixth columns of thelateral faces, and the events hitting rather deep region 3 < w < 4 cm are used, to suppress
the other contribution by rejecting PMTs near the γ hit position. The even-odd resolution ismeasured to be 1.46% at the statistics of 1.06 × 104 photoelectrons. The enhancement of the√statistical contribution from the PMTs is estimated to be 1.50 (= 1.46%× 1.06 × 104 ) at most.
This is too small to explain the observed degradation by a factor of 2.5.
As a consequence of this observation, it turns out that the unknown contribution is not due
to a stochastic process on each PMT. Another possibility like unexpected non-uniformity of thereadout by an incident angle dependence of the PMT QE also seems not the case, since its eﬀect
should be independent of the γ-ray energy at the leading order. Therefore, the PMT behavior
is not favored as a source of the unknown contribution, and replacing the PMTs to the MPPCs
does probably not help its reduction.

9.3 Energy measurement performance in MEG II
9.3.1 Expected energy resolution in pilot run
In the pilot runs, only a quarter of the photosensors was read out due to the limited numberof channels, and the energy of γ-ray was reconstructed from the sum of their signals. To ensurethat the most of the signals are contained in the readout region, following event selections areapplied for the energy resolution study. Events hitting the central area of the MPPC readout
region shown in Fig. 9.2 (|u| < 9 cm and |v + 17| < 9 cm) are selected. Events hitting very deep
region (w > 12 cm) are rejected, since their scintillation light distributes wider than the MPPC
readout area. Cosmic-ray events are also rejected by applying a selection of “Eγ (MPPC) >Eγ (PMT)/6”. This selection works since the cosmic-rays do not enter the LXe detector fromthe inner face and a fraction of the observed charge on the MPPCs becomes smaller than thatfor the γ-rays.
Fig. 9.3 shows the simulated energy spectrum for the monochromatic signal γ-rays. Here, the107Resolution [%]Chapter 9 Energy resolution

108

6

60

5

MEG Data : 108/Eγ (MeV)+1.22 %4

MEG MC : 17/Eγ (MeV)+0.7 %

50

2

40

3

30

2

20

1

10

0
0

20

40

60

80

100

120

140

0
−0.1

−0.05

0

0.05
0.1
0.15
E(even)-E(odd) / (E(even)+E(odd))

Energy [MeV]

(a)

(b)

Figure 9.1 (a) Energy resolution in MEG as a function of the γ-ray energy. The resolution
for deep events (w > 2 cm) is shown where the unknown contribution is more obvious. The
measured resolution (red) is taken from [43]. The expected resolution from MC (blue) is
added by the author. (b) Diﬀerence of reconstructed energies for even channel and odd
channel in the CW-Li data in MEG, (Eγ (even) − Eγ (odd))/(Eγ (even) + Eγ (odd)). Events
hitting in a local region “|u| < 10 cm & |v| < 10 cm & 3 < w < 4 cm” are selected. Due tothe limitation of the granularity of the readout, the electromagnetic shower looks diﬀerently
from the even channels and the odd channels, and the peak position is slightly deviatedfrom zero.

100
80
60
40
20
0
20
40
60
80
100
100

Figure 9.2 Analysis area in run 2019. Green shows MPPC readout area, and red box(18(u) × 18(v) cm2 ) shows the area used for the energy resolution estimation. Each green
box in the right figure corresponds to a group of 4 × 4 MPPCs.

measured photosensor performance is simualted including the lower PMT gain and the lower
MPPC PDE. The energy resolution is defined from the spread of the upper side of this spectrum
as shown in Table 9.1. The same energy resolution is achievable with the limited channel readout
by applying the event selection. The low energy tail of this spectrum is caused by the energy
escape from the electromagnetic shower and the energy loss before reaching the detector, and isalso not aﬀected by the readout channels.

Chapter 9 Energy resolution

140

Full channel readout

120

Limitted channel readout

109

Full channel readout

250
Limitted channel readout

200

100
80

150

60
100
40
50

20
0
48

49

50

51

52

53

54

55
56
Energy (MeV)

0
48

49

50

51

(a)

52

53

54

55
56
Energy (MeV)(b)

Figure 9.3 Reconstructed energy spectrum in the simulation for signal 52.8 MeV γ-ray
after the event selection described in the main text. (a) Shallow event (w < 2 cm), (b)deep event (w > 2 cm).

Table 9.1 Expected energy resolution in MEG II for the signal 52.8 MeV γ-ray

Full channel readout

Limited channel readoutw < 2 cm

0.72(1)%0.73(1)%

w > 2 cm

0.70(1)%0.76(1)%

9.3.2 Energy oﬀset
In the pilot run, a fluctuation of the reconstructed energy oﬀset was found. The oﬀset fluctuation was monitored by the random trigger. Fig. 9.4(a) shows the averaged random trigger
waveforms of a channel measured at diﬀerent temperatures of the readout electronics. A slopeof the waveforms correlated with a temperature can be seen. This is probably due to a temperature dependence of a leakage current of the DRS cells. As is described in Section 1.8, in the
WaveDREAM system a waveform is stored in the DRS cells when the trigger is fired and thecharge in each cell is read out in the order of time. Some part of the stored charges can be lost
due to the leakage current from the cells depending on the elapsed time before the readout, andthis leads to a slope of the waveforms. The leakage current is known to be dependent on thetemperature of the electronics which is aﬀected by the temperature of the detector hut. The
heat generation at the amplifiers implemented on the WDBs, which can be turned on and oﬀ
for each purpose, is another source of the temperature fluctuation.
To correct this oﬀset, the temperature of each DRS chips was read out during the data-taking.
A template of the slope like Fig. 9.4(a) was generated at each temperature for each channel,
and is used for the correction. Fig. 9.4(b) shows the energy oﬀset history in the run 2018. The
fluctuation in the peak-to-peak is reduced from 0.9 MeV to 0.1 MeV by this correction, and asuﬃcient stability for the search of µ → eγ is achieved*1 . Additionally, an air-conditioning*1 Long term stability of the γ-ray energy was measured to be 0.2% in MEG. It was included as a systematics

in the analysis, and its eﬀect on the branching ratio sensitivity was negligible.

amplitude (V)Chapter 9 Energy resolution

110−0.0005−0.001

before correction
after correction

MeV−0.0015−0.002−0.0025−0.00353.5 deg
54.5 deg
55.5 deg
56.5 deg
57.6 deg
58.5 deg
−0.8

−0.7

−0.6

−0.5

−0.4

−0.3

×10
−0.1
0
time (sec)

−0.2

−6

(a)

(b)

×10

3

20

240

18
16

220

14

200

12
180

10
8

160

6

140

4
120
100

2
−8

−6

−4

−2

0

2

4

6

(a)

8
u (cm)

0weighted sum of number of photon (a.u.)weighted sum of number of photon (a.u.)

Figure 9.4 (a) Averaged random trigger waveforms of a channel at diﬀerent temperature ofelectronics. Declining slope is observed at higher temperature due to larger leakage current.
(b) History of energy oﬀset in run 2018 calculated from the random trigger waveforms of
all read out channels.

×10

6

18
16

11

14

10

12
9
10
8

8

7

6

6

4
2

5
−8

−6

−4

−2

0

2

4

6

8
u (cm)

0(b)

Figure 9.5 Reconstructed γ-ray energy as a function of the γ-ray hit position for shallow
events (w < 1.5 cm). The same scale of the y-axis is used for both plots. Measured
spectrum of 17.6 MeV γ-ray from CW-Li is shown. The energy before correcting the hit
position dependence is shown. (a) MEG, (b) MEG II.

system was introduced in the detector hut from 2019. This improved the daily temperaturefluctuation from about 2 K in the run 2018 to about 0.6 K in the run 2019 (peak-to-peak).

9.3.3 Uniformity of the readout
In MEG, there was a periodical bias on the reconstructed energy for the shallow events correlated with the PMTs placed with 6.2 cm spacing. This bias is expected to be reduced in MEG II
thanks to the uniformity of the readout realized by the MPPCs. Fig. 9.5 compares a position
dependence of the reconstructed energy measured in MEG and MEG II. An improvement in theuniformity is observed in MEG II.

Chapter 9 Energy resolution

111

450
160

400

140

350

120

300
250

100

200

80

150

60

100

40

50

20

0
12

13

14

15

16

17

18

19
20
Energy (MeV)

0
−4

−3

−2

(a)

−1

0

1

2

3
4
Energy (MeV)(b)

Figure 9.6 (a) Reconstructed energy spectrum of the CW-Li. (b) Reconstructed energyof the random trigger waveform. This is calculated from a random trigger run, and theeﬀect of the oﬀset fluctuation (Section 9.3.2) is negligible in one run.

9.3.4 Energy resolution at low energy (17.6 MeV γ-ray)
The energy resolution for the 17.6 MeV γ-ray was measured by using the CW-Li (Section 2.5).
This measurement is useful to know the unknown contribution which is more obvious for the
low energy γ-rays, though it does not directly give us the resolution for the signal energy γ-ray.
Fig. 9.6(a) shows the reconstructed energy distribution after the non-uniformity correction. Theenergy resolution is estimated to be 3.1(1)% from the 17.6 MeV peak. This is much worse than
the 1.0% resolution expected from the MC.
A part of the diﬀerence between the MC and the data is due to a noise from the readout
electronics. Fig. 9.6(b) shows the reconstructed energy distribution of the random trigger waveform, and its spread is 0.21 MeV. This corresponds to 1.2% of the CW-Li energy. Thus, theintrinsic energy resolution of the LXe detector should be 2.8(1)%. This is consistent with the
2.8% resolution achieved in MEG for the deep events (w > 2 cm). The unknown contribution
seems still existing in MEG II.
Fig. 9.7 shows the conversion depth dependence of the fitted spread of the 17.6 MeV peak.
The spread of the peak is aﬀected by an energy escape from the electromagnetic shower because
the escape peak at 17.1 MeV is smeared by the energy resolution of about 0.5 MeV. The energy
escape can happen more often for the shallow events, and the fitted spread becomes larger for
those events, even if the energy resolution is independent of the conversion depth. Fig. 9.7
also shows the expected spread of the 17.6 MeV peak assuming an additional unknown term of
2.6% independent of the depth. The observed depth dependence can be explained by a constantenergy resolution.
Possible causes of the worse energy resolution are examined, and the results are summarized
below.

energy resolution (%)

Chapter 9 Energy resolution

112

5
Data

4.5
MC + 2.6% contribution

4
3.5
3
2.5
2
1.5
1
0.5
0
0

2

4

6

8

10
12
conversion depth (cm)

16

90

14

80
70

12

60

10

Energy (MeV)

Energy (MeV)

Figure 9.7 Fitted sigma for the 17.6 MeV peak of CW-Li. Observed depth dependence isconsistent with an expectation from the simulation.

90

16

80
14
70
12
60
10
50

50
8

8

40

40
6

30

4

20

6

20
10

2

10

2

0
0

0

0
0

2

4

6

8

(a)

10

12
depth (cm)

30

4

2

4

6

8

10

12
depth (cm)0(b)

Figure 9.8 Measured energy of CW-Li as a function of the conversion depth, (a) only fromMPPC signals, (b) only from PMT signals.

MPPC and PMT
The reconstructed energy only from the MPPCs and the PMTs are compared between the
MC and the data. If we decompose the γ-ray energy for the CW-Li into the MPPC energy
and the PMT energy, each of them have a conversion depth dependence as shown in Fig. 9.8.
Fig. 9.9 shows their reconstructed energy spectra after correcting the dependence on the conversion depth. The spread of the upper side of the measured spectrum is larger than MC for
both energies. Therefore, the degradation of the resolution does not seem to depend on thephotosensor type.
Stability
An instability of the signal gain can lead to a worse resolution. Fig. 9.10 shows the fitted
CW-Li peak as a function of the time. No significant fluctuation is observed, and cannot be areason of the worse resolution.

Chapter 9 Energy resolution

113

Data

350

Data

600

MC

MC

300

500

250

400

200
300
150
200
100
100

50
0
2000

2200

2400

2600

2800

3000

3200

×10
3400 3600 3800 4000
sum of number of photon

3

0
3000

3500

4000

4500

5000

(a)

5500

×10
6000
6500
7000
sum of number of photon

3(b)Energy (MeV)

Figure 9.9 The energy spectrum of CW-Li, (a) only from MPPC signals, (b) only from
PMT signals. The excess of the both measured spectra in the lower energy region are justbecause the event rate of 14.7 MeV peak is not correctly simulated.

19.5
40
19
35

18.5

30

18

25

17.5

20

17
16.5

15

16

10

15.5

5

15

26-20h26-22h27-00h27-02h27-04h27-06h27-08h27-10hTime

0Figure 9.10 Reconstructed energy of the CW-Li as a function of time. Red markers show
the fitted peak.

9.3.5 Energy resolution at signal energy (52.8 MeV γ-ray)
The energy resolution for the signal energy γ-ray is evaluated. The background γ-rays whichmainly come from the RMDs on the target are used, instead of the quasi-monochromatic 55 MeV
γ-ray from the CEX used in MEG.
The measured spectrum of the background γ-ray in the run 2019 is fitted by an expected
spectrum. The fit is performed by a binned-likelihood method. The likelihood L(p), and its
negative log likelihood nll are defined as
L(p) :=

N
−1
∏
b=0

fb (p)hb e−fb (p),hb !

nll := − ln L(p) = −N−1∑{hb ln fb (p) − fb (p)} + const. ,b=0where {hb |0 ≤ b < N } is a N -bin histogram of the measured spectrum, and {fb (p)|0 ≤ b < N }is that of the expected spectrum. The expected spectrum is a function of the fit parametersChapter 9 Energy resolution114

p = (N orm, Scale, σ):∫f (x|p) = N orm ×

fMC (x/Scale + s)e−s /2σ ds + fCR (x).
22

The simulated energy spectrum fMC is convoluted with an additional resolution σ. An energy
scale Scale and an overall rate N orm are also considered as nuisance parameters. A contribution
from the energy spectrum without the beam usage fCR is also included based on the spectrum
measured without muon beam*2 .
Fig. 9.11 shows the background spectrum measured at the reduced intensity (0.7 × 107 µ/s)
and at the MEG II intensity (7 × 107 µ/s), together with the expected spectra. Fig. 9.12 show
the excesses of the negative log likelihood from their local minimum. The best estimate of thefitted parameters are
Scale = 1.013(3), N orm = 1.16, σ = 1.6(2)%(for Reduced intensity),

Scale = 1.007(1), N orm = 1.13, σ = 1.5(1)%(for MEG II intensity).

The larger uncertainty of the reduced intensity data is just due to the limited statistics. The
fitted energy scales of the background γ-rays agree with that of the CW-Li γ within 1% precision.
The uncertainty in the energy scale will be reduced in the physics data-taking by the CEX
measurement whose energy (55 MeV) is much closer to the signal energy (52.8 MeV) than the
CW-Li (17.6 MeV). The overall rate of the background γ-rays estimated from the fitting is
10–20% higher than that expected at the MEG II beam intensity. This is likely due to the beam
rate higher than the MEG II intensity as mentioned in Section 3.1.3. The energy resolution
is estimated to be 1.7(2)% for the reduced intensity, and 1.7(1)% for the MEG II intensity,
respectively, from a combination of the fitted σ and the 0.7% energy resolution in the simulation(Section 9.3.1). These resolutions should include the noise contribution, but it is only 0.4%
for the signal energy γ-ray (Fig. 9.6(b)) and is negligible. These are consistent with the 1.8%
resolution in MEG for the deep events. This implies that the unknown contribution remains in
MEG II.
To estimate the depth dependence of the resolution, the events are grouped into three categories (0 < w < 2 cm, 2 < w < 5 cm, and 5 < w < 12 cm), and the spectra are fitted independently. To consider a possible error of energy scale depending on the conversion depth, thenuisance parameters are also fitted independently. The energy spectra of the MEG II intensity
are used in order to ensure the suﬃcient statistics. Fig. 9.13 shows the result. An improvementof the energy resolution for the shallow events is confirmed.

9.3.6 Even-Odd resolution
As is done for MEG data, even-odd energy resolution is estimated also for MEG II. Since the
MPPCs and the PMTs can have diﬀerent ENF, the resolution of the MPPCs and the PMTs
are estimated separately. It is estimated both from the CW-Li data and the background γ-ray*2 It mainly comes from cosmic rays, and neutrons from the accelerator captured by the LXe.

115

Event rate (Hz)Event rate (Hz)

Chapter 9 Energy resolution

Measured spectrum

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

10

1

10 2

10

Measured spectrum

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

1

10 1

3

2

10

42

44

46

48

50

52

54

56

42

Energy (MeV)

44

46

48

(a)

50

52

54

56

Energy (MeV)(b)

additional sigma (%)

5

5
2

2

4.5

1.9

4

1.8

3.5

1.7

3

1.7

3

1.6

2.5

1.6

2.5

1.5

2

1.5

2

1.4

1.5

1.4

1.5

1.3

1

1.3

1

1.2

0.5

1.2

0.5

1.1
1.006

0

1.1

1.008

1.01

1.012

1.014

1.016

1.018
energy scale

4.5

1.9

4

1.8

3.5

1

1.002

1.004

(a)

1.006

1.008

1.01

1.012
energy scale(b)

Figure 9.12 Excess of the doubled negative log likelihood (2×nll) from its local minimum.
(a) At the reduced intensity, (b) at the MEG II intensity.

Resolution (%)

additional sigma (%)

Figure 9.11 Measured energy spectrum of the background γ-ray fitted by the expected
spectrum. The expected spectrum at better and worse resolution than best fit are also
shown for comparison. (a) At the reduced intensity, (b) at the MEG II intensity.

3

MEG measured
MEG II measured
MEG II expected

2.5

2

1.5

1

0.5

0
0

2

4

6

8

10

12

Conversion depth (cm)Figure 9.13 Energy resolution as a function of the conversion depth estimated from background γ-rays at MEG II intensity.

0Resolution(%)

Chapter 9 Energy resolution

3

116

MPPC
PMT
1/sqrt(# of p.e.)

2.5

2

1.5

1

0.5

0
0

5000

10000 15000 20000 25000 30000 35000 40000 45000 50000

number of photoelectron

Figure 9.14 Even-odd energy resolution in MEG II as a function of the number of photoelectrons estimated from the partial sums of the CW-Li events and the background γ
events. The measured energy resolutions for CW-Li and background γ-rays are also shownas black data series for comparison. Three gray lines correspond to the ENF of 1.22 , 1.42 ,and 3.72 , respectively.

data, and events hitting a selected local region are used. In addition to the energy from theeven channels and the odd channels, the energies from many kinds of partial sums are utilized
to estimate the resolution at diﬀerent photoelectron statistics.
The results are shown in Fig. 9.14, and the ENF is estimated to be as large as 2.0 for both
the MPPCs and the PMTs, which can be due to the stochastic process in the photosensors as
explained in Section 2.1.3. Similar to MEG, this is too small to explain the observed unknown
contribution.

9.4 Summary and discussion
The energy resolution was measured by using the CW-Li γ-rays and the background γ-rays.
Thanks to the better uniformity realized by the MPPCs in MEG II, the energy resolution for theshallow events has been improved. On the other hand, the energy resolution for the deep events
shown in Fig. 9.15 is not improved from that in MEG. This is probably due to the unknown
contribution also observed in MEG.
Though the cause of the unknown term has not been understood, there are several possibilities
which may result in the unknown contribution. One possibility is a problem of our detector
system such as a convection of the LXe in the cryostat. Another possibility is an event-by-event
fluctuation of the shower development which is not correctly simulated for some reason. Anotherpossibility is an intrinsic property of the LXe scintillation. A part of the energy deposit in the
LXe can be used for a generation of the charged carriers or an emission of the scintillation lightin the infrared region. The fraction of the energy used for the emission of the scintillation lightResolution [%]Chapter 9 Energy resolution

117

6

MEG Data : 108/Eγ (MeV)+1.22 %52

MC : 17/Eγ (MeV)+0.7 %4

MEG II Data

3

2

1

0
0

20

40

60

80

100

120

140

Energy [MeV]

Figure 9.15 Energy resolution of MEG II as a function of the γ-ray energy compared tothat of MEG for the deep events (w > 2 cm). Noise contribution is subtracted to show the
intrinsic detector resolution.

in the VUV range may fluctuate event-by-event. These possibilities cannot be investigated inthis thesis, and further studies are needed for a better understanding.

118

Chapter 10

Pileup elimination performance
The LXe detector performances in the previous chapters focus on that without any pileup
γ-rays. The position and the timing resolutions will not be aﬀected by pileups because they
are reconstructed from the local information only around the hit position. Fig. 10.1 shows thepileup eﬀect on the reconstructed position and timing of the signal γ-rays. The reconstructedtimings of some of the signal γ-rays are biased by the pileup γ-rays as shown in the long tail ofFig. 10.1(b). This leads to an analysis ineﬃciency for the signal events, but it is only 3%, andeﬀect on the branching ratio sensitivity is almost negligible.
On the other hand, the energy is reconstructed from a global sum of the number of photons,
and its reconstruction largely deteriorates with pileups. Thus, this chapter focuses on the pileup
eﬀect on the reconstructed energy. In the Section 10.1, sources of pileup γ-rays in MEG II are
explained. Two complementary methods to identify and eliminate the pileups are described in
Section 10.2 and 10.3.

without pileup
10

10

3

3

with pileup

without pileup
with pileup

102

102

10

10

1

1
−10

−5

0

5

10

−2000

−1500

−1000

−500

0

u (cm) (reco. - truth)

(a)

500

1000

1500

2000

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

Figure 10.1 Pileup eﬀect on the position and timing reconstruction of the signal γ-rays(MC). The diﬀerences between the reconstructed variable and its truth are shown. (a) Hit
position (u-direction). (b) Hit timing.

10− 210from radiative decay
from Michel decay

−3

10− 4

10

119

event rate (Hz)prob. /500 keV

Chapter 10 Pileup elimination performancew/ pileup from MEG II beam

10

w/o pileup

1

−5

10−1

10

−6

10−2

10− 7

−8

10 0

10

20

30

40

50
Energy (MeV)

10−3
42

44

46

48

(a)

50

52

54

56
energy (MeV)(b)

Figure 10.2 (a) Simulated energy deposit from a muon decay on target. The y-axis is normalized to the probability from a single muon decay. (b) Reconstructed energy spectra ofbackground γ in the simulation without applying any pileup elimination analyses assuming(red) no pileups and (black) pileups from the MEG II beam.

10.1 Sources of pileup
10.1.1 Accidental pileup γ from another muon decay
The first type of pileup events is accidental pileup γ-rays from other muon decays. In the
MEG II experiment, 7 × 107 muons per second decay on the target. Some of them emit γ-raysin the radiative decay, and they can pile up in the detector. Some of the Michel positrons canalso emit γ-rays via interactions with materials. Fig. 10.2(a) shows simulated energy deposit in
the LXe detector originating from the muon decays on the target. A single muon decay emits a
γ-ray which deposits energy in the LXe with a probability of 1.5%. Thus, one pileup γ comesto the LXe detector in 1 µs time window on average.
Fig. 10.3 shows a typical pileup γ event. Additional charge caused by the pileups can bias theenergy reconstruction, which is based on the global sum of the number of photons. Fig. 10.2(b)shows an simulated energy spectrum of background γ without pileup elimination analyses. Many
events are reconstructed at higher energies, and the number of events near the signal energy
becomes much larger due to the pileups. This is not acceptable to search for µ → eγ decay, andsome pileup elimination analysis is needed.

10.1.2 Two γ event from annihilation in flight
In addition to the accidental pileups, two coincident γ-rays can come even from a single muon
decay. Most of the Michel positrons are swept from the MEG II detectors by the gradientmagnetic field of the COBRA, but some of them can annihilate in flight with materials (AIF)
and emit two γ-rays which are boosted in the direction of the flight.
The background events with the AIF reconstructed to be signal-like energy can be classified
into two groups shown in Fig. 10.4. In the first type, one of the emitted γ-rays comes to theChapter 10 Pileup elimination performance120

Figure 10.3 Typical event display of a pileup event.

ν
γ

ν
γ

(a)

γ

e

ν

ν

e

γ

(b)

Figure 10.4 Two types of high energy background γ from AIF. (a) AIF 1γ, (b) AIF 2γ.

LXe detector with a large energy up to 52.8 MeV. Since one of the emitted two γ-rays carries
most of the positron energy, the other γ-ray is emitted nearly backward, and cannot come tothe detector. This type of event is called AIF 1γ event. In the second type, the opening angle oftwo γ-rays is relatively small, and both γ-rays come to the LXe detector. If the hit positions are
too close to identify them as two independent γ-rays, they look like a single high energy γ-ray.
This type of event is called AIF 2γ event.
From the full simulation of the background γ (Section 4.3), this AIF 2γ event is found to havea dominant contribution among all types of the backgrounds near the signal energy. Fig. 10.5
shows the energy spectrum of the background γ-ray of each class. The number of the γ-rays
from the RMDs rapidly decreases as it goes to higher energy, while that from the AIFs only
gradually decreases due to the shape of the Michel positron spectrum (Fig. 1.5(a)). In reality,
the large fraction of the AIF 2γ events near the signal energy is smeared by the energy resolution

AIF 2 gamma

102

121

Fraction

event rate (Hz)

Chapter 10 Pileup elimination performance

AIF 1 gamma

1.2

AIF 2 gamma
AIF 1 gamma
RMD

1

RMD

10

0.8

0.6

1

0.4
10

−1

0.2
10− 2
42

44

46

48

50

52

54

0

56
energy (MeV)

42

44

(a)

46

48

50

52

54

56
58
energy (MeV)(b)

Fraction of AIF two gamma

Figure 10.5 (a) Energy spectrum of the background γ. Simulated energy deposit in the
LXe is shown. Events above mµ /2 come from muon decays before stopped on the target.
Muon momentum can boost decay products in these events. (b) Fraction of the backgroundγ-rays of each type calculated from (a).

0.9resolution 0.6%

0.8resolution 1.2%

0.7

resolution 1.7%

0.6
0.5
0.4
0.3
0.2
0.1
0

42

44

46

48

50

52

54

56
58
energy (MeV)

Figure 10.6 Expected fraction of the AIF 2γ events taking the energy resolutions into account (MC).

as shown in Fig. 10.6. Even with the 1.7% energy resolution measured in run 2019, which isworse than expected (Chapter 9), the AIF 2γ events still have 34% contribution near the signal
energy*1 (51.5 < Eγ < 54 MeV). Therefore, an identification of the AIF 2γ events leads to an
additional reduction of the background γ and can result in an improvement in the branchingratio sensitivity.

*1 This region is defined to be ±1.5σ for a rough and qualitative discussion on the eﬀect of the pileups. Since

the MEG II physics analysis adopts a likelihood fitting instead of a cut-counting analysis, a real eﬀect
on the branching ratio sensitivity can be diﬀerent. The qualitative estimation of the eﬀect is given in
Chapter 11.

Chapter 10 Pileup elimination performance

10.2 Pileup elimination by sum waveform
10.2.1 Elimination algorithm
This method tries to eliminate pileup γ-rays from the accidental muon decays. It starts froma calculation of summed waveforms of all MPPCs and PMTs. In the calculation of the sum
waveform, the weights and the photosensor performances used in the energy reconstruction(Equation 9.1) are applied, so that the γ-ray energy can be directly reconstructed from thearea of the sum waveform. Template waveforms are created from the sum waveform of many
γ-ray events as shown in Fig. 10.7, and are used for the peak search in the waveform. The datataken at the reduced intensity is used to eliminate the contamination of the pileup pulses inthe template waveform. A relative event-by-event fluctuation in the waveform is also calculated
from the standard deviation of Fig. 10.7, as shown in Fig. 10.8. A typical fluctuation is below
1.5% of the peak amplitude in 1σ, except for a time window near the peak. Thus, 2.4 MeV(= 52.8 MeV × 1.5% × 3) pileups in the signal events can be identified if we search for a deviation
larger than 3σ from the template.
The pileup identification of each event starts from a fitting of the sum waveform by the
template assuming no pileup in this event. If a local significant deviation from the template
above 3σ is found, another template for the pileup is added in the fit function, and the sum
waveform is re-fitted assuming two γ-rays. This step is repeated until the fitting gets converged.
The sum waveform is deconvoluted to several pulses by the fit, from which energy of each γ-ray isreconstructed. Fig. 10.9 shows a typical sum waveform with pileups. Excesses of the chi-squarevalue from the template around −50 ns and +150 ns are solved by adding a pileup γ-ray for
each, and the sum waveform is successfully deconvoluted to three γ-rays.
In the current implementation, only the sum waveform of the PMTs is used for a identificationof the pileups in the waveform. The MPPC sum waveform is fitted and deconvoluted by assuming
the pileup γ-rays found in the PMT. This is to avoid picking up fake peaks due to the larger
statistical fluctuation and noise fluctuation when the MPPC PDE will get reduced. The pileup
search in the MPPC waveform may be included, once a better understanding on the fluctuationof the MPPC waveform is obtained from the γ-ray data operated at lower PDE in the future.

10.2.2 Performance measurement at run 2019
The performance of this algorithm is tested both in the simulation and in the real data at
the MEG II beam intensity. Fig. 10.10 compares the reconstructed spectra of the backgroundγ-ray with and without applying this algorithm. The high energy tails are largely suppressedby this method both in data and MC. The energy spectrum of data after the elimination agrees
with MC as shown in Fig. 10.11(a). The number of background events in the “signal region”(51.5 < Eγ < 54 MeV) is 1.4(1) Hz in Data, and 1.47(3) Hz in MC.
Fig. 10.11(b) shows a simulated energy spectrum after applying this algorithm compared tothat without pileup. Some of the pileups are still not identified, and this increases the number

122Chapter 10 Pileup elimination performance

123

70
0

0.2

amplitude

amplitude

0.2

100

0

60

80

−0.2

−0.2
50

−0.4
−0.6

60

−0.4

40

−0.6

30

−0.8

20

−0.8

−1

10

−1

0

−1.2
0

40

20

−1.2
0

50

100

150

200

250

300

350

400

450
500
time (ns)

50

100

150

200

(a)

250

300

350

400

0

450
500
time (ns)(b)

fluctuation

0.05
0.045
0.04
0.035

0.05
0.045
0.04
0.035

0.03

0.03

0.025

0.025

0.02

0.02

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0.015

0.01

0.01

0.005

0.005

0
0

50

100

150

200

250

300

350

400

0
0

450
500
time (ns)

50

100

150

(a)

200

250

300

350

400

450
500
time (ns)

(b)

chi2

Figure 10.8 Event-by-event fluctuation of the summed waveform (Fig. 10.7) as a functionof time. (a) MPPC, (b) PMT. The fluctuation is normalized by the peak amplitude of
the sum waveform. The local minimum at 140 ns (MPPC)/120 ns (PMT) are due to the
waveform normalization at the peak of the waveform.

amplitude (V)fluctuation

Figure 10.7 Summed waveforms of the (a) MPPCs, (b) PMTs, which are produced byoverlaying 1000 events. The peak amplitude and peak timing of each event are normalized
and shifted. The second peak in the PMT waveform at 300 ns is due to a reflection.

0

−0.2

103

102

−0.4
10
−0.6

−0.8

1

−1
−6

−0.05

0

0.05

0.1

(a)

0.15

0.2

0.25

0.3
time (sec)

×10

10−1

−6

−0.05

0

0.05

0.1

0.15

0.2

0.25

0.3
time (sec)

×10

(b)

Figure 10.9 Pileup elimination by sum waveform for a typical waveform with pileups. (a)The original PMT sum waveform (black) is deconvoluted to three identified pulses (red,blue, and green). (b) Chi-square of this event assuming (black) signal γ-ray, and (red)three γ-rays.

w/o pileup elimination

10

w/ pileup elimination

124

event rate (Hz)event rate (Hz)

Chapter 10 Pileup elimination performancew/ pileup elimination

1

1

10−1

10−1

10−2

10−2

10−3
42

44

46

48

50

52

54

10−3
42

56
energy (MeV)

w/o pileup elimination

10

44

46

48

(a)

50

52

54

56
energy (MeV)

(b)

Data

10

MC

event rate (Hz)event rate (Hz)Figure 10.10 Comparison of the energy spectrum of the background γ-ray at the MEG II
beam intensity with and without applying pileup elimination by the sum waveform for(a) MC and (b) data. The spectrum of the MC is smeared to match the worse energy
resolution in data (Section 9.3.5).

with pileup of MEG II beam

1

1

10−1

10−1

10−2

10−2

10−3
42

44

46

48

50

52

54

56
energy (MeV)(a)

without pileup

10

10−3
42

44

46

48

50

52

54

56
energy (MeV)(b)

Figure 10.11 (a) Comparison of the background γ spectrum at the MEG II beam intensity
between MC (in Fig. 10.10(a)) and data (in Fig. 10.10(b)) with the pileup elimination by
the sum waveform. The normalization of the spectrum is also adjusted to match the dataat the low energy region. (b) Comparison of the simulated background γ spectra between
that assuming no pileup (black), and that assuming pileup from MEG II muon beam (red).
The spectra are smeared to match worse energy resolution in data.

of events in the “signal region” by 13%. Most of these events are the pileups which accidently
come at the similar timing to the triggered γ, and they are the target of another elimination
method in the next section.
In the search of pileup candidates, some of the single γ-ray events can be misidentified as an
event with pileups. Energy of these events can be reconstructed to be smaller than the realenergy deposit, and this leads to an analysis ineﬃciency of the signal events. In the simulation,
this ineﬃciency is estimated to be only 0.2%.
To confirm the little ineﬃciency in the data, a fraction of the events reconstructed as two
γ-rays in the background γ data is utilized. These events are composed of the true pileup

40
35

p0

0.3442 ± 0.2257

p1

26.14 ± 0.4925

125

Fraction of pileup event (%)

Fraction of pileup event (%)

Chapter 10 Pileup elimination performance

30
25
20
15

40
35

20
15

5

5

0.2

0.4

0.6

0.8

1

1.2

29.78 ± 0.6464

25

10

0

−0.4548 ± 0.3425

30

10

0

p0
p1

0

0

0.2

beam rate (relative to 7e7 muon/s)

(a)

0.4

0.6

0.8

1

1.2

beam rate (relative to 7e7 muon/s)(b)

Figure 10.12 Fraction of the background events (40 < Eγ < 42 MeV) reconstructed as
two γ events as a function of the beam rate (a) in MC and (b) in data.

events and the misidentified single γ events, and they are distinguished from the beam ratedependence. Fig. 10.12(a) shows the fraction as a function of the beam rate in the low energy
region (40 < Eγ < 42 MeV*2 ). The beam rate dependence of the fraction is fitted with a linear
function except for the data point at x = 0 (namely without pileup γ-rays), and the ineﬃciency
to the pure single γ events is estimated to be 0.3(2)% from its y-intercept. This result is
consistent with 0.2% ineﬃciency. The same analysis is applied for measured background γ-raysin the run 2019. As shown in Fig. 10.12(b), the y-intercept is fitted to be −0.5(3)%, and theineﬃciency is found to be negligible also in the data.

10.3 Pileup rejection by charge distribution
10.3.1 Identification algorithm
This method searches for a local maximum in the charge distribution on the MPPCs to identify
the events having more than one peak due to the pileup γ-rays. The peak search algorithm isdesigned to avoid picking up fake peaks in the charge distribution. Firstly, the granularity of
the MPPC readout is re-binned by a factor of two to suppress an event-by-event fluctuation of
the charge distribution. Secondly, a low-pass filter is applied by a moving average of 3 × 3 bins.
Thirdly, small peaks whose excess is below a given threshold (typically 200 photon) are ignoredin the peak search. Fourthly, each identified peak is fitted by a two-dimensional Gaussian sothat we can roughly reconstruct its energy from the integrated volume of the Gaussian*3 . The
identified peaks less than 1 MeV are ignored. Note that peak caused by the triggered γ-ray isalso counted as one peak.
Events having more than one peak is discarded from the analysis. In the current implemen-*2 This is the lowest energy region available in data.
*3 Currently dependence on the conversion depth is not corrected. This can be improved in the future.

Chapter 10 Pileup elimination performance

Figure 10.13 Example of two peak event from single γ-ray in MC. In this event, a 50 MeV
γ-ray from RMD creates two peaks in the detector.

tation, the algorithm is applied only to the events where no pileup γ-rays are identified in thesum waveform method. In other words, we rely on the sum waveform method for the events
whose pileup is identified by both methods. This implementation can be improved in the future
to deal with three γ-rays events in which one pileup is identified by the sum waveform method,
and the other by this method.
This is a complementary method to the identification by the sum waveform because it issensitive to the pileup hits coming at the same or similar timing. Since the time window of thecharge integration is defined around the timing of the main γ-ray, the pileup hits coming at thesame or similar timing tend to have larger charges than the other pileups.
If a signal event is rejected by this analysis, it leads to an ineﬃciency. There are two sourcesthat causes the second peak in the signal event. One is the accidental pileup γ-ray coincident
with the signal event, but its contribution is limited. The ineﬃciency is estimated to be only
0.3% in the signal MC with pileups. The other ineﬃciency, which is dominant, is due to theevents where a second peak on the charge distribution is created by the signal γ-ray itself.
Fig. 10.13 shows an example event of this type, and Fig. 10.14 shows particle tracks in thisevent. A γ-ray escaped from the main electromagnetic shower is converted in a distant place,and creates a second peak on the inner face.

10.3.2 Expected performance with full channel readout
The expected performance of this algorithm is evaluated by the simulation assuming a fullchannel readout.
Fig. 10.15 shows the reconstructed energy spectrum of the background γ-ray from the RMDwith accidental pileups. The fraction of the background events due to the overlooked pileups inthe “signal region” is 13% only with the pileup elimination by sum waveform, and it is improved
to 5% also applying this algorithm.

126

y[cm]

Chapter 10 Pileup elimination performance

127

1
60

0.9
0.8

40

0.7
20
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−60
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−70

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−50

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−30

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−10

0

10
x[cm]

0

event rate (Hz)Figure 10.14 Particle track in the simulated event of Fig. 10.13. Each black line shows a
track of a γ-ray. A gamma-ray escaped from the shower converted at the top side of thedetector. The energy deposit on each point is overlaid. The scale of the gray bar is in theunit of MeV.

10

1

10 1

10 2

10 3
44

w/ pileup, identification by waveform.
w/ pileup, identification bothby waveform and light distribution.
w/o pileup
46

48

50

52

54

56
energy (MeV)

Figure 10.15 Reconstructed energy spectrum of the simulated background γ. The background event only from RMD is shown. (black) no pileup is simulated. (blue) pileup issimualted, and eliminated by sum waveform method. (red) pileup is simulated and eliminated by both the sum waveform and the charge distribution.

Fig. 10.16 shows the expected performance for the AIF 2γ identification. The identificationeﬃciency of the AIF 2γ events ef f and analysis ineﬃciency to the single signal γ events inef f
are shown at several peak search thresholds. To have a naive impression on the improvement of
the branching ratio sensitivity, the inverse of the significance in the “signal region” is defined asfollows, as a figure of merit f om of this analysis.
√√
1 − c ∗ ef f − (1 − c) ∗ inef f
NBG
f om :==.
Nsig
1 − inef f(10.1)

Here, c = 0.29 is the fraction of AIF 2γ event in the “signal region” (Fig. 10.6). The branchingratio sensitivity of MEG II will get improved by a factor of this f om, if the statistics is suﬃcient.

0.3

128

Figure of merit

Inefficiency

Chapter 10 Pileup elimination performance

0.25

1.05

w/o AIF reduction
1

0.2
0.95
0.15
0.9
0.1
0.85

0.05

0
0

0.2

0.4

0.6

0.8

0.8
0

1
Efficiency

100

200

300

(a)

400

500
600
Threshold (# of photon)(b)

Efficiency

Figure 10.16 (a) Identification eﬃciency of AIF 2γ event and ineﬃciency to single γ-ray
at various peak search threshold (MC). (b) Figure of merit defined in equation 10.1 as afunction of peak search threshold (MC).

1.2

1

0.8
0.7
0.6

0.8

0.5

0.6

0.4
0.3

0.4

0.2
0.2
0.1
0

5

10

15

20

25

(a)

30

35

40

45

50

Distance (cm)

0

10

20

30

40

50

Distance (cm)(b)

Figure 10.17 (a) Distribution of the distance between two γ-rays from AIF 2γ (MC). (b)Identification eﬃciency of AIF 2γ event as a function of its distance (MC).

Nominal threshold (200 photon) for the peak search is set near the optimal threshold which
minimizes the f om, and a significance improvement by 8% is expected at the ef f = 68%,
inef f = 3%.
The identification eﬃciency of AIF 2γ events depends on the distance between two γ-rays.
Fig. 10.17 shows a distribution of the distance between two γ-rays, and the identification eﬃciency as a function of the distance. The typical distance is 20 − 30 cm, and this algorithm issensitive to them. The AIF 2γ events closer than 15 cm are diﬃcult to be identified since two
peaks are overlapped, but those are very rare. On the other hand, the longer the distance is,the smaller the energy of the second γ-ray tends to be. Therefore, the identification eﬃciency
decreases above 20 cm . Some of the second γ-rays which convert in the deep region of thedetector are not identified due to its small observed charge on the inner face. These γ-rays may
be identified by also using charge distribution on other faces in the future.

Chapter 10 Pileup elimination performance

129

100
80
60
40
20
0
20
40
60
80
100
100

Figure 10.18 Analysis area in run 2019. Green shows MPPC readout area, and red box(24(u) × 36(v) cm2 ) shows area used in this search.

10.3.3 Performance measurement at run 2019
The eﬃciency and ineﬃciency of this algorithm were measured in the 2019 run. Due tothe limited readout area, the pileup γ-ray which hitting outside the area cannot be identified.
Since the distance between AIF 2γ is shorter than that between the accidental γ-rays which are
uniformly distributed, most of the identified two γ events in 2019 run come from AIF 2γ.
In the analysis of 2019 data, two γ events where both γ-rays hit the central area shown in
Fig. 10.18 are used. This area is defined to have 3 cm (two MPPCs) margin from the edge of thereadout area, in order to veto events whose true hit positions are outside the area. Even though
the most of the AIF 2γ events hitting the whole detector cannot be identified with the limited
readout area, a reasonable eﬃciency is expected for the events hitting this region as shown in
Table 10.1.
Table 10.1 Identification probability of AIF 2γ in MC

Peak search in whole detector
Peak search in 2019 area

AIF 2γ in whole detector

AIF 2γ in 2019 area

78(1)%

80(5)%-

67(4)%

Fig. 10.19(a) shows a fraction of two γ events in the background γ-rays as a function of
the energy. The high energy events have a larger fraction of two γ events as expected. The
major component of the identified two γ events is not the accidental pileups since the fraction
is independent of the beam intensity. This result qualitatively shows that the identification of
the AIF 2γ events works correctly.
Fig. 10.19(b) compares the fraction of two γ events at the reduced beam intensity between
MC and data. The measured fraction of two γ-ray events in the low energy region (40 < Eγ <45 MeV) is twice larger than expected. It is confirmed that those identified two γ events in data
really have two signal-like peaks on the charge distribution, and not due to a noise or mistakes

0.14

MEG II
0.12

130Fraction

Fraction

Chapter 10 Pileup elimination performance

LOW

0.14

MC
0.12

0.1

0.1

0.08

0.08

0.06

0.06

0.04

0.04

0.02

0.02

0

40

45

50

55

60
Energy (MeV)

(a)

0

Data

40

45

50

55

60
Energy (MeV)(b)

Figure 10.19 Fraction of 2 γ event. (a) Comparison between reduced intensity and MEG II
intensity in Data. (b) Comparison between MC and data at reduced beam intensity.

in the analysis. Since this excess is observed in both the reduced intensity data and the MEG II
intensity data, it should not be due to the accidental pileups, but due to some two γ events froma single muon decay.
There are two possibilities which explain this inconsistency. One is due to some materials
which produce AIF 2γ events but are not implemented in the MC. Since the excess by a factorof two is observed only in the low energy region, the material should not be located in the central
part of the beam line, but be located where only the Michel positrons after some energy loss canhit. The other is that the current MC simulation underestimates the probability of having thesecond peak in the single γ event for some reason. In this case, the ineﬃciency for signal γ-ray
becomes twice larger than expected.
Since the second possibility cannot be rejected, it is diﬃcult to evaluate the ineﬃciency from2019 data with a good precision. The ineﬃciency of this method should be directly measured
with reading all the MPPCs in the future.

131

Chapter 11

Expected branching ratio sensitivity of
MEG II
In the design stage of the MEG II experiment shown in Section 1.9, the branching ratio
sensitivity was estimated in the expected detector performance from the simulation at thattime. In this chapter, the sensitivity is updated based on the measured LXe detector performancesummarized in the previous chapters.
The calculation procedure of the MEG II branching ratio sensitivity is summarized in Section 11.1.
In this thesis, many improvements and degradations on the detector performance are discussed.
Their eﬀects on the sensitivity are discussed separately in this chapter. In the Section 11.2, thesensitivity achieved by the detector performances measured in the pilot run is discussed. This
includes eﬀects from the improved resolutions realized by the MPPCs, and a degradation fromthe worse energy resolution than expected.
Due to the PDE degradation of the MPPCs, original DAQ plan of MEG II assuming continuous
120 days data-taking may not be possible (Section 6.3.4). Section 11.3 and 11.4 discusses theeﬀect of the PDE degradation including the expected detector resolution with lower MPPCPDE.
A conclusion on the achievable branching ratio sensitivity with the developed LXe detector
by a reasonable data-taking time is given in Section 11.6.

11.1 Calculation procedure of branching ratio sensitivity
11.1.1 PDF in likelihood analysis
In the physics search of µ → eγ in MEG II, the number of signal events is estimated bya maximal likelihood method. An analysis region where the likelihood fitting is performed isdefined as follows: 48 < Eγ < 58 MeV, 50 < Ee < 56 MeV, |teγ | < 0.7 ns, |θeγ | < 50 mrad, |ϕeγ | <75 mrad. A time-sideband is defined around the analysis region as 1 < |teγ | < 3 ns, and an
energy-sideband is defined as 43 < Eγ < 48 MeV, 48 < Ee < 53 MeV, |θeγ | < 300 mrad, |ϕeγ | <Chapter 11 Expected branching ratio sensitivity of MEG II

132

300 mrad.
The likelihood function is defined from a probability density function (PDF) for signal, RMD,
and accidental background events as shown in Equation 11.1.
(N
−⟨N
⟩)
RMD ⟩)− BG 2 BGe−(Nsig +NRMD +NBG ) − (NRMD2σ−⟨N
2
2σ
RMD
BG
e
e
Nobs !
N
obs∏
×(Nsig S(x⃗i ) + NRMD R(x⃗i ) + NBG B(x⃗i )).
2

L(Nsig , NRMD , NBG ) :=2

(11.1)

i=1

Here, Nobs is the number of events observed in the analysis region. Nsig , NRMD , and NBG
are the expected value of the number of signal, RMD, and accidental background events inthe analysis region. These are the fitting parameters determined in the maximum likelihood
analysis. ⟨NRMD ⟩, ⟨NBG ⟩, σRMD , and σBG are the expected numbers of RMD and accidental
background events and their uncertainties estimated from the sidebands. S(x⃗i ), R(x⃗i ), andB(x⃗i ) are the PDFs of signal, RMD, and accidental background events as a function of thedsobservables x⃗i = (Eγ , Ee , teγ , ϕeγ , θeγ , tds
rdc , Erdc ) defined in Section 1.3.

These PDFs are calculated from the theoretical expectations and the detector resolutions. For
example, the signal PDF S(x⃗i ) is composed of PDFs of each variable as follows,ds
S(Eγ , Ee , teγ , ϕeγ , θeγ , tds⃗i ) = S(teγ ) × S(Eγ )rdc , Erdc |wγ , y× S(ϕeγ |wγ , y⃗i ) × S(θeγ |wγ , y⃗i )× S(Ee |⃗yi )ds
× S(tds
rdc , Erdc |Eγ ),where wγ is the conversion depth of a γ-ray, and y⃗i is a set of reconstructed positron variables
such as direction, decay vertex, and tracking quality. To estimate the sensitivity, signal PDFs
related to the γ-ray are prepared from the measured performance given in the previous chapters.
The positron detector performance is assumed to be the same as that in the design summarizedin Table 1.1.
The signal PDF of the γ-ray energy S(Eγ ) is created from the simulated energy distribution
for the signal γ-ray. The simulated spectrum is smeared by an additional Gaussian to match themeasured energy resolution as shown in Fig. 11.1(a). The signal PDF of the timing teγ is defined
as a Gaussian of the teγ resolution. The teγ resolution is a combination of the timing resolutionsof the γ-rays and the positrons (Table 1.1). The angular PDFs are the combination of the
γ-ray position resolution, the positron vertex resolution, and the positron direction resolution.
Conversion depth dependence of the γ position resolution is also included.
Similar to the signal PDF, the background PDF B(x⃗i ) is also composed of the PDFs of eachvariable. Fig. 11.1(b) shows the background Eγ PDFs generated from the simulated background
spectrum. Pileup events from the MEG II beam are included. It is already confirmed that thegenerated background spectrum from the simulation agrees with data as shown in Fig. 9.11. The
pileup rejection by the charge distribution is not adopted in this thesis since its performance
was not confirmed from the data. Thus, only the pileup elimination by the sum waveform isapplied.

Chapter 11 Expected branching ratio sensitivity of MEG II

1
0.9
0.8
0.7

133

1

resolution 1.1%

resolution 1.1%

resolution 1.7%

10resolution 1.7%

−1resolution 2.1%

resolution 2.1%

0.6

10

−2

0.5
0.4

10

−3

0.3
10− 4

0.2
0.1
0
48

−5

49

50

51

52

53

54

55

56

10 48

49

50

51

52

energy (MeV)

(a)

53

54

55

56

energy (MeV)(b)

Figure 11.1 Simulated Eγ PDFs assuming several resolutions. (a) For signal. (b) For
accidental background.

The background PDF of the RDC parameters are updated from the MEG II design. Fractionof the background events identified by the RDC is dependent on the gamma-ray energy as shownin Fig. 10.5(b), and this dependence is newly included in the calculation.

11.1.2 Accumulated number of muon decays
The accumulated number of muon decays is another input parameter needed for the calculationof the branching ratio sensitivity. In the nominal configuration, it is estimated as follows, basedon the original DAQ plan of the MEG II experiments.
• beam rate : 7 × 107 µ/s• geometrical acceptance : 10.8%• positron eﬃciency : 70%• γ eﬃciency : 69%• trigger and analysis eﬃciency : 91% (same as the first half of MEG)
• DAQ time : Three years. 20 week data-taking per year with 84% live fraction.
With these parameters, the total number of muon decays called k-factor becomes k = 1.03×1014 .

11.1.3 Sensitivity calculation from toy experiments
The branching ratio sensitivity of MEG II is calculated by simulating many (O(103 –104 )) toy
experiments. In each toy experiment, a set of MEG II observables are simulated from the PDFs
assuming a background-only hypothesis. The generated number of the RMD and the accidental
background events are calculated from the simulation. Their statistical fluctuations are also
taken into account. The best estimate of the number of signals Nsig of each toy experiment iscalculated by maximizing the likelihood function in Equation 11.1, and the upper limit of Nsig
at 90% confidence level is calculated by asymptotic formulae in [62].

Chapter 11 Expected branching ratio sensitivity of MEG II

134

35
30
25
20
15
10
5
0
0

5

10

15

20

25

90% C.L. upper limit of Nsig

Figure 11.2 The upper limits of the number of signal Nsig for 5000 toy experiments assuming nominal detector performance in MEG II, and DAQ time. Red arrow shows themedian of this distribution.

Fig. 11.2 shows a distribution of the upper limits of Nsig at 90% confidence level. “Branchingratio sensitivity” of the MEG II experiment is obtained from the median of the upper limits
divided by the k-factor.

11.2 Sensitivity imporvement by LXe detector
In this section, the achieved improvement on the branching ratio sensitivity is shown for eachdetector resolution.
Here, the resolutions measured at the MPPC PDE of 8% are used. Note that it does notreflect the eﬀect of further degradation of PDE in the future, which will be discussed in the next
sections.
In the comparisons of the branching ratio sensitivity shown below, resolutions other thanthat being compared are fixed to the measured resolutions in the pilot run, and the nominal
data-taking time in the original MEG II DAQ plan is assumed. A sensitivity improvement by
the RDC depends on the γ-ray energy resolution because the fraction of the RMD events in the
backgrounds near the signal energy depends on it (Section 10.1.2). Thus, the RDC observables
are not used in the likelihood analysis in these comparisons to see a pure eﬀect of the γ-ray
resolution on the sensitivity.
Position resolution
The position resolution is improved by the better granularity realized by MPPCs in MEG II
especially for shallow events. This leads to a 30% improvement of the branching ratio sensitivity
as shown in Fig. 11.3(a). On the other hand, in the pilot run, a slight degradation of theresolution for the deep events was observed (Chapter 7). This results in a 4% degradation of
the sensitivity, and thus a 26% sensitivity improvement from MEG is achieved in MEG II.

Chapter 11 Expected branching ratio sensitivity of MEG II
Timing resolution
A better timing resolution than the design is achieved by the analysis optimization (Chapter 8).
As shown in Fig. 11.3(b), this leads to an improvement of the branching ratio sensitivity by
about 7% from the design. The timing resolution is also better than that in MEG, thanks to themore precise estimation of time of flight by the improved position resolution. The sensitivity
improvement from MEG is a few percent.
Energy resolution
As discussed in Chapter 9, the energy resolution is measured to be worse than the expectationfrom the simulation, probably due to the unknown contribution also observed in MEG. Since
the branching ratio sensitivity in the MEG II design assumes only a half of the unknown contribution (Section 1.9), the sensitivity gets worse than the estimation in the design. As shownin Fig. 11.3(c), about 10% degradation of the sensitivity from the design is expected. Even
with the same or even worse energy resolution for the deep events than MEG, the better energy
resolution for the shallow events improves the sensitivity by about 15% compared to that in
MEG.
PileupFig. 11.3(d) shows a comparison of the branching ratio sensitivity with and without the accidental pileups. Since the pileup elimination by the charge distribution is not applied, someof the accidental pileups near the signal energy are still left (Section 10.2.2, Fig. 10.15). This
results in a sensitivity degradation by about 10% at MEG II intensity.
Eﬀect of measured resolution uncertainties
Each measured resolution of the LXe detector in the pilot runs has an uncertainty. For
example, the energy resolution for the shallow events (w < 2 cm) have a 0.2% uncertainty fromthe energy spectrum fitting (Fig. 9.13). The expected branching ratio sensitivity improvement
mentioned above uses the best estimate of the resolution, and the result has an uncertainty
coming from that of the resolutions. The size of the uncertainty is estimated by calculating a
resolution dependence of the sensitivity.
The uncerainty from the 0.2% energy resolution uncertainty for the shallow events is estimatedto be 2.6%. The position resolution for the shallow events (w < 4 cm) have a 0.2 mm fit
uncertainty at most (Fig. 7.6(b)). Eﬀect of this is calculated to be a sensitivity uncertainty ofless than 0.9%. Eﬀects from other resolution uncertainties, such as the resolutions for the deep
events and the timing resolution, are smaller than these and are negligible. The uncertainty ofthe sensitivity is less than 5% in total if we sum up the eﬀects from the all resolutions.

135

Branching ratio sensitivity (a.u.)

Branching ratio sensitivity (a.u.)

Chapter 11 Expected branching ratio sensitivity of MEG II

1.3

1.25

1.2

1.15

1.1

1.05

136

1.15

1.1

1.05

1

0.95

0.9

0.85

MEG II

1

MEG II design

MEG II meas.

0.8

MEG

50

MEG
60

MEG II design
65

70

75

80

time resolution (ns)(b)

Branching ratio sensitivity (a.u.)(a)Branching ratio sensitivity (a.u.)

55

1.15

1.1

1.05

1

0.95

0.9

1.15

1.1

1.05

1

0.95

0.9

0.85

MEG II design

MEG II

0.85

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

MEG

0.8

w/o pileup

w/ pileupw/ pileup

energy resolution (%)

(c)

(d)

Figure 11.3 Relative size of the branching ratio sensitivity as a function of the LXe detector
resolution. A smaller value on the vertical axis corresponds to a better performance of theexperiment as defined in Section 11.1.3. (a) Position resolution, (b) timing resolution, (c)energy resolution. Other resolutions are fixed to the resolution measured in the pilot run.
The DAQ time in the original MEG II plan is assumed. (d) Eﬀect of the accidental pileups
on the sensitivity.

11.3 Eﬀect of PDE degradation: detector performance
As is shown in Section 6.3, a radiation damage to our MPPC was found, which aﬀects the
PDE for VUV light. Even though there is still a large uncertainty in the PDE extrapolation to
the future, its degradation is too fast to be ignored, and the PDE can become zero after 70 daysof detector operation in the worst case.
This degradation will aﬀect the branching ratio sensitivity of MEG II by two processes. The
first one is the degradation of the detector resolutions by the decreased PDE. The expected
detector resolution at MPPC PDE of 2–22% , and its eﬀect on the sensitivity will be discussed
in this section.
The second one is the limitation to the DAQ time. In the most pessimistic scenario, the MEG II
DAQ plan which assumes 120 days of continuous data-taking in each year is not possible, andwe have to reduce the beam time or the beam rate. This leads to a smaller statistics and aChapter 11 Expected branching ratio sensitivity of MEG II
worse sensitivity. This eﬀect will be discussed in the next section (Section 11.4).

The PDE degradation can aﬀect the detector resolution through two contributions. The firstone is the statistical fluctuation by the reduced number of photoelectrons. In the original detector
concept, statistical fluctuation does not limit the γ resolutions, but it becomes non-negligible
when the PDE becomes very small.
The second contribution is the signal to noise ratio of the MPPC waveforms. As is discussed in
Section 8.4 and 9.3, noise from electronics is not negligible in energy and timing reconstructions.
This noise contribution will become larger with a lower PDE.
This can be cured by increasing an amplifier gain on the frontend of the electronics, as longas the noise before the amplification is negligible. The gain is easily switchable from the DAQ
software. In the original detector design, the amplifier is not used for the physics data-taking tokeep the maximum signal amplitude of the MPPCs in the dynamic range of the readout. Since
the MPPC signals get smaller with lower PDE, an amplification shown in Table 11.1 can beapplied. It is defined to keep the maximum signal amplitude after the amplification, while afurther tuning may be possible in the future, including an usage of a smaller operating voltageof the MPPCs.
Table 11.1 List of assumed amplifier gain

PDE

amplifier gain

8% < P DE ≤ 22%

1

4% < P DE ≤ 8%

2.5

2% < P DE ≤ 4%

50% < P DE ≤ 2%

10

11.3.1 Degradation of position resolution
The hit positions of the γ-rays are reconstructed by fitting charge distribution on the MPPCs.
An increased statistical fluctuation due to the reduced PDE can aﬀect the position resolution
through the fit uncertainty. Fig. 11.4 shows the position resolution for the signal γ-ray simulated
at various MPPC PDEs. A degradation of the resolution is observed mainly for deep events.
This is because the fit uncertainty becomes larger for the deep events due to the smaller numberof photoelectrons on the inner face, while the contribution from the event-by-event fluctuation
depending on the direction of the shower development is dominant for the shallow events.
The noise contribution should not be a problem because no noise issue was found in the
resolution measurement by 17.6 MeVγ-ray from the CW-Li at the PDE of 7%, whose signal tonoise ratio is equivalent to that at the PDE of 2.3% for the signal γ-ray.
Fig. 11.5 shows the eﬀect on the sensitivity by this position resolution degradation, and its

137PDE 16 %0.9
PDE 8 %
0.8
0.7
0.6

PDE 4 %

1
PDE 16 %0.9
PDE 8 %
0.8
0.7

PDE 2 %

138

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

Chapter 11 Expected branching ratio sensitivity of MEG II

0.6

0.5

0.5

0.4

0.4

0.3

0.3

0.2

0.2

0.1

0.1

PDE 16 %1.6
PDE 8 %
1.4

PDE 4 %

PDE 4 %
1.2

PDE 2 %

PDE 2 %
1

0.8

0.6

0
0

2

4

6

8

0.4

0.2

0
0

10
12
depth (cm)

2

4

6

(a)

8

0
0

10
12
depth (cm)

(b)

2

4

6

8

10
12
depth (cm)(c)

Branching ratio sensitivity (a.u.)

Figure 11.4 Position resolution in the simulation as a function of the conversion depth atvarious PDE for (a) u, (b) v, and (c) w direction.

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 11.5 Eﬀect on the branching ratio sensitivity from the position resolution degradation at diﬀerent MPPC PDEs.

eﬀect is found to be less than a few percent. Here, the observed degradation for the deep eventsis included assuming that the degradation does not decrease even if the resolution improves at
the higher photoelectron statistics than the measurement.

11.3.2 Degradation of timing resolution
The hit timing of γ-ray is reconstructed from the timing information of all the channels. The
timing resolution of each photosensor can become worse both by the worse S/N ratio, and thelarger statistical fluctuation, and this leads to a degradation of the timing resolution.
The degradation of the S/N ratio can be recovered to some extent by using the amplifier.
Table 11.2 presents the noise level at each amplifier configuration measured in the run 2019.
The increase of the noise level is not proportional to the gain of the amplification, and therelative noise level is improved by the amplification.

Chapter 11 Expected branching ratio sensitivity of MEG II

139

2.5

2

amplifier gain

1

2.5

5

10

Noise level

0.7 mV

0.8 mV

0.9 mV

1.3 mV

resolution (ps)timing resolution (ns)Table 11.2 Noise level (RMS of random trigger waveform) at each amplifier gain in the run 2019.

amp gain 1
amp gain 2.5
amp gain 5
amp gain 10

200

gain 1
gain 2.5
gain 5gain 10

180
160
140

1.5

120
100
80

1

60 PMT precision
0.5

40
20

0
0

0.02

0.04

0.06

0.08

0.1

0.12
0.14
1/sqrt(# of p.e.)

0
0

2

4

6

(a)

8

10

12

14

16

18

20

22
24
PDE (%)(b)

Figure 11.6 (a) Timing resolution of an MPPC channel as a function of the number ofphotoelectrons (MC). (b) Accumulated timing precision of all the MPPCs as a function of
the MPPC PDE (MC).

Fig. 11.6(a) shows the simulated timing resolution of each MPPC channel. The real noise
situation in Table 11.2 is directly included in the simulation by simply adding the measured
random trigger waveform to the simulated waveform. As can be seen, smaller number of thephotoelectrons will lead to a worse resolution, while part of the degradation can be compensatedby increasing the amplifier gain. The improvement of the timing resolution is saturated at theamplifier gain of 5–10, and the gain larger than 10 is not useful.
Fig. 11.6(b) shows the accumulated timing precision of all the MPPCs defined in Equation
8.2 calculated from the plot of Fig. 11.6(a). The resolution defined only by the MPPCs will
become much worse than that defined by the PMTs when the PDE gets low. Since the detector
timing resolution will be determined by the combination of the MPPCs and the PMTs, thedetector resolution will be defined only by the PMTs under such condition. It is notable that theaccumulated precision of the PMTs is already measured to be consistent with MC (Section 8.4,
and Table 8.2).
Fig. 11.7(a) shows simulated absolute and intrinsic timing resolutions. The degradation of the
branching ratio sensitivity is shown in Fig. 11.7(b). Its eﬀect is found to be up to 5%.

11.3.3 Degradation of energy resolution
The γ-ray energy is reconstructed from the sum of the photosensor signals, and can be aﬀectedboth by a statistical fluctuation and a noise on the signals.
The eﬀect of the statistical fluctuation on the energy resolution is not crucial at the nominal
PDE. When the PDE is 8%, the total number of photoelectrons observed on the MPPCs is90absolute
80 MEG II design

intrinsic

70
MEG LXe
60
50
40
30
20

Branching ratio sensitivity (a.u.)

resolution (ps)

Chapter 11 Expected branching ratio sensitivity of MEG II

1.25

1.2

1.15

1.1

1.05

1

0.95

10
0
0

140

2

4

6

8

10

12

14

16

18

20

0.9
0

22
24
PDE (%)

2

4

6

8

10

12

14

16

18

20

22

24

PDE (%)

(a)

(b)

1.4

Energy resolution
1.2

Statistical fluctuation

resolution (%)

resolution (%)

Figure 11.7 (a) Simulated timing resolution as a function of the MPPC PDE. (b) Eﬀect
on the branching ratio sensitivity from the timing resolution degradation at the diﬀerent
MPPC PDE. A sensitivity degradation up to 5% is expected at lower MPPC PDE.

2.4

1

2

0.8

1.8

0.6

1.6

0.4

1.4

0.2

1.2

0
0

2

4

6

8

10

12

(a)

14

16

18

20

22
24
PDE (%)

Energy resolution + 1.5%

2.2

1
0

2

4

6

8

10

12

14

16

18

20

22
24
PDE (%)(b)

Figure 11.8 Expected energy resolution for the signal γ-ray as a function of the PDE.
The ENF of 2.0 is assumed. (a) Expected energy resolution in MC. (b) Expected energy
resolution including the unknown contribution of 1.5%.

typically 2 × 104 . Since the MPPC signal contributes to one third of the total energy, the√√statistical fluctuation is only 0.4% (= 100/ 2 × 104 /3 × 4%), even if we take into accountENF of 4.0 (from Section 9.3.6, with some margin). This is negligible compared to the 1.0%
energy resolution goal.
This fluctuation becomes larger with lower PDE. Fig. 11.8 shows the simulated energy resolution of the signal γ-ray, and the contribution of statistical fluctuation on it. The energy
resolution increases from 0.8% to 1.0% by the lower PDE. This degradation becomes small if wetake the unknown contribution of 1.5% observed in the detector into account. It is notable thatthe statistical fluctuation is directly measured by the even-odd analysis, and the results confirm
that the unknown contribution is not related to the statistical fluctuation term.
Fig. 11.9(a) shows the noise contribution evaluated from the random trigger data in run 2019

1.4

amp gain 1
1.2

amp gain 2.5
amp gain 5

1
0.8
0.6
0.4
0.2
0
0

Branching ratio sensitivity (a.u.)energy resolution (%)

Chapter 11 Expected branching ratio sensitivity of MEG II

141

1.25

1.2

1.15

1.1

1.05

1

0.95

2

4

6

8

10

12

14

16

18

20

22
24
PDE (%)

0.9
0

2

4

6

8

(a)

10

12

14

16

18

20

22

24

PDE (%)(b)

Figure 11.9 (a) Noise contribution in energy resolution. Based on the measurement at each
amplification configuration in the run 2019. (b) Eﬀect on the branching ratio sensitivity
from the energy resolution degradation at diﬀerent MPPC PDEs. Assuming the existenceof unknown contribution of 1.5%. A slight sensitivity degradation is expected at lower
MPPC PDE.

taken at each amplifier configuration. It is still less than 0.6% at 2% of PDE by applying theamplification, and will not be a limiting factor.
Fig. 11.9(b) shows the sensitivity degradation by the energy resolution degradation, where
both the statistical fluctuation and the noise contribution are included. A slight degradation by
4% is expected.

11.3.4 Degradation of pileup elimination by sum waveform
The pileup elimination by the sum waveform consists of a pileup identification by the deviationfrom the template and a waveform fitting with found pileups.
The pileup identification performance is not aﬀected by the lower MPPC PDE since only the
PMT sum waveform is used for the pileup identification in the current implementation. The
precision of the waveform fitting can be aﬀected by lower PDE. Fig. 11.10 shows the precisionof the reconstructed energy A slight degradation of the energy resolution is just due to thestatistical fluctuation discussed in the energy resolution section.

11.3.5 Summary of performance degradation
Fig. 11.11 shows the degradation of the sensitivity which combines that of all the resolutions
at the low PDE. Degradation by 10% is expected in the case of the 2% PDE compared to the
22% PDE. It is notable that the real eﬀect will be smaller than this, roughly half of this, because
the PDE will gradually decrease during the data-taking.

Chapter 11 Expected branching ratio sensitivity of MEG II

142

90

PDE 13%80

PDE 2%

70
60
50
40
30
20
10
0
−2

−1.5

−1

−0.5

0

0.5

1

1.5
2
Energy (MeV)

Branching ratio sensitivity (a.u.)

Figure 11.10 Diﬀerence between the reconstructed energy by the pileup elimination andthe true energy in MC. The simulation including the pileups from the MEG II intensity
beam is used.

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 11.11 MEG II branching ratio sensitivity as a function of MPPC PDE. Eﬀect ofall detector resolutions are included. A smaller value on the vertical axis corresponds to abetter performance of the experiment as defined in Section 11.1.3.

11.4 Eﬀect of PDE degradation: detector operation
More crucial eﬀect of the PDE degradation than the resolution degradation is a limitation on
the maximal operational days without any annealings in the middle. As is shown in Fig. 6.19,
it will take only 60–80 days to reach 2% PDE in the MEG II muon beam in the worst case.
Even though the annealing of the all MPPCs can be performed during the annual accelerator
maintenance period, it is impossible to carry out the planned data-taking for 120 days (84% live
fraction in 140 days beam time) in each year. The degradation in Fig. 6.19 may be biased to befaster as discussed in Section 6.3.4, but here we rely on it for a conservative discussion. In thissection, three alternative plans of the annual data-taking in Table 11.3 are compared, assuming
the PDE degradation in the worst case.

Chapter 11 Expected branching ratio sensitivity of MEG II

143

Plan A : 60 days DAQ at MEG II beam intensity
The first plan is just taking data as long as the LXe detector can be operated. The LXedetector can be operated for 60 days, and the accumulated statistics gets reduced by a factor of
two.
Plan B : 120 days DAQ at halved beam intensity
The second plan is to reduce the beam intensity by a factor of two so that we can keep our
detector operating for 120 days. Since the accidental backgrounds are the dominant backgrounds√
in the search of µ → eγ, the significance Nsig / NBG gets improved than plan A, and theachievable branching ratio sensitivity becomes better than plan A.
Data-taking at the halved beam intensity also improves pileup conditions, and this is anotheradvantage of this plan. The sensitivity degradation by 10% due to the pileup γ-rays shown in
Fig. 11.3(d) is expected to be halved.
In addition to that, preliminary studies suggest that a reconstruction performance of thepositron track is aﬀected by the pileups. A reduced beam intensity can result in an increased
eﬃciency of the positron. This can also be an advantage of this plan, while it is not taken into
account in this thesis since it is not quantified yet.
Plan C : DAQ at MEG II beam intensity + annealing in the middle
The other plan is to anneal all the MPPCs during the beam time. It will take about 40 days
to anneal all the MPPCs*1 . In addition, since the annealing of the MPPCs will be performedat room temperature, detector temperature has to be raised up before the annealing and to becooled down after the annealing. It takes 1–2 weeks for each temperature control. In total, it
will take about 60 days to finish all the annealing processes, and other 80 days can be used forthe data-taking. Advantage of this plan is a higher PDE than the plan A and B thanks to theannealing.
Table 11.3 Comparison of the alternative data-taking plans. The number of the signals
and the backgrounds is normalized by that in original MEG II plan.

plannumber of signal

number of background

PDE

Plan A

0.5

0.5

2–16%

Plan B

0.5

0.25

2–16%

Plan C

0.57

0.57

5–16%

Branching ratio sensitivity in alternative DAQ plans
Fig. 11.12 shows the expected sensitivities for these scenarios. The gradual degradation of
the detector performances by that of the PDE discussed in the previous section is included.
The sensitivity improvement by the RDC is also included. The plan B has the best sensitivity*1 This is the current best estimate, and may include some ambiguity.

Branching ratio sensitivity

Chapter 11 Expected branching ratio sensitivity of MEG II

144

A: 60 days/year at MEG II beam
B: 120 days/year at halved beam intensity
C: 67 days/year at MEG II beam + annealing

10−13

10−14

0

1

2

3

4

5

6

7

year
Figure 11.12 Branching ratio sensitivity as a function of time in three DAQ scenario. The
PDE degradation in the most pessimistic scenario is assumed.

among these three plans as expected from the best significance, since the MEG II branchingratio sensitivity is dominated by the number of accidental backgrounds not by the single event
sensitivity.
Also in the case of the slower PDE degradation, reducing the beam intensity to keep the
PDEs above 2% during the whole beam time like the plan B will be the best option because thesensitivity in the plan C is limited by the time needed for annealing. It is notable that a study
on the faster and easier annealing procedure is ongoing, in which all the MPPCs are heated at
the same time by heating up the cryostat by flowing hot water in a pipe. If the annealing canbe performed more shortly, the plan C may outperform the plan B.

11.5 Eﬀect of pileup rejection by charge distribution
As is discussed in the Section 10.3.3, the performance of the pileup rejection by the charge distribution was not able to be validated from the pilot run. Thus, this method is not applied in thesensitivity discussed above. In this section, its eﬀect on the MEG II branching ratio sensitivity
is discussed for a future reference assuming the expected performance in the simulation.
This method aﬀects the sensitivity by several aspects. Firstly, it identifies about 60% of thepileup events whose energy is reconstructed near the signal energy (Fig. 10.11(b)). As shownin Fig. 11.13(a), a part of the sensitivity degradation by the pileups is suppressed, and 7%
improvement of the sensitivity is expected by this method.
Secondly, this method identifies and rejects about 60% of the AIF 2γ event. Fig. 11.13(b)shows the sensitivity improvement as a function of the reduction power of AIF 2γ events. About

Branching ratio sensitivity (a.u.)

Branching ratio sensitivity (a.u.)

Chapter 11 Expected branching ratio sensitivity of MEG II

1.15

1.1

1.05

1

0.95

0.9

1.15

energy resolution 0.8%
1.1

energy resolution 1.7%

1.05

1
0.95
0.9
0.85

0.85

0.8

145

w/o pileup

w/ pileup, elimination
by sum waveform

w/ pileup, elimination
by both methods

0.8

0

(a)

20

40

60

80

100

AIF reduction power (%)(b)

Figure 11.13 (a) Eﬀect of the pileups and the elimination analysis to the branching ratio
sensitivity. A smaller value on the vertical axis corresponds to a better performance ofthe experiment. (b) Relative branching ratio sensitivity as a function of the AIF reduction
power, assuming a zero ineﬃciency. Due to the smearing of the large fraction of the AIF 2γ
events near the signal energy, the performance depends on the energy resolution.

7 % improvement is expected.
Thirdly, some of the signal γ-ray events are rejected by identifying accidental pileup γ-rayscoming at the same time by this method. The ineﬃciency is estimated to be only 0.3% (Section 10.3.1), and the eﬀect to the sensitivity is negligible.
Fourthly, some of the single γ-ray create a second peak on the charge distribution. This
results in another ineﬃciency of the signal event about 2.4%. The degradation of the sensitivity
is expected to be about 1.6% from a k-factor dependence of the senstivity.
In summary, 12% improvement on the branching ratio sensitivity is expected by this method
if it works as expected in the simulation. Even if the ineﬃciency is doubled, 10% improvement
is expected.
At lower PDE, the statistical fluctuation becomes larger and a misidentification probability
can become larger. For example, as shown in Fig. 11.14, ineﬃciency gets larger at lower PDE
especially at 2%. Since its performance was not validated at the PDE of 8%, the expected performance at lower PDE may not be reliable. Further study should be done after the inconsistency
is understood by further measurements.

11.6 Branching ratio sensitivity of MEG II experiment
The branching ratio sensitivity of MEG II with the developed LXe detector is calculated.
This calculation includes all the eﬀect discussed in the previous sections, except for the improvement by the AIF2γ reduction analysis whose performance has not yet been validated withthe measurement. Table 11.4 and 11.5 show the comparison of the resolution and sensitivity
improvement from MEG.

Inefficiency

Chapter 11 Expected branching ratio sensitivity of MEG II

146

0.1
0.09
0.08
0.07
0.06
0.05
0.04

PDE 12%0.03

PDE 8%

0.02

PDE 6%
PDE 4%

0.01
00

PDE 2%
0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9
1
Efficiency

Figure 11.14 Expected ineﬃcney of the signal event and eﬃciency of the AIF 2γ events
at various PDE.

Fig. 11.15 shows the branching ratio sensitivity as a function of the beam time. The sensitivity
with three years of data-taking will be 6.0–6.6 × 10−14 depending on the PDE degradation speed
in the future. Even in the worst case of the PDE degradation of the MPPCs, the sensitivity
is much better than 8.8 × 10−14 achievable with the MEG LXe detector only with the PMTs,
and thus an upgrade of the LXe detector is meaningful. Since the ambiguity of the estimatedsensitivity comes from that of the PDE degradation speed extrapolated in the future, a further
pilot run or a physics run will reduce the ambiguity.
Table 11.4 Summary of the resolution

MEG

MEG II design

MEG II measured

Position (w < 4 cm/ 4 cm < w)

4.1/3.8 mm

2.4/3.6 mm

2.4/4.8 mm

Energy (w < 2 cm/ 2 cm < w)

2.5%/1.8%

1.1%/1.0%

1.8%/1.8%

62 ps

76 ps

55 ps

Timing

The planned branching ratio sensitivity of 5 × 10−14 can be achieved by extending the datataking time. As shown in Table 11.6, the required data-taking time is 4.0–4.6 year depending on
the PDE degradation speed in the future. This is still within a realistic time and the extensionof the beam time is a significant option*2 . It is notable that the longer data-taking time thanthe original MEG II plan is not a problem from the view point of the PMT lifetime because
most of the PMTs are operatable for five years by reducing the gain (Section 5.1.3) and the
reduced beam intensity will mitigate the PMT gain degradation.

*2 Actually, MEG data-taking was performed for 4.5 years from 2009 to 2013

Chapter 11 Expected branching ratio sensitivity of MEG II

147

Table 11.5 Summary of the sensitivity improvement/degradation from
MEG. A negative value in this table corresponds to a better performanceof the experiment as defined in Section 11.1.3. The ambiguity comesfrom that of the PDE degradation speed in the future.

MEG II design

MEG II measured

Position resolution

−23%

−20%

Energy resolution

−22%

−13%

Timing resolution

+7%

−3%

Detection and analysis eﬃciency

−6%

−4%

PDE degradation0%+0–10%

0%

−12%

−32%

−32–−25%−32%−40–−34%

AIF2γ reduction (MC)Total (without AIF2γ reduction)
Total
*

*

*

Due to the eﬀect of single event senstivity and the senstivity improvement by
the RDC, the sum of each component is not equal to the overall improvement.

Table 11.6 Required time to achieve the branching ratio sensitivity of 5 × 10−14

required time
MEG II design

3.0 year

MEG II LXe detector. Optimal PDE degradation saturated at PDE of 6%.

4.0 year

MEG II LXe detector. Pessimistic PDE degradation (Plan B).

4.6 year

MEG LXe detector + other MEG II detectors

7.6 yearBranching ratio sensitivity

Chapter 11 Expected branching ratio sensitivity of MEG II

148

MEG II. Optimistic PDE degradation
MEG II. Pessimistic PDE degradation

−12

10

MEG LXe detector + the other MEG II detectors.

MEG Final Result

10−13

10−14
0

1

2

3

4

5

6

year
Figure 11.15 Branching ratio sensitivity as a function of time. (Black) With the MEG II
LXe detector in the optimal PDE degradation saturated at PDE of 6%. (Red) With the
MEG II LXe detector in the pessimistic PDE degradation. DAQ at the halved beam
intensity is assumed. (Blue) With the MEG LXe detector, and other MEG II detectors.

149

Chapter 12Conclusion
Conclusion
MEG II experiment is planned to improve the branching ratio sensitivity of a charged lepton
flavor violating decay of a muon, µ → eγ, by one order of magnitude. Improvements on thedetector resolutions are mandatory in MEG II because the performance of the previous MEG
experiment was limited by the number of accidental backgrounds. For this purpose, a new
LXe γ-ray detector has been developed. It utilizes a large area VUV-sensitive MPPC newly
developed to improve the granularity and the uniformity of the scintillation readout.
A series of the pilot runs was performed under the high intensity muon beam. Detector
resolutions were evaluated from the obtained data. An improvement in the position resolution
for the shallow events is confirmed. The timing resolution is estimated to be 55 ps, which
is better than the resolutions in the previous studies thanks to an optimal threshold for thetiming extraction. The energy resolution for the signal energy γ-ray is evaluated by fitting theenergy spectrum of the background γ-rays. Thanks to the better uniformity of the readout,an improvement in the energy resolution for the shallow events (w < 2 cm) is confirmed. Theenergy resolution for the deep events (w > 2 cm) is measured to be worse than expected. Thisis probably due to an unknown contribution also observed in MEG.
A degradation correlated with the beam usage is found on the MPPC PDE for the xenon
scintillation light. This kind of radiation damage was neither reported nor expected. A recoveryof the damage by an annealing process is confirmed. In the most pessimistic scenario of the PDE
degradation in the future, muon beam intensity in the MEG II data-taking has to be halved tokeep a suﬃcient PDE for a suﬃcient resolution.
The branching ratio sensitivity of MEG II with this LXe detector is estimated to be 6.0–
6.6 × 10−14 with three years of data-taking. The ambiguity of the sensitivity comes from that of
the PDE degradation speed in the future. This is worse than the planned sensitivity of 5 × 10−14
mainly due to the worse energy resolution and the PDE degradation. Nonetheless, the planned
sensitivity is found to be still achievable by a realistic extension of the beam time up to 4.6
years. Therefore, it is concluded that the LXe detector has a suﬃcient performance to search
for the µ → eγ decay with a branching ratio sensitivity of 5 × 10−14 .

Chapter 12 Conclusion
Prospect
For a furthur improvement of the sensitivity, a faster annealing procedure should be tried ina future work, which can mitigate the eﬀect of the PDE degradation. Future work should alsomeasure the performance of the pileup rejection by the charge distribution with a full channel
readout to confirm another 12% improvement on the sensitivity. For a better understanding of
the detector, the source of the PDE degradation and the source of the unknown contribution on
the energy resolution should also be investigated.
The MEG II experiment will start the physics data-taking from 2021 by utilizing the LXedetector developed in this thesis, to search for a charged lepton flavor violation and thus aphysics beyond the Standard Model.

150

151

Appendix A

Data reduction algorithm
As mentioned in Section 1.8, to store the obtained data from the MEG II physics data-taking,a data size reduction by a factor of a few is needed before it is written in the disk. Two kindsof data reduction algorithms for the LXe detector are briefly shown in this chapter.
One is a re-binning of the waveforms. In this algorithm, peak regions are defined around peaks
above a threshold (40 photoelectron) in each photosensor waveform, which are important for the
γ-ray reconstruction. Only the signal amplitudes in the peak regions are stored as it is, and thosein the other time regions are re-binned with adjacent time bins by a factor of 8 (Fig. A.1). Since
the threshold is set suﬃciently low, this method does not aﬀect the performances of the γ-ray
reconstruction. This algorithm reduces the number of sampling point, and the data size. The
size of the LXe detector waveforms is expected to be reduced from 3.4 MB/event to 0.7 MB/eventin the simulation, and thus this is a promising method.
Another reduction algorithm called “waveform clustering” is also considered as an option.
This algorithm reduces the granularity of the MPPC readout where no γ-rays hit. The MPPCs
on the inner face are grouped into the adjacent 4×4 MPPCs, and a pulse amplitude of a summed
waveform of each group is calculated. If the pulse amplitude is below a given threshold, waveformof each MPPC in the group is discarded, and only the sum of them are stored. As shown in
Fig. A.2, the granularity of the MPPC readout is reduced in the oﬀ-peak regions, while it is kept
in the on-peak region needed for the hit position reconstruction. This reduces the data size byanother 30% in addition to the waveform re-binning.
These algorithms were not applied in the pilot runs because only the MPPCs near the γ-ray
hit position were read out by the limitted number of channels, and there was little room for thedata reduction. The performances of these methods should be checked with data once the full
readout channels gets available. Especially eﬀects of the reduced granularity should be checkedon the pileup rejection algorithm by charge distribution and on some possible analyses utilizing
the MEG II granularity developed in the future.

Appendix A Data reduction algorithm

152

Waveform

Waveform

00−0.005−0.005

−0.01

−0.01

−0.015−0.015

−0.02

−6

−0.6

−0.5

−0.4

−0.3

(a)

−0.2

−0.1

×10
0

−0.02

−6

−0.6

−0.5

−0.4

−0.3

−0.2

−0.1

×10

(b)

Figure A.1 Data reduction by the waveform re-binning in a simulated example channel.
(a) Before reduction. (b) After reduction.

(a)

(b)

Figure A.2 Data reduction by the waveform clustering in a simulated example event. (a)Before reduction. (b) After reduction.

153

Appendix B

Threshold dependence of timing resolutionof a channel
As disused in Section 8.3, and Fig. 8.5, better timing resolution can be achieved if we use
lower threshold for the timing extraction from the waveforms. In this chapter, a simple model
which explains this behavior is given.
In the scintillation of the signal γ-ray, many photons come to each photosensor. Emitted
photons follow the time distribution of the scintillation (typically an exponential). For thetiming reconstruction of the γ-ray, starting time of this distribution needs to be reconstructedfrom the photosensor waveforms.
First, let’s start discussion when the scintillation time distribution is a constant distribution.
In this case, photons come to a sensor at a constant frequency A [Hz]. Timing of the n-th arriving
photon tn from the start time of the scintillation follows a following relation
ti+1 = ti + δi
, where δi follows a probability distribution of f (t) = A exp (−At). Since δi (0 ≤ i ≤ n) is
independent each other, event-by-event spread of tn becomes,
v
u n
u∑
√
√
σ(tn ) = tσ(δi )2 = nσ(t0 ) = n/A
i=0Fig. B.1(a) shows the spread of tn estimated in a toy simulation, and it follows this expectation.
In reality, scintillation time distribution is not a constant, and σ(ti ) will be diﬀerent. Alsoin those cases, due to the stochastic fluctuation of δi , σ(ti + 1) becomes larger than σ(ti ).
Fig. B.1(b) shows the spread of the n-th photon timing for the exponential distribution of thexenon scintillation time constant.
The better timing resolution by the smaller threshold comes from this statistical fluctuationof the photon arriving timing. By using the smaller threshold, we can extract the timing of aphoton coming earlier, and the better timing resolution can be achieved. Fig. B.2 shows timing
resolution as a function of the constant fraction, where only the fluctuation of the photon arriving
time is considered. It shows a roughly consistent dependence with that in Fig. 8.5.

5 ×10−9

time spread (sec)time spread (sec)Appendix B Threshold dependence of timing resolution of a channel

4.5
4
3.5

5 ×10

4
3.5

3

3
2.5

2

2

1.5

1.5

1

1

0.5

0.5
20

40

60

80

0
0

100
n-th photon

−9

4.5

2.5

0
0

154

20

40

(a)

60

80

100
n-th photon(b)

Figure B.1 Spread of n-th photon estimated from a toy simulation. Spread for 200 photoelectron signal. (a) Assuming a uniform (2.2 MHz) scintillation time distribution. (b)Assuming an exponential (τ = 45 ns) time distribution.

1.4

×10

−9

1.2

1

0.8

0.6

0.4

0.2

0
0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Figure B.2 Timing resolution from photon arriving time fluctuation for 200 photoelectron signal. Assuming xenon scintillation time constant, and single photoelectron MPPC
waveform in Fig. 4.3.

155

Appendix C

List of abbreviations
AIF,AIF 1γ,AIF 2γ

annihilation in flight

Page.119

BTS

beam transport solenoid (magnet)

Page.9CEX

charge exchange (reaction)

Page.51

COBRA

constant bending radius (magnet)

Page.9CW, CW-Li

Cockcroft-Walton (accelerator)

Page.50

LXeliquid xenon

Page.16

PDF

probability density function

Page.132

PSI

Paul Scherrer InstitutePage.5

RMD

radiative muon decay

Page.6

VUV

vacuum ultra violet

Page.17

CE/QE

collection/quantum eﬃciency (of PMT)

Page.67

ECF

excess charge factor

Page.37

ENF

excess noise factor

Page.38

MPPC

multi-pixel photon counter

Page.22

PDE

photon detection eﬃciency (of MPPC)

Page.38

PMT

photomultiplier tube

Page.12SiPM

silicon photo-multiplierPage.13

DCB

data concentrator board

Page.27

DRS

domino ring sampler

Page.27

TCB

trigger concentrator boards

Page.27WDB

WaveDREAM boards

Page.27

photosensor

electronics

156

Acknowledgements
Fist of all, I would like to express my gratitude to Prof. Toshinori Mori who supervised me
and gave me an opportunity to participate the MEG II experiment. I also express my great
appreciation to Prof. Wataru Ootani, and Dr. Toshiyuki Iwamoto who led the development of
the LXe detector. This work would not be completed without their large amount of supports.
I would like to oﬀer my special thanks for Dr. Kei Ieki, Prof. Satoshi Mihara, Prof. William
Molzon, Prof. Ryu Sawada, and Dr. Yusuke Uchiyama for their insightful advices and comments
which are essential in this study.
I would like to express my thanks to all the MEG II colleagues contributing to the experiment.
I would particularly like to thank the members of the LXe group, Dr. Daisuke Kaneko, Satoru
Kobayashi, Rina Onda, and Kazuki Toyoda, who work together with me. I also would like tothank Dr. Marco Francesconi, and Dr. Luca Galli for their supports on the data-taking.
Finally, I am deeply grateful to my family for their support and heartful encouragement.

157

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