Master Thesis

Research and Development on Calibrationof MEG II Gamma Ray Detector（MEG II 実験ガンマ線検出器の較正に関する研究開発）

Department of Physics, School of Science,
The University of Tokyo
35-186077

Kazuki Toyoda
31st, January, 2020

i

Abstract
It is the main interest in the field of particle physics to search for a clue to new physics.
The MEG II experiment searches for the µ → eγ decay, which can be observed only under
new physics. High resolution detectors have been developed to measure the decay products
precisely. A liquid xenon scintillator calorimeter measures the direction, energy and timingof the gamma ray. In order to achieve high resolution, precise calibration of photosensors
and complete understanding of detector response are necessary.
In this thesis three topics on calibration of the gamma ray detector are discussed. First one
is a general study on photosensor calibration methods. Two diﬀerent methods of monitoring
gain of silicon photomultipliers are discussed. One uses the statistical characteristics of thecharge distribution, which is robust to noise. In the other method, gain variation is monitored
by waveform shapes, which allows calibration without a special setup. The second one iscalibration and monitoring of the photosensors in the liquid xenon calorimeter. The gainfrom both methods was confirmed to be correlated to the one obtained from the usual onephotoelectron method. The response of photomultiplier tubes in the calorimeter in operation
were monitored by alpha rays and LED light with the precision of 4%, which satisfies therequirement. The problem of aging of the photomultiplier tubes was also solved by lowering
the high voltage. The third one is about calibration of the detector response using gamma
rays. A new pion beam detector is proposed and is being developed for a possible improvementin the most important calibration method for the liquid xenon calorimeter.

Contents
1 Preface

1

I

2

Introduction

2 Physics of µ → eγ
2.1 Standard Model and New Physics . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Lepton Flavor Violation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Theory of µ → eγ Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.1 µ → eγ in Standard Model . . . . . . . . . . . . . . . . . . . . . . . .
2.3.2 µ → eγ in New Physics . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 µ → eγ Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.1 Signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3
3
4
5
5
6
7
7
8

3 MEG II Experiment
3.1 MEG Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1 Beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.2 Target . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.3 COBRA Magnet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.4 Drift Chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.5 Timing Counter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.6 LXe Calorimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.7 Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.8 Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 MEG II Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Target . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.2 Cylindrical Drift Chamber . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.3 Pixelated Timing Counter . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.4 LXe Calorimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.5 Radiative Decay Counter . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.6 Trigger and Data Acquisition . . . . . . . . . . . . . . . . . . . . . . .
3.2.7 Expected Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10
10
10
12
12
12
13
13
13
14
14
15
15
16
17
19
19
20

ii

Contentsiii

4 LXe Calorimeter
4.1 Hardware . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.1 Characteristics of LXe . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.2 Photomultiplier Tube . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.3 Silicon Photomultiplier . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Event Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.1 Waveform Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.2 Position Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.3 Energy Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.4 Timing Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.1 Photosensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.2 Cockcroft-Walton-Litheum Calibration . . . . . . . . . . . . . . . . . .
4.3.3 Charge Exchange Calibration . . . . . . . . . . . . . . . . . . . . . . .
4.4 Status . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

22
22
22
25
27
32
32
35
36
36
37
37
42
42
43

II

45

Photosensor Calibration

5 Comparison of Gain Monitoring Methods for SiPM
5.1 Gain of SiPM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Statistical Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.1 Previous Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.2 Validation Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.3 Relation between Variance and Mean . . . . . . . . . . . . . . . . . .
5.3 Waveform Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.1 Previous Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.2 Validation Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.3 Application for SiPM . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

46
46
46
47
48
49
52
52
54
55
59

6 PMT Monitoring
6.1 Pre-Engineering Run . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1.1 2018 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1.2 2019 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1.3 Readout Region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1.4 Requirement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2 Calibration Methods and Precision . . . . . . . . . . . . . . . . . . . . . . . .
6.2.1 Alpha Ray . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.2 LED . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3 Cause of Variation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3.1 Eﬀect of Magnetic Field . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3.2 Short-term Variation under Muon Beam . . . . . . . . . . . . . . . . .
6.3.3 Aging Caused by Muon Beam . . . . . . . . . . . . . . . . . . . . . . .

60
60
60
61
61
62
64
64
65
65
65
66
71

Contents

iv

6.4

72
72
73
76
76
78

6.5

III

Gain Decrease . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4.1 Expectation from MEG . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4.2 Beam Rate Dependence . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4.3 Gain Dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Calibration of Detector Response

79

7 Improvement of Charge Exchange Calibration
7.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2 Requirement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.3 Scintillating Fiber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.3.1 Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.3.2 Particle Identification . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.3.3 Radiation Hardness . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.4 Active Target . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.4.1 Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.4.2 Charge Exchange Reaction in Scintillator . . . . . . . . . . . . . . . .
7.4.3 Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.4.4 Energy Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.5 Test of Active Target . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.5.1 Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.5.2 Construction of Prototype . . . . . . . . . . . . . . . . . . . . . . . . .
7.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

80
80
81
82
82
83
84
88
89
91
91
91
93
93
94
94

IV

96

Conclusion

8 Conclusion
8.1 SiPM Gain Monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8.2 PMT Monitoring during Pilot Run . . . . . . . . . . . . . . . . . . . . . . . .
8.3 Development of Pion Beam Detector . . . . . . . . . . . . . . . . . . . . . . .

97
97
97
98

Acknowledgement

99

Bibliography

105

Chapter 1

Preface
Searching for a clue to new physics is the main interest in the field of particle physics.
One of the most powerful ways of looking for a signature of new physics is the µ → eγ search,and its physics overview is explained in Chapter 2. The MEG II experiment is the upgradeof the MEG experiment, which searched for the decay with the best sensitivity in the world,
and they are explained in Chapter 3.
For the MEG II experiment, high resolution detectors have been developed to measure
the decay products precisely. The dedicated detectors have been developed, and all thecomponents will be ready in 2020 at the earliest.
The liquid xenon scintillator calorimeter (LXe Calorimeter) measures the direction, energy
and timing of the gamma ray. The detector construction was finished in 2017, and the next
step is to understand the detector response and to evaluate the performance. In order toachieve high resolution, precise calibration of photosensors and complete understanding ofdetector response are necessary. The detector and the calibration are explained in Chapter 4.
This study aims at developing the calibration methods of the MEG II LXe Calorimeter.
In this paper some topics on the calibration are discussed. The first topic is a general study
on photosensor calibration methods, and two diﬀerent methods of monitoring gain of silicon
photomultipliers are discussed in Chapter 5. The second is the calibration and monitoring of
the photosensors in the LXe Calorimeter. The gain of photomultiplier tubes are monitored
and their sustainability is discussed in Chapter 6. The third is about the overall calibrationof the detector response. A new pion beam detector is proposed and is being developed fora possible improvement in the most important calibration method for the LXe Calorimeter.
This is reported in Chapter 7.
The study is summarized and concluded in Chapter 8.

1Part I

Introduction

2

Chapter 2

Physics of µ → eγ
In this chapter the physics and the motivation of the µ → eγ search are described. In
Sec. 2.1, the current status of the particle physics and methods of searches for new physics are
introduced. One of the most powerful probes for new physics is the search for charged lepton
flavor violation (cLFV) and it is explained in Sec. 2.2. Among some cLFV modes, the targetof the MEG II experiment is µ → eγ decay, whose physics and experimental characteristics
are discussed in Sec. 2.3

2.1

Standard Model and New Physics

The theory of everything has been explored by particle physicists for years, and they
established the Standard Model (SM). Although the SM explains low energy phenomena
very precisely, it does not seem to be the complete theory. There are some experimental facts
that cannot be explained by the SM such as the neutrino oscillation [1]. From the theoreticalpoint of view, it contains some unnatural properties in itself such as the light Higgs massand three generations of the fermion. Moreover, cosmological mysteries such as baryogenesis,
dark matter and dark energy still remain to be solved.
Theorists have been trying to construct an improved theory which compensates for somecracks of the SM. Most of the new physics models contain some new particles, which havenot been observed owing to their high energy scale or their small coupling to SM particles.
All we experimentalists have to do is to find the evidence of the new physics, or thenon SM particles. One major approach is to search for the new particles directly, either
by achieving the ultra low background from SM particles, or by producing a new particle
artificially by colliding SM particles in very high energy. The other approach is to search
for a small discrepancy of an observable from the prediction of the SM. Loop eﬀects from a
new particle can induce a deviation, or even bring about a prohibited reaction in the SM.
A violation of a conservation law of the SM is one of the most eﬀective tools because theSM background is highly suppressed. Lepton flavor conservation is such a representative
conservation law of the SM and explained in detail in the next section.

3

Chapter 2. Physics of µ → eγ

4Figure 2.1: Elementary particles in the SM [2]. The particles in the left side are those which
compose matter. Those in the left bottom are not subject to the strong interaction and called
leptons.

2.2

Lepton Flavor Violation

Figure 2.1 shows the elementary particles in the SM. The particles in the left tables arethose which compose matter and they are called fermions. They have three generations andeach generation is represented as a column. The quarks are fermions which are subject to thestrong interaction while the leptons do not interact by that interaction. In the SM, quarks
can change between themselves over generations while leptons cannot do so. This property
is called the lepton flavor conservation.
The lepton flavor conservation in the electrically neutral sector was found to be violatedby the discovery of the neutrino oscillation [3]. The oscillation attributes to the existence ofmass of neutral leptons, and it can also originate the violation of the charged lepton flavor
conservation. However, a naive extension of the SM cannot make the charged lepton flavor
violation (cLFV) in an observable scale because the masses of neutrinos are too small to mix
the charged leptons enough, as discussed in the next section.
There are a number of extension models of the SM and some of them predict sizableviolation of charged lepton flavor conservation. Although it depends on the size of the couplings or the details of each model, the search for cLFV can probe up to more than PeV scale
physics as shown in Fig. 2.2. The reach is much higher than the future direct production
experiment using high energy colliders.
The muon is a suitable object for a cLFV search. It can be easily produced becuase it
is not so heavy. The physics processes are simple because it is not subject to the strong
interaction. The most powerful historical search is the search for its rare decay µ → eγ, andexplained in the next section.

Chapter 2. Physics of µ → eγ

de

μN→eN

107
106

100

direct reach
EW precision

t→cγ

t→cZ
t→uγ

101

t→uZ

t→ch

h→μe

102

h→τμ

dn

μ→eee

μ→eγ

103

τ →μγ

104

ΔmB
ΔmBs

105

ϵK

106

AΓ
ΔmK

Scale [TeV]

107

5

105
104
103
102
101
100

Observable

Figure 2.2: Reach in the new physics scale of various searches of current and future facilities
estimated from generic six-dimensional operators [4]. The operator coeﬃcients are taken tobe either ∼ 1 (plain colored) or suppressed by Minimal Flavor Violation factors (hatch filled).
Light colors correspond to present data. Cancellations among higher-dimension operators or
the eﬀect of one-loop diagram mediated by SM particles are not taken into account. Someobservables combine the insights from other flavor physics.

2.3

Theory of µ → eγ Decay

2.3.1µ → eγ in Standard ModelIn the minimal extended Standard Model, the main contribution to the µ → eγ decay
is the one-loop process caused by neutrino oscillation as shown in Fig. 2.3. This process isseverely suppressed owing to the tiny masses of neutrinos, and so the branching ratio is
3α ∑ ∗∆m2i1
B(µ → eγ) =Uµi Uei32πMW2< 10−50 ,

(2.1)

i=2,3

where α is fine-structure constant, Uij is the Pontecorvo-Maki-Nakagawa-Sakata matrix,∆mij is the mass diﬀerence of neutrinos, and MW is the mass of the W boson [6]. Thisbranching ratio is quite small compared to the experimental reach, and so the discovery ofthis process is direct evidence of the new physics.

Chapter 2. Physics of µ → eγ

6

W

+

γ

µ+

e+
νµ

νe

Figure 2.3: Feynman diagram of the µ → eγ process in the minimal extended Standard
Model [5].

2.3.2

µ → eγ in New Physics

The SM Lagrangian can be extended as follows using the Eﬀective Field Theory assuming
only that the scale of the new physics is much larger than the electromagnetic scale [7];L = LSM +1 ∑ (6) (6)1 ∑ (5) (5)Ca Qa + 2
C Q + ··· ,Λ aΛ a a a(2.2)

where LSM is the Lagrangian of the SM, Λ is the energy scale of new degrees of freedom that(D)(D)
give rise to the operators once integrated out, Ca are dimensionless coeﬃcients, and Qa
are non-renormalizable operators. Since the operators with D = 5 can induce cLFV onlyat the loop level, the eﬀects arise at the dimension-six level. Considering only dimension-six
dipole operators for simplicity, the following expression for the decay rate can be obtained;Γ(µ → eγ) =m3µ v 2
eµ 2
µe 2
(|Ceγ
| + |Ceγ
| ),
8πΛ4

(2.3)

where mµ is the muon mass and v is the vacuum expectation value of the Higgs field. Thus
µ → eγ can occur under new physics where the energy scale is relatively small or the coeﬃcients of the relevant operators are large.
These parameters depend largely on each model. One of the main theoretical frameworks
which motivates experimental eﬀorts is the Supersymmetry (SUSY) models, which are attractive because they explain the Higgs naturalness problems. Under some of the SUSY models
three kinds of (electromagetic, weak and strong) interactions are unified. SUSY combinedwith the seesaw mechanism can explain the origin of the observed small neutrino masses.
SUSY models enhance the µ → eγ decay because neutrinos in the Fig. 2.3 can be replaced
by SUSY particles and W bosons, and the suppression caused by the separation between theelectromagnetic scale and the neutrino mass scale now disappears. The size of the cLFV
eﬀect caused by the SUSY has been studied in various models. Figure 2.4 shows branchingChapter 2. Physics of µ → eγ

7

Figure 2.4: Rates of µ → e processes predicted in a SUSY seesaw with large slepton mixing [7].
The orange line is the branching ratio of the µ → eγ decay. The purple and green lines are
the branching ratio of the µ → eee and the conversion rate of µN → eN , respectively. The
parameters are chosen aiming at maximising the cLFV eﬀects.
ratios expected from one of the SUSY models, SUSY-seesaw under SO(10) gauge symmetry.
When choosing some parameters to maximize the cLFV eﬀect, the MEG experiment has
already explored new physics up to the SUSY scale of a few TeV, and the µ → eγ decay canbe observed at anytime by succeeding experiments. It shows the importance of increasing
the precision of the µ → eγ search to find the new physics.

2.4µ → eγ Search

2.4.1

SignalSince µ → eγ is a two-body decay, the decay products have the following signatures in
the rest frame of the muon:• coming out in the opposite directions• being produced at the same timing• having the same amount of momentum (mµ /2)
as shown in Fig. 2.5. These distinctive characteristics make it possible to distinguish a signal
from SM decays of the muon.

Chapter 2. Physics of µ → eγ

8

e+

180°

μ+

γ

Figure 2.5: Kinematicsof thesignal event [5]. The decay particles are generated at the same
SatoruKobayashi
timing and go to the opposite directions having the same amount of momentum.

2.4.2

Background

There are two kinds of backgrounds, a physical background and an accidental background.
Physics Background
The muon has a decay mode which emits both a gamma ray and an electron, µ → eν ν̄γ(Fig. 2.6), which is called the Radiative Muon Decay (RMD). When the energy of the twoneutrinos are small, this decay looks similar to the two-body decay signal. The branchingratio of the RMD is (6.0 ± 0.5) × 10−8 when looking at the energy range of Ee > 45 MeV
and Eγ > 40 MeV [8].
Accidental Background
Even when a gamma ray and an electron are not generated from a single source, they canimitate the signal when they accidentally fly in the opposite directions with the same amountof momentum at the same time. The most common source of an electron is the Michel
decay of muons, which accounts for almost 100% of the muon decay branching ratio [9]. The
gamma ray comes mainly from the following two sources. One is the RMD, which is also asource of the physics background. The other is the annihilation of positrons in flight of apositron generated by the Michel decay, which is depicted in Fig. 2.7. The decay positron
can annihilate combining with an electron and generate a gamma ray in material such as amuon stopping target, detectors or beamline components.

!29

Chapter 2. Physics of µ → eγ

9

e+
e-

νe

γ

e+

μ+
νe

μ+

γ

νμ

γ

νμ

Satoru Kobayashi

!29

!28

Satoru Kobayashi

Figure 2.6: Kinematics of the physics background, the Radiative Muon Decay [5]. It
can also be a gamma ray source of an accidental background.

Figure 2.7: Kinematics of the annihilationin flight of the positron from a Michel decay[5].

The number of the accidental backgrounds NBG can be written as follows [10];2NBG ∝ Rµ2 · ∆Eγ2 · ∆pe · ∆θeγ
· ∆teγ(2.4)

where Rµ is the number of the muons decayed in unit time, Eγ is the energy of the gamma ray,pe is the momentum of the positron, θeγ is the opening angle of the two decay particles, teγ isthe generation time diﬀerence between the gamma ray and the positron, and ∆ represents theresolution of detectors for each variable. It is necessary to increase the statistics to improve
the sensitivity with limited time, but the number of the background events increases withthe square of the beam rate. Thus, detectors which have very high resolution are needed toeﬀectively increase the statistics by utilizing a high rate beam.

Chapter 3

MEG II Experiment
3.1

MEG Experiment

The current best limit of the branching ratio of the µ → eγ decay is set by the MEG experiment, which was operated from 2008 to 2013 at Paul Scherrer Institute (PSI) in Switzerland.
Figure 3.1 shows a schematic view of the experiment. Right-handed coordinate wasdefined so that the z axis coincided with the muon beam direction, and the y axis directed
upward vertically. An antimuon beam was generated by a proton accelerator complex at PSI.
An antimuon stopped at a plastic target and it decayed into some particles: positrons, gamma
rays and neutrinos. Positrons flew in a spiral trajectory due to a gradient magnetic fieldcreated by the constant bending radius (COBRA) magnet. Positron tracks were recordedby the Drift Chamber and the timing is measured by the Timing Counter. Gamma rays
were detected by the LXe Calorimeter after going through a thin aluminum window on the
COBRA wall. All waveforms were recorded using waveform digitizers. Each component isbriefly described below.

3.1.1

Beam

PSI has provided 590 MeV proton beam accelerated by the large proton cyclotron (Fig. 3.2).
The current of the proton was 2.2 mA at maximum. The protons collided into a graphitetarget and generated positive pions. The pions decayed into antimuons through the reaction
π + → µ+ + νµ . When the pion was at rest when it decays, a completely polarized muon(Pµ = −1) was generated whose momentum was 29.8 MeV/c. Those produced around thesurface of the target selectively went into the πE5 beamline, and went through a separator
and the Beam Transport Solenoid (BTS), and finally were stopped by a plastic target. They
were unpolarized during this transportation, and their polarization became Pµ ≃ −0.85 at
the target [13]. Figure 3.3 shows a schematic view of the MEG beamline.
At the πE5 beamline the world’s highest DC muon beam intensity was available. However,beam rate was reduced because the number of accidental backgrounds increases proportional
to the square of the beam rate as discussed in Sec. 2.4.2, and it was better to operate at lower
intensity considering the detector performance.

10Chapter 3. MEG II Experiment

11

Figure 3.1: Schematic view of the MEG experiment [11]. Positrons and gamma rays generated
from muons were detected using three diﬀerent detectors: the Drift Chamber, the Timing
Counter and the LXe Calorimeter.

Figure 3.2: Large proton cyclotron at PSI. [12] It produces protons of which energy is 590
MeV and the current is 2.2 mA at maximum.

Chapter 3. MEG II Experiment

12

Figure 3.3: Schematic view of the MEG beamline [10]. Protons generated from a cyclotron
were converted into pions and they decayed into muons. The muons were transported to thetarget through the πE5 beamline, a separator and the BTS.

3.1.2

Target

The target was 205 µm thick and has an elliptical shape. It was tilted by 20◦ to the beamaxis in order to increase the muon stopping eﬃciency while suppressing interactions with the
decay products.

3.1.3

COBRA Magnet

The COnstant Bending RAdius (COBRA) magnet was designed to make a gradient magnetic field which kept the radius of the positron constant independent of the emission angle
at the target as schematically depicted in Fig. 3.4. Thus, the radius only depended on thepositron momentum, and only those with the momentum around that of signal (52.8MeV/c)
could reach the detectors. Positrons emitted almost perpendicular to the beam axis did notstay in the spectrometer and they were quickly swept away. This mechanism reduced thepileup in the spectrometer caused by the large number of Michel positron backgrounds.
The magnetic field strength was 1.27 T at the center and 0.5 T at each end. The photomultiplier tubes (PMTs) used in the LXe Calorimeter were aﬀected by the magnetic field. Therefore there were compensation coils which reduced the magnetic field around the calorimeterto under 5 mT.

3.1.4

Drift Chamber

Positron tracks were recorded by the Drift Chamber. Gas in the chamber was ionized bya positron and charge was induced to wires. Sixteen drift chambers were installed inside the
COBRA magnet and wires were stretched parallel to the beam axis. The signals were readout by anode wires and zigzag-shaped cathode pads.
The chambers are placed a little away from the beam axis in order to avoid pileups fromlow momentum Michel positrons which flew in a small radius region.

Chapter 3. MEG II Experiment

13

Figure 3.4: Schematic view of the cross section of the COBRA magnet and the positron spectrometer [14]. The gradient magnetic field made the radius of the positron track independentof the emission angle.

3.1.5

Timing Counter

The time of the positron was measured by the Timing Counter. It was made of 80 cm longplastic scintillator bars. The scintillation photons were read out by fine-mesh PMTs attachedat either side of the scintillator bars. Thirty bars were installed just outside the Drift Chamber
and inside COBRA magnet, and the bars measured the azimuthal angle of a positron hit
discretely. The position in the beam direction was measured by the time diﬀerence between
the PMTs at either side. The information about the reconstructed positions was used tomatch each hit with the Drift Chamber track.

3.1.6

LXe Calorimeter

The gamma ray detection is the key for the background reduction because the number ofaccidental backgrounds is proportional to the square of the energy and position resolution of
the gamma ray as shown in Eq. (2.4). In the MEG experiment, LXe was used as a scintillator
and PMTs detected the scintillation photons. The main component of the calorimeter was
900 L LXe and it was stored in a C-shaped cryostat shown in Fig. 3.5, which covered 11%of the solid angle from the target. The PMTs are on all of the 6 inner faces: inner, outer,
lateral (upstream and downstream), top and bottom. The detail will be explained in Chap. 4
because the gamma ray detector of the MEG II experiment, which is the main topic of thisthesis, is based on this MEG LXe Calorimeter.

3.1.7

Data Acquisition

A fast waveform digitizer was utilized in the MEG experiment, because pileup identification was important under the high intensity muon beam. The digitizer is named Domino
Ring Sampler (DRS).

Chapter 3. MEG II Experiment

14

Figure 3.5: Outlook of the LXe Calorimeter [14]. It has a unique C-shape to cover a largesolid angle.

Fig. 3.6 shows the principle of the DRS. The voltage information is sampled in high speed
and the sampling signals transfer through the inverter delay chain circle. When a trigger
signal is input, the rotation of the signals stops and the voltage value is sequently read out
by a shift resister. The sampling frequency can be chosen from 0.5 GHz to 5 GHz. The LXeCalorimeter and the Timing Counter, which were responsible for the timing measurement,
used 1.6 GHz sampling, and the Drift Chamber used 0.8 GHz.
The MIDAS system [16] was used as a data acquisition system.

3.1.8

ResultDuring the physics run period from 2008 to 2013, 7.5 × 1014 muons were stopped at thetarget [11]. A blind and maximum likelihood analysis resulted in the null consistent numberof signals, and the world best upper limit was set on the branching ratio: B(µ → eγ) <4.2 × 10−13 (90% C.L.) [11], while the sensitivity was estimated to be 5.3 × 10−13 . The main
source of the systematic uncertainty was the target deformation. It degraded the sensitivity
by about 13% while the total contribution of the other systematics were less than 1%.

3.2

MEG II Experiment

The MEG collaboration decided to terminate the MEG experiment in 2013 and to concentrate on the upgrade of the experiment because they considered it ineﬃcient to continue

Chapter 3. MEG II Experiment

15

Figure 3.6: Principle of DRS [15]. Rotating inverter chain stores the voltage in condensers,
and it is read out by a shift resister.

it with the reduced muon beam rate. The upgraded experiment was named the MEG II
experiment and the key point of this upgrade is to utilize the full muon beam intensity. The
muon stopping rate at the target will reach 7 × 107 µ/s, which is more than twice larger thanthat in the MEG experiment. As discussed in Sec. 2.4.2, the number of accidental background is proportional to the square of the beam rate. In order to overcome this problem,
the resolution of each measured variable is supposed to be twice better than in the MEG
experiment. The detectors also have to become robust aginst the increase of pileup events.
The upgrade of each components is summarized below.

3.2.1

Target

The MEG II stopping target is made of a scintillating plastic film with the average thickness of 174 µm, and it is placed at 15.0◦ to the beam axis. The smaller thickness and angle
reduce the material budget. Stopping eﬃciency is maximized by adjusting the beam degrader
thickness.
The main source of the systematic uncertainty of the MEG experiment was the vertex
estimation resulting from the target distortion. Therefore, two cameras are installed forthe monitoring of the target shape in the MEG II experiment, and the deformation will bemonitored by the dots printed on the target. Figure 3.7 is the picture of the target and thetwo cameras in the beamline.

3.2.2

Cylindrical Drift Chamber

In the MEG experiment, positron detection eﬃciency was reduced by scattering of thepositrons by the mechanical frame or the electronics of the Drift Chamber before entering
the Timing Counter. For the MEG II experiment a single-volume drift chamber, the Cylindrical Drift Chamber, has been developed and there is no unnecessary material between the
Cylindrical Drift Chamber and the timing counter. The length of the chamber is 193 cm andthe inner (outer) radius is 17 cm (29 cm). The stereo angle structure of the wires provides

Chapter 3. MEG II Experiment

16

Figure 3.7: Picture of the target and the two cameras installed in the beamline [17].
the position information along the beam axis. The hyperbolic shape due to the stereo angle
wiring is visible in Fig. 3.8. It can endure the high rate backgrounds owing to the small
drift cells (6.6–9 mm). In a cell a 20 µm-diameter gold-plated W sense wire is surrounded by
40 µm-diameter silver-plated Al field wires. A radiation length per track turn is 1.58×10−3 X0
when the chamber is filled with a gas mixture of helium and isobutane in the ratio 90:10,
compared to 2.0 × 10−3 X0 in the MEG experiment.
It was mounted inside COBRA magnet in 2018, and the stability of the current under
the intense muon beam is studied with the limited number of readout channels in 2019.

3.2.3

Pixelated Timing Counter

The scintillators used for the Timing Counter of the MEG experiment was so large that
there was large variation of the optical photon paths, leading to worse resolution. It would
also lead to more pileups if it was used in the higher rate environment.
The timing of the positron is measured by the Pixelated Timing Counter in the MEG II
experiment. Each counter is made of a small plastic scintillator read out by series-connected
6 SiPMs at either side. The size of each counter is (40 or 50) × 120 × 5 mm3 . The timing
resolution of a single counter is about 80 ps [10]. One module consists of 256 counters asshown in 3.9 and it was placed at each of the upstream and the downstream side of the target.
By measuring the timing by 9 counters per track on average, even better timing resolution
can be achieved. The measured resolution at a pilot run in 2017 was 38.5 ps [18]. The
pixelated structure also enables the operation under a large number of backgrounds because
there are a small number of pileups at each counter. This structure also enables the trackingof the positron only by the Timing Counter itself, possibly resulting in the improvement ofChapter 3. MEG II Experiment

17

Figure 3.8: Cylindrical Drift Chamber of the MEG II experiment [10]. There is no unnecessary material in the path to the Pixelated Timing Counter.
the matching eﬃciency with the Cylindrical Drift Chamber.

3.2.4

LXe Calorimeter

The largest change of the gamma ray detector from the MEG experiment is the photosensors at the gamma ray incident face. In the MEG experiment, gamma rays which converted
in the shallow region had worse resolution than those in the deep region on account of the
non-uniformity caused by large PMTs. The MEG II experiment employs smaller sensors,silicon photomultipliers (SiPMs), at the incident face. The sizes can be compared with eachother in Fig. 3.10 which shows inside the calorimeter. The SiPM is only 15 × 15 mm2 while
the PMT is 57 mm in diameter. The uniformity improves by placing sensors with smallergaps, which leads to the better energy resolution for shallow events and twice better position
resolution. Furthermore, the high granularity will also improve the performance of the pileup
identification. Owing to the decrease of the amount of material at the incident face, thedetection eﬃciency of the gamma rays is expected to become higher by absolutely about 5%
than the MEG experiment.
Another upgrade is the change in the placement of the photosensors. The incident facehas become wider by 10% in the beam direction, which reduces the energy leakage for eventsnear the lateral face. The PMTs on the lateral faces are tilted so that all the photocathodes
will lie in the same plane, which minimizes the eﬀect of the fluctuation in the electromagnetic
shower development.

Chapter 3. MEG II Experiment

18

Figure 3.9: Pixelated Timing Counter of the MEG II experiment. The pixelated configuration
reduces the pileups, improves the resolution, and enables the self tracking.

Figure 3.10: Inside of the LXe Calorimeter of the MEG II experiment. The PMTs on theincident face (bottom of this picture) are replaced with small SiPMs.

Chapter 3. MEG II Experiment

19

Figure 3.11: Concept of the RMD active detection [10]. The low energy positron from the
RMD is be detected by a counter put on the beam axis.

3.2.5

Radiative Decay CounterA radiative decay counter is newly introduced in the MEG II experiment for the purposeof the active detection of the RMD background events, which are the main source of a gamma
ray background. RMD emits a positron whose energy is around 3 MeV, corresponding to the
gamma ray which has energy similar to that of the signal (52.8 MeV). This low energy positronis trapped around the beam axis owing to the magnetic field produced by the COBRA magnet.
Therefore, a detector put on the beam axis can detect the RMD positrons selectively as
schematically depicted in Fig. 3.11. A low energy positron detected simultaneously with agamma ray will be recognized as the RMD positron.
The half of the RMD positrons go toward upstream. The upstream counter must be
put on the muon beam path in order to detect low energy positrons. On account of thediﬃculty in avoiding the interaction with muon beam, development of only the downstreamside counter has been already finished. It consists of two parts, a timing counter made of 12
plastic scintillators, and a calorimeter made of 76 Lutetium Yttrium Orthosilicate (LYSO)
crystals, as shown in Fig. 3.12. The photons are read out by SiPMs. The timing information
is used to take a coincidence with the gamma ray signal, and the energy information is used
to distinguish lower energy RMD events from higher energy Michel events.

3.2.6

Trigger and Data Acquisition

Owing to the higher segmentation of each detector, signals from about 9000 channels must
be read out, which are three times more than those in the MEG experiment. Channels for
SiPMs should have the function of a high voltage supply. In addition, a flexible amplification
was necessary for SiPMs because small gain is used to observe gamma ray signals without
saturation while large gain is needed for calibration by a single-photoelectron peak explainedin Sec. 4.3.1.
For these reasons, the WaveDAQ system has been developed for the MEG II experiment.
It is an integrated system of triggering and data acquisition. The DRS4 based readout module

Chapter 3. MEG II Experiment

20

Figure 3.12: Schematic image of the radiative decay counter in the downstream side [10].
A timing counter made of plastic scintillators is in front of a calorimeter which consists of
LYSO crystals.

(WaveDREAM) boards are used for data acquisition, and they have several components suchas amplifiers, DRS chips, shapers and a high voltage source. The gain of the amplifier canbe chosen from 0.5 to 100. Sixteen channels are read out by one board, and 16 boards are
put in one crate. They are synchronized within 20 ps over diﬀerent crate modules [19]. The
MIDAS system [16] is used as a data acquisition system.

3.2.7

Expected Sensitivity

The expected performance of the MEG II detector is shown in Tab. 3.1. Based on thisperformance evaluation, the 90% confidence level sensitivity of the µ → eγ branching ratio is
calculated as a function of the data acquisition time as shown in Fig. 3.13. After three years
operation, the sensitivity will reach 6 × 10−14 .

Chapter 3. MEG II Experiment

21

Table 3.1: Expected performance of the MEG II detectors [10].
parameter
energy resolution of e+angular resolution of e+ at target
position resolution of e+ at target
energy resolution of γ (at deep, at shallow)
position resolution of γ conversion point
resolution of decay time diﬀerence
detection eﬃciency of γ
detection eﬃciency of e+σEeσθe , σeϕ
σxe
σEγ /Eγ
σu , σv , σw
σteγ
ϵγ
ϵe+

MEG
306 keV
9.4 mrad, 8.7 mrad
1.2 mm, 2.4 mm
1.7%, 2.4%
5 mm, 5 mm, 6 mm
122 ps63%
30%

MEG II
130 keV
5.3 mrad, 3.7 mrad
0.7 mm, 1.6 mm
1.0%, 1.1%
2.6 mm, 2.2 mm, 5 mm
84 ps
69%
70%

Figure 3.13: Sensitivity for the branching ratio of µ → eγ decay [10]. 6 × 10−14 is expected
after three years operation.

Chapter 4

LXe Calorimeter
Since the studies in this thesis aims at the improvement of the performance of the gamma
ray reconstruction, the gamma ray detector is explained in more detail here. The first section
is about the hardware. The event reconstruction is explained in the next section. The
calibration, which is necessary for the proper reconstruction and is the main topic of thisstudy, is explained in the third section.

4.1

Hardware

The gamma ray detector of the MEG II experiment is a LXe scintillation calorimeter,and scintillation photons are read out by PMTs and SiPMs located on the inner wall.

4.1.1

Characteristics of LXe

LXe is an optimal scintillator for the MEG experiment. The basic properties of LXe issummarized in Tab. 4.1.
The advantages of LXe as a scintillator are as follows;• uniformity• no self absorption

Table 4.1: Characteristics of LXe.
atomic number
54
atomic weight131.293 [9]density
2.98 g/cm3 [20]radiative length
2.77 cm [9]W value for electron
21.6 eV/photon [21]W value for α particle
19.6 eV/photon [22]wavelength of scintillation light 174.8 nm [23]Rayleigh scattering length
45 cm [24]22Chapter 4. LXe Calorimeter

23

Figure 4.1: Phase diagram of the LXe [25]. A careful operation is needed to keep the liquid
phase.
• short radiation length (2.77 cm)• short time constant for gamma ray (45 ns)• particle identification by waveforms
In contrast, following concerns should be carefully treated;• necessity of being kept in low temperature (165 K)• short wavelength of the scintillation photon (175 nm)• short Rayleigh scattering length (45 cm)• change of properties such as a light yield and light propagation by impurity
As shown in Fig. 4.1 the pressure and the temperature must be kept in a quite narrow region
in the phase diagram in order to keep the liquid phase. For example, the temperature should
be kept between 161 K and 165 K at 1 atom. Figure 4.2 shows that the absorption length isquite sensitive to the impurity.
When an energetic particle interacts with xenon, xenon atoms can be excited or ionized [27]. The excitation leads to fast scintillation. The excited xenon atom combines toChapter 4. LXe Calorimeter24

Figure 4.2: Eﬀect of impurity on the absorption length of LXe [26]. The absorption length
becomes comparable with the detector size especially when large amount of H2 O is contaminated.

Chapter 4. LXe Calorimeter25

Table 4.2: Basic properties of the PMT used in the MEG II experiment (R9869) [29].
size
57 mmϕsize of sensitive area
45 mmϕlength32 mmmaterial of photocathode K-Cs-Sb
type of dynodemetal channel
number of dynode12
another atom to make excited molecular state. This state immediately de-excites and emitsa scintillation photon;Xe∗ + Xe + Xe → Xe∗2 + Xe,(4.1a)

Xe∗2 → 2Xe + hν.

(4.1b)On the other hand, the ionization leads to slow scintillation. Although the ionized xenon also
finally results in the emission of a scintillation photon, the process chain is more complicatedthan that of the excited xenon atom.
Xe+ + Xe → Xe+2,−

Xe2 + e → Xe

∗∗

∗∗

∗

+

+ Xe,

(4.2b)→ Xe + heat,(4.2c)+ Xe + Xe → Xe∗2 + Xe,
Xe∗2 → 2Xe + hν.

(4.2d)

Xe
Xe∗(4.2a)(4.2e)

The fraction of these processes depends on the size of the energy deposit in unit volume,and diﬀerent depending on the particle as shown in Fig. 4.3. The alpha ray deposits large
energy in unit volume and it makes fast scintillation, whose time constant is 4.2 ns or 22 ns.
The gamma ray generates electrons in LXe and they deposit smaller energy in unit volume.
It makes slow scintillation, whose time constant is 45 ns. This diﬀerence in the scintillation
time constant enables particle identification. Since the final process is the same as that of
the excitation case, the wavelength of the scintillation light is the same.

4.1.2

Photomultiplier Tube

The photomultiplier tubes (PMTs) for the MEG experiment were developed with Hamamatsu photonics [28] to have enough sensitivity for the scintillation photons from xenon whose
wavelength is around 175 nm. The basic properties is shown in Tab. 4.2. The window of the
PMT is synthetic quartz glass and it is transparent for the wavelength down to 160 nm. The
transmittance for the xenon scintillation wavelength (175 nm) is about 80%. To keep highquantum eﬃciency even at LXe temperature (165 K), an aluminum strip pattern is printed
on the photocathode as can be seen in Fig. 4.4, which keeps low surface resistance. The metalchannel dynode structure realizes the fast response and the compactness, and it enables theoperation under the COBRA magnetic field (50 Gauss).

Chapter 4. LXe Calorimeter

26

Figure 4.3: Time constant of the scintillation of LXe [27]. The response to alpha particles isfast while that to electrons are slow.

Chapter 4. LXe Calorimeter

27

Figure 4.4: PMT used in the LXe Calorimeter (R9869). An Aluminum strip pattern maintains high quantum eﬃciency even at low temperature.
The divider circuit is shown in Fig. 4.5. Two Zener diodes play a role in keeping thevoltage applied to the latter dynodes constant. It prevents from the voltage drop caused bylarge current, and the uniform distribution of the voltage between the dynodes is secured
even under high rate signals.

4.1.3

Silicon PhotomultiplierIn the MEG II experiment, silicon photomultipliers are newly introduced to increase thegranularity and the uniformity of the photon detection on the gamma ray incident face.
Operating Principle
A SiPM is a kind of semiconductor photon detector. By applying inverse bias voltage on
p-n junction, a depletion layer is made. The photon entering the layer makes an electronhole pair and it works as the seed of the signal. This electron is also called photoelectron.
The photoelectron is accelerated by the electric field and make an avalanche multiplication.
During the multiplication process, electrons and holes collide with the lattice of the silicon
crystal, and new electron-hole pairs are sequently produced. SiPMs work in the Geiger modeand the operating voltage is larger than the breakdown voltage. The operation under theGeiger mode results in multiplication whose gain is about 106 , and it is called a Geiger
discharge. The principle of an avalanche multiplication is schematically depicted in Fig. 4.6.
In order to control the multiplication, each pixel is connected in series to a quenching
resister (Fig. 4.7), which makes the voltage drop and finishes the multiplication. Since eachChapter 4. LXe Calorimeter

28

Figure 4.5: Divider circuit for the PMT [29]. Two Zener diodes (Z1 and Z2) keep the voltage
distribution uniform even under the high rate beam.

Figure 4.6: Visualization of an avalanche multiplication [30]. An avalanche is caused in a
depletion layer.

Chapter 4. LXe Calorimeter

29

Figure 4.7: Quenching resisters in a SiPM [30]. The voltage drop caused by them finishes
the avalanche multiplication.
pixel can detect a photon digitally, the SiPM can count the number of incident photons byconnecting pixels in parallel.
Characteristics
The SiPM has the following advantages compared to the PMT.
• good single photon counting ability• can be operated under a magnetic field• low bias voltage• smallOn the other hand, the following properties must be carefully treated.
Dark Count Thermal excitation or tunneling eﬀect can generate a one-photoelectron signal even when no photon enters the SiPM. It can be reduced by keeping the SiPM at low
temperature as shown in Fig. 4.8. The dark count rate at the LXe temperature is known tobe low enough to neglect.
Crosstalk Even when only one pixel makes a Geiger discharge primarily, a photon generated in the avalanche process can cause another Geiger discharge at another pixel, resulting
in a two-photoelectron signal. It is called a prompt crosstalk. Sometimes the secondary
photon is absorbed in the base and a career scatters, making a Geiger discharge at anotherpixel later. This is called a delayed crosstalk.

Chapter 4. LXe Calorimeter

30

Figure 4.8: Dark count rate at low temperature for 3 mm2 samples [10]. The dark countrate at the LXe temperature (165 K) is about 100 Hz which can be neglected in the MEG II
experiment.

Chapter 4. LXe Calorimeter

31

Figure 4.9: Saturation eﬀect of a SiPM. When the number of photoelectrons is comparable
to the number of pixels, the response becomes non-linear on account of the saturation.
Afterpulsing When an electron in avalanche multiplication is trapped to an energy level
made by a lattice defect or impurity, it can make another avalanche in the same pixel later. It
is called afterpulsing. Since it happens in the same pixel with the primary Geiger discharge,
the signal height depends on the recovery time of quenching.
Saturation Since a SiPM counts the number of photons by the number of fired pixels,
it cannot detect the photons entering simultaneously to the same pixel. Thus the response
becomes non-linear when the number of photoelectrons is comparable to the number of pixels
as shown in Fig. 4.9. The saturation is not a problem in the MEG II calorimeter becauseeven the events which have conversion points close to the incident face do not generate somany photons as to saturate the SiPM [10].
Temperature Dependence The breakdown voltage of the SiPM depends on temperature
because the interaction between the career and the phonon decreases at low temperature andthe careers are easily accelerated.
Radiation Hardness Semiconducting detectors generally require careful handling concerning radiation hardness. In particular, the irradiation by the neutron increases the darkcount rate. The expected 1.6 × 108 n/cm2 irradiation during the MEG II experiment [10] willlead to 2–3 times larger dark count rate [31], but it is not a problem at low temperature in
LXe. The gamma ray irradiation increases the leak current when the dose is over 200 Gy [32].
Since the expected dose is only 0.6 Gy in the MEG II experiment [10], it is not a problem
either.

Chapter 4. LXe Calorimeter32

Development
There are the following requirements for the SiPMs used in the MEG II experiment.
• high sensitivity to the VUV light (175 nm)• operational under low temperature (165 K)• large area per channel (12 mm × 12 mm)• shorter time constant than that of the scintillation (45 ns)
The high sensitivity to the VUV light was achieved by thinning the contact layer andreplacing the protecting layer with a VUV-transparent quartz window. In order to cover thelarge area by one readout channel, 4 chips are read out as one channel. The size of each chipis 6 × 6 mm2 . A hybrid connection scheme was developed to apply the bias voltage in parallel
while reading the signal in series, and it is shown in Fig. 4.10. The parallel connection of
the high voltage line keeps the total high voltage small and prevents from the discharges
between chips. The series connection of the readout line makes the time constant of thesignal waveform small because it reduces capacitance.

4.2

Event Reconstruction

In this section the reconstruction method of each variable is explained. The goal of
the reconstruction of the LXe Calorimeter is to obtain three key variables of a gamma ray;the position of the first conversion point, the timing of the first conversion, the energy ofthe gamma ray. The reconstruction flow is shown in Fig. 4.11. First the charge and thetiming are obtained from the waveform of each sensor. Then the charge is converted to
the number of primary photoelectrons (Npe ) and the number of incident photons (Npho ).
From the position distribution of Npho in the incident face, the first conversion point isreconstructed. The energy and the timing are reconstructed using the distribution of Nphoand timing, respectively. The reconstructed position of the conversion point is also used forthe reconstruction of those variables.

4.2.1

Waveform Analysis

Charge and timing of the signal detected by each photosensors are extracted by waveform
analysis. Before that, a baseline slope and coherent noises are reduced by noise reduction.
The baseline of a waveform of a WaveDREAM board has a slope as shown in Fig. 4.12,
which is considered to be due to the current leakage at the DRS. The voltage stored in thecapacitors are sequently read out. If the voltage decreases at the same speed by a leakage,
the bins which are read out later have lower voltage, resulting in the slope of the baseline.
Since the slope is correlated to the temperature of the WaveDAQ board, it is corrected using
the templates prepared for each temperature by the pedestal data taken periodically.
In order to synchronize all the readout channels, a clock signal is input to one channel
in the DRS. The coherent noise synchronized to this clock signal is reduced using a noiseChapter 4. LXe Calorimeter

33

Figure 4.10: Hybrid connection scheme [33]. Parallel connection and series connection is
combined incorporating the benefits.

Chapter 4. LXe Calorimeter34

waveform
chargeeach sensor

time

Npe
Npho
positiongamma rayenergytimingFigure 4.11: Reconstruction flow of the LXe Calorimeter. Charge and timing are obtained
from waveforms of each channel, and they are used to reconstruct the position, timing andenergy of the gamma ray.

Voltage[V]Sum Waveform

0.2
0
−0.2
−0.4
−0.6
−0.8
−1
−1.2
−1.4
−800−700−600−500−400−300−200−100
Time[ns]

Figure 4.12: Baseline slope of the waveform before (black) and after (red) correction [5]. The
slope is considered to be caused by the current leakage at the DRS.

Amplitude [a.u.]

Chapter 4. LXe Calorimeter35
FFT of MPPC sum WF

10

1

10−1
0

100

200

300

Frequency

400

500 MHz
600

Figure 4.13: Amplitude spectrum of the sum waveform of 640 SiPMs before (black) and after(red) the noise subtraction.
template made from the pedestal runs after the baseline subtraction. Fig. 4.13 shows theperformance of the noise subtraction.
The timing is extracted by the constant fraction method to avoid a time-walk eﬀect tomake it independent of the signal height.
The charge is extracted by integrating the waveform. The baseline charge is also calculatedusing the region before the waveform, and subtracted from the signal charge. The obtained
charge is transformed to Npe , which denotes the number of photoelectrons (for PMT) or thenumber of primary Geiger discharges (for SiPM), using a calibration factor 1/(G·ECF ). HereG denotes the gain, and ECF is the excess charge factor, which corresponds to the charge
excess due to crosstalks and afterpulses of the SiPM. Npe is converted to the number ofincident photons, Npho , by a calibration factor 1/P DE, where P DE is the photon detection
eﬃciency. These factors are obtained by diﬀerent calibration methods and explained in detailin the next section.

4.2.2

Position Reconstruction

The position of the first conversion point x is reconstructed by minimizing the following
chi squared;
sensors∑ ( Npho, i − C · Ωi (x) )2
2
,
(4.3)
χ =
σNpho, iiwhere C is a nuisance parameter representing the total light yield, Ωi (x) is the solid angle ofthe sensor i viewed from a position x, and σ is the statistical uncertainty of the estimation of
the Npho, i . In reality, the photon distribution depends on the direction of the electromagnetic

Chapter 4. LXe Calorimeter

36

shower development and the eﬀect is corrected.

4.2.3

Energy Reconstruction

The energy is reconstructed basically by summing the number of photons entering eachsensor. There are actually some corrections and the equation of the reconstruction is asfollows;
sensors∑Eγ = C · FE (x) ·(αi · Npho, i ),(4.4)
iwhere C is a calibration constant to convert the number of photons to the energy, FE (x) isthe correction function which correct the position dependence of the detector response, αi isgeometrical weight for each sensor. αi is fixed by the geometry, and C and FE is determinedby dedicated calibration experiments explained in Sec. 4.3.3

4.2.4

Timing Reconstruction

First of all, the timing of the first conversion is estimated channel by channel using thefollowing equation;
tconv, i = tsensor, i − tdelay (di , ηi , Npe, i ) − toﬀset, i ,(4.5)

where i denotes each sensor. tsensor, i is the constant fraction time obtained by the waveform
analysis. tdelay (di , ηi , Npe, i ) is a correction function which depends on the distance between
the conversion point and the sensor di , the angle between the conversion point and the sensor
ηi , and Npe, i . toﬀset, i is a channel by channel oﬀset due to the cable and the electronics
synchronization. tdelay is described by three components,
tdelay (di , ηi , Npe, i ) = tToF (di ) + tindir (ηi ) + twalk, α (Npe, i ).

(4.6)

tToF is the time of the photon propagation from the conversion point to the sensor. tindiris the eﬀect of a delay of the arrival of photons scattered somewhere and it is a function of
ηi , because the number of indirect photons increases with the angle between the light source
and the sensor. twalk is the time walk which cannot be completely eliminated by the constantfraction method. Since the waveform is diﬀerent for the PMTs and the SiPMs, and for the
production lots of the SiPM, the time-walk correction function is prepared separately forthem as indicated by α in the equation.
The conversion time tconv is estimated by the maximum likelihood method using tconv, iof each sensor. The likelihood function is written as follows;∏L(tconv ) =f (tconv, i − tconv , Npe, i ),(4.7a)if (dt, Npe ) = ExpGaus(dt; σ(Npe ), τ (Npe )),()
 exp − dt22
(dt < σ 2 /τ )( 2σ)ExpGaus(dt; σ, τ ) =,2 /τ )
 exp − dt + σ22
(dt
>
σ
τ
2τ

(4.7b)(4.7c)

Chapter 4. LXe Calorimeter

37

where σ(Npe ) is the timing resolution, and τ (Npe ) is the eﬀect that scintillation photons do
not come probabilistically when the number of photoelectrons is small. Both functions are
determined by a dedicated calibration run explained in Sec. 4.3.3.
A simulation study shows that the obtained tconv still depends on the conversion position
although the cause is not understood [34]. Thus finally it is corrected by a global correction
function which provides a correction factor depending on the conversion position. This global
function is also obtained by a calibration run.

4.3

Calibration

The event reconstruction requires various calibration parameters. In the MEG II experiment, the photosensors are calibrated using LEDs and alpha ray sources, and the overall
detector response is calibrated by two diﬀerent gamma ray sources.

4.3.1

Photosensor

When Npho photons enters the sensitive area of the photosensor, the charge Q obtained
from the waveform is written as follows;
Npe = Npho · P DE,
Q = Npe · ECF · G · e.

(4.8a)(4.8b)The photon goes through the window and is detected generating a photoelectron with Photon
Detection Eﬃciency (P DE). P DE of a PMT is written as the product of the quantum
eﬃciency (QE) and the collection eﬃciency (CE). QE is the probability of an incident
photon producing a photoelectron on the photocathode, and it depends on the wavelength ofthe photon. CE is the probability of the photoelectron being caught by the first dynode andresulting in the multiplication, and it depends on the applied voltage and the surrounding
magnetic field. The photoelectron is multiplied by a gain factor (G), and observed as charge(Q) which can be obtained by multiplying elementary charge (e). In the SiPM case, thenumber of photoelectrons is larger than the number of primary Geiger discharges (Npe )owing to the existence of the crosstalk and afterpulsing. This eﬀect is represented by Excess
Charge Factor (ECF ).
In order to estimate Npe and Npho , the calibration factors P DE and G·ECF are necessary.
G · ECF is obtained by an LED run while P DE is estimated from an α run. The calibration
methods are explained in detail below;
Setup
LED G · ECF is measured using photons from blue LEDs. The LEDs are put on the innerwall of the detector as shown in Fig. 4.14. Light from the LEDs which were also used in
the MEG experiment is reduced by an aluminum sheet with pinholes and diﬀused uniformly
by teflon as shown in Fig. 4.15. These LEDs are located on the lateral faces, and they areused for the PMT gain calibration. Some LEDs have been newly installed for the MEG II

Chapter 4. LXe Calorimeter

38

Top

Outer
old LED
from MEG
new LED
from MEG II

DS

BottomUSz axisFigure 4.14: Position of the LEDs [5]. The LEDs used from the MEG experiment are shownin green and the others in blue.
Table 4.3: Basic properties of the 241 Am sources for calibration.
half-life 432.6 years [36]activity 200 Bq [35]energy5.4856 MeV (84.5%) [36]5.4429 MeV (13.2%) [36]experiment mainly on the outer face to provide more uniform light for the incident face, andthey are used for the SiPM calibration. The light from some of them is also reduced andscattered by teflon as shown in Fig. 4.16. The purpose of the light reduction is to reduce therelative fluctuation of LED light intensity by applying large voltage.
Alpha Ray Source Since P DE depends on the wavelength of the photons, it shouldbe measured with the xenon scintillation light. For the PDE calibration, five wires with
241 Am [35] are put in the detector as alpha ray sources. The basic properties of the 241 Am
source is summarized in Tab. 4.3. Five sources are on a 100 µm diameter tungsten wire at
12.4 cm interval. Each source is covered by 1.5 µm thick gold as shown in Fig. 4.17. The
position of the wires is diﬀerent in height as shown in Fig. 4.18.
MethodPMT Gain Since gain of the PMTs used in the MEG and MEG II experiment has a large
dependence on the incident position on the photocathode, one-photoelectron signals cannot
be distinguished from pedestal events. Therefore, gain is measured using the property of theChapter 4. LXe Calorimeter

39

Figure 4.15: LEDs used from the MEG experiment. The light is reduced by an Aluminum pinhole and scattered by teflon.

Figure 4.16: Newly installed LEDs. The
teflon reduces and scatters the light fromthe LEDs.

Figure 4.17: 241 Am alpha ray source covered in gold [35].

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 4.18: Position of the alpha ray sources [5]. 25 sources in total are put on 5 wires inSatoru Kobayashi
28
the detector.

Chapter 4. LXe Calorimeter

40

Poisson statistics of the number of photoelectrons. Only a small part of the LED photons
enters the PMT surface, goes through the quartz window, and makes photoelectrons. Thus
the number of photoelectrons Npe follows Poisson distribution if the fluctuation of the LED
light is small enough compared to the Poisson variance. The probability of obtaining Npe
photoelectrons can be written as follows by denoting the mean by N̄pe ;P (Npe ) = PoissonN̄pe (Npe ),Poissonλ (k) =λk e−λk!

,(4.9a)(4.9b)

when a certain intensity of LED light is used. Assuming the gain G fluctuate by Normal
distribution whose mean is Ḡ and standard deviation is σG , and there is white noise whosemean is Q0 and RMS is σ0 , the distribution of charge Q is written as follows;∫∑
P (Q) =
PoissonN̄pe (k) dG NormḠ, σG (G) · NormkGe+Q0 , σ0 (Q),(4.10a)k()
1(x − µ)2
Normµ, σ (x) = √
exp −
.
2σ 2
2πσ

(4.10b)2 of this charge distribution can be written as
Then the mean Q̄ and the variance σQ

Q̄ = N̄pe Ḡe + Q0
2
σQ
= σ02 + Ḡe(Q̄ − Q0 )

{

}
2
σG
1 + 2 (1 + N̄pe ) .
Ḡ

(4.11)(4.12)

When σG is small enough compared to Ḡ, the relation between Q̄ and σQ becomes simple;2
σQ= σ02 + Ḡe(Q̄ − Q0 ).

(4.13)

Since the noise level does not depend on the LED intensity, the linear plot like Fig. 4.19
can be obtained by analyzing the charge distributions from diﬀerent LED intensities. The
slope of the plot corresponds to the gain. The gain of the PMTs in the calorimeter has beenmonitored during pilot runs and is discussed in Chap. 6.
SiPM Gain and ECF The one-photoelectron peak can be resolved in charge distributionof SiPMs after reducing the noise. The typical charge distribution for weak LED light isshown in Fig. 4.20.
ECF is the ratio between the actually measured charge and the charge expected only
from the primary Geiger discharge. It is more than one in the SiPM case owing to thecorrelated noise such as crosstalk and afterpulsing. In order to estimate the number of primary
photoelectrons, again the Poisson statistics is utilized. Although the charge distribution is
distorted from the Poisson distribution owing to the correlated noise, the number of eventsin the pedestal peak is not aﬀected. According to the Poisson statistics, the fraction of thepedestal events can be written as
f0 = PoissonN̄pe (0) = e−N̄pe .

(4.14)

Chapter 4. LXe Calorimeter

41

variance [(109e)2]-xecwfcl.chargeArray[2001][3]0.0025
Number of Events [a.u.]

htemp

0.002

0.00150.001

0.0005

EntriesMean
Std Dev

2503023
0.057450.06606

200
150
100
50
0

0

0.1

0.2

0.3

0.4

0.5

-xecwfcl.chargeArray[2001][3]charge[10^9e]

0
0

0.2

0.4

0.6

0.8

1

1.2

charge [109e]

Figure 4.19: Relation between the varianceand the mean of the charge distribution
from the constant LED signal. The slopeof this plot corresponds to the gain of the
PMT.

Figure 4.20: Charge distribution of a SiPM
for weak LED light [5]. The peak of the
one-photoelectron signal is resolved. The
fraction of the pedestal events can be used
to estimate Npe .

Then, the number of primary Geiger discharge Npe is
Npe = − ln f0 .

(4.15)

G · ECF can be calculated by
Q̄/e
.
ln f0
Other methods of monitoring SiPM gain are discussed in Sec. 5.
G · ECF = −(4.16)PDE Although the alpha ray from the 241 Am source has monochromatic energy, it loses
some energy in the gold cover and converts the remaining energy into scintillation photons.
Some photons reach a photosensor directly, and some are scattered by LXe and finally aredetected, while others are absorbed by LXe or detector walls. The whole process is simulatedby Geant4 [37] version 10.4.p02 and the number of photons entering the sensors is calculated.
Then PDE is calculated as
Npe
P DE =,(4.17)
Npho
where Npho is the calculated value by simulation and Npe is obtained using G·ECF measured
in the method described above.

Chapter 4. LXe Calorimeter

42

Figure 4.21: CW beam line [38]. Protons are accelerated by Cockcroft-Walton accelerator
located at the downstream side of the MEG II detectors.

4.3.2

Cockcroft-Walton-Litheum Calibration

As shown in Fig. 4.21, the MEG II collaboration has a Cockcroft-Walton (CW) accelerator
in the downstream side of the detectors. It accelerates protons to 440 keV. When the proton
is stopped on a Li2 B4 O7 target, a 17.6 MeV monochromatic gamma ray is generated fromthe reaction 7 Li(p, γ)8 Be. The muon target is replaced with a LiBO target, and it is tilted by
45 degrees so that it will not prevent the gamma ray directing to the xenon calorimeter. The
exchange of the beamline can be done easily because CW beam comes from the downstreamside and it does not conflict with the muon beam line. It enables the frequent calibrationand it was used twice a week in the MEG experiment. This calibration is called the CW-Li
calibration. The main purpose of this calibration is to monitor the energy scale stability,
which can be aﬀected by the change of the optical property of the LXe (the light yield or
attenuation length) due to the purity variation, or by the miscalibration of the photosensors.

4.3.3

Charge Exchange Calibration

The MEG II beam line can switch the beam particle from muon to pion. The negative
pion is used for the calibration of the LXe Calorimeter through charge exchange (CEX)
reaction;π − p → π 0 n.
(4.18)The experimental setup of the CEX calibration is schematically depicted in Fig. 4.22. Whena negative pion is injected to a liquid hydrogen target and stops inside it, a neutral pion is
generated and decays into two gamma rays immediately;
π 0 → γγ.

(4.19)

Chapter 4. LXe Calorimeter

43

Tagging Counter

Figure 4.22: Overview of the CEX calibration [29]. A negative pion is converted into aneutral pion in the liquid hydrogen target, and the gamma rays generated from the decay of
the neutral pion are detected by the LXe Calorimeter and a tagging detector. The tagging
detector is explained in Sec.7.1
These gamma rays are used for the calibration of the calorimeter.
Since the CEX reaction occurs after the negative pion has stopped and the gamma rays
are generated from a two body decay, the energy of the gamma ray can be calculated kinematically. By choosing the events where the two gamma rays are emitted into the opposite
directions, a specific energy can be obtained; 54.9 MeV and 82.9 MeV. Since 54.9 MeV is near
the signal energy (52.8 MeV), important calibration and performance evaluation is conductedusing this gamma ray. This calibration method is called CEX calibration. The improvementof the CEX calibration is discussed in Chap. 7.

4.4

StatusConstruction of the LXe Calorimeter has been finished in 2017, and the next step is toachieve and confirm the required performance. As explained in this chapter, reconstructionof observables needs calibration. In the following sections three topics on calibration are
discussed. First of all, calibration of photosensors is necessary. New calibration methods ofgain of SiPMs, which has been newly introduced in the MEG II experiment, was developed.
PMTs were also calibrated by the methods used in the MEG experiment, and aging of
PMTs which is important in the high beam rate environment was investigated. The CEX
calibration is most important for investigating the overall detector performance. In order toChapter 4. LXe Calorimeter44

improve precision of the CEX calibration corresponding to the improvement of resolution, a
new beam monitoring detector was proposed and developed.

Part II

Photosensor Calibration

45

Chapter 5

Comparison of Gain Monitoring
Methods for SiPM
Scintillation photons are detected by photosensors located on the inner wall of the calorimeter. Photosensors convert photons into electrons and multiply them, providing detectableelectronic signals. In order to reconstruct the number of incident photons, it is necessary toknow the properties of the photosensors. One of the most important parameters is the gain,
which represents how many electrons are generated from an initial single electron.
In this chapter, methods of measuring the gain of SiPMs are discussed. A conventional
method is explained in the first section with its disadvantages. Two alternative methods
which can overcome the disadvantages are discussed in the following sections.

5.1

Gain of SiPM

A SiPM is a photosensor which can detect a single photon. Therefore, the gain can beobtained directly from the size of the single-photon signals. Although this method is simple
and powerful, it has some disadvantages. First, this method is available only when a singlephotoelectron peak is resolved. In other words, gain cannot be obtained in noisy environmentby this method. Second, this method needs a specific setup for the measurement because itis necessary to prepare a light source which provides optimal intensity.
Recently two other methods have been proposed, which might overcome the disadvantagesof the standard method. The first one is the statistical method which uses a statisticalproperty of charge distribution obtained by a SiPM. The second one analyzes the shape of
the waveform to extract information concerning gain.

5.2

Statistical Method

The statistical method has been used for the PMT gain calibration in the MEG and MEG
II experiment. The application of this method to a SiPM has been tested in Ref [39]. In thisstudy, the statistical method is applied to a SiPM (MPPC S13360-3050CS by Hamamatsu[40]) and a solution to a newly found problem is provided.
46

Chapter 5. Comparison of Gain Monitoring Methods for SiPM

5.2.1

47

Previous Study

Photons emitted by an LED generate an electron-hole pair and trigger avalanche multiplication with small probability. Thus, it can be assumed that the number of the primary
Geiger discharges follows Poisson distribution. In this case gain can be obtained from therelation between variance and mean of the charge distribution as discussed in Sec. 4.3.1.
However, the SiPM has a peculiar characteristics and additional signals come from correlated noises: the crosstalk and the afterpulsing. A model to include the eﬀect of crosstalkis proposed in Ref. [39]. When the number of photoelectrons made by crosstalks (CT) fromone primary Geiger discharge follows Poisson distribution with mean λCT , the total numberof photoelectrons (n) follows Generalized Poisson distribution GPN̄pe , λCT (n). N̄pe is mean
number of primary Geiger discharges, and Generalized Poisson distribution is represented asfollows;µ(µ + nλ)n−1 e−(µ+nλ).
(5.1)
GPµ, λ (n) =n!
Mean and variance of the Generalized Poisson distribution are µ/(1 − λ) and µ/(1 − λ)3 ,respectively. The number of photoelectrons actually bocomes smaller than this disribution
when λCT is too large, because crosstalks usually occur only in the neighboring cells andthere should be limitation in the number of crosstalks in reality. The charge distributionchanges from Eq. 4.10b as follows in accordance with the introduction of the crosstalk eﬀect;∫∑
P (Q) =
GPN̄pe , λCT (k) dG NormḠ, σG (G) · NormkGe+Q0 , σ0 (Q),(5.2)
kQ̄ = ḠeN̄pe+ Q0 ,
1 − λCTN̄pe(1 − λCT )31= σ02 +Ḡe(Q̄ − Q0 )(1 − λCT )22σQ≃ σ02 + Ḡ2 e2(5.3)(5.4a)(5.4b)

Once 1/(1 − λCT )2 is known, the gain can be calculated from the relation between varianceand mean of the charge distribution with the same procedure with the case without crosstalks.
The conversion factor 1/(1 − λCT )2 is needed to convert the slope of variance vs meanplot to the gain. The conversion factor can be obtained from a measurement with weak LED.
Using Eq. 5.3 and Eq. 5.4, the conversion factor can be represented as follows;
2 − σ2σQ
10= N̄pe.
1 − λCT(Q̄ − Q0 )2(5.5)

N̄pe can be obtained using the pedestal fraction;
f0 = GPN̄pe , λCT (0) = e−N̄pe .

(5.6)

Chapter 5. Comparison of Gain Monitoring Methods for SiPM

48

Figure 5.1: Setup for the gain measurement of the statistical method [41]. The SiPM detects
constant intensity LED light.

The advantage of this method is that once the conversion factor is known, the gain canbe obtained only from a simple statistical property; mean and variance. The gain can bemonitored even when a single-photoelectron peak is not resolved, although in order to obtain
the absolute value the conversion factor must be known beforehand by counting the numberof pedestal events.

5.2.2

Validation Test

A validation test of this principle was conducted. The experimental setup is shown in
Fig. 5.1. A blue LED in pulse operation is used as a light source. MPPC S13360-3050CS is
used as a SiPM sample, and the MPPC signals are read out by a DRS evaluation board after
the amplification by a factor of about 70. The LED, the SiPM and the amplifier are placedin a thermal chamber which keeps the temperature around 25 ◦ C.
Fig. 5.2 shows the charge distribution obtained by a measurement with weak LED light.
The conversion factor can be calculated from the fraction of the pedestal events. Fig. 5.3
shows the relation between variance and mean obtained by analyzing charge distributions
with diﬀerent light intensity runs. One point corresponds to one run with constant intensity
LED light.
According to the model with Generalized Poisson distribution, variance depends linearlyon mean, and the gain can be calculated using the slope. However, the measured relationin Fig. 5.3 is rather quadratic than linear. The reason of this non-linearity is discussed
in the next section although the cause has not become clear. In any case, the gain was
successfully extracted from the relation between variance and mean as follows. Assumingthat the over-linearity is an additional eﬀect on the Generalized Poisson statistics which
occurs only when a large number of photoelectrons are generated, the slope around the origin
was compared to the gain. What was actually done is fitting the variance vs mean plot
2 = c + c · Q̄ + c · Q̄2 , and calculating gain multiplying cby the quadratic function, σQ
0
1
2
1
by (1 − λCT )2 obtained from a measurement using weak LED light. The measurement was
repeated with some diﬀerent overvoltages, and λCT was 20–40% depending on the overvoltage.
The calculated gains were compared with those obtained by the usual single-photoelectron
method. As shown in Fig. 5.4, the calculated gains are consistent with those measured byChapter 5. Comparison of Gain Monitoring Methods for SiPM

49

Variance [(109e)2]

Vov = 2.2 V

number [a.u.]

0.035
0.03
0.025
0.02
0.015
0.01
0.005
0
0

0.2



0.4

0.6





0.8



1
Mean [109e]charge [a.u.]

Figure 5.2: Charge distribution obtained bya measurement using weak LED light.

Figure 5.3: Variance as a function of mean[41]. The relation is rather quadratic thanlinear.

the single-photoelectron method. The precision was 2.5% in RMS.

5.2.3

Relation between Variance and Mean

The measured relation between variance and mean was rather quadratic although it should
be linear in principle based on the model using Generalized Poisson distribution. The causeof this relation is investigated as follows.
Linearity of Amplifier Linearity of the readout system was first checked. A DRS Evaluation Board developed by PSI was used as a waveform digitizer and full waveforms wereobtained. This board has the dynamic range of 1 V, and the range was set to [−50 mV,+950 mV]. Signals from the SiPM was amplified before being read out. The amplifier is also
developed by PSI, and its circuit is shown in Fig. 5.5. The SiPM is biased through the signal
line which is AC-coupled to the amplification stage.
The linearity of this amplifier was measured with the setup shown in Fig. 5.6. A signal
from the SiPM is divided into two signals after amplification. One goes directly to the DRS
and the other is amplified again by an additional amplifier. By comparing the two signals,
linearity of the additional amplifier can be obtained.
The result is shown in Fig. 5.7. Considering that the output from the amplifier is attenuated by a factor 4, the linearity is guaranteed when the output signal height is less than
1.6 V.
Eﬀect of Afterpulsing The non-linearity of the relation between mean and variance mightcome from certain characteristics of the SiPM which is not taken into account in modelingof charge distribution, such as afterpulsing. The assumed Generalized Poisson distributionof the number of photoelectrons takes only the crosstalk into account. The afterpulsing is
diﬀerent from the crosstalk in that the signal size is not constant and it depends on thetime diﬀerence between the primary discharge and the afterpulse. Since it is rather diﬃcult
to take it into account analytically, a waveform simulation was conducted and the eﬀect ofafterpulsing on the charge distribution was investigated.

Chapter 5. Comparison of Gain Monitoring Methods for SiPM

50Gain [109e/pe]Single photoelectron & Statistical Gain

0.05
0.04

Gain from Single photoelectron Method
Gain from Statistical Method

0.03
0.02
0.01
0
0

1

2

3

4

5
Overvoltage [V]Figure 5.4: Gain obtained from the usual single-photoelectron method and from this statistical method as a function of overvoltage [41]. Statistical uncertainty is shown as error
bars.

Figure 5.5: Circuit diagram of the amplifier [42].

Chapter 5. Comparison of Gain Monitoring Methods for SiPM

51

VAM P

MPPC

AMP1

Attenuator

Divider

VM P P C

AMP2Divider

LED
Divider
IN2
Pulse Generator

IN1
TRIGGER

DRS

Figure 5.6: Setup for the measurement of the saturation of the readout system. The signals
before and after amplified are compared.

Figure 5.7: Linearity of the amplifier. The input signal (x-axis) is amplified and output as
the height in y-axis.

Chapter 5. Comparison of Gain Monitoring Methods for SiPM

52

It is necessary to make a model to simulate the SiPM waveform which takes the afterpulsing into consideration. The waveform from a single photoelectron is assumed to riseup instantly and decay exponentially with the time constant τdecay . Time distribution ofemission of photons from an LED is also assumed to be exponential with the time constantτLED = 40 ns. Since there are quenching resisters in each cell of a SiPM, the size of thepulses which start after a main pulse is smaller. The later the pulse occurs, the larger thepulse becomes, because the voltage recovers gradually. Assuming that time distribution ofafterpulsing is exponential with the time constant τAP and the cell recovers with the sametime constant with that of waveform, the timing distribution of afterpulsing and the heightof the afterpulse signal are written as follows;
dp
1 −tAP /τAP
=
e
,
dtAP
τAP
HAP = (1 − e−tAP /τdecay )H1pe ,

(5.7)
(5.8)

where H means the height of the signal and H1pe is that of a one photoelectron pulse.
In the simulation, the number of primary Geiger discharges follow Poisson distribution,and each discharge generates crosstalks whose number is determined also by Poisson distribution. A fired cell can be followed by an afterpulse whose timing distribution and the signal
size are defined by the equations above with certain probability. Changing the mean numberof the primary Geiger discharges corresponds to changing the intensity of LED light.
By changing the probability and the time constant of afterpusing, the eﬀect on the charge
distribution was qualitatively investigated. Since an afterpulse increases the charge by making
an addtional pulse which is smaller than the standard one-photoelectron signal, the photoelectron peaks in the charge distribution become to have a tail. The probability of afterpulsing
changes the size of the tail, while the time constant of the afterpulsing probability changes
the shape of the tail.
To see the eﬀect on the relation between variance and mean, the simulation was repeatedwith diﬀerent Npe . The parameters used in the simulation is summarized in Tab. 5.1. τdecay
was determined by the waveform shape, and τAP was selected to reproduce the tail of thecharge distribution. The noise RMS is the same with the measured value. The other parameters were obtained by fitting. The resulting charge distribution is shown in Fig. 5.8 and it
is comparable with the actual charge distribution (Fig. 5.2). The obtained relation between
variance and mean is shown in Fig. 5.9. The points are on a straight line and the quadratic
behavior cannot be seen. The relation keeps linear even when increasing the crosstalk orafterpulsing probability deliberately up to 40%.

5.3

Waveform Method

5.3.1

Previous Study

Gain is the number of electrons generated from one photoelectron. Therefore, the gain
can be obtained once how many photoelectrons has generated a signal is known. This method
extracts information concerning the number of photoelectrons contained in a signal by usinga waveform shape.

Chapter 5. Comparison of Gain Monitoring Methods for SiPM

53

Table 5.1: Parameter settings for the waveform simulation.
mean number of crosstalks from one pixel 0.01
probability of generating an afterpulse
0.14
gain including an amplifier
4.5 × 107
decay time constant of a waveform τdecay 30 ns
time constant of afterpulsing τAP
20 ns
noise RMS
0.6 mV
number [a.u.]charge [a.u.]

Figure 5.8: Charge distribution obtained by a simulation using the parameters shown in
Tab. 5.1.
variance [a.u.]mean [a.u.]

Figure 5.9: Relation between mean and variance of charge distribution obtained by a waveform simulation considering afterpulsing eﬀect.

Chapter 5. Comparison of Gain Monitoring Methods for SiPM

54

It is known that in the PMT case a variable proportional to gain can be extracted from the
waveforms themselves by analyzing them statistically [43]. The waveform from photosensors
such as PMTs or SiPMs is in principle a sequence of single-photoelectron signals. Insteadof directly counting each single-photoelectron signal, an integration of signal height squared(HS) is used to represent how jagged the waveform is;∫
HS = dt {f (t)}2 ,(5.9)
where f (t) is the amplitude of the waveform as a function of time.
As an example, a case in which the signals from each photoelectron are completely separated over time is discussed. When there are two peaks from photoelectrons and they do not
overlap with each other, HS is∫
HS = 2 dt {f1pe (t)}2 ,(5.10)
where f1pe is the waveform of one photoelectron. f1pe does not always have the same form
because the distribution of the arrival time of each electron diﬀers from time to time. But
when the gain is large enough, the shape of f1pe is almost same owing to the large statisticsof the electrons. Thus f1pe is assumed to be proportional to the gain;
f1pe (t) ∝ G.

(5.11)

Then,∫
HS = Npe∫

Q = Npedt {f1pe (t)}2 ,(5.12)

dt · f1pe (t),(5.13)

HS.
Q(5.14)and these equations lead toG∝

In reality, some signals from electrons overlap with each other. For making HS sensitive
to the arrival time diﬀerence of the signals, the derivative of the waveform is useful. The
second derivative is used in the previous study because the correlation with gain becomesstrongest.
The advantage of this method is that a dedicated light source is not needed in constrast
to the other methods where one needs LEDs which emit photons following Poisson statistics,
or appropriate weak light source which enables you to see a clear one-photoelectron peak.

5.3.2

Validation Test

Before considering applying this method to the SiPM case, the validation test with PMT
was conducted. Some PMTs in the LXe Calorimeter were read out by WaveDREAM boards,
and LEDs in the calorimeter were used as a light source. The sampling frequency of thehist2D02

hist2D0

1.8

Entries
Mean x

1.084

1.6

Mean y0.8734

Std Dev x

0.5137

1.4

Std Dev y0.2569

70

44669

60

HS [a.u.]

Chapter 5. Comparison of Gain Monitoring Methods for SiPM
hist2D1

hist2D2

1.4

1.2

1.2
1

40

0.8

30

0.6

44701

Mean x0.7097

Mean y0.6303

0.6

0
0

0.5

1

1.5

2

1
50

Entries

44875

Mean x0.4405

Mean y0.5125

Std Dev x

0.2011

Std Dev y

0.0693

40

0.8
40
30

30
0.6
20

20

0.4

20

10

0.2

10

0

0
0

0.4
0.2

50

hist2D2

60

Std Dev y 0.1252

1
0.8

1.2

hist2D1
Entries

Std Dev x 0.3312

50

55

0.2

0.4

0.6

0.8

1

0.4
10

0.2

0
0
1.2 Charge [109e] 0

0.2

0.4

0.6

0.8

0

Figure 5.10: Linear relation between thehist2D5
charge and HS obtained by PMTs in the calorimeter.
hist2D4
hist2D6
1

The slope corresponds to the
PMT gain.
1
hist2D4

0.9

Entries

44743

Mean x0.16830.8

Mean y

0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0

0.434

40
35

hist2D5

0.9

Entries

44736

Mean x0.11180.8

Mean y0.423345
40

1

hist2D6

0.9

Entries

44817

Mean x0.04835

0.8

Mean ywaveform digitizer was 1.2 GHz. In order to check the linearity
between HS and charge in a
35
0.7
0.7 entered each PMT.
wide range, LED intensity
was changed and roughly 30 to 500 photons
30
30 information of the arrival time
The second derivative was 0.6
used to calculate HS so that much
0.6
25
diﬀerence can be extracted. The linearity was confirmed as 25
shown in Fig. 5.10.
0.5
0.5
In order to see20the correlation
with the gain, data must be takenwith diﬀerent gain.
20
0.4 configurations were used to realize the0.4
Seven diﬀerent high voltage
diﬀerent gain sets. For
each high voltage 15
set, the0.3HS vs charge plot was made andwas calculated for
15 the slope
0.3each set. Fig. 5.11
shows
the
correlation
between
the
slope
and
the
gain
obtained from
10
10
0.2
0.2
the usual variance vs mean relation. The cause of the small discrepancy from the linear
5 and the0.1dependence is diﬀerent channel 5by channel.
0.1 Although it is not a
relation is not clear,complete proportional
relation,
the
gain
can
be
monitored
once
therelationfor each channel
00000.05 0.1 is
0.15
0.2
0.25
0.3
0
0.05
0.1
0.15
0.2
0
0.02
0.04
0.06
measured beforehand.

5.3.3

Std Dev x

0.07352

Std Dev y

0.04689

Std Dev x

0.04948

Std Dev y

0.04552

0.01795

Std Dev y

0.04482

Application for SiPM

Applying this waveform method for the SiPM is not straight-forward because it has
so-called correlated noises as explained in Sec. 4.1.3. A pulse from a crosstalk is almost
simultaneous with its primary signal, and the assumption that each pulse can be separated
is no longer reasonable. The second eﬀect is afterpulsing and the problem is that the size ofthe signal from an afterpulse depends on its generation time. In addition, when considering
finally applying this gain monitoring method for the LXe Calorimeter, a large noise willchange the waveform. How the noise contributes to this method must be examined. For

25

0.4156

Std Dev x

20

15

10
5

0.08

0

56

Slope [a.u.]

Chapter 5. Comparison of Gain Monitoring Methods for SiPM

Gain from Standard Method

Figure 5.11: Correlation between the obtained slope and the gain.

these reasons, a new modeling of the SiPM waveform is discussed in this section.
First let’s discuss how to treat crosstalk. Crosstalk occurs almost completely simultaneously with the original hit. When Npe pulses completely overlap, HS and charge become∫
dt {Npe f1pe (t)}2∫2= Npe dt {f1pe (t)}2 ,HS =(5.15a)(5.15b)∫
Q = Npedt {f1pe (t)},(5.16)

so now the relation between charge and HS is not linear, and HS is quadratically depends
on charge.
The signal of an afterpulse is smaller than the one photoelectron signal. When smaller
signals come without overlapping, HS and charge does not scale equally and HS is more
aﬀected than charge.
The eﬀect of noise is estimated assuming white noise for simplicity. The white noise iscancelled when it is integrated;∫
dt Vnoise (t) = 0,(5.17)

where Vnoise (t) is the height of the noise waveform at time t. While it does not change thecharge of the signal waveform, it aﬀects HS as follows;∫
HS = dt {f (t) + Vnoise (t)}2(5.18a)∫≃ dt [{f (t)}2 + {Vnoise (t)}2 ],(5.18b)Chapter 5. Comparison of Gain Monitoring Methods for SiPM
number of event [a.u.]

57

HS [a.u.]charge [109e]# of pCT

Figure 5.12: Simulated number of prompt crosstalk events for diﬀerent regions in a HS vscharge plot. The number of prompt crosstalk is large in high HS region.

offset [a.u.]slope [a.u.]

noise [a.u.]

noise [a.u.]

Figure 5.13: Oﬀset (left) and the slope (right) of the HS vs charge plot. Eﬀect of noise canbe seen only in oﬀset.
∫
where the term dt f (t)Vnoise (t) is neglected assuming
the frequency composition of a signal∫
is slow enough compared to that of noise. Since dt {Vnoise }2 does not depend on Npe , thewhite noise works as a constant term in the HS-charge relation.
Simulation
These eﬀects are validated by a toy Monte-Carlo simulation. First the crosstalk is simulated and it is found that a tail in large HS appears owing to crosstalk. Figure 5.12 showsthat the number of prompt crosstalk is actually large in the large HS events.
The noise eﬀect is also confirmed. A random noise which follows Gaussian distribution isadded to the signal. With a large noise level, the oﬀset becomes large but the slope does notchange as shown in Fig. 5.13.

Noisepower

Chapter 5. Comparison of Gain Monitoring Methods for SiPM

58

OV = 2.2 V

×103

105

1400
104

1200
1000

103

800
102

600
400

10
200
0
0

0.5

1

1.5

1
9

charge [10 e]

Figure 5.14: HS vs charge plot for data [41]. The blackline describes the peak positions of thehistogram projected to the y axis. The 2D histogram is broad owing to the prompt crosstalkand the afterpulsing. The oﬀset is considered to be due to the noise. The distribution isquadratic.

Test
The setup is the same as that for the statistical method which is explained in Sec. 5.2.2.
The sampling frequency was 1.6 GHz. The waveform of SiPM was obtained changing LED
intensity. The obtained HS vs charge plot is shown in Fig. 5.14. The distribution is broader
in HS direction especially in the large charge region, which is considered to be due to thecrosstalk eﬀect. The oﬀset exists but it is smaller than the PMT case, because the noiselevel is lower comparing to the measurement of the PMTs in the LXe Calorimeter. The
overlapping makes the quadratic shape.
In order to extract the gain-related information from this plot, the slope around theorigin was calculated. First the peak positions at each x bin were estimated by fitting thehistogram projected to y axis around the peak with a Gaussian function, and then the peaks
are fitted by a quadratic function. The first order coeﬃcient corresponds to the slope at theorigin. This measurement was repeated nine times and the bias voltage was changed every
time. Since gain is known to have a linear relation with overvoltage, the correlation of theextracted slope and gain can be confirmed by checking the relation between the slope and theovervoltage. A clear linear relation was observed as shown in Fig 5.15. Although the scalecannot be determined only by this waveform method, it can be used as a online monitoringtool.

gain [a.u]Chapter 5. Comparison of Gain Monitoring Methods for SiPM

59

Gain vs Overvoltage

×103
300
250
200
150
100
50
0
0

1

2

3

4

5
Overvoltage [V]Figure 5.15: Correlation between slope of HS vs charge plot and overvoltage [41]. There isa clear linear relation.

5.4

Conclusion

Two independent methods of monitoring the gain of SiPMs were investigated. The statistical method uses a statistical property of the charge distribution from a Poisson light source.
It has an advantage in the robustness to noise, and the gain can be monitored even after
it is damaged by irradiation and so the usual one-photoelectron method cannot be applied.
However, it still needs a clear separation of the pedestal to calculate the conversion factor
and to get the absolute gain. The absolute gain was consistent with the gain from standard
single-photoelectron method with the precision of 2.5% in RMS. The waveform method extracts gain-related information directly from the waveform. It does not need any dedicatedsetup for monitoring the gain and make the in-situ monitoring possible, although the absolute
gain cannot be obtained.
Although the gain extracted by the alternative methods is confirmed to be highly correlated with that obtained from the standard one-photoelectron method by changing theovervoltage, it is not guaranteed that these methods are robust. The most important thing
to be cared is the variation of the afterpulsing eﬀect. An afterpulse is generated when a carrier is trapped by an energy level made by a lattice defect or impurity. Thus, the probability
or other properties of afterpulsing can change independently of overvoltage for example byradiation damage, which means the variation of afterpulsing properties can lead to wrong
estimation of the gain. In the statistical method the non-linearity of the relation between
variance and mean has not been understood, and the possibility that the change of suchproperties as afterpulsing aﬀects the result cannot be denied. The waveform method directly
uses the waveform and it is very sensitive to afterpulses. These eﬀect should be carefully
treated and it would be the next step to do.

Chapter 6

PMT Monitoring
In 2018 and 2019, the MEG II collaboration conducted pilot runs, where the performanceof the detectors were evaluated with a limited number of readout electronics in priparation forthe coming physics run. A response of the LXe Calorimeter variates owing to a change in a
Xe purity or responses of photosensors. In order to achieve 1% energy resolution, photosensor
calibration parameters such as gain and QE must be monitored with good precision. The
photosensors were monitored by LEDs and alpha ray sources as explained in Sec. 4.3.1 during
the pilot runs. It was necessary to deal with some problems for a long-term operation of thedetector such as a long-term decrease of PMT gain. This chapter focuses on the PMT
monitoring in the pilot runs.
In the first section the purpose of each run is explained and the requirements for the
PMT calibration is discussed. Two kinds of calibration, the alpha ray calibration and the
LED calibration are compared and the precision is discussed in the second section. Somefeatures in the change of PMT response were observed during the pre-engineering runs, andthey are discussed in the third section. Among those features, the investigation of the decreaseof the PMT response by muon beam is one of the main objectives for the run in 2019 and it
is discussed in the fourth section.

6.1

Pre-Engineering Run

6.1.1

2018

The main purposes of the pilot run in 2018 are as follows:• measure the energy spectrum of the gamma ray with the nominal intensity muon beam
(7 × 107 µ/s)
• measure the energy resolution at 17.6 MeV by the CW-Li calibration• measure the position resolution by the CW-Li calibration• evaluate the performance of the pileup reduction using the muon beam of various intensities
60

Chapter 6. PMT Monitoring

61

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

0

100

200

300

Figure 6.1: Photosensors read out in the pilot runs.
• check the stability of a photosensor response under high muon beam rate environment
The important point for the PMT calibration is that there were many activities in diﬀerent
environments. The PMT response can change when the muon beam intensity or the magnetic
field changes. The beam intensity was changed for the study of the pileup reduction. The
CW-Li calibration runs were taken under diﬀerent magnetic field conditions on account of theinstability of the magnet for the beam transportation. It was required to follow the changeof the environment and connect the gain history with appropriate points.

6.1.2

2019

In 2018, the size of the response of both PMTs and SiPMs decreased. One of the main
purpose for the pilot run in 2019 was to investigate the decrease problem. Since the investigation of the photosensors is the target in 2019, a good calibration precision is required.
As for SiPMs, what is decreasing is considered to be the PDE for VUV light. In order tomeasure the VUV response of the SiPMs, optical properties of LXe such as light yield must
be known. Since the PMTs provide important information on the optical properties of the
LXe, the precision of the calibration was the key point for the study of the SiPM response.

6.1.3

Readout Region

Since the number of electronics was still limited in the pilot runs, only a part of thephotosensors were read out. The sensors read out in the pilot runs are shown in Fig. 6.1. 640
SiPMs and 350 PMTs were read out.

Chapter 6. PMT Monitoring

6.1.4

62

Requirement

Channel by Channel Calibration
Wrong calibraiton of the PMTs does not aﬀect the position reconstruction because it isbased on the photon distribution on the incident face. However, the reconstruction of energy
would depend on the gamma ray position when the PMTs are wrongly calibrated channel
by channel. It would result in worse energy resolution, being aﬀected by the fluctuationof the electromagnetic shower development. The eﬀect of the precision of the photosensor
calibration on the performance of the LXe Calorimter was studied using Monte Carlo simulation. Signal gamma rays were injected to the LXe Calorimter, and the propagation of
the scintillation photons were simulated. A Gaussian fluctuation was added to the detected
number of photoelectrons of each sensor. Since the statistical uncertainty of the estimation of
SiPM response has already been evaluated in Ref [44], the fluctuation added to the numberof photoelectrons detected by SiPMs was fixed to the evaluated value, 4%. The individual
diﬀerence of the measured PMT QE is relatively 26% in standard deviation, which means the
maximum error of the QE calibration is 26%. Therefore, the fluctuation added on the PMTs
ranged from 0% to 20% The energy was reconstructed according to the procedure explainedin Sec. 4.2.3. The reconstructed energy is shown in Fig. 6.2, and the following function was
fitted to the spectrum;( {}){A exp (σt2 2t − (x−x)(x ≤ x0 + t)
0)
f (x) =
(6.1)
(x−x0 )2
A exp − 2σ2(x > x0 + t)
where A means a scale, x0 means a peak position, t means a transition point, and σ represents
energy resolution. The low energy tail is due to interactions with material in front of thefiducial volume and shower escapes mainly from the inner face. In Fig. 6.3, the resolution
parameter σ is shown as a function of the size of the additional fluctuation which corresponds
to the calibration precision. When the fluctuation becomes larger than 5%, the resolution
becomes worse and the estimated resolution fluctuates much. The large fluctuation of theestimated resolution is considered to be because the position dependence of reconstructed energy becomes larger when wrongly calibrated PMTs accidentally distribute locally. Althoughsystematic errors caused by bad channels or position dependence might have larger impact
on the resolution, at least the statistical precision of channel by channel calibration should
be under 5%.
Stability of Averaged Response
The averaged response of all the PMTs provides information on the light yield of LXe or
energy scale of the calorimeter response.
In the MEG experiment, energy scale was calibrated by the 55 MeV peak of the CEX
reaction and monitored by the 17.6 MeV peak of the CW-Li reaction and energy spectrumof background gamma rays. The CW-Li calibration was conducted only about twice a week
to save time. The estimation of the energy scale from the gentle slope of the background
spectrum has an uncertainty caused by the finite detector resolution. Therefore, the averagehistResult0
histResult0
EntriesMean
Std Dev

250

10453
0.92370.04137200
150

Chapter 6. 100PMT Monitoring

63

50

Number of Events

0
0.8

0.85

0.9

0.95

1

histResult1

900

histResult1
EntriesMean
Std Dev

800

17331
0.933
0.03514

700
600
500
400
300
200
100
0
0.8

0.85

0.9

0.95

1

Reconstructed Energy [a.u.]

Energy Resolution [%]Figure 6.2: Reconstructed energy spectrum without additional fluctuation of detected numberof photons for photosensors.

1.6

1.4

1.2

1

0.8

5

10
15
20
Calibration Precision [%]

0

5

10
15
20
Calibration Precision [%]Figure 6.3: Energy resolution as a function of the size of the additional fluctuation of thecalibration of photosensors.

Chapter 6. PMT Monitoring64of the PMT response to the alpha ray events was used as a auxiliary tool for frequent andaccurate monitoring. The uncertainty of the energy scale was estimated to be 0.2% in the
MEG experiment [45]. This level of the uncertainty should be achieved also in the MEG II
experiment.
As for the pilot run in 2019, the light yield monitoring was also important for the investigation of the problem of the SiPM response to VUV light. Since the response to the VUVlight can be measured only using the scintillation of the LXe, VUV response of photosensors
and the light yield of LXe cannot be distinguished from each other. If the variation of response to VUV light is consistent with that to LED light, it is natural to think that there is
no wavelength dependence of the variation of the response and that the light yield of LXe isconstant, because the response to light from LEDs is independent of the LXe property. On
the other hand, the distinguishment is impossible if the variation of response to VUV lightis inconsistent with that to LEDs. In that case an upper limit of the light yield variation canbe set by the inconsistency. The VUV response of the SiPM was found to have decreased byabsolutely 3% while no variation of the gain was observed [44] [46]. In order to confirm that
it is not the decrease of light yield but the decrease of the SiPM response, the consistency of
the PMT response to alpha rays and LEDs should be measured within a precision of 1%.

6.2

Calibration Methods and Precision

There are two kinds of calibration sources for the photosensors installed in the LXeCalorimeter: alpha ray sources and LEDs. The principle of the calibration is explained inSec. 4.3.1. Here the advantage and the disadvantage of the two calibration methods arecompared and the statistical precision and the possible systematic errors of each calibration
are discussed.

6.2.1

Alpha RayA variation over time and an individual diﬀerence of VUV response is calibrated by alpha
ray signals. The alpha ray source is 241 Am covered by 1.5 µm thick gold, and it emits alpharays whose energy distribution is always same. The positions of the sources are determinedby the position of the wires and they do not move. Thus, they are ideal VUV-photon sources
which provide constant photon distribution. Furthermore, the absolute size of the signal fora certain number of photons can be obtained because the absolute light yield is known. Since
the energy distribution is not monochromatic on account of the energy loss in the gold cover,the spectrum is calculated by the Geant4 simulation and its mean is compared to that ofmeasured distribution.
The short-term stability of the calibration was estimated by repeating some measurements
under the same condition. The mean of the charge distribution for alpha ray events was
obtained for each PMT. The measurement was repeated 11 runs in 2 days. The standard
deviation of the mean values for 350 PMTs is shown in Fig. 6.4. It shows that the PMT
response to the alpha ray is stable within 4% in a short term. The stability of the averaged
response of all the PMTs was 0.2%. The required precision has been achieved at least fromthe point of view of the short-term stability.

Chapter 6. PMT Monitoring65

It is notable that there may be a systematic error in the calibration. From the point ofview of the energy scale monitoring, it is aﬀected by the characteristics of the LXe because thelight yield, scattering length or absorption length of LXe depends on the purity and can varyover time. It is therefore diﬃcult to reproduce the detector environment in the simulation.
The noise of the readout electronics or the bias caused by trigger threshold can also changeover time. From the point of view of a channel-by-channel absolute PDE measurement,
those which do not change over time also aﬀect the measurement, such as the reflection by
inner walls or PMT surfaces, and the distance between an alpha source and a PMT, because
the simulation input can be diﬀerent from the actual reflectance or the alignment of thecomponents.

6.2.2

LED

Although the absolute number of emitted photon is unknown, the variation of the PMT
response can be tracked by the response to LED light. The LED light has three advantages
compared to the alpha ray as a calibration source. The first one is that the charge distribution
is simply Poisson distribution of the number of photons, and thus the precision of the mean
estimation is good compared to the broad distribution of the alpha ray spectrum. The second
advantage is that large amount of photons are available, which also leads to good precision.
The third advantage is that the data can be taken triggering on the LED flashing, while thetiming of alpha ray events is not known. It makes it possible to take calibration data evenunder muon beam.
The short-term stability of the monitoring by LED was also estimated by repeating thesame measurement 17 times. Figure 6.5 shows the standard deviation of mean of charge
distribution for constant intensity LED runs. The typical number of photons detected by a
PMT is 700. The short-term stability within 1% was confirmed.
Although the stability is better than the alpha ray calibration, it should be noted that itis the response to visible light and it can be diﬀerent from that to VUV light. It is notablethat there could be long-term instablity in the LED output or variation of the baseline of the
waveform.

6.3

Cause of Variation

There are some features of the variation of the PMT response which are known from theexperience of the MEG experiment. Those variations were investigated and tracked by thealpha ray or the LED light during the pilot runs.

6.3.1

Eﬀect of Magnetic Field

In 2018, the CW-Li calibration runs were taken under three diﬀerent configurations shownin Tab. 6.1 The magnetic field generated by the COBRA magnet is symmetric for the plane on
the target position perpendicular to the beam axis. The upstream side of the LXe detector
has a non-negligible eﬀect from the stray field from the BTS, which transports the muon
beam to the MEG detector.

Chapter 6. PMT Monitoring
Number of PMTs

hist
hist
EntriesMean
Std Dev346
2.371
0.6821

Number [a.u.]

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

66

ChargeEntriesMean
Std Dev30

350
0.41870.3079

25
20
15
10

1

2

3

4

5

Precision[%]Figure 6.4: Standard deviation of response
to alpha ray measured 11 times. In eachmeasurement the mean of the charge distribution is converted to the number of photoelectrons, and then compared to that ofsimulation.

5
0
0

0.5

1

1.5

2

2.5
3
Std. Dev. [%]Figure 6.5: Standard deviation of mean ofcharge distributions for constant intensity
LED runs taken 17 times.

Table 6.1: Magnetic field configurations
COBRA BTS
oﬀ
oﬀ
on
oﬀ
on
on
The dynode structure of PMTs is optimized for the eﬃcient multiplication. The gain
and the collection eﬃciency is expected to decrease under the magnetic field because theelectron trajectory will be modified. The tolerance to the magnetic field was measured by
the producer, the Hamamatsu Photonics, as shown in Fig. 6.6. The amount of decreasedepends on the direction of the magnetic field owing to the metal channel dynode structure.
The magnetic field calculated for the diﬀerent PMT locations is shown in Fig. 6.7. The PMTs
are rotated to the direction where the eﬀect from the magnetic field becomes minimal.
The PMT response was measured under diﬀerent magnetic field configurations. The sizeof the signal from the nearest alpha source under COBRA and BTS B-field is compared tothat without B-field, and it is shown in Fig. 6.8. The response of the PMTs especially at theedge of the outer face decreases by the B-field. The asymmetry between the upstream anddownstream side is because the BTS compensates for the B-field produced by COBRA in the
upstream side.

6.3.2

Short-term Variation under Muon Beam

The PMT charge for LED light changes under high rate signals of gamma rays from thetarget. There is a correlation between the size of the charge variation and the intensity ofthe muon beam as shown in Fig. 6.9. The amount of the change under the nominal intensity(7 × 107 µ/s) muon beam is shown in Fig. 6.10.

Chapter 6. PMT Monitoring

67

Figure 6.6: Dependence of the PMT response to the magnetic field [47]. The amount of thedecrease depends on the direction of the magnetic field because it adapts a metal channel
dynode structure.
Correction
The muon beam sometimes stops and restarts again owing to unpredictable stops of the
proton supply or the necessity of conducting calibration runs without beam. Therefore, thetime constant of the variation by muon beam is important in terms of the tracking of thephotosensor response. In order to study the time development of PMT response, LED data
were taken for about an hour after the opening/closing of the beam blocker. Figure 6.11
shows the response of a PMT to light from LEDs after the beam blocker is opened (top) andclosed (bottom). The variation lasts for about 60 minutes.
Some correction should be applied because it is not eﬃcient to start taking the physics
data before the response stabilizes. Assuming that the physics data taking starts ten minutes
after the beam blocker opens, template functions were made by fitting the variation with an
exponential function,
)}]
[
{
(
t − t0 − tBB,(6.2)
f (t) = a 1 + b 1 − exp −τwhere a and b are scale factors, t0 is an oﬀset parameter, τ is a time constant parameter,
and tBB is the time of the operation of the beam blocker. Since the size of the variation bor the time constant τ is diﬀerent channel by channel, the template functions were made foreach channel. The parameters a and b were determined using the initial region and the final
region of the plot. The data taken in initial 10 minutes after the opening of the beam blocker
are ignored for now because the variation is especially large.

Chapter 6. PMT Monitoring

68

Figure 6.7: Calculated magnetic field along the boundary path of the LXe Calorimter where
the PMTs are arranged [47]. The top (bottom) figure is the profile of the component parallel(perpendicular) to the tube axis. The dashed line indicates the field strength where therelative gain of the PMT is reduced by 50%.

Chapter 6. PMT Monitoring

69

100

1.5

80

100

60

80

40

60

20

40

0

20

1.4

1.2

1.1

0

1.0

−20
0.9

−40
−60

0.7

−80
0.6

−100
−100

0

100

200

300

z

0.5

% muon/second)
Ratio
Ratio(7×10(7e7 muon/second)

Figure 6.8: Eﬀect of the magnetic field on PMT response to VUV light. The color shows thesignal size under the magnetic field relative to that under no field.

Correlation

1.15

Entries

349

Mean x

1.003

Mean y1.008

Std Dev x 0.007379
Std Dev y

18
16
14

0.02029

12

1.1

10
8

1.05

6
4

1

2
0.95
0.95

1

1.05
1.1
1.15
%
Ratio
(3e8
muon/second)
Ratio (3×10 muon/second)0

Figure 6.9: Correlation between the change of PMT response under weak and intense muon
beam. The larger change can be seen under more intense muon beam.

Chapter 6. PMT Monitoring

70

Number [a.u.]

Beam Effect
hist

50

EntriesMean
Std Dev349
1.008
0.02029

40
30
20
10
0

1

1.05

1.1

1.15
Ratio

Charge [a.u.]

Figure 6.10: Relative change of the charge from LED light due to the high rate signals. The
response of some PMTs increase under muon beam.

0.5
0.49
0.48
0.47
0.46
0.45
0.44
0.43
0.42
0.41
0.4

0

20

40

60

Charge [a.u.]Time [minute]

0.5
0.49
0.48
0.47
0.46
0.45
0.44
0.43
0.42
0.41
0.4

0

20

40

60
Time [minute]

Figure 6.11: LED response after opening (top) and closing (bottom) the beam blocker. Every
red point is mean of 100 actual data points. The variation lasts for about 60 minutes.

Chapter 6. PMT Monitoring

71
Run: 347981

0.49

0.49

0.48

0.5

0.49

0.48

0.47

0.48

0.47

0.47

0.46

0.46

0.46

0.45

0.45

0.45

0.44

0.44

0.44

0.43

0.43

0.43

0.42

0.42

0.42

0.41

0.41

0.4
−5

0

5

10

0.4

15
20
time [minute]

0.41
0Run: 348650

20

0.4

40
60
time [minute]

0.49

0.48

0.5

0.47

0.46

0.46

0.46

0.45

0.45

0.45

0.44

0.44

0.44

0.43

0.43

0.43

0.42

0.42

0.42

0.41

0.41
10

20
time [minute]

0.4

15
20
time [minute]

0.48

0.47

0

10

0.49

0.48

0.47

5

Run: 349204

0.5Charge [a.u.]

0.49

0.4

0

Run: 348862

0.5Charge [a.u.]

Charge [a.u.]

Run: 348279

0.5

Charge [a.u.]

Charge [a.u.]

Charge [a.u.]

Run: 347623

0.5

0.41
−5

0

5

10
time [minute]

0.4

− 10

0

10
20
time [minute]

Figure 6.12: Variation of response of a PMT just after opening the beam blocker for diﬀerent
runs under the same intensity muon beam. Each red points is the mean of the charge of 100
events. The blue line is the template function obtained from one long run, and the functionis scaled using the events before opening the beam blocker.
The obtained function was compared with the diﬀerent runs under the same intensity
muon beam as shown in Fig. 6.12, in order to confirm that the variation is the same every
time. The parameter a was determined using the data points before opening the beam blocker,
and the other parameters were fixed with those obtained from the long run. Although there
is still a small discrepancy whose cause is yet to be understood, the rough shape of the timedependent variation is almost same every time. Therefore, the variation can be correctedusing this template function.
However, it is possible that the change of the response to the VUV light is diﬀerent fromthe response to LED light. The eﬀect of the muon beam on the VUV light detection has
not been studied and this would be a future task. Since the time constant of the variation islong, it might be possible to compare the response to the gamma rays from a muon decay,
beween just after opening the beam blocker and an hour after the operation.

6.3.3

Aging Caused by Muon Beam

The charge response of the PMT is known to decrease under muon beam, and a rapid
decrease was observed in the pilot runs. Figure 6.13 shows the variation of three observables;
gain, charge for LEDs, and charge for alpha rays.

Chapter 6. PMT Monitoring72

Responsegain
LEDalpha ray

1
0.98
0.96
0.94
0.92
20/10

24/10

27/10

date

Figure 6.13: Variation of PMT gain (red circle), charge for LED (green square) and charge
for alpha ray (blue triangle) under muon beam. They are normalized channel by channel,
and the average of about 350 PMTs is plotted.
In a few days the response decreased by about 8%. The decreases observed for the threeobservables were consistent within 1% over a week. It means that the main cause of thedecrease of the PMT total response is the gain decrease. If the decrease of the VUV response
is caused only by the gain decrease, the alpha ray calibrations can be interpolated by LED
calibration, which needs less time. However, it is also possible that there is an additional
wavelength dependent QE variation. There is in fact 1% inconsistency between gain decrease
and charge decrease, and it should be carefully investigated for longer period.
The decrease speed was more rapid than expected from the MEG experiment, and it is aserious problem The problem is discussed in the next section.

6.4

Gain Decrease

6.4.1

Expectation from MEG

The PMT response is known to decrease with muon beam irradiation as can be seen in
the gain history during the MEG experiment shown in Fig. 6.14.
Although the decrease of the gain can be compensated by increasing high voltage, toomuch voltage would lead to severer damage on the PMT and would finally result in breakdown. Using the dependence of the gain on the voltage shown in Fig. 6.15, the final voltage
necessary at the end of the MEG II experiment was estimated in 2013 [49]. The assumptions
were as follows;Chapter 6. PMT Monitoring

73

×10

Gain

3

2100
2000
1900
1800
1700
1600

02/07/10

31/12/10

02/07/11

01/01/12

01/07/12

31/12/12

02/07/13
Date

Figure 6.14: PMT gain history during the MEG I experiment from 2010 to 2013 [48]. Red
circles were taken without operation of magnets. Blue triangles (green squares) were taken
under (without) muon beam. Yellow inverse triangles were taken under pion beam. The highvoltage was adjusted every year so that the PMTs would have high enough gain.
• Voltage is adjusted for the gain to become 1.8 × 106 at the beginning of every year.
• G = a(V − V0 )k , where G is gain and V is applied voltage.
• V0 and k does not change by irradiation.
• The decrease is exponential and the rate is proportional to the muon beam rate.
• The voltage cannot exceed 1400 V.
The result is shown in Fig. 6.16. After running for three years, the required voltage would
be still below the upper limit of 1400 V for most PMTs, although for some PMTs it would
have already been beyond the limit. The PMTs whose decrease rate was small were selected
to be used also in the MEG II experiment because the number of PMTs decreases by 216
owing to the introduction of SiPMs on the incident face. An important point here is that it
is assumed that the gain decrease rate is proportional to the muon beam rate. It has to bevalidated under higher beam rate.

6.4.2

Beam Rate Dependence

Figure 6.17 shows the history of response of a PMT monitored by LED in 2017. Since three
diﬀerent muon beam rates were tested during this period, the dependence of the decrease
speed on the beam rate can be extracted. Although the decrease rate seems to decrease with
irradiated time, the initial slope is fitted by linear function and the speed is extracted. In
2018 muon beam rate reached the MEG II nominal intensity (7 × 107 µ/s) and the decrease
rate at this high irradiation environment was also extracted. As a result, the dependence isfound out not to be proportional to the beam rate, and the decrease under MEG II nominal
intensity is much faster than expected in 2013 as shown in Fig. 6.18.
For now there is basically no method of increasing the gain except for applying higher
voltage. Decreasing the beam rate is one solution for the PMT survival, but the doubling of
the muon beam rate from the MEG experiment is necessary to reach the sensitivity goal inthree years. Based on the observed speed of gain decrease, the high voltage necessary after athree-years run was calculated for each PMT and it is shown in Fig. 6.19. Most PMTs would

Gain

Chapter 6. PMT Monitoring74

CH: 4347

×103
3000
2500
2000
1500
1000
500
750

800

850

900
HV [V]

Figure 6.15: High voltage dependence of the PMT gain. The points are data including
statistical uncertainty, and the line is the fitted power function. The gain is proportional tothe power of applied high voltage.

12

Number of PMTs

X1

X3

X5

40

current
after 1 year
after 3 years
after 5 years

35
30
25
20
15
10
5

DEAD

1380

1300

12

1340

1260

1180

1220

1100

1140

1020

1060

940

980

900

820

860

780

700

740

0

Voltage [V]Figure 6.16: PMT high voltage necessary to keep enough gain simulated in 2013 (labels andlegends replaced for visibility from [49]). Most PMTs would not need more than 1400 V after
the 3 years run.

Chapter 6. PMT Monitoring

75

Charge of a PMT (normalized)
beam intensity(relative to MEG II)

78%
72%
31%

date
Figure 6.17: Response of a PMT monitored by LED in 2017 [48]. The yellow inverted triangles
are points taken under 78% of the MEG II nominal beam rate. The blue triangles and thered circles correspond to 72% and 31%, respectively.

charge decrease rate[%/day]MEG II

MEG I

beam intensity (relative to MEG II)
Figure 6.18: Beam rate dependence of the gain decrease rate [48]. The relation is not proportional and the decrease under MEG II intensity is much faster than expected. Note that
not all of the PMTs shown in Fig. 6.1 is used in this plot because some of them were notread out in the MEG experiment or in 2017.

Chapter 6. PMT Monitoring76

histHV

10

EntriesMean
Std Dev

203
1615
528.6

8
6
4
2
0

1000

2000

3000

4000
HV [V]

Figure 6.19: High Voltage necessary at the end of a three-years run estimated from the gain
decrease speed observed with the same intensity muon beam with that in the MEG II physics
run.
require more tha and they would be in dahave a risk of failure. To overcome the problem,the possibility of operating the PMTs with lower gain to prolong thir lives was studied atpilot run in 2019.

6.4.3

Gain Dependence

One possibility of the cause of the gain decrease is a degradation of dynodes in the PMT.
The damage can possibly be mitigated when the number of electrons hitting the dynodes isreduced by a lower gain operation. The decrease rate of the average gain of 200 PMTs wascompared under diﬀerent high voltages. As shown in Fig. 6.20, the decrease rate became
small under the halved gain. A recovery of the gain was observed after leaving the PMTs forseveral month at room temperature, but it was very small (a few percent). Using the slopeof the gain decrease curve and the high voltage dependence of the gain, the high voltage
necessary after the three years run was estimated channel by channel. The result is shown in
Fig. 6.21 and most of the PMTs can be operated with reasonable voltage.

6.4.4

Discussion

In order to keep the applied high voltage in the safe region, it seems necessary to operate
the PMTs with lower gain. The largest disadvantage of using lower gain is that the signalto-noise ratio (S/N) becomes worse. One possible solution for this problem is to increase thegain of the amplifier of WaveDREAM boards from 1. If the major component of the noise
arises between the amplifier and the waveform digitizer, the loss of the signal size can becompensated by the amplifier because the noise level does not change by the amplifier.
The noise level was actually compared between the cases with gain 1 and gain about
2.3 [50]. The result is shown in Fig. 6.22 and the total noise level increased only 13% afterChapter 6. PMT Monitoring77

Normalized Gain
1
0.99
0.98

0.8M: 0.4(2)%/day
1.6M: 1.80(8)%/day

0.97
0.96
0.95
0.94
0

1

2

3

Day

Figure 6.20: Gain decrease under the diﬀerent voltage as a function of the irradiation days.
Average gain of about 200 PMTs measured by LED. The decrease rate is smaller when smaller
voltage is applied.

histHV
EntriesMean
Std Dev

10

203
992.8
162.8

8
6
4
2
0

600

800

1000

1200

1400

1600
HV [V]

Figure 6.21: High voltage necessary after a three years run estimated from the gain decrease
rate and the high voltage dependence of gain.

Chapter 6. PMT Monitoring

78

Figure 6.22: Noise waveform without an amplifier (left) and with an amplifier gain about 2.3(right) [50]. The total noise level diﬀers only about 13%.
inserting an amplifier. This imply that the lower gain operation of PMTs does not aﬀect theperformance of the detector.
The eﬀect of the lower gain operation on the detector performance should be investigatedusing signal-like gamma rays and it is planned to be done by the charge exchange experimentin 2020.

6.5

Conclusion

The PMT response was monitored during the MEG II pre-engineering runs conducted
in 2018 and 2019. The dependence on the magnetic field and muon beam was carefully
investigated. The response of one PMT to alpha rays was calibrated with 4% precision. The
precision of the estimation of the average of 350 PMTs was 0.2%. The response of one PMT
to LED light was calibrated with 1% precision. The aging by the muon beam irradiation
was found to be severer than expected from the experience in the MEG experiment, but asolution of lower gain operation was found out to be eﬀective. The eﬀect of the lower gain
operation on the detector performance will be investigated by the CEX calibration in 2020.

Part III

Calibration of Detector Response79

Chapter 7

Improvement of Charge Exchange
Calibration
7.1

Motivation

Global calibration parameters necessary for the event reconstruction (see Sec. 4.2) will be
extracted using the gamma rays generated in the charge exchange (CEX) reaction of pions
explained in Sec. 4.3.3. For example, the position dependence of the total number of photons
detected by photosensors must be corrected in order to reconstruct energy, and the correction
function is made by the CEX calibration. The detector performance will be evaluated also in
the CEX calibration using the extracted calibration parameters. From these points of view,
the CEX calibration is the most important calibration and the precision of the calibration is
the key to the best performance of the LXe Calorimeter.
In order to calibrate something, the reference value has to be more precise than the target
precision of the calibration. In the case of LXe Calorimeter, the position, energy and timingof the gamma ray should be known very precisely.
A lead collimator has been developed to restrict the region where gamma rays enter forthe position study [5].
The timing of the gamma ray injected into the LXe Calorimeter is estimated from thatof the other gamma ray. It is detected by the pre-shower counter which consists of lead
conversion plate and two plastic scintillators read out by SiPMs, whose timing resolution
is 40 ps [33]. The pre-shower counter is shown in Fig. 7.1. The timing at the pion decay
vertex position is calculated using the flight length of the gamma ray, and then the measured
generation time of the two gamma rays is compared to each other. However, there is another uncertainty from the vertex position because the pion beam is broad in the direction
perpendicular to the beam axis. It makes an uncertainty in the time of flight estimation(2 × 10 mm/c ∼ 70 ps in sigma).
The energy of the gamma ray is around 55 MeV when selecting the events where two
gamma rays are emitted in the opposite direction in the laboratory frame and lower energy
one enters the LXe Calorimeter. More precise estimation is possible using the opening angleof the two gamma rays from a neutral pion decay because there is a relation determined by80

Chapter 7. Improvement of Charge Exchange Calibration

Figure 7.1: Pre-shower counter [33]. A
plastic scintillator read out by SiPMs iswrapped by a light shield.

81

Figure 7.2: BGO counter [51]. 4 × 4 BGO
crystals are optically connected to PMTs.

the kinematics between the opening angle and the gamma ray energy as shown in Fig. 7.3.
The precision of the angle is determined by the position resolution of the LXe Calorimeter(a few mm) and the tagging detector (∼ 10 mm), and the variance of the vertex position(∼ 10 mm). It corresponds to an uncertainty of several hundred keV. The BGO calorimeter(Fig. 7.2) is used as the tagging detector in the energy calibration. It is a 4 × 4 array of BGO
crystals (46 × 46 × 200 mm3 each), each of which is optically connected to a fine mesh PMT(H8409-70 by Hamamatsu).
Thus, the estimation of the energy and the timing of the gamma ray suﬀer from theuncertainty of the vertex position of the neutral pion decay. In order to overcome the problem,
two types of detectors were considered. The first one is a scintillating fiber detector for the
charged pion beam, and the second one is an active target which made of scintillating material.
They are explained in detail below.

7.2

Requirement

The role of this detector is to measure the vertex position of the neutral pion decay. The
required position resolution depends on the resolution of the other detectors, and the detector
geometry is optimized using simulation as described below. Since this position measurement
should be done event by event, timing resolution and pileups should also be taken into
account. The maximum charged pion beam rate is 1.4 MHz, which means the requirement
for the timing performance is not severe, O(µs). Another concern is the contamination in
the beam. There are 26 times more electrons than pions in the beam, and they must be
distinguished from the pions. In addition, the detector must be radiation hard. The CEX
calibration was conducted for 10 days per month in the MEG experiment. Therefore, 50 days
irradiation is assumed in the following study.

Chapter 7. Improvement of Charge Exchange Calibration

82

Figure 7.3: Relation between the opening angle and the energy of a gamma ray [29]. The
black points are data taken in 2009 and the line is the theoretical prediction based on the
kinematics.

7.3

Scintillating Fiber

7.3.1

Concept

Since the lifetime of the neutral pion is very short, the x-y position of the decay vertex
is almost equal to the beam position at the target. This detector is designed to measure
the beam position just in front of the target as shown in Fig. 7.4. When the charged pion
goes through the scintillating fiber, the pion deposits some energy on the fiber and some
scintillation photons are emitted. By detecting the photons by the SiPMs attached at theend of the fibers, discrete information of the beam position is obtained. Since scintillatingfibers are very thin (∼ 250 µm), some fibers are put together to make a bundle to read manyfibers by one SiPM. One layer can measure only one dimensional position. Therefore, thenext layer is put orthogonally to the previous layer to enable a two-dimensional measurement.
The small thickness of scintillating fibers reduces influence on the pion beam. If the charged
pion is scattered too much by the detector, the vertex position will be diﬀerent from thedetected position.
The detector performance was simulated using Geant4 vesion 10.3.1 [37]. In the simulationa pion beam is generated imitating the actual beam used in the CEX calibration at the MEG
experiment, and the momentum and the width of the pion beam are normally distributed.
The expected resolution of the calorimeter and the tagging detector is also reproduced in
the simulation. The simulation setting is summarized in Tab. 7.1. The eﬀect on the energyChapter 7. Improvement of Charge Exchange Calibration

83

・・・

・・・

Al
degradermylarwindow

SiPM
fiber bundle

𝜋 " beam
LH2

3 mm 1 mm

50 mm

75 mm

Figure 7.4: Schematic design of a pion beam monitor. Scintillating fibers detect the pion
beam without aﬀecting the beam property so much.
Table 7.1: Settings in the simulation of a pion beam position detector.
central value of beam momentum
70.5 MeV/cfluctuation of beam momentum
3%
beam width in horizontal direction
8.5 mmbeam width in vertical direction
7.5 mmtiming resolution of pre-shower counter
40 ps
position resolution of pre-shower counter 7 mm
position resolution of BGO calorimeter
10 mmposition resolution of LXe Calorimter
O(mm) (depends on conversion depth)
physics model
FTFP BERT
estimation and the timing estimation was studied for diﬀerent thicknesses of the bundles. Theenergy and the timing of the gamma ray injected to the LXe Calotimeter were reconstructedusing the reconstructed information of tagged gamma ray and the vertex position. The
simulation is repeated for diﬀerent bundling configurations of the fiber detector, and thereconstructed variables were compared with the true values. Accuracy was defined as thestandared deviation of the distribution of the diﬀerence between the reconstructed variable
and its true value. The result is shown in Fig. 7.5.
Since this type of detectors provide discrete information, highly segmented bundles lead
to better position resolution. In our case, however, the improvement saturates at around 10
bundles, which corresponds to the thickness of 5 mm per bundle, because the eﬀect of theresolution of other detectors becomes donimant.

7.3.2

Particle Identification

The negative pion beam is contaminated by 26 times larger number of electrons. Thesecan be eliminated by the timing and the signal size.
The pions are generated from protons accelerated by a large proton cyclotron, and the

84

Accuracy [MeV]

Chapter 7. Improvement of Charge Exchange Calibration

Figure 7.5: Accuracy of the estimated energy and timing of the gamma ray [52]. Although
the large number of bundles leads to better estimation, ∼10 bundles (5 mm/bundle) areenough owing to the resolution of other detectors.
ejected protons have a bunch structure. Since a pion is heavier than an electron, the velocity
of a pion is diﬀerent from that of an electron when the momentum is the same. Thus thepions can be distinguished from the electrons by the arrival time.
The energy deposit of the pion is also diﬀerent from that of the electron. The electron
behaves like a minimum ionizing particle at the beam momentum of 70.5 MeV/c, while thepion does not and it deposits larger energy. The simulated diﬀerence of the energy deposit
is shown in Fig. 7.6.
These methods of particle identification have been already verified using a diﬀerent beamline at PSI as shown in Fig. 7.7 [53] although the momentum of the particles is ∼ 60% larger
than our case.

7.3.3

Radiation Hardness

Since the pion beam monitor will always be irradiated by the beam, some radiation
damage is expected. In addition to the charged pion beam and the electron contamination,neutrons from the CEX reaction or gamma rays from the neutral pion decay should be also
taken into account. The possible eﬀect of the radiation is discussed separately for eachcomponent; the scintillating fiber and the SiPM.
Scintillating Fiber
The light yield and the transmittance of the scintillating fiber are expected to decreaseby radiation damage. It can lead to small signals and bad S/N.

Chapter 7. Improvement of Charge Exchange Calibration

85

π-

e-

Figure 7.6: Energy deposit on 250 µm thick scintillator from pions (top) and from electrons(bottom). The signal from a pion is larger than that from an electron.

Chapter 7. Improvement of Charge Exchange Calibration

86

Figure 7.7: Result of the particle identification test performed at the πM1 beamline at PSI
using 115 MeV/c beam [53]. The three clusters are associated to electrons, pions and muons,reading the spectrum from left to right. The charge spectra of the muons and pions are scaled
by a factor of twenty for visibility.

Chapter 7. Improvement of Charge Exchange Calibration

87

Table 7.2: Scintillation light yield of diﬀerent type of plastic scintillators before and after
irradiation [54].

Figure 7.8: Radiation-induced optical absorption coeﬃcients at 440 nm [55].
Light Yield The light yield of scintillating fibers decreases by irradiation. Table 7.2 shows
the light yield of various scintillators after irradiated by the gamma ray. In our case the doseis 1.5×104 Gy at the center fiber, and the irradiation source is negative pions, which makes it
diﬃcult to directly compare them with each other. If it is assumed that the radiation eﬀect
by negative pions is not so much diﬀerent from that of gamma rays, the light yield of BC
series scintillators will be 60% even after suﬀering from twice larger dose.
Transmittance Figure 7.8 shows the radiation eﬀect to the absorption coeﬃcient of ascintillator for the neutron and the gamma ray. The fraction of light which reaches the end of
the scintillator after 5 years run was calculated using the absorption coeﬃcient. More than
40% of light can be detected after propagating 10 cm even after the irradiation.

Chapter 7. Improvement of Charge Exchange Calibration

88

Eﬀect on Signal Size The initial performance of the photon detection is estimated using
the energy deposit and the transmittance. The number of photon Npho is written as follows;()∆Ω
dNpho = W · E ·exp −· P DE,(7.1)
4π
λwhere W ∼ 8, 000 photons/MeV [56] is the scintillation performance of the scintillating fiber,
E ≳ 0.2 MeV is the energy deposit on the scintillator, ∆Ω/4π ∼ 7% is the fraction of thesolid angle looking into SiPM, d < 10 cm is the distance between the scintillation position
and the sensor, λ ∼ 15 cm [56] is the attenuation length of the fiber, and P DE ∼ 40% [40]is the photon detection eﬃciency of the SiPM. The solid angle was calculated assuming thephotons are generated at the end of a 5 × 5 × 100 mm3 scintillator, and only those directly
reach a SiPM at the other end of the bar are considered. About 23 photons are expected to
be detected. Even after the experiment of 50 days, more than 10 photons can be detectedbased on the radiation damage estimation above and it is large enough to distinguish signals
from dark noise.
SiPM
The radiation damage on SiPM can be classified into two types: ionizing process and bulk
damage.
Ionizing Process When SiPM is irradiated with ionizing particles such as gamma rays,
the p-n structure changes and leak current increases. A significant increase of leak current
after 160 Gy/h gamma ray irradiation is reported in Ref. [32]. In our case, the width of thepion beam is about 8 mm in sigma and if the length of a scintillating fiber is 100 mm, almost
no beam particles enters SiPM directly. Then only possible ionizing particle is a gamma ray
from a pion decay. The expected dose on the silicon is calculated and it is only 0.48 Gy after
50 days calibration. Thus this eﬀect will be negligible.
Bulk Damage The other type of damage is called bulk damage and it is induced typicallyby neutron. The increase of dark noise caused by 53 MeV proton is reported in Ref. [57] andthe broadening of the one photoelectron peak was observed after 9.1×109 1 MeV-neq /cm2 .
In order to estimate the radiation level of the neutron in our case, the energy spectrum of
the neutron was simulated. The kinetic energy of the neutron generated in the CEX reactionis 420 keV, and the energy distribution after 25 mm flight in the liquid hydrogen target is likeFig. 7.9. 109-10 1 MeV-neq /cm2 is expected during the calibration run of 50 days, and it will
worsen the energy resolution. In our case the precise energy is not required to distinguisha signal hit from background. Thus the worsening of the resolution in this level is not a
problem.

7.4

Active Target

The beam monitor can provide information of the beam position only in the plane perpendicular to the beam axis, and cannot provide the information on z position of the vertex,

Chapter 7. Improvement of Charge Exchange Calibration

89

Figure 7.9: Energy distribution of the neutron generated by charge exchange reaction after
the flight of 25 cm, simulated by Geant4.
which is most important for the energy estimation because it is sensitive to the opening angleof two gamma rays. An active target is one solution which makes it possible to measure
the vertex position along the beam axis. By replacing the passive liquid hydrogen target
by an active scintillating target, three dimensional position information of the vertex can beextracted.

7.4.1

Concept

The detector concept is depicted in Fig. 7.10. The basic idea is shared with the scintillatingfiber beam monitor. It is made of some layers and each layer detects only the one-dimensional
position. The significant diﬀerence is that each layer is designed to be thick so that the charged
pion can stop in the scintillator while the beam monitor was designed to be thin enough not
to aﬀect the beam.
The detector performance is compared with the case of using scintillating fiber beam
monitor, for the case where the width and the thickness of the scintillating materials are
5 mm. The result is summarized in Tab. 7.3. Not only the timing estimation but also theenergy estimation improves thanks to the capability of estimation of the position along thebeam axis.
The radiation hardness of the plastic scintillator is similar to that of the scintillating fiber,
while the light yield is larger thanks to the large thickness.
On the other hand, there are two possible disadvantages discussed below.

Chapter 7. Improvement of Charge Exchange Calibration

90

Scintillator bars𝜋"
1 1
y x1 1yz
Figure 7.10: Design of an active target. Each layer is thicker than the scintillating fiber andsome layers are piled up to obtain the position along the beam axis.

Table 7.3: Performance of the estimation of the gamma ray timing and energy using diﬀerent
type of detectors.
Detector type
Timing Energy
No Detector
73 ps
320 keV
Scintillating Fiber
51 ps
300 keV
Scintillating Target 39 ps
230 keVChapter 7. Improvement of Charge Exchange Calibration

7.4.2

91

Charge Exchange Reaction in Scintillator

While the liquid hydrogen target consists of purely hydrogen atoms, a scintillator contains
carbon atoms. Therefore, the reaction of the charged pions in the target is diﬀerent. The
negative pion causes two types of reaction in a scintillator.
The first one is coherent reaction [58]. A stopped negative pion is captured by a molecule
which consists of C and H with probability proportional to Z −1 , where Z indicates the atomic
number. Then the captured pion moves from a molecular orbital to an atomic orbital. This
probability is proportional to Z 2 , which means that the probability that the pion moves tothe hydrogen orbital is 100 times smaller than that to the carbon orbital. The CEX reaction
does not happen in a pionic carbon owing to the energy diﬀerence between the carbon andthe boron. This will probably result in a significant decrease of the reaction rate.
The second type is incoherent reaction. The moving pion can directly collide with anucleus with small probability. When a moving pion causes CEX reaction with a proton in
the carbon nucleus, the momentum of generated neutral pion is no more 28 MeV/c because
the negative pion is moving and the proton has Fermi momentum in the carbon atom. The
diﬀerent momentum of the neutral pion leads to the diﬀerent energy of the gamma ray. Thismight result in changing the energy spectrum of the gamma ray.

7.4.3

Rate

The rate of the charge exchange reaction on various materials has been studied as shownin Fig. 7.11. It shows the probability of a pion charge exchange reaction on diﬀerent materials
compared to that on liquid hydrogen. When using CH2 as target material, the probabilityof reaction becomes around 1% of that with liquid hydrogen target. The minimum rate of
the charge exchange reaction on CH2 which has been found in the literature is 0.77% of thaton liquid hydrogen [60], and the maximum is 1.45% [61]. In the MEG experiment, the DAQ
rate of the charge exchange calibration with a LH2 target was 12.5 Hz and it took 2.5 hours
to store the necessary statistics for a particular region defined as a patch. The decrease of
the probability of the charge exchange reaction demands 250-500 hours with an active target
and it is unreasonable. However, in the charge exchange calibration of the MEG experiment,
the beam rate was intentionally reduced to prevent from pileups and radiation damage on
detectors. By fully opening the beam slit, 20 times larger beam rate can be obtained. It
improves the reaction rate up to 1.5-3 Hz, which leads to 10-20 hours/patch. Although it
is still longer, it is worth investigating more because it is instead possible to save the target
preparation time which is necessary in the liquid hydrogen target case. The cumbersome lowtemperature operation is not needed anymore with the scintillator active target.

7.4.4

Energy Spectrum

The active target for the pion charge exchange reaction has been already used in the
MEGA experiment [62]. Fig. 7.12 shows the energy spectrum obtained in the MEGA experiment using a scintillating target. The tail events in the low energy region is explained as the
charge exchange reaction in flight on carbon nuclears, and the tail in the large energy region
is explained as events which have small opening angle. High energy tail can be eliminated byChapter 7. Improvement of Charge Exchange Calibration

92

Figure 7.11: Probability of a pion charge exchange reaction on diﬀerent materials comparedto that on liquid hydrogen [59]. The probability of the reaction is around 1% of that on liquidhydrogen target when using CH2 as a target.

Chapter 7. Improvement of Charge Exchange Calibration

93

Figure 7.12: Energy spectrum of reconstructed photons which converted in the outer layer inthe MEGA experiment [62]. The points come from data and the solid line shows reconstructedenergy from simulated events.
the improved angle reconstruction owing to the vertex information. The lower energy events
coming from the CEX reaction on carbon nuclears cannot be separated from those due todetector response. It disturbs the extraction of the detector response function, and need to
be investigated by experimental test.

7.5

Test of Active Target

In the previous two sections, two types of vertex detectors were considered. The active
target provides more precise estimation of the properties of the gamma ray although it has
two possible disadvantages. In order to investigate the possible problems, a test experiment
was planned to be conducted in December 2019.

7.5.1

PurposeThe main purpose is to check the rate of gamma ray from the charge exchange reaction
with an active target, and to compare the energy spectrum with that obtained from thenormal liquid hydrogen target. In addition, the improvement of the timing and energy
estimation should be confirmed using the vertex reconstruction.

Chapter 7. Improvement of Charge Exchange Calibration

94

Figure 7.13: One layer of the active target before wrapped by shading cloth.

7.5.2

Construction of Prototype

In order to achieve these purposes, a prototype target has been developed. Figure 7.13
shows one layer of the constructed target. The support structure is made of plastic, and it can
fix the scintillators in three dimensions. Plastic scintillators EJ-232 provided by Eljen [63]cut into pieces with a size of 90 mm × 4.8 mm × 4 mm are used as a scintillating target.
The scintillation photons are read out by a SiPM attached at the end of the scintillator,
which is optically connected by optical cement. One layer consists of eight scintillators andthey are optically separated by reflectors (3M ESR, 65 µm-thick [64]) with each other. The
SiPMs are only at one end to reduce the number of readout channels, and the other end iscovered by the reflector. Four layers are stacked up to provide enough material to stop thepion beam. Each layer is wrapped by shading cloth. In front of first layer, a degrader madeof 3 mm thick aluminum is placed. The thickness of the degrader was determined by a flight
length simulation shown in Fig. 7.14.

7.6

Conclusion

Obtaining information on the position of the neutral pion decay vertex leads to better
estimation of the energy and timing of the gamma ray entering the LXe Calorimeter, resulting
in more precise calibration and performance estimation. Two diﬀerent types of modules wereconsidered as a vertex position detector, the scintillating fiber beam monitor and the plastic
scintillator active target, and the performance and the radiation hardness were inspected.
The active target provides the position information along the beam axis although there aresome possible disadvantages which should be tested experimentally. A prototype of theEvents

Chapter 7. Improvement of Charge Exchange Calibration

95

htemp

45

EntriesMean
Std Dev

40

995
8.124
1.693

35
30
25
20
15
10
5
0
0

2

4

6

8

10

12

14
z [mm]

Figure 7.14: Simulated flight length of the negative pion in the plastic when a 3 mm thickAluminum degrader is placed in front of the scintillators.
active target has been developed for the test experiment which was planned in December
2019, although the test was postponed on account of a failure of a beam transport solenoid.
It will be repaired and the test of the active target is planned in 2020.

Part IV

Conclusion

96

Chapter 8

Conclusion
Several studies concerning the calibration of the LXe Calorimeter were conducted. The
photosensors were successfully calibrated and monitored during the pilot runs. The new
calibration methods of the photosensors and the new detector for the coming CEX calibration have been studied, which are expected to contribute to the more convenient or precise
calibration after some more sophisticated studies.

8.1

SiPM Gain Monitoring

Two independent methods of monitoring the gain of SiPMs were studied to compensate
for some disadvantages of the standard method. One method uses a statistical property of thecharge distribution from a Poisson light source. It has an advantage in the robustness to noise,and the gain can be measured even after heavily irradiated where usual one-photoelectron
method cannot be applied, although a conversion factor has to somehow be obtained to
calculate the absolute gain. The behavior of the statistics was diﬀerent from expected one,but the gain was successfully extracted.
The other method extracts gain-related information directly from the waveform and it
does not need special setup for measuring the gain. Although this method was originallydeveloped for PMT gain monitoring in the previous study, it was successfully applied to
SiPMs in this study with a method improved by taking into account the eﬀect of overlapping
waveforms.
The gain extracted by these methods is confirmed to be highly correlated to the one
obtained from the standard one-photoelectron method. However, it must be checked thatchanges in other properties such as afterpulsing does not aﬀect these methods, and it would
be the next step to do.

8.2

PMT Monitoring during Pilot Run

The PMT response was monitored during the MEG II pilot runs conducted in 2018 and2019. The eﬀects of high rate muon beam were especially carefully investigated because thebeam rate is more than twice larger than in the MEG experiment. The response to alpha97

Chapter 8. Conclusion

98

rays was calibrated with 4% precision channel by channel, and the precision of the averageof 350 PMTs was 0.2%, which fulfills the requirement. The response to LED light wascalibrated with 1% precision channel by channel, and the variation of response to LED lightcaused by aging seems correlated with that to alpha rays. The gain decrease by the muon
beam irradiation was found to be severer than expected from the experience in the MEG
experiment, but a solution of lower gain operation was found out to be eﬀective. The eﬀectof the lower gain operation on the detector performance will be investigated by a calibration
run with the CEX reaction in 2020.

8.3

Development of Pion Beam Detector

Obtaining information on the position of the neutral pion decay vertex leads to better
estimation of the energy and timing of the gamma ray entering the LXe Calorimeter, resulting
in more precise calibration and performance estimation. Two diﬀerent types of modules wereconsidered as a vertex position detector, the scintillating fiber beam monitor and the plastic
scintillator active target, and the performance and the radiation hardness were inspected.
The active target provides the position information along the beam axis although there aresome possible disadvantages which should be tested experimentally. A prototype of theactive target has been developed for the test experiment which was planned in December
2019, although the test was postponed on account of a failure of a beam transport solenoid.
It will be repaired and the test of the active target is planned in 2020.

Acknowledgement
First, I want to thank Prof. Toshinori Mori for giving me the chance for this study. I
had a precious experience of taking part in an international collaboration locally at PSI andstudying together with overseas researchers. He gives us essential comments at the right timeand makes us collaborators brace ourselves. Prof. Wataru Ootani has given me important
advice in every meeting. I am grateful of his equal interest to all the studies of students andpointed questions. Dr. Toshiyuki Iwamoto has given me kind support both on research andon life in Switzerland. He always kindly answers my questions despite being very busy withwork as a run coordinator. Dr. Yusuke Uchiyama always points out critical points I missed
in my study. I was often moved by his presentations or questions which get straight to thepoint. I always rely on Dr. Kei Ieki for technical support both in hardware and software.
I respect that he tries a lot of new ideas himself while paying attention to students’ work.
Mr. Shinji Ogawa, Mr. Satoru Kobayashi and Ms. Rina Onda were necessary for proceeding
my study. I could not have conducted my study at all without their kind support.
Dr. Satoshi Mihara gave me important insight on the PMT gain decrease and the pion
charge exchange reaction ina scintillator. Dr. Peter-Raymond Kettle, Dr. Giovanni Signorelli
and Dr. Angela Papa provided me necessary information on making a prototype target.
Dr. Akos Schreiber and Dr. Florian Barchetti made a support on making the target. The
discussion with Mr. Kosuke Yanai and Mr. Atsushi Oya was necessary on the SiPM gain
study, and they have also always supported me as good friends.
I want to thank the member of the laboratory, Dr. Miki Nishimura, Mr. Mitsutaka Nakao,
Mr. Masashi Usami, Mr. Linghui Liu, Mr. Nobuo Matsuzawa, Mr. Naoki Tsuji, Mr. Tatsuro Torimaru, Mr. Kohei Shimada, Mr. Taku Yonemoto, Mr. Kensuke Yamamoto and
Mr. Ryunosuke Masuda, for advice in the meeting and for enjoyable research life. I would liketo thank all the people in the MEG II collaboration and my friends in Japan and Switzerland.
Finally I would like to thank my family for accepting my decision in studying abroad andfor their warm support throughout my life.

99

Bibliography[1] Y. Fukuda et al. (Super-Kamiokande Collaboration), Evidence for oscillation of atmospheric neutrinos. Phys. Rev. Lett. 81, 1562–1567 (1998). doi:10.1103/PhysRevLett.
81.1562. https://link.aps.org/doi/10.1103/PhysRevLett.81.1562[2] CERN website. https://home.cern/science/physics/standard-model, cited 22nd
December 2019[3] Y. Fukuda et al., Evidence for oscillation of atmospheric neutrinos. Physical Review
Letters (1998). doi:10.1103/PhysRevLett.81.1562, arXiv:9807003[4] European Strategy for Particle Physics Preparatory Group, Physics Briefing Book
(2019). arXiv:1910.11775. http://arxiv.org/abs/1910.11775[5] S. Kobayashi. Research on precise gamma-ray position measurement with MEG II liquid
xenon detector. Master’s thesis, The University of Tokyo (2019). https://www.icepp.
s.u-tokyo.ac.jp/download/master/m2018_kobayashi.pdf[6] S. M. Bilenky, S. T. Petcov, B. Pontecorvo, Lepton mixing, µ → e + γ decay and neutrino
oscillations. Physics Letters B (1977). doi:10.1016/0370-2693(77)90379-3[7] L. Calibbi, G. Signorelli, Charged Lepton Flavour Violation: An Experimental and Theoretical Introduction. Riv. Nuovo Cimento 41 (2017). doi:10.1393/ncr/i2018-10144-0,
arXiv:1709.00294. https://arxiv.org/abs/1709.00294[8] The MEG Collaboration et al., Measurement of the radiative decay of polarized muons in
the meg experiment. The European Physical Journal C 76(3), 108 (2016). doi:10.1140/
epjc/s10052-016-3947-6. https://doi.org/10.1140/epjc/s10052-016-3947-6[9] M. Tanabashi et al., Review of Particle Physics. Physical Review D 98(3), 030001(2018). doi:10.1103/PhysRevD.98.030001. https://link.aps.org/doi/10.1103/
PhysRevD.98.030001[10] A. M. Baldini et al., The design of the MEG II experiment. The European PhysicalJournal C 78(5), 380 (2018). doi:10.1140/epjc/s10052-018-5845-6. https://doi.
org/10.1140/epjc/s10052-018-5845-6

100

Bibliography101[11] A. M. Baldini et al., Search for the lepton flavour violating decay µ+ → e+ γ with thefull dataset of the MEG experiment. The European Physical Journal C 76(8), 434(2016). doi:10.1140/epjc/s10052-016-4271-x. https://doi.org/10.1140/epjc/
s10052-016-4271-x[12] PSI website. https://www.psi.ch/en, cited 22nd December 2019[13] A. M. Baldini et al., Muon polarization in the MEG experiment: predictions and measurements. The European Physical Journal C 76(4), 223 (2016). doi:10.1140/epjc/
s10052-016-4047-3. https://doi.org/10.1140/epjc/s10052-016-4047-3[14] J. Adam et al., The MEG detector for µ+ → e+ γ decay search. European PhysicalJournal C (2013). doi:10.1140/epjc/s10052-013-2365-2, arXiv:1303.2348[15] S. Ritt, The DRS chip: cheap waveform digitizing in the GHz range. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 518(1), 470 – 471 (2004). doi:https://doi.org/
10.1016/j.nima.2003.11.059. http://www.sciencedirect.com/science/article/
pii/S016890020302922X[16] MIDAS webpage.
https://midas.triumf.ca/MidasWiki/index.php/Main_Page,cited 22nd December 2019[17] G. Cavoto et al. A photogrammetric method for a periodic monitoring of the target
position in MEG-II. Technical report, MEG II colaboration (2018)[18] M. Nishimura, Positron Timing Mesurement to Seach for Lepton Flavor Violating Decay
in MEG II. PhD thesis, The University of Tokyo. https://www.icepp.s.u-tokyo.ac.
jp/download/doctor/phD2018_nishimura.pdf[19] Y. Uchiyama, The MEG II experiment in search of µ → eγ. in The APS Division of Particles and Fields Meeting (2019). https://indico.cern.ch/event/782953/
contributions/3441675/attachments/1887140/3111341/APS-DPF2019.pdf[20] D. R. Lide, Handbook of Chemistry and Physics, 85th. Boca Raton, FL: CRC (2004).
https://archive.org/details/B-001-003-529/page/n1019[21] T. Doke et al., Absolute scintillation yields in liquid argon and xenon for various particles.
Japanese Journal of Applied Physics 41(Part 1, No. 3A), 1538–1545 (2002). doi:10.
1143/jjap.41.1538. https://doi.org/10.1143%2Fjjap.41.1538[22] T. Doke, K. Masuda, Present status of liquid rare gas scintillation detectors and their new
application to gamma-ray calorimeters. Nuclear Instruments and Methods in Physics
Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment
420(1), 62 – 80 (1999). doi:https://doi.org/10.1016/S0168-9002(98)00933-4.
http://www.sciencedirect.com/science/article/pii/S0168900298009334

Bibliography102[23] K. Fujii et al., High-accuracy measurement of the emission spectrum of liquid xenon in
the vacuum ultraviolet region. Nuclear Instruments and Methods in Physics Research,
Section A: Accelerators, Spectrometers, Detectors and Associated Equipment (2015).
doi:10.1016/j.nima.2015.05.065[24] A. Baldini et al., Liquid xenon scintillation calorimetry and Xe optical properties. inIEEE Transactions on Dielectrics and Electrical Insulation (2006). doi:10.1109/TDEI.
2006.1657967, arXiv:0401072[25] E. Aprile, T. Doke, Liquid xenon detectors for particle physics and astrophysics. Reviewsof Modern Physics (2010). doi:10.1103/RevModPhys.82.2053, arXiv:0910.4956[26] R. Sawada, A liquid xenon scintillation detector to search for the lepton flavor violating
muon decay with a sensitivity of 10−13 . PhD thesis, The University of Tokyo. https://www.icepp.s.u-tokyo.ac.jp/download/doctor/phD2008_sawada.pdf[27] A. Hitachi et al., Eﬀect of ionization density on the time dependence of luminescence fromliquid argon and xenon. Physical Review B (1983). doi:10.1103/PhysRevB.27.5279[28] Hamamatsu Photonics Web page. https://www.hamamatsu.com/, cited 9th December
2019[29] Y. Nishimura, A Search for the Decay µ+ → e+ γ Using a High-Resolution Liquid Xenon
Gamma-Ray Detector. PhD thesis, The University of Tokyo. https://www.icepp.s.
u-tokyo.ac.jp/download/doctor/phD2010_nishimura.pdf[30] MPPC handbook. https://www.hamamatsu.com/resources/pdf/ssd/03_handbook.
pdf, cited 22nd December 2019[31] T. Matsumura et al., Eﬀects of radiation damage caused by proton irradiation on MultiPixel Photon Counters (MPPCs). Nuclear Instruments and Methods in Physics Research, Section A: Accelerators, Spectrometers, Detectors and Associated Equipment(2009). doi:10.1016/j.nima.2009.02.022, arXiv:0901.2430[32] T. Matsubara et al., Radiation damage of MPPC by γ-ray irradiation with 60Co.
in Proceedings of Science (2007). https://www.researchgate.net/publication/
293079737_Radiation_damage_of_MPPC_by_g-ray_irradiation_with_60Co[33] R. Onda. Research and Development on Time Calibration and Background Reductionfor γ-ray Detection in MEG II Experiment. Master’s thesis, The University of Tokyo(2019). https://www.icepp.s.u-tokyo.ac.jp/download/master/m2018_onda.pdf[34] S. Ogawa. MEG II 実験のための真空紫外光に感度のある大型 MPPC を用いた高精細読出
し液体キセノンガンマ線検出器の開発. Master’s thesis, The University of Tokyo (2016).
https://www.icepp.s.u-tokyo.ac.jp/download/master/m2015_ogawa.pdf[35] A. Baldini et al., A radioactive point-source lattice for calibrating and monitoring theliquid xenon calorimeter of the MEG experiment. Nuclear Instruments and Methods

Bibliography

103

in Physics Research, Section A: Accelerators, Spectrometers, Detectors and AssociatedEquipment (2006). doi:10.1016/j.nima.2006.06.055[36] M.-M. Bé et al.
Table of Radionuclides, volume 5 of Monographie BIPM5.
Bureau International des Poids et Mesures, Pavillon de Breteuil, F-92310
Sèvres, France (2010). http://www.bipm.org/utils/common/pdf/monographieRI/
Monographie_BIPM-5_Tables_Vol5.pdf[37] Geant4 webpage. https://geant4.web.cern.ch/, cited 6th December 2019[38] J. Adam et al., Calibration and monitoring of the MEG experiment by a proton beamfrom a CockcroftWalton accelerator. Nuclear Instruments and Methods in Physics Research, Section A: Accelerators, Spectrometers, Detectors and Associated Equipment(2011). doi:10.1016/j.nima.2011.03.048[39] V. Chmill et al., On the characterisation of SiPMs from pulse-height spectra. Nuclear
Instruments and Methods in Physics Research, Section A: Accelerators, Spectrometers,
Detectors and Associated Equipment 854, 70–81 (2017). doi:10.1016/j.nima.2017.
02.049, arXiv:1609.01181[40] Hamamtsu Photonics. MPPC S13360 series datasheet (2016). https://www.hamamatsu.
com/resources/pdf/ssd/s13360_series_kapd1052e.pdf[41] A. Oya et al., A comparative study on various methods for SiPM gain calibration.
in Proceedings of the 5th International Workshop on New Photon-Detectors (PD18).
(Journal of the Physical Society of Japan) (2019). doi:10.7566/PD18, arXiv:https://journals.jps.jp/doi/pdf/10.7566/PD18. https://journals.jps.jp/doi/abs/10.
7566/PD18[42] P. W. Cattaneo et al., Development of high precision timing counter based on plastic
scintillator with sipm readout. IEEE Transactions on Nuclear Science 61(5), 2657–2666(2014). https://ieeexplore.ieee.org/document/6898046[43] J. Stein et al., Experiment and modeling of scintillation photon-counting and current
measurement for pmt gain stabilization. Nuclear Instruments and Methods in Physics
Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment
782, 20 – 27 (2015). doi:https://doi.org/10.1016/j.nima.2015.01.101. http://www.sciencedirect.com/science/article/pii/S0168900215001515[44] S. Kobayashi et al., Calibration of VUV-sensitive MPPCs of MEG II Liquid Xenon
Gamma-ray Detector.
in Physics of fundamental Symmetries and Interactions,
number 133 (2019). https://indico.psi.ch/event/6857/contributions/18967/
attachments/15252/20923/kobayashi_2019PSI_v2.pdf[45] F. Yuki, Search for the Lepton Flavor Violating Muon Decay µ+ → e+ γ with a Sensitivity
below 10−12 in the MEG Experiment. PhD thesis, The University of Tokyo. https://www.icepp.s.u-tokyo.ac.jp/download/doctor/phD2013_fujii.pdf

Bibliography104[46] S. Kobayashi, XEC: MPPC PDE & WD2G in PreEng2019. internal meeting report(2020)[47] W. Ootani et al. Technical Report on the COBRA Magnet. Technical report, MEG
Collaboration (2002)[48] K. Toyoda et al., Study on Aging of Photomultiplier Tubes for MEG II Liquid Xenon
Calorimeter. in Physics of funcdamental Symmetries and Interactions (2019). https://indico.psi.ch/event/6857/contributions/18974/[49] D. Kaneko. Internal meeting report (2013)[50] K. Ieki. Internal meeting report (2019)[51] D. Kaneko, The final result of µ+ → e+ γ search with the MEG experiment. PhD thesis,
The University of Tokyo. https://www.icepp.s.u-tokyo.ac.jp/download/doctor/
phD2016_kaneko.pdf[52] K. Toyoda on behalf of the MEG II Collaboration, The Development of a π Beam
Position Detector for the Calibration of the MEG II Liquid Xe Detector. in Japan
Physics Society Annual Meeting (2019). https://kds.kek.jp/indico/event/30559/
contributions/112372/attachments/88184/104724/17aK104-2.pdf[53] G. Rutar, In search of charged lepton flavor violating decays at psi. PhD thesis, ETH
Zürich. http://meg.icepp.s.u-tokyo.ac.jp/docs/theses/giada_phd.pdf[54] Y. Protopopov, V. Vasil’chenko, Radiation damage in plastic scintillators and opticalfibers. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms 95(4), 496 – 500 (1995). doi:https://doi.org/10.
1016/0168-583X(94)00599-0. http://www.sciencedirect.com/science/article/
pii/0168583X94005990[55] B. Bodmann, U. Holm, Neutron-irradiated plastic scintillators. Nuclear Instruments andMethods in Physics Research Section B: Beam Interactions with Materials and Atoms
185(1), 299 – 304 (2001). doi:https://doi.org/10.1016/S0168-583X(01)00762-5.
http://www.sciencedirect.com/science/article/pii/S0168583X01007625[56] Saint-Gobain Crystals. Fiber product sheet. https://www.crystals.saint-gobain.
com/products/scintillating-fiber, cited 22nd December 2019[57] T. Matsumura, 高感度光検出器 MPPC の放射線耐性. in Japan Physics Society Autumn
Meeting (2008). http://www.nda.ac.jp/cc/radiation/presen/JPS200809_toru.pdf[58] S. S. Gershteı̆n et al., MESOATOMIC PROCESSES AND MODEL OF
LARGE MESIC MOLECULES.
Soviet Physics Uspekhi 12(1), 1–19
doi:10.1070/pu1969v012n01abeh003914.
https://doi.org/10.1070%(1969).
2Fpu1969v012n01abeh003914

Bibliography105[59] Z. V. Krumshtein et al., INVESTIGATION OF π − -MESON CAPTURE BY HYDROGEN IN HYDROGENOUS SUBSTANCES 27(6), 906 (1968). http://jetp.ac.ru/
cgi-bin/dn/e_027_06_0906.pdf[60] A. F. Dunaitsev, V. I. Petsukhin, Y. D. Prokoshkin, Measurements of stopped π- meson
absorption probability by bound hydrogen nuclei. Il Nuovo Cimento (1955-1965) 34(3),521–528 (1964). doi:10.1007/BF02749995. https://doi.org/10.1007/BF02749995[61] V. Petrukhin, V. Suvorov, Study of atomic capture and recapture of pions minus in mixtures of hydrogen with other gases. Zhurnal Ehksperimental’noj i Teoreticheskoj Fiziki
70(4), 1145–1151 (1976). https://inis.iaea.org/search/search.aspx?orig{_}q=
RN:9355912[62] M. Ahmed et al. (MEGA Collaboration), Search for the lepton-family-number nonconserving decay µ+ → e+ γ. Phys. Rev. D 65, 112002 (2002). doi:10.1103/PhysRevD.
65.112002. https://link.aps.org/doi/10.1103/PhysRevD.65.112002[63] Eljen Technology. Data sheet of EJ-232. https://eljentechnology.com/products/
plastic-scintillators/ej-232-ej-232q, cited 9th December 2019[64] 3M. Vikuiti Enhanced Specular Reflector (ESR). https://www.digikey.ch/Site/
Global/Layouts/DownloadPdf.ashx?pdfUrl=AFE70E6B414C436184B8A9900F1C4831,
cited 22nd December 2019