Doctoral Dissertation
博士論文

Innovative positron spectrometerfor µ+ → e+γ search beyond 10−13 sensitivity
with most intense µ+ beam
（最大強度 µ+ ビームを用いた
10−13 を超える感度の µ+ → e+γ 探索のための
革新的な陽電子スペクトロメータ）

A Dissertation Submitted for the Degree of Doctor of Philosophy
May 2021
令和 3 年 5 月博士（理学）申請
Department of Physics, Graduate School of Science,
The University of Tokyo東京大学大学院理学系研究科
物理学専攻

Usami Masashi
宇佐見正志

i

iii

Abstract
The µ+ → e+ γ decay is one of the charged lepton ﬂavor violation (cLFV) phenomena. It is strongly suppressedin the standard model but predicted to occur around the branching ratio of O(10−13 – 10−15 ) in the physics
beyond the standard model. The discovery of µ+ → e+ γ will, therefore, be unambiguous evidence of the newphysics. Innovative detectors have been developed for the MEG II experiment to achieve the µ+ → e+ γ searchin a branching ratio of O(10−14 ), which is one order better than the current upper limit of 4.2 × 10−13 (90% conﬁdence level) by the MEG experiment. The positron spectrometer is composed of two detectors, the pixelated
timing counter (pTC) for timing measurement and the cylindrical drift chamber (CDCH) for track reconstruction, and a spectrometer magnet. The requirement of the positron spectrometer in the MEG II experiment is
twice better positron-tracking resolution and positron-reconstruction eﬃciency than the MEG experiment undertwice higher beam intensity. The commissioning of the positron spectrometer was performed to demonstrate thedetector performance. The radiation damage of the pTC, which deteriorates the timing resolution signiﬁcantly,
was observed during the commissioning in 2015. The new cooling system was developed to minimize the deterioration, and the stable operation of the pTC was demonstrated. The performance of the full pTC was evaluatedin the commissioning in 2017 – 2019, and time resolution of 34.3 ps was achieved with newly developed reconstruction algorithms. As for the CDCH, the noise analysis and the waveform analysis were performed to
implement the realistic performances in the simulation. The global tracking algorithms which utilize both thepTC and the CDCH information were newly developed to evaluate the performance of the MEG II positron
spectrometer. With realistic simulations and newly developed algorithms, it is demonstrated that new MEG-II
positron spectrometer has twice better tracking eﬃciency and resolution than the MEG experiment under twice
higher beam rate. As a results, the projected sensitivity of µ+ → e+ γ search is improved by one order of magnitude better than that of the the MEG experiment, 6.0 × 10−14 , which is powerful probe to discover the newphysics.

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Contents
Abstractiii

Introduction

1

Chapter 1

Physics Motivation

13

1.1

Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

13

1.2

Beyond the Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

13

1.2.1

SUper-SYmmetric (SUSY) Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

14

1.2.2

Seesaw Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

15

1.2.3

Grand Uniﬁed Theory (GUT) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

15

1.3

Overview of Charged Lepton Flavor Violation (cLFV) Search . . . . . . . . . . . . . . . . . . . . .

15

1.4

Muon Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

16

1.4.1

Basic Properties of Muon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

16

1.4.2

Interactions and Decay Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

16

Motivation of cLFV Search Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

18

1.5.1

Energy Frontier and Intensity Frontier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

18

1.5.2

µ → eγ Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

19

1.5.3

Prospect of µ → eγ Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

20

1.5

Chapter 2

2.1

2.2

2.3

MEG and MEG II Experiment

23

Experimental Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

23

2.1.1

Signal Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

23

2.1.2

Background Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24

2.1.3

Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

26

MEG Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

26

2.2.1

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

27

2.2.2

Result and Limitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

27

2.2.3

Proposal of the MEG II Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

29

MEG II Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

30

2.3.1

Coordinate systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

31

2.3.2

Muon Beam Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

32

2.3.3

Target . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

33

2.3.4

Liquid Xenon (LXe) photon Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

34

2.3.5

Radiative Decay Counter (RDC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

36

2.3.6

Trigger and Data Acquisition (TDAQ) System . . . . . . . . . . . . . . . . . . . . . . . . .

37

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vi
2.4

Chapter 3

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

40

2.4.1

Concept of Upgrade from MEG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

40

2.4.2

Pixelated Timing Counter (pTC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

41

2.4.3

Cylindrical Drift CHamber (CDCH) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

46

2.4.4

COnstant Bending RAdius (COBRA) Magnet . . . . . . . . . . . . . . . . . . . . . . . . . .

50

Investigation of Radiation Damage for pTC

53

3.1

Radiation Damage on Series Connected SiPMs . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

53

3.2

Total Fluence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

54

3.3

Irradiation on SiPMs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

54

3.3.1

SiPM Irradiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

54

Eﬀect on pTC Performance by Dark Current Increase . . . . . . . . . . . . . . . . . . . . . . . . . .

55

3.4.1

IV Curves for Each Damage Level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

55

3.4.2

Timing Measurement Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

55

3.4.3

Deterioration of Time Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

55

3.4.4

Cooling System for pTC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

57

3.4

Chapter 4

Commissioning Runs from 2017 to 2019

63

4.1

Commissioning Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

63

4.2

Status of Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

63

4.3

DAQ for Positron Spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

63

4.3.1

Readout Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

63

4.3.2

Triggers for Positron Spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

66

4.3.3

Muon Beam Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

66

4.3.4

Data Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

67

Chapter 5

Overview of Positron Analysis Flow

69

5.1

Data Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

69

5.2

Event Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

70

5.2.1

Simulation of Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

70

5.2.2

Simulation of Detector Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

70

5.3

Positron Reconstruction Chain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

70

5.4

Updates from MEG II Oﬃcial Previous Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

71

Performance of the pTC

73

6.1

Goal of This Chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

73

6.2

Overview of Timing Reconstruction Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

73

6.3

Algorithms for pTC Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

73

6.3.1

Waveform Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

73

6.3.2

Hit Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

74

6.3.3

Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

77

6.3.4

Standalone pTC Track Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

78

6.3.5

Timing Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

80

Chapter 6

vii
6.3.6
6.4

6.5

6.6
Chapter 7

7.1

7.2

7.3

Reﬁnement of the Timing Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . .

84

Performance of pTC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

86

6.4.1

Even-Odd Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

86

6.4.2

Overall Timing Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

87

Performance Studies Using MC Simulations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

88

6.5.1

Tuning of S/N . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

89

6.5.2

Hit Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

89

6.5.3

Tracking Quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

90

6.5.4

Position Dependence of Tracks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

91

6.5.5

Evaluation with MC Truth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

91

6.5.6

Implementation of Systematics by Hit Position . . . . . . . . . . . . . . . . . . . . . . . . .

91

Performance of pTC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

92

CDCH Analysis

97

Waveform Analysis of CDCH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

97

7.1.1

Signal Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

97

7.1.2

Cross-Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

97

Analysis of Low Rate Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

98

7.2.1

Noise Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

98

7.2.2

Observed S/N . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

Reproduction of Commissioning Data by MC Simulations . . . . . . . . . . . . . . . . . . . . . . . 101
7.3.1

Update of Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

7.3.2

Space-Charge Eﬀect for High Rate Environment . . . . . . . . . . . . . . . . . . . . . . . . 102

7.4

Comparison between MC and Commissioning Data at MEG II Beam Rate . . . . . . . . . . . . . . . 102

7.5

CDCH Tracking Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

Chapter 8

8.1

8.2

7.5.1

Hit Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

7.5.2

Track Finding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

7.5.3

CDCH Track Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

Performance of Positron Spectrometer

109

CDCH-pTC Combined Analysis for Global Tracking . . . . . . . . . . . . . . . . . . . . . . . . . . 109
8.1.1

CDCH-pTC Matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

8.1.2

pTC-CDCH Global Track Reﬁnment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

Positron Spectrometer Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
8.2.1

Deﬁnition of Reconstruction Eﬃciency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

8.2.2

Global Track Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

8.2.3

Truth Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

8.2.4

Tail Cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

8.2.5

Angle Correlation Correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

8.2.6

Resolution and Eﬃciency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

8.2.7

Breakdown of Ineﬃciency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

8.2.8

Rate Dependence of pTC and CDCH Eﬃciencies . . . . . . . . . . . . . . . . . . . . . . . . 118

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viii
Chapter 9

9.1

9.2

9.3

Projected Sensitivity of MEG II

123

Maximum Likelihood Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
9.1.1

Maximum Likelihood Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

9.1.2

Probability Density Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

9.1.3

Discriminant Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

9.1.4

Expected Number of Muon Decays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

9.1.5

Systematic Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

9.1.6

Conﬁdence Interval and Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

Comparison with MEG Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
9.2.1

Extension of MEG Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

9.2.2

Several Upgrade Cases from MEG Experiment . . . . . . . . . . . . . . . . . . . . . . . . . 127

Comparison with MEG II Design Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
9.3.1

Sensitivity with Design Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

9.3.2

Impact of Update . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

9.4

Comparison with Previous Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

9.5

Possible Other Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
9.5.1

Gain Improvement and Software Optimization . . . . . . . . . . . . . . . . . . . . . . . . . 129

9.5.2

Additive Gas Impact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

9.5.3

New Detector Installation: CDCH II/US-RDC . . . . . . . . . . . . . . . . . . . . . . . . . 130

9.5.4

Reduced Muon Stopping Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

Chapter 10

Conclusions

133

A

Laser components

135

B

Radiation damage with differently damaged SiPMs

137

B.1

SiPMs Irradiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

B.2

Patterns for SiPMs Connection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

B.3

IV Curves for Each Pattern . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

B.4

New SiPM test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

C

Online Synchronization in 2018 - 2019

C.1

D

143

Analysis of Online Synchronization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
C.1.1

Clock Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

C.1.2

12.5 ns Jump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

C.1.3

Out-of-synchronization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

Kalman Filter Algorithm

145

D.1

Kalman Filter Formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

D.2

Deterministic Annealing Filter (DAF) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

E

Track Extrapolation from pTC to CDCH

E.1

149

Extrapolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

ix
F

Noise Spectrum from Commissioning 2020

151

F.1

Noise Spectrum and Noise Level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

F.2

Expected Performances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152

G

Performance Evaluated with Reconstructed Kinematics

G.1

Performance Evaluated with Reconstructed Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . 153
G.1.1

Reference

153

CDCH Tracking Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
159

1

Introduction
The MEG II experiment is designed to search for µ+ → e+ γ which is known as one of the charged lepton ﬂavor violation(cLFV) phenomena. The cLFV phenomena are prohibited in the standard model of particle physics, or even if the tiny
neutrino mass is included, the expected rate is too low to be detected in an experiment. However, in new theories called“beyond the standard models (BSM)” the cLFV phenomena are predicted to occur within the experimental reach - thismeans that to ﬁnd the cLFV phenomena means to ﬁnd the new physics.
The current most strict upper limit of BR(µ+ → e+ γ) < 4.2 × 10−13 (90% C.L.) was set by the MEG experiment [1]. The
region of Br(µ+ → e+ γ) ∼ O(10−14 ), where some of the BSM predict, has not been explored yet. MEG II experiment was
proposed in 2013 to improve the sensitivity by one order of magnitude. One of the largest upgrades from the MEG to the
MEG II experiment is the positron spectrometer which is fully replaced with the new detectors. The sensitivity to 10−14
region is reachable by improving the positron reconstruction eﬃciency and resolution by a factor of two under twice higher
muon beam intensity.
Two innovative positron detectors were constructed to achieve the twice better eﬃciency and resolution of positronreconstruction; one is the pixelated timing counter (pTC), and the other is the cylindrical drift chamber (CDCH). The
pTC is composed of 512 small scintillation counters with series-connected Silicon-PhotoMultipliers (SiPMs) readout. The
segmented design of the pTC is tolerant to the event pileup under high muon beam intensity and improves the timing
resolution by a factor of two by using the multiple-hit information. As for the CDCH, the high-granularity readout andultra-low material improve the precision of the positron tracking. Also, the large tracking volume with the cylindrical shapegreatly improves the matching eﬃciency and the path-length estimation between the pTC and CDCH.
Structure of This Thesis

This thesis describes the details of the performance of the positron spectrometer in the MEG II experiment. Chap. 1
summarizes the physics motivation of the cLFV search. The apparatus of the MEG II experiment is described in Chap. 2.
In early 2015 commissioning runs, a rapid current increase of the pTC channels by the radiation damage was observed.
The author performed the dedicated studies to mitigate the deterioration of the pTC performance and this is described in
Chap. 3, and 2017 - 2019 commissioning runs with pTC cooling systems are summarized in Chap. 4. The analysis overview
and the simulation framework are introduced in Chap. 5. The performance of the pTC was demonstrated in Chap. 6 withthe reﬁned algorithms for the timing reconstruction, which lead twice better resolution than the MEG experiment and
15% improvement from the previous studies, which used the not-optimal timing reconstruction algorithms without any
tracking information. The CDCH analysis from commissioning runs in 2017 – 2019 is described in Chap. 7. The realistic
simulations, which take into account detector response obtained from analysis, were developed. The signal-noise ratio of
the simulated waveforms was tuned to reproduce the observed waveforms. The performance of the positron spectrometer
was demonstrated with the simulation in Chap. 8. The global tracking algorithms which utilizes both the pTC informationand the CDCH information were developed. Finally, a realistic estimation of the MEG II sensitivity is reported in Chap. 9.
Then this thesis is concluded in Chap. 10.

2Introduction

Author’s Contribution

The author played a central role for the construction and the operation of the pTC with the collaboration of the MEG II
pTC group; construction of the pTC counters, development of the calibration systems and algorithms, dedicated studies
for the radiation damage eﬀect on the timing resolution, preparation of temperature and cooling systems, data taking in
the commissioning at site in 2017 – 2019. The author had the large contribution on the development of the reconstruction
algorithms and the analysis of the commissioning data taken in 2017 – 2019 with the collaboration of the MEG II positron
analysis group; establishment and reﬁnement of the positron reconstruction algorithms, performance evaluation of the pTC,
raw data analysis of the positron spectrometer, check of the consistency between the simulation and the commissioning
data. The author performed an up-to-date calculation of the achievable sensitivity with the collaboration of the MEG II
positron analysis group, the LXe group, and the RDC group.

3

List of Tables
1.1

Basic parameters of muon from the experiment summarized by the Particle Data Group (PDG)[2] . . . . .

16

1.2

Decay modes of muons in standard model [2]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

17

2.1

The detector performance of MEG and expected performance of MEG II [3]. . . . . . . . . . . . . . . . .

28

2.2

The list of the systematic uncertainties considered in the physics analysis in the MEG experiment [4]. The
fractions of “All the other” are also shown in parentheses. . . . . . . . . . . . . . . . . . . . . . . . . . .

30

2.3

The materials for a pTC counter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

43

2.4

The basic properties of BC-422 from the datasheet [5]. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

43

2.5

The datasheet values ( provided by AdvanSiD [6]) of SiPMs used for the pTC ounter. . . . . . . . . . . .

44

2.6

The CDCH wires. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

48

3.1

Summary of the damage level of the SiPMs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

54

4.1

The number of the maximum readout channels for pTC and CDCH each year. . . . . . . . . . . . . . . .

64

5.1

Data mainly used in the following chapters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

72

6.1

Parameters extracted from the position calibration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

76

6.2

The summary of the uncertainties for the laser-based calibration. . . . . . . . . . . . . . . . . . . . . . .

81

6.3

Comparison between two time calibration methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

83

6.4

The pTC performance evaluation with the commissioning data: comparison of the updated studies andprevious studies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

88

6.5

The pTC performance evaluation with the commissioning data and MC. . . . . . . . . . . . . . . . . . .

91

6.6

The pTC performance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

92

7.1

The major updates of the CDCH waveform analysis after 2018 [7]. . . . . . . . . . . . . . . . . . . . . . 101

8.1

The timing resolution (calculated from the pTC performance in Table 6.6 and the path length estimationof the CDCH in Fig. 7.15) at the vertex. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

8.2

The criteria for the 5σ eﬃciency cut. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

8.3

The performance of the positron reconstruction under the several beam rates. The “optimistic” case uses
the 3.7 times better S/N condition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

8.4

The breakdown of the ineﬃciency of the positron measurement with pileups of 7×107 Michel positrons. . 118

8.5

The eﬃciency of CDCH tracking, CDCH-pTC matching, and pTC timing reconstruction under the beamof the MEG II intensity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

8.6

The rate dependence of CDCH tracking, CDCH-pTC matching, and pTC timing reconstruction eﬃciency. 119

List of Tables

4
9.1

Default values for the sensitivity calculation of MEG II experiment. . . . . . . . . . . . . . . . . . . . . . 125

9.2

The number of background events obtained in the MEG experiment, and that expected in the MEG II
experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

9.3

The input parameters of the positron spectrometer for the likelihood analysis with several possible scenarios.127

9.4

Summary of the contribution for the results in this thesis. . . . . . . . . . . . . . . . . . . . . . . . . . . 129

A.1

Optical components used in the laser calibration system [8] . . . . . . . . . . . . . . . . . . . . . . . . . 136

B.1

Vbr values of Pattern A and Pattern D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

F.1

The positron reconstruction resolution under the several beam rates. . . . . . . . . . . . . . . . . . . . . . 152

G.1

The extracted and estimated resolutions for the detector. . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

G.2

Comparison of the results from Michel-Fit with MEG II expected and MEG 2013 data. . . . . . . . . . . 154

5

List of Figures
1.1

The particles to describe the fundamental interactions and matters. . . . . . . . . . . . . . . . . . . . . .

1.2

The coupling constants of three gauge groups calculated in the standard model framework and in theminimal supersymmetric standard model (MSSM) framework [2]. . . . . . . . . . . . . . . . . . . . . .

1.3

13
15

The positron energy spectrum from the polarized Michel decay. (a), (b), (c) shows the case of cosθe = 0,cosθe = +1 and cosθe = -1 respectively [9]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

17

1.4

The energy spectrum of RMD gamma ray [9]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

18

1.5

The diagram of µ → eγ in the standard model with the neutrino oscillation [10]. . . . . . . . . . . . . . .

19

1.6

An example of the diagram of µ → eγ with the TeV scale SUSY particles [10]. . . . . . . . . . . . . . . .

19

1.7

The expected branching ratios of µ → eγ and τ → µγ in the CMSSM with seesaw mechanism [11]. . . . .

19

1.8

Br(µ → eγ) as functions of the universal scaler mass m0 and tanβ for MN = 3 × 10

15

GeV, M1/2 = m0 ,a0 = 0, and sign(µ) > 0 in the mSUGRA. Numbers of the ﬁgures correspond to the values of Br(µ → eγ).
Dark green, light green, and dashed green region for mh [GeV] correspond to the region of 125 < mh <127, 124 < mh < 128, and 120 < mh < 130, respectively [12]. . . . . . . . . . . . . . . . . . . . . . . . .
1.9Br(µ → eγ) as functions of the universal scaler mass m0 and tanβ for MN = 3 × 10

13

20

GeV, M1/2 = m0 ,a0 = 0, and sign(µ) > 0 in the mSUGRA. r = 2.2 is one of the CI parameters. With the increase of r value,
the Yukawa coupling can become larger. The detail of the other CI parameters can be found in [13]. The
black lines are for Higgs mass of 125 GeV, and the dashed/dot lines are ± 1 GeV/2 GeV from the Higgs
mass. The current upper limit of electron EDM de < 1.1 × 10−29 e cm [14] is shown with the green dashedline, which is almost equivalent to the current upper limit of Br(µ → eγ) by the MEG experiment (shownwith the brawn dashed line) in this parameter space. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

21

1.10

The history of the upper limits of three cLFV phenomena [3]. . . . . . . . . . . . . . . . . . . . . . . . .

22

2.1

The schematics of a signal event and background events (accidental and RMD). . . . . . . . . . . . . . .

23

2.2

Eﬀective branching ratio of the RMD background as a function of the positron energy (δx) and gamma-ray
energy (δy) [9]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.3

25

Eﬀective branching ratios of the accidental and RMD background into the kinematic window of MEG
experiment deﬁned by Ee+ ,min < Ee+ < 53.5 MeV, Eγ,min < Eγ < 53.5 MeV, |te+ γ | < 0.24 ns and cosΘe+ γ <−0.9996. (a) Accidental background from the side-band data. (b) RMD background calculated with thetheoretical formula folded with the MEG detector response [1]. . . . . . . . . . . . . . . . . . . . . . . .

2.4

The overview of the apparatus used in MEG experiment. The picture of DRS chip and board from [15].
The picture of the LXe from [3]. The other pictures and sketch from [1]. . . . . . . . . . . . . . . . . . .

2.5

25
27

Event distributions for the 2009 – 2013 full dataset on the (Ee+ , Eγ )-plane with the selections of cos Θe+ γ <-0.99963 and |te+ γ | < 0.24 ns (left), and (cosΘe+ γ , te+ γ )-plane (right) with 51.0 < Eγ < 55.5 MeV and 52.4

2.6

< Ee+ < 55.0 MeV. The contours of the averaged signal PDFs (1σ, 1.64σ and 2σ) are superimposed [1]. .

28

The branching ratio sensitivity as a function of the DAQ days in the MEG experiment [4]. . . . . . . . . .

29

List of Figures6
2.7

The overview of the MEG II experiment [3]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

30

2.8

The global coordinate system of MEG II positron spectrometer. . . . . . . . . . . . . . . . . . . . . . . .

31

2.9

The local coordinate on a CDCH wire. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

31

2.10

The local coordinate of a pTC counter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

31

2.11

The dedicated coordinate of the LXe detector (u, v, w) [16]. . . . . . . . . . . . . . . . . . . . . . . . . .

31

2.12

The coordinate of the target ellipse. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

31

2.13

The Cockcroft-Walton pre-accelerator [17]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

32

2.14

The large proton ring accelerator [17]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

32

2.15

The πE5 beam line [18]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

33

2.16

The MEG II scintillator target [3]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

33

2.17

The distribution of positron reconstructed position at the target with 2011 MEG data [3]. . . . . . . . . . .

34

2.18

The perspective corrected and 2D gaussian ﬁtted beam image viewed originally under 15◦ to the target
plane and taken in 2016 commissioning [3]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

34

2.19

The picture of the LXe photon detector [3]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

34

2.20

The sketch of a large area VUV sensitive MPPC used in MEG II LXe photon detector [19]. . . . . . . . .

35

2.21

A large area MPPC used in MEG II LXe photon detector [19]. . . . . . . . . . . . . . . . . . . . . . . .

35

2.22

Example of scintillation light distribution detected by PMTs (left) and MPPCs (right) for a same simulated
event [3]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.23

The schematic view of the RDC. The horizontal long plates in front are the plastic scintillator bars and the
cubes behind are the LYSO crystals [3]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.24

37

The expected (MC) energy distribution at the RDC for RMD events with Eγ >48 MeV (red) and forMichel events (blue) [3]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.26

36

The expected (MC) distribution of the timing diﬀerence between the RDC and LXe. Red line shows theaccidental background events and blue line shows the signal events [3]. . . . . . . . . . . . . . . . . . . .

2.25

35

37

The sketch of the single WaveDAQ crate [20]. The green boards are WDB, magenta DCB and blue
TCB. CMB is drawn on the right side. Arrows show connections in the backplane: red arrows for datatransmission to backend machines, blue for trigger serial links, orange to distribute back the trigger signal
and green for hardware compensated clock distribution, and brown shows low level access for slow control
and conﬁguration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

37

2.27

The schematics of the WDB [3]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

38

2.28

The mechanism of the Domino Ring Sampler chip (DRS chip). . . . . . . . . . . . . . . . . . . . . . . .

38

2.29

The online timing distribution of positrons in MC (black) ﬁtted with multiple gaussian function (red) [7]. .

39

2.30

The comparison of the online te+ γ trigger selection eﬃciency of the MEG II expected (blue) timing window
and the MEG (red) timing window. The width (FWHM) is reduced from 20 ns (MEG) to 14 ns (MEG II)[3]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.31

39

The overview of the MEG (up) and MEG II (down) experiment [21]. The blue line shows the gamma
ray and the red positron. The positron tracker volume (green region) was extended to the pTC interface,which increased the number of CDCH hits for one track and improved the trajectory and timing integration(matching eﬃciency). The timing counter (light blue region) was segmentalized into small pixels. . . . . .

40

2.32

The design of pTC detector [3]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

41

2.33

The picture of pTC detector. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

41

2.34

The backplanes on the pTC support structure [7]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

41

7
2.35

The signal lines of the backplane [7]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.36

A simulated signal positron trajectory (blue line) and the pTC counters (yellow). The positron crossed thered counters [3]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.37

41
42

(Left) The picture of single pTC counter. The picture of the two types of PCBs are also shown in rightsketch [3]. (Right) The sketch of the counter design pattern. L-shape and mix-shape counters were
designed to put counters on inner step of the support structure. . . . . . . . . . . . . . . . . . . . . . . .

2.38(Left) A mounted ﬂat-type counter on the backplane. (Right) Mounted L-shape counters on the inner stepof the support structure [7]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.39

The pTC counter map [22]. Counter region is ∼20 –110 along the beam axis (z-axis) for both downstream

2.40

The diﬀerence of the pulse shape with diﬀerent connections of 3 SiPMs (3-SiPM parallel, single, andand upstream. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-SiPM series) with BC422 with HPK SiPM (S10362-33-050C) [23]. . . . . . . . . . . . . . . . . . . . .
2.41

42
43
44
45

The counter resolution measured in the lab-test with 4 cm counters (pink-line) and 5 cm counters (blueline), which include type-I and type-II SiPMs [24]. The histograms ﬁlled with pink and blue show theresolution with type-III SiPMs for 4 cm and 5 cm counters, respectively. . . . . . . . . . . . . . . . . . .

45

2.42

The support structure viewed from the bottom side [7]. Cooling pipes and laser optical ﬁbers can be seen.

46

2.43

The schematics of humidity and temperature sensor positions. . . . . . . . . . . . . . . . . . . . . . . . .

46

2.44

(a) Schematic and (b) picture of the laser-based calibration system for the MEG II pTC (from [25]). The
individual components are described in the Table A.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

47

2.45

The mechanical sketch of cylindrical drift chamber [3]. . . . . . . . . . . . . . . . . . . . . . . . . . . .

47

2.46

The picture of CDCH mounted all wires [3]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

48

2.47

The layer structure in the CDCH [26]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

49

2.48

Drift cell conﬁguration of MEG II CDCH. Top: Simpliﬁed sketch of a single drift cell (an anode circle
and cathode circles are depicted). Bottom: schematic view of the wires in the CDCH [26]. . . . . . . . . .

2.49

49

Isochrones for a single 6 × 6 mm drift cell [26]. The vertical color is ns. The drift lines are curved and2

the isochrone map is distorted by the magnetic ﬁeld. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

49

2.50

Front-end electronics for CDCH [3]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

50

2.51

COBRA magnet [27]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

51

2.52

The concept of the COBRA gradient magnetic ﬁeld [1]. (a) Positrons with the same momentum have thealmost same bending radius, even with the diﬀerent emission angles. (b) Positrons with low longitudinal

3.1
3.2

momentum are quickly swept away. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

51

The pTC current of each channel (16 channels are shown with colored lines) in 2015 commissioning. . . .

53◦

The I-V curves of the six electron-irradiated SiPMs. The I-V data of each SiPM were taken at 30 C (a–e),
and the breakdown voltages are plotted in (f). The I-V data of six series-connected SiPMs were taken at
30◦ C (g) and 10◦ C (h).

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

56

3.3

The timing resolution measurement setup for the radiation tolerance test. . . . . . . . . . . . . . . . . . .

57

3.4

The schematics of the ampliﬁer [23]. The pole-zero cancellation ﬁlter can be applied by tuning the ad-

3.5
3.6

justable resistor in the circuit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

57

The example of the waveform at each damage level. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

58

◦

◦

Timing resolution versus over-voltage at 30 C (left) and 10 C (right). The CFD fraction is 20%. . . . . .

59

List of Figures8
3.7

The timing resolution with theq diﬀerent damage level at the ﬁxed 3 applied voltage (157.5, 160 and 162.5
V). The dashed curves σt =3.8

Relation between
q the dark current and the RMS noise at 30 C for three applied voltages. The dashed
αIdark + N02 are ﬁtted to the data.

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

59◦

Relation betweenqthe RMS noise and the timing resolution at 30 C for three applied voltages. The dashedcurves are σt =

3.10

59

◦

curves NRMS =3.9

βIdark + σ20 are ﬁtted to the data. . . . . . . . . . . . . . . . . . . . . . . .

2γNRMS+ σ20 ﬁtted to the data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

60

The system for pTC cooling. The pictures for a chiller, water pipes, a heat exchanger, air lines are also
shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

60

3.11

The picture of pTC for the low temperature operation. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

61

3.12

The temperature and humidity measured on the pTC sensors. . . . . . . . . . . . . . . . . . . . . . . . .

61

4.1

The pTC counter map with identiﬁcation number (0-511). In 2017, all of the counters (512) were tested,in 2018 and 2019 128 counters were tested (# 128 - 255 in 2018 and # 304 - 431 in 2019). The colorsof the counters show the counter types (inner magenta: 4cm-L, yellow: 4cm-Mix, light blue: 5 cm-Flat,outer magenta: 4cm-Flat). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.2

The CDCH readout in 2018 commissioning [26]. Data acquisition was conducted with the readout in S3(L1-3) and S4 (L1-3). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.3

64
65

The CDCH readout in 2019 commissioning [26]. Data acquisition was conducted mainly with the readout
in S4 (L1 - 6). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

65

5.1

The overview of the MEG II analysis framework. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

69

5.2

The overview of the MEG II positron reconstruction algorithms. . . . . . . . . . . . . . . . . . . . . . .

71

5.3

The ﬁxed combinations of counters used in [7] for the evaluation of the pTC resolution. . . . . . . . . . .

71

6.1

The sine waveform in the clock channel for the pTC WDB synchronization. . . . . . . . . . . . . . . . .

74

6.2

The template noise extracted from the pedestal data taken in 2017 in the experimental area [28]. . . . . . .

74

6.3

The pedestal waveforms of the pTC (left black) and their amplitude of the power spectrum (right red)
before / after the noise reduction (up / down) [28]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

75

6.4

The RMS-noise of each pTC channel with pedestal data before / after the noise reduction [28]. . . . . . .

75

6.5

The extracted waveform from a pTC counter [29]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

75

6.6

An example of the x-position histogram of a counter. The green line is the original histogram, black after
the moving average, blue-dashed the trapezoid function. The ﬁtting result is shown with red line. The
center of the ﬁt result corresponds to the relative oﬀset between the two channels [30]. . . . . . . . . . . .

76

6.7

The position distributions of counters before/after the calibration [30]. . . . . . . . . . . . . . . . . . . .

76

6.8

The position calibration diﬀerence in 2017 and 2018, and the outlier examples. . . . . . . . . . . . . . . .

77

6.9

The deﬁnition of the geometrical order in pTC (left) and the distribution of the geometrical order from theﬁrst hit and timing from the ﬁrst hit [7]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.10

A typical tail event of pTC cluster. After crossing a ﬁrst cluster (orange), that positron loses the momentum
by material eﬀects and its turn radius becomes small, and it soon comes back to the pTC region (green). .

6.11

77
78

The hit addition to the cluster by using the projected hit position. The green counter in the left plot cannot
be assigned to the purple cluster only with the timing information, but it can be assigned to the purple
cluster with the cross-check of the timing information and the position information. The positron passed
through under the counters in the middle of the cluster. . . . . . . . . . . . . . . . . . . . . . . . . . . .

78

9
6.12

The schematics of the ylocal estimation algorithm (left) and its result (right). . . . . . . . . . . . . . . . . .

79

6.13

The sketch of KF algorithm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

80

6.14

The reconstructed positron track by GENFIT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

80

6.15

The time oﬀset history of a counter in a month [8]. The histogram of the RMS of monitored counters is
also shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

82

6.16

The concept of track-based calibration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

82

6.17

The result of track-based calibration compared with the simulation random oﬀset. The standard deviation
is estimated to be ∼13 ps. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

83

6.18

The consistency between two pTC timing calibration methods with 2017 commissioning data [8]. . . . . .

84

6.19

The hit position dependence of the channel by channel time oﬀset after the correction of the time oﬀset inx direction for 4 cm counters [24]. The left plot shows channel 1, and right plot shows channel 2. . . . . .

6.20

84

The hit position dependence of the channel timing resolution (right) for 4 cm counters [24]. The left plotshows channel 1, and right plot shows channel 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

85

6.21

The relation between the energy deposit and the time oﬀset (left) and the timing resolution (right) [24]. . .

85

6.22

The hit position dependence of the counter timing oﬀset (left) and the timing resolution [24]. . . . . . . .

86

6.23

The timing resolution from even-odd analysis with 2017 commissioning data with the latest analysis. . . .

87

6.24

The probability distribution of the number of pTC hits for signal positrons. . . . . . . . . . . . . . . . . .

88

6.25

2017 pTC amplitude.

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

89

6.26

2017 pTC RMS-noise .

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

89

6.27

pTC amplitude (MC). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

89

6.28

pTC RMS-noise (MC). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

89

6.29

The timing distribution of the pTC hits in 2018 data with the muon beam. Triggered events can be seenaround 410 ns – 430 ns. For the rate calculation, the ﬂat region (pedestal region) is used with the assumption of the Poisson distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.30

90

Hit rates calculated with 2017 data (magenta) and MC (black) with MEG II nominal beam rate settings[7]. Larger discrepancy between the MC and the data was observed in the large |Z| region (position ∼200
- 256/∼450 - 512). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

93

6.31

Hit rates calculated with 2017, 2018, and 2019 data with MEG II nominal beam rate settings each year. . .

94

6.32

The 2D scatter plot of the diﬀerence between the estimated position and the MC truth. The magenta line
shows the resolution, white square shows the mean of the distribution at each counter. . . . . . . . . . . .

94

6.33

Timing resolution from even-odd analysis with 2017 commissioning data at several |z| position of tracks. .

95

6.34

Timing resolution from even-odd analysis with MC at several |z| position of tracks. . . . . . . . . . . . . .

95

6.35

The y-dependence of the timing center in a counter at the edge (xhit > 5 cm) with 2017 data [24]. . . . . .

95

6.36

The y-dependence of the timing center in a counter at the edge (xhit > 5 cm) with MC to reproduce the2017 data [24]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.37

95

Position dependence of the time center in a counter at x = −4.25 cm. The applied voltage was ﬁxed to162.5 V at 30◦ C [31]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

96

6.38

The y-dependence of the timing center in a counter at x = −4.25 cm [24]. . . . . . . . . . . . . . . . . . .

96

6.39

The y-dependence of the timing center in a counter at the edge (xhit > 5 cm) with 1.8 times increased
dependence, i.e. 108 (4 cm counters)/135 ps (5 cm counters) time oﬀset between adjacent SiPMs [24]. . .

96

List of Figures10
7.1

The example of the simulated CDCH waveforms and the cross-ﬁtting algorithm. The sky-blue horizontal
line shows the threshold for the signal ﬁnding, and the orange, green, magenta, and blue lines on the
waveform shows the ﬁtted results, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

98

7.2

The noise spectrum of the CDCH noise in 2018. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

98

7.3

The example of the CDCH waveform with the muon beam rate of 1.34 × 10 taken in 2018 commissioning. 99

7.4(Black) The observed 50 MHz noise in the 2019 commissioning. (Red) The template noise spectrum

7

extracted from the waveform themselves by the sine ﬁtting. . . . . . . . . . . . . . . . . . . . . . . . . .

99

7.5

The signal amplitude histograms from the commissioning data taken in 2018 and 2019. . . . . . . . . . . 100

7.6

The RMS-noise histograms from the commissioning data taken in 2018 and 2019. The dashed line shows
the RMS-noise calculated from the raw waveform and the solid line shows that after the noise subtraction
by the moving average ﬁlter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

7.7

The distributions of simulated RMS-noise (dashed line: before noise subtraction, solid line: after noise
subtraction) and signal amplitude. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

7.8

The scatter plots of the simulated signal amplitude at ch1 (x-axis) and ch2 (y-axis). Left plot is before
the update of the gain parameters, center plot is after the update, and right plot is from the commissioning
data in 2018 (1.34×107 rate at 1460V). Note that the scale of the axis is one-order diﬀerent between left
plot and center/right plot. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

7.9

The signal height and the RMS-noise under the MEG II nominal beam rate. . . . . . . . . . . . . . . . . 103

7.10

S/N distributions from the commissioning data and the simulation. S from the commissioning data and N
from the simulated mean (0.8 mV) is also shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

7.11

The diﬀerence in z between the MC truth and the reconstruction (left: time diﬀerence, center: charge
division). The right histogram shows the consistency between the two methods under the MEG II expectedmuon decay rate (7 × 107 ). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

7.12

The diﬀerence in z between the MC truth and the measurement (left: time diﬀerence, center: charge
division). The right histogram shows the consistency between the two methods under the single Michel
decay. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

7.13

The illustration of the CDCH seeding procedure. The blue and green circles show the drift circle, andthe dashed lines are the candidate of the track (left-right for each circle). The yellow line shows theconstructed track seed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

7.14

Event monitor with a simulated signal positron from the x-y projected view (left) and the 3-D monitor
from the top view (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

7.15

The estimated ﬂight time precision (σTOF ≈ 6.9 ps) in the CDCH region with the simulation. . . . . . . . 108

8.1

The diﬀerence between the pTC hit position and the CDCH extrapolated position. . . . . . . . . . . . . . 109

8.2

The timing diﬀerence between the pTC clusters and the CDCH tracks. ±15 ns timing window for thematching is applied. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

8.3

The number of matched cluters for one CDCH track. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

8.4

The propagation length from the CDCH region to the pTC counter which is illustrated in the histogram:the length of the pink line is the propagation length, the black circle is the CDCH outer foil, and yellow
boxes are pTC counters. The red histogram shows the after 5σ resolution cut. . . . . . . . . . . . . . . . 110

8.5

The distribution of (x, y) matched positions in the counter local coordinate. Up: 4cm counters (the counterregion is ±6 cm for x and ±2 cm for y), down: 5 cm counters (±6 cm for x and ±2.5 cm for y). . . . . . . 110

11
8.6

The matched |z|-position. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

8.7

The impact parameter resolutions with a simulated signal positron. The blue histogram was updated to
the red histogram by the pTC-CDCH track re-ﬁtting. The resolution changed from 106 µm to 85 µm (thestandard deviation from 123 µm to 112 µm). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

8.8

The impact parameter resolutions with a simulated signal positron and 7 × 107 Michel positrons. The blue
histogram was updated to the red histogram by the pTC-CDCH track re-ﬁtting. The resolution changed
from 111 µm to 84 µm (the standard deviation from 130 µm to 114 µm). . . . . . . . . . . . . . . . . . . 111

8.9

The number of positron tracks in each event with no selections (black), those with the track pre-selection(purple), and those with the track quality selection (red). . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

8.10

The distribution of the per-errors of MEG II kinematic parameters. . . . . . . . . . . . . . . . . . . . . . 115

8.11

The distribution of the χ2 of tracks (black) and selected tracks with good quality (red, within 5σ tail cut). . 116

8.12

The relation between the θ and ϕ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

8.13

The diﬀerence between the MC truth and the reconstructed kinematics with the pileup of 7 × 107 e+ /s. The
red region contains the eﬀective events after the tail cut. The tail cut will reduce the eﬃciency 10% (75.5%→ 65.2%) at this rate. The blue line shows the double-gaussian ﬁtting without tail cut, and the light blueshows the single gaussian ﬁtting after the tail cut. The resolution is extracted from the σ of the latter ﬁtting. 118

8.14

The relation between the eﬃciency of the hit reconstruction by signal positrons and the beam rate. . . . . 120

8.15

An example of an ineﬃciency event by turn merge failure from ± stereo view. The green-dot segment andthe blue-dot segment were not merged. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

8.16

Distribution of the number of hits in one signal track under the MEG II beam intensity before (black) andafter (red) the tail cut. One track segment has ∼20 hits (ﬁrst peak), and these segments are merged to
improve the quality of the tracks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

9.1

The distribution of the upper limits of Nsig /Nobs at 90% C.L. for 3000 pseudo-experiments with null-signal
medianhypothesis. The obtained median is Nsig
= 5.6, and the sensitivity is 6.0 × 10−14 . . . . . . . . . . . . . 126

9.2

The distribution of the upper limits of seudo-experiments in the MEG experiment [4]. Vertical dashed line
shows the search sensitivity from the median calculation (5.3 × 10−13 ), and two arrows show the upper
limits obtained from the timing sidebands. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

9.3

The generated signal event in the pseudo-experiments. Red histogram is made with the assumption of σ p= 93 keV and blue histogram σ p = 130 keV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

9.4

The generated background event in the pseudo-experiments. Red histogram is made with the assumptionof σ p = 93 keV and blue histogram σ p = 130 keV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

9.5

The distribution of the upper limits of Nsig at 90% C.L. for 3000 pseudo-experiments with null-signal
medianhypothesis at a half rate beam. The obtained median is Nsig
= 3.2. . . . . . . . . . . . . . . . . . . . . 130

9.6

The example event distribution within 1.64σ angles, positions, and timing resolution at half rate beam.
Nsig = 2.2 was obtained in this pseudo-experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

9.7

The example of event distribution within 1.64σ angles, positions, and timing resolution at MEG II nominal
beam. Nsig = 7.4 was obtained in this pseudo-experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . 131

9.8

The branching ratio sensitivity as a function of the DAQ years. (Black) With the updated resolutions under7 × 107 µ/s. (Red) With the updated resolutions under 3.5 × 107 µ/s. . . . . . . . . . . . . . . . . . . . . . 132

B.1

Schematic of SiPMs’ pattern A, pattern B, pattern C in normal order and pattern A in reverse order. The
SiPMs with highest dark currents are in black, those with lowest in white. . . . . . . . . . . . . . . . . . 138

List of Figures

12B.2

I-V curves of each SiPM used for pattern A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

B.3

I-V curves of each SiPM used for pattern B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

B.4

I-V curves of each SiPM used for pattern C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

B.5

I-V curves of several patterns of series-connected SiPMs measured at 30◦ C. . . . . . . . . . . . . . . . . 139

B.6

I-V curves of several patterns of series-connected SiPMs measured at 10◦ C. . . . . . . . . . . . . . . . . 139

B.7

The explanation of breakdown voltage shift arising from the diﬀerence in dark currents. If n SiPMs havethe same dark current I at the breakdown voltage Vbr , the breakdown voltage of the series-connected
SiPMs is expected to be n × Vbr . In pattern A, the breakdown voltage becomes 6 × Vbr + 4 × δVbr , and inpattern B, 6 × Vbr + 2 × δVbr to accommodate the same current I + δI at the breakdown voltage. . . . . . . 139

B.8

The irradiation test setup at BTF. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

B.9

The IV curves of the SiPMs after irradiation at 10◦ C and 30◦ C. The type-II SiPMs shown in ”New”. . . . 141

B.10

The bias scan of the timing resolution of type-II SiPMs (shown as “New”) after irradiation at 10◦ C and30◦ C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

C.1

The relation among the clock, PLL and DRS cycle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

C.2

The reconstructed hit positions on CDCH wires (left) and the timing diﬀerence between both ends (right).
Clearly unphysical jump can be seen. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

C.3

The cell-zero chip-id diﬀerence from the reference chip. If the synchronization completely works and notrigger jitter, the diﬀerence should be zero. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

C.4

Drift of the diﬀerence of the cell-zero from the reference chip during a run which caused the out-ofsynchronization problem. The cell-zero id of the chip drifted to the one direction. . . . . . . . . . . . . . 144

D.1

The coordinate system of the wire measurement in GENFIT [32]. . . . . . . . . . . . . . . . . . . . . . . 145

D.2

Illustration of the probability assignment with deterministic annealing ﬁlter [33]. (a) The algorithm starts
with high temperature and all measurements (green circles) in the same layer have the similar weight. (b)At the lower temperature, the measurements far from the estimate obtain the lower assignment probabilities. (c) Finally, the assignments are frozen out. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

E.1

A positron partial track reconstructed with pTC hits and CDCH hits (MC). Blue rectangular planes show
pTC hits, blue cylinders show drift circles of CDCH hits, and gray planes show CDCH hits. . . . . . . . . 149

F.1

The noise spectrum observed in 2020 with the standard FE card. . . . . . . . . . . . . . . . . . . . . . . 151

F.2

The RMS-noise sin 2020 with the standard FE card. The muon rate is MEG II nominal (7 × 107 /s) . . . . 151

F.3

The waveforms in the 2020 commissioning under the muon beam. (Left) before the noise subtraction,(right) after the noise subtraction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152

G.1

The distributions of CDCH tracks between the ﬁrst turn and the second turn. . . . . . . . . . . . . . . . . 154

G.2

Michel-Fit with the reconstructed energy spectrum (MC). The grey line shows the theoretical Michel
spectrum, the blue dashed line response function, and the red line is the ﬁtting result.

G.3. . . . . . . . . . . 155

The acceptance function of MEG II (MC, blue) and MEG 2013 data (red) normalized at 52.8 MeV. The
relative eﬃciency (normalized at 52.8 MeV) from the reconstructed tracks in the range of 43 – 53 MeV/2
MeV is also shown with cross marks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

G.4

The momentum dependence of the momentum resolution with Michel positrons. . . . . . . . . . . . . . . 155

13

Chapter 1

Physics Motivation
In this chapter, the physics motivation for the µ+ → e+ γ search is discussed.

1.1Standard Model
Generations

I

II

III

Fig. 1.1: The particles to describe the fundamental interactions and matters.

The standard model in particle physics is one of the most fundamental theories of physics, which well explains theinteractions with 17 elementary particles (12 fermions for matters and 5 bosons for interactions). Fig. 1.1 shows theelementary particles in the Standard Model.
Theoretically, the Standard Model Lagrangian has the gauge symmetry of SU(3)C × SU(2)L × U(1)Y , and this symmetry
describes the three fundamental interactions: strong interaction, weak interaction, and electromagnetic interaction. The
gauge bosons are derived from the gauge ﬁelds, and the Higgs boson is derived from the Higgs mechanism and provides
the mass term for gauge bosons (W / Z).
In 2012, the Higgs boson was discovered in ATLAS and CMS experiments [34, 35], and all of the elementary particles
predicted in the Standard Model were experimentally observed.

1.2

Beyond the Standard Model

Though the Standard Model explains the fundamental interactions and reproduces most of the experimental observations
up to the electroweak energy scale (O(100) GeV), it is not a perfect theory to explain all of the interactions and particles in
the Universe.
The major mysteries that the Standard Model does not explain are summarized as follows:Chapter 1 Physics Motivation

14• The Standard Model does not explain the dark matter and the dark energy in the Universe. It does not explain thegravitational force which is also considered as the fundamental interaction in nature.
• The mass of the Higgs particle (125 GeV) suggests the diﬃculties for the extension of the Standard Model to the GUT
scale (Grand-Uniﬁed-Theory energy scale where the electromagnetic-weak interaction and the strong interaction
are considered to be uniﬁed in O(1016 ) GeV) or Planck scale (gravitational interaction is considered to be uniﬁedin O(1019 ) GeV), and this is known as the hierarchy problem. To be consistent with GUT region, the quantum
correction term for the Higgs mass must be ﬁne-tuned precisely.
• In the Standard Model, neutrinos are assumed to be massless. However, the neutrino oscillation [36] indicates thatthe neutrino has a tiny mass. The inconsistency between the experiments and the theories suggests the necessity forthe extension of the model.
Currently, the Standard Model is considered as an approximation of a more general and fundamental model in the low
energy region, which is called Beyond Standard Model (BSM). Promising BSMs are shortly summarized in the following
sections.

1.2.1

SUper-SYmmetric (SUSY) Model

The supersymmetric (SUSY) model can solve the hierarchy problem. In this model, new supersymmetric fermion (boson) partners are introduced for all the standard model boson (fermion) under the symmetry of the fermion and bosontransformation:
Q|Fermion⟩ = |Boson⟩, Q|Boson⟩ = |Fermion⟩,(1.1)

where Q is the operator that generates the SUSY transformation. The SUSY partner’s sign of the radiative correction termfor Higgs mass is inverse from the original particle, so the correction terms (quadratically divergent terms) are canceled out[37]. In addition, the lightest SUSY particle, which is stable, electrically neutral, and weakly interacts with the ordinary
matter, can be an attractive candidate for the dark matter [38, 39]. For these reasons, the SUSY model is considered as oneof the promising BSM theories.
The general SUSY models have too many soft SUSY parameters and reasonable constrains for the models are often
introduced. One of the typical constraints are called mSUGRA (minimal SUperGRAvity) for the constraint on minimal
SUSY models (MSSM) with ﬁve parameters, (m0 , a0 , M1/2 , tanβ, sign(µ)). The soft SUSY breaking parameters satisfy themSUGRA boundary conditions; the soft scalar mass-squared parameters at the Planck scale are assumed to be universal(m20 , universal scaler mass) and the tri-linear scalar couplings (A-terms) are proportional to the corresponding Yukawa
couplings with the coeﬃcient of a0 . M1/2 is the universal gaugino mass at the Planck scale, and tanβ is the ratio of thevacuum expectation of up-type and down-type of Higgs bosons, and µ is the supersymmetric Higgs mass parameter. Withthe universal assumption, the source of ﬂavor violation from SUSY particles is absent at the Planck scale, which solves
the so-called SUSY ﬂavor problem. Even in such a case, the ﬂavor violation source in the neutrino Yukawa enters into theslepton mass matrix through the renormalization group equation, and an avoidable ﬂavor violation source is introduced at
the low energy.

1.3 Overview of Charged Lepton Flavor Violation (cLFV) Search

1.2.2

15

Seesaw Mechanism

The seesaw mechanism can explain the neutrino tiny mass. In this mechanism, the neutrino is assumed to be a Majorana
particle and the heavy right-handed neutrino is introduced. The neutrino mass term can be described as follows:!
0 mD(N1 N2 ),(N1 N2 )
mD mR

(1.2)

where N1 and N2 are the Majorana ﬁelds, mD is the Dirac mass, mR is the Majorana mass of the right-handed neutrino,
respectively. By calculating the eigenvalues of this mass matrix with the assumption of mR ≫ mD , we can obtain two
neutrino masses of:m2D, mR .
mR

(1.3)

m2

These two masses suggest that mDR of left-handed neutrino mass, which is observed in the experiments, becomes tiny whenmR of right-handed neutrino mass, which is not yet observed, is huge.

1.2.3

Grand Uniﬁed Theory (GUT)

Fig. 1.2: The coupling constants of three gauge groups calculated in the standard model framework and in the minimal
supersymmetric standard model (MSSM) framework [2].
In the GUT model, three gauge groups, SU(3)C × SU(2)L × U(1)Y , are assumed to be uniﬁed to a single and larger groupat a very high energy scale (GUT scale). Actually, it is known that the running coupling constants of three interactions
become close to each other around O(1016 ) GeV, and if the SUSY particles exist at the TeV scale, they are well uniﬁed asshown in Fig. 1.2.

1.3

Overview of Charged Lepton Flavor Violation (cLFV) Search

The Standard Model fermions with the same charge have three generations depending on their masses, which are called
ﬂavors. It is already observed that quark and neutrino ﬂavors can mutate to ﬂavors in the diﬀerent generations (this phenomenon is called ﬂavor mixing), while it is not observed in the charged lepton sector, i.e. among e, µ, and τ.
The ﬂavor mixing in the quark sector is explained in the framework of the Standard Model through the CKM matrix.The
observation of the neutrino oscillation, which showed the evidence of the ﬂavor mixing in the neutrino sector, gave a strongChapter 1 Physics Motivation

16

impact on the particle physics. Actually, the conservation of the lepton ﬂavor derives from not fundamental symmetries but
the assumption of the mass-less neutrino and the non-observation of the ﬂavor mixing in the lepton sector.
Now, the ﬂavor mixing in the charged lepton sector, which is called charged Lepton Flavor Violation (cLFV), is one ofprobes for the new physics. If the cLFV is observed in an experiment, it is clearly evidence of the new physics beyond theStandard Model. Even if the cLFVs are not observed, the upper limit for the branching ratio gives a strict constraint on the
BSM theories.

1.4

Muon Properties

Muon is widely used as a probe of new physics because of its relatively long lifetime and availability of the intense beam as
explained in the next chapter. In this section, the important properties of a muon for the search of µ → eγ are summarized,
and the physics motivations of µ → eγ search are discussed.

1.4.1

Basic Properties of Muon
Table 1.1: Basic parameters of muon from the experiment summarized by the Particle Data Group (PDG)[2]Parameter

Value

Mean Lifetime(2.1969811 ± 0.0000022) ×10−6 s

Mass105.6583745 ± 0.0000024 MeV

g −2
Magnetic Moment Anomaly ( µ2 )(11659208.9 ± 5.4 ± 3.3) ×10−10

Electric Dipole Moment (EDM)(-0.1 ± 0.9) ×10−19 e cm

Table 1.1 summarizes the basic parameters of a muon. The muon mass is ∼ 200 times larger than the electron’s one.
The muon decay is characterized by the weak interaction, and therefore the lifetime of the muon is relatively longer thanthe particles whose decays are caused by the electromagnetic interaction or the strong interaction. The gµ − 2 and EDM
measurements are also considered as one of the attractive measurements for new physics [40].

1.4.2Interactions and Decay Modes

In the Standard Model, the muon interaction is given as follows:
L = eµγµ µAµg− √ (νµL γµ µL Wµ+ + µL γµ νµL Wµ− )2q1− g2 + g′2 (µL γµ (− + sin2 θW )µL + µR γµ sin2 θW µR )Zµ0
2
mµ
−
µµH,
v

(1.4)

where g and g′ are the coupling constants from SU(2) and U(1) interactions, θW is the Weinberg angle (sin θW = √ g2′

g +g′2),mµ is the muon mass. Each line corresponds to the interaction with photon (ﬁrst line), W boson (second line), Z boson(third lines) and Higgs boson (ﬁnal line).
The decay modes of muon are summarized in Table 1.2. In the MEG II experiment we use a positive muon beam to avoid
the formation of the muonic atoms. So in the following sections, we basically discuss not the negative muon decay but thepositive muon decay.

1.4 Muon Properties

17
Table 1.2: Decay modes of muons in standard model [2].

ModeFractionµ− → e − ν µ ν e
−

−

−

−

≈1

µ → e νµ νe γ

Michel Decay

6.0 ± 0.5 × 10

+ −µ → e νµ νe e eµ → eγNote−8(3.4 ± 0.4) × 10

Radiative Muon Decay, Eγ >40 MeV and Ee >45 MeV−5< 4.2 × 10−13 (90% C.L.)[1]

Michel Decay

Fig. 1.3: The positron energy spectrum from the polarized Michel decay. (a), (b), (c) shows the case of cosθe = 0, cosθe =+1 and cosθe = -1 respectively [9].
µ+ → e+ νe νµ , called Michel decay, is described by the weak interaction mediated by a W boson. The Michel decay isthe dominant source of the background positrons for µ+ → e+ γ search. The diﬀerential decay rate is described as [9]:5 2d2 Γ(µ± → e± νν) mµG F 2=
x [(3 − 2x) ± Pµ cosθe (2x − 1)],
dx dcosθe
192π3
2

(1.5)

2m

where G F is the Fermi constant (G F = 4 √g2m2 ), x = m2 +mµ 2 Ee , Pµ is the polarization of µ, θe is the angle between theWµeµ polarization and the electron (positron) momentum. Fig. 1.3 shows the energy spectrum of polarized (Pµ = 1) Michel

positron*1 . In the MEG II simulation and analysis software, the radiative correction calculated in Ref.[41] is also used inaddition to (1.5).
Radiative Muon Decay (RMD)

Radiative Muon Decay (RMD) can be included as a kind of radiative correction for the Michel decay with the lowest-order.
RMD emits a positron and a gamma ray at the same time, and if the neutrinos go out with a tiny momentum, the decay
mimics the signal decay µ+ → e+ γ and becomes the background event. In addition, when a high energy γ is emitted from a*1 We count the positron from the all direction in the experiment, so we can eﬀectively assume the distribution of (a), which is equivalent to unpolarized

muon case.

Chapter 1 Physics Motivation

18

Fig. 1.4: The energy spectrum of RMD gamma ray [9].

RMD and a high energy positron is emitted from a Michel decay at the same timing, they become the accidental background
event. The diﬀerential branching ratio of the radiative muon decay is expressed by [9]:dB(µ → eννγ) 1= (J+ (y)(1 ± Pµ cosθγ ) + J− (y)(1 ∓ Pµ cosθγ )),dydcosθγ
y

(1.6)

2E

where y = mµγ , θγ is the angle between muon polarization and γ momentum. J+ (y) and J− (y) is deﬁned as follows:
"
!
!
!
#
1 − y 171−y
1 − y 13α(1 − y) 3ln−+ −3ln+ 7 (1 − y) + 2ln+(1 − y)2 ,
6π
r
2
r
r
3

(1.7)

"
!
!
!
#
α
1 − y 93
1 − y 29
1 − y 55
(1 − y)2 3ln−+ −4ln+(1 − y) + 2ln−(1 − y)2 ,
6π
r
12
r
3
r
12

(1.8)

J+ =

J− =

where r = ( mmµe )2 . Fig. 1.4 shows the energy spectrum of the RMD gamma ray from unpolarized muons.

1.5

Motivation of cLFV Search Experiment

1.5.1

Energy Frontier and Intensity Frontier

In the search of the BSM candidates, “energy frontier” experiments like ATLAS and CMS at the LHC and “intensity
frontier” experiments like the MEG are both important. The LHC experiment directly searches the new particles in BSM
through the strong interaction. Its discovery reach is limited by the beam energy and luminosity. On the other hand,
the MEG II experiment can indirectly reach for the BSM whose energy scale is much higher than the energy scale of
the LHC and it is sensitive to new particles interacting through the weak interaction. Therefore, the two approaches arecomplementary.
The search for the TeV-scale SUSY particles has been one of the motivations of the LHC experiments. However, theresults so far have been negative for masses up to 1 - 2 TeV [42, 43]. Considering that the LHC has not yet observed
signiﬁcant signs of new physics, it is eﬀective to take a diﬀerent strategy from the energy frontier: indirect search of the
new particles in the intensity frontier.

1.5 Motivation of cLFV Search Experiment

19

Fig. 1.5: The diagram of µ → eγ in the standard modelwith the neutrino oscillation [10].

Fig. 1.6: An example of the diagram of µ → eγ with
the TeV scale SUSY particles [10].

Fig. 1.7: The expected branching ratios of µ → eγ and τ → µγ in the CMSSM with seesaw mechanism [11].

1.5.2 µ → eγ Decay
This thesis shows the latest progress of the MEG II experiment which searches for one of the cLFV phenomena, µ → eγ.
This decay violates the lepton ﬂavor conservation and is strongly suppressed in the Standard Model. Taking the neutrinomass into account, the µ → eγ can occur within the Standard Model by the process shown in Fig. 1.5 and the rate is
calculated as [10]:Br(µ → eγ) =

∆m2
3α
∗
Σi=2,3 Uµi
Uei 2i132πMW2∼ 10−54 .

(1.9)

The most strict upper limit is currently set by MEG experiment, Br(µ → eγ) < 4.2 × 10−13 (90% C.L.) [1]. In the BSM, thebranching ratio of this decay becomes much larger by introducing heavy new particles like SUSY particles or right-handed
neutrinos. Fig. 1.6 shows the diagram of the µ → eγ with SUSY particles.
The limit by the MEG experiment already puts a stringent constraint on some of the BSMs and improving the experimental sensitivity by another order of magnitude will cover the majority of the parameter space. As an example, the expected

Chapter 1 Physics Motivation

20

Fig. 1.8: Br(µ → eγ) as functions of the universal scaler mass m0 and tanβ for MN = 3 × 1015 GeV, M1/2 = m0 , a0 = 0, andsign(µ) > 0 in the mSUGRA. Numbers of the ﬁgures correspond to the values of Br(µ → eγ). Dark green, light green, anddashed green region for mh [GeV] correspond to the region of 125 < mh < 127, 124 < mh < 128, and 120 < mh < 130,
respectively [12].

µ → eγ branching ratio in the constrained-MSSM (CMSSM) with seesaw mechanism is shown in Fig. 1.7. The neutrino
mixing angle θ13 ∼ 9◦ [44] suggests a higher branching ratio for µ → eγ, and the search of O(10−14 ) region approaches theparameter region of the heaviest right-handed neutrino mass around 1012 GeV for SPS 1a parameters*2 .
Fig. 1.8 shows the relation between mSUGRA parameters (m0 , a0 , M1/2 , tanβ, sign(µ)), the branching ratio of µ → eγ
and the Higgs mass [12] with the heavy right-handed neutrino (MN = 3 × 1015 ). The limit by the MEG experiment already
explored the parameter space of m0 around 5 TeV at mh = 126 GeV. If the MEG II experiment is completed and the oneorder higher sensitivity of O(10−14 ) is achieved, the access to the parameter space of the new particles up to around O(10TeV), which is not achievable by the direct search experiments, becomes feasible.
Another example is shown in Fig. 1.9 [13]. In this paper, several parameters pointed out by Casas and Ibarra [46] (CIparameters), which complicate the mixing structure of the neutrino Yukawa matrix and aﬀect the CP and ﬂavor violating
observables by enhancing the oﬀ-diagonal elements of the mass matrix, are studied carefully. They showed that the proper
introduction of the CI parameters has a signiﬁcant impact on the CP and ﬂavor violating observables, and thus Br(µ → eγ) isenhanced. The MEG II experiments has an enough sensitivity to explore the parameter space of the heavy SUSY particles,O(10 TeV).

1.5.3

Prospect of µ → eγ Search

Fig. 1.10 shows the history of the searches for these three major cLFV phenomena. The sensitivity of µ+ → e+ γ searches
have reached O(10−11 − 10−13 ) region in the past ∼ 30 years, which is already within the predicted region of some BSM*2 The “Snowmass Points and Slopes” (SPS) are a set of benchmark points and parameter lines in the MSSM parameter space corresponding to

diﬀerent scenarios in the search for Supersymmetry at present and future experiments [45].

1.5 Motivation of cLFV Search Experiment21

Fig. 1.9: Br(µ → eγ) as functions of the universal scaler mass m0 and tanβ for MN = 3 × 1013 GeV, M1/2 = m0 , a0 = 0,
and sign(µ) > 0 in the mSUGRA. r = 2.2 is one of the CI parameters. With the increase of r value, the Yukawa coupling
can become larger. The detail of the other CI parameters can be found in [13]. The black lines are for Higgs mass of
125 GeV, and the dashed/dot lines are ± 1 GeV/2 GeV from the Higgs mass. The current upper limit of electron EDM
de < 1.1 × 10−29 e cm [14] is shown with the green dashed line, which is almost equivalent to the current upper limit ofBr(µ → eγ) by the MEG experiment (shown with the brawn dashed line) in this parameter space.

theories. The experimental sensitivity of µ → eγ continues to be improved toward O(10−14 ) region. The unprecedented
sensitivities are achieved by the improvement of the detectors (new apparatus and sophisticated design like Sec. 2.2: MEG
and Sec. 2.3: MEG II) and beam technologies (surface muon beam explained in Sec. 2.3.2).

Chapter 1 Physics Motivation

22

90% C.L. Limit

History of CLFV experiments with muons
1
10−1
10−2
10−3

µ → eγµN → eNµ → 3e

10−4
10−5
10−6
10−7
10−8
10−9
10−10
10−11
10−12
10−13
10−14
1940 1950 1960 1970 1980 1990 2000 2010 2020
Year

Fig. 1.10: The history of the upper limits of three cLFV phenomena [3].

23

Chapter 2

MEG and MEG II ExperimentThis chapter describes experiential requirements for µ+ → e+ γ detection. An overview of the MEG experiment and its
limitation in the past searches are summarized. Then, MEG II upgrade is explained in details.

2.1

Experimental Requirements

The signal event and two main background (accidental background event and RMD event) events in the µ+ → e+ γ search
are shown in Fig. 2.1. The signal and RMD events are single physics phenomena while the accidental background event iscomposed of two physics phenomena close in time.

2.1.1

Signal Events

The signal event, µ+ → e+ γ, is a two-body decay and the kinematics of the signal positron and the signal gamma-ray canbe characterized as follows:• te+ γ = 0,
• Θe+ γ = 180◦ ,• Ee+ = Eγ = mµ /2,
where te+ γ is the time diﬀerence between the positron and the gamma-ray at the vertex, Θe+ γ is the opening angle between
the positron and the gamma-ray, Ee+ and Eγ are the energies of the positron and the gamma-ray, respectively, and mµ is themuon mass (mµ /2 ≃ 52.8 MeV).

γ
ν#

γ

ν"

µ!
e!

Signal Event

ν#

γ
µ!

µ!
e!

Accidental Background Event(Michel Positron + Gamma Ray)ν"e!

RMD EventFig. 2.1: The schematics of a signal event and background events (accidental and RMD).

Chapter 2 MEG and MEG II Experiment24
The number of the expected signal events can be written as follows:
Nsig = Rµ × T × Ω × B × ϵγ × ϵe × ϵ s ,(2.1)

where Rµ is the rate of stopped muons, T is the total data acquisition (DAQ) live time, Ω is the solid angle of the detectors,
B is the branching ratio of the signal decay, ϵγ , ϵe , ϵ s are the eﬃciencies of the gamma-ray, positron, and event selection by
the trigger and the oﬄine analysis, respectively.

2.1.2

Background Events

The major background events are the accidental coincidence between gamma-rays and positrons. The main source of theaccidental positron is the Michel decay, µ+ → e+ νν. The accidental gamma-rays are from the RMD event µ+ → e+ ννγ,
bremsstrahlung, and positron annihilation-in-ﬂight (AIF). Another background source is the RMD when the emitted neutrinos carry a low momentum. Fig. 2.1 shows these schematics.
Here these two types of backgrounds are summarized based on [9]. For the discussion, the following 4 parameters,
x = 2Ee+ /mµ , y = 2Eγ /mµ , z = θe+ γ − π, and te+ γ are used and the signal region is deﬁned as below:
1 − δx ≤x ≤ 1 + δx,(2.2a)

1 − δy ≤y ≤ 1 + δy,(2.2b)

0 ≤z ≤ δz,(2.2c)−δte+ γ ≤te+ γ ≤ δte+ γ ,(2.2d)

where δx, δy, δz and δte+ γ is the signal region for each variable. For example, by using the design resolutions obtained inRef. [1], the signal region in the MEG experiment can be deﬁned to have 90% coverage:
δx ≈0.015,(2.3a)

δy ≈0.019,(2.3b)δz ≈20 mrad,(2.3c)

δteγ ≈200 ps.

(2.3d)RMD Events

One of the backgrounds for the µ+ → e+ + γ search is the radiative muon decay (RMD), µ → e+ ννγ, when the positron andgamma ray are emitted back to back with two neutrinos carrying oﬀ little energy (x ≈ 1, y ≈ 1 and z ≈ 0). The backgroundfraction from the RMD (dBRMD ) can be calculated by integrating the RMD diﬀerential branching ratio (dB(µ+ → e+ ννγ))
over the signal region:dBRMD =

Z 1+δxZ 1+δy
dx

1−δx

Z δz
dy

1−δy

dz
0

dB(µ+ → e+ ννγ).
dxdydz(2.4)

Then the number of the RMD background events can be estimated as follows:
NRMD = Rµ × T × Ω × dBRMD × ϵγ × ϵe ,(2.5)

Fig. 2.2 shows the achievable sensitivity for RMD with the given δx and δy values. For example, the eﬀective branchingratio of the RMD background in the MEG experiment was ∼ 1 × 10−14 , which was almost negligible compared to the single
event sensitivity*1 of (5.84 ± 0.21) × 10−14 . To achieve the sensitivity of O(10−15 ) level, which will be the target for the
MEG II experiment, both δx and δy should be on less than 0.01. In the MEG II experiment, the resolution of the positron
momentum will be improved by a factor of three (∼90 keV), and the that of the gamma-ray will be by a factor of two. Thisrequirement can be satisﬁed and the RMD background will not be a dominant source of the background.
*1 The single event sensitivity (SES) is deﬁned as B in Nsignal , which is the sensitivity value for the experiment to see one signal event.

2.1 Experimental Requirements

25

Fig. 2.2: Eﬀective branching ratio of the RMD background as a function of the positron energy (δx) and gamma-ray energy(δy) [9].

Fig. 2.3: Eﬀective branching ratios of the accidental and RMD background into the kinematic window of MEG experimentdeﬁned by Ee+ ,min < Ee+ < 53.5 MeV, Eγ,min < Eγ < 53.5 MeV, |te+ γ | < 0.24 ns and cosΘe+ γ < −0.9996. (a) Accidental
background from the side-band data. (b) RMD background calculated with the theoretical formula folded with the MEG
detector response [1].

Accidental Background

Under the very high rate environment like the MEG and MEG II experiment, the accidental background becomes more
important than the RMD background. Fig. 2.3 shows the eﬀective branching ratio of the RMD and accidental backgroundin the MEG experiment.
The accidental background rate (Bacc ) can be estimated by:
Bacc = Rµ · fe0 · fγ0 · δteγ ·

δωeγ
,
4π

(2.6)

Chapter 2 MEG and MEG II Experiment26

where Rµ is the muon beam rate, fe0 and fγ0 are the integrated fractions of the spectrum of the positron and the gamma-ray
from the muon decay within the signal region, ∆teγ is the full width of the timing coincidence, ∆ωeγ is that of the angularconstraint of the back-to-back kinematics.
The energy spectrum of the positron and gamma ray are shown in Fig. 1.3 and Fig. 1.4, respectively. fe0 can be estimatedby integrating the ﬂat part of the Michel spectrum (x ≈ 1), yielding fe0 ≈ 2δx. As for the gamma ray, if the main source of
background gamma ray is the RMD*2 , it can be calculated by the integral of the spectrum over 2π for θγ and over the signal
region for gamma ray energy. fγ0 is given by:
fγ0 ≈Z 1+δy

Z 2π
dy

1−δy

d(cosθγ )0dB(µ → e+ ννγ)α
≈ ( )(δy)2 [ln(δy) + 7.33].
dyd(cosθγ )
2π

(2.7)

Given the angular resolution δθeγ , the back-to-back resolution (∆ωeγ /4π) can be presented by (δθeγ )2 /4.
From the above, the eﬀective branching ratio of accidental background is given by:
Bacc = Rµ · (2δx) · [(δθeγ )2α(δy)2 (ln(δy) + 7.33)] ·· 2δteγ .
2π
4

(2.8)

Thus, the number of accidental background events can be written as follows:
Nacc = Rµ × T × Ω × Bacc × ϵγ × ϵe
∝ R2µ × ∆Eγ2 × ∆Pe × ∆Θ2eγ × ∆teγ × T.

(2.9)

where ∆Eγ , ∆Ee+ is the energy/momentum resolution for gamma-ray and positron, ∆Θe+ γ is the resolution for the opening
angle between positron and gamma-ray, ∆te+ γ is the resolution for the time diﬀerence between positron and gamma-ray.

2.1.3

Requirements

To maximize the Nsig in Eq. 2.1, it is important to increase the beam rate Rµ , the DAQ period T , the eﬃciency ϵγ , ϵe , ϵ s andthe detector acceptance Ω.
On the other hand, the accidental background events also increase quadratically with the increase of Rµ . In high rate
experiments like the MEG II experiment, both the accidental overlap of a positron and a gamma-ray and the pileups ofpositrons (gamma-rays) in a detector have signiﬁcant impacts. Detectors must separate the accidental background and must
be tolerant for the pileups. Eq. 2.9 also indicates that having good resolutions of position, timing, angle, and energy is the
key to reduce the background events.
Considering the realistic DAQ period (three-year for MEG II), the important points can be summarized as follows:• Design the detectors, which are tolerable under high radiation and preserve good resolutions and high eﬃciencies
under intense muon beam.
• Develop the reconstruction algorithms to cope with high pileup environment under intense muon beam and to preserve good resolutions and high eﬃciencies.

2.2

MEG Experiment

The most stringent upper limit on the µ → eγ was established by the MEG experiment [1], Br(µ → eγ) < 4.2 × 10−13 (90%C.L.).
*2 Another main background source of the gamma-ray around the signal region is the AIF gamma-ray. However, the spectrum of the AIF gamma-ray

depends on the material distribution of the experiments and diﬃcult to discuss generally. In the MEG II experiment, the materials are reduced from
the MEG experiment and the RMD events are dominant.

2.2 MEG Experiment27

Fig. 2.4: The overview of the apparatus used in MEG experiment. The picture of DRS chip and board from [15]. The
picture of the LXe from [3]. The other pictures and sketch from [1].

2.2.1

Apparatus

Fig. 2.4 summarizes the apparatus. The MEG experiment was conducted at the Paul Scherrer Institute with an intense
continuous muon beam (3 × 107 µ / s). Muons were stopped at a stopping target made of polyethylene and polyester.
Gamma-rays were measured with a liquid xenon photon detector with 846 VUV sensitive photomultiplier tubes. Positrons
were measured by a positron spectrometer, which was composed of 16 drift chamber modules and a timing counter madeof the plastic scintillation bars. For the data acquisition, Domino-Ring-Sampler 4 (DRS4) chips [15] were used.
Table 2.1 shows the resolution and eﬃciencies achieved by MEG experiment (those proposed by the MEG II uprade arealso shown). As for the detector performance of the positron detectors, the large scintillator used in the MEG timing counter(4 × 4 × 80cm3 ) caused the additional timing variation of scintillation photons by longitudinal propagation, incident angle,
position dependence and so on. In addition, the performance of the PMTs used in the magnetic ﬁeld were degraded during
operation. The positron-crossing timing resolution achieved with the MEG timing counter (σTC ≈ 70 ps) was much worse
than the designed value (σTC ≈ 40 ps). The event rate of the timing counter (1 MHz) also limited the beam rate of the MEG
experiment.
The module-type drift chamber had mainly two crucial problems. Firstly, due to relatively large detector materials(including support structure and readout electronics of each module), the multiple scattering deteriorated resolutions andreconstruction eﬃciency. Secondly, the tracking volume and the number of layers were not enough to precisely associate
the positron tracks with the hit positrons in the timing counters and with the vertex points on the stopping target, resulting
in large uncertainties of the global tracking and lower reconstruction eﬃciency of 30%.

2.2.2

Result and Limitation

The MEG experiment ﬁnished data taking in 2013, and its ﬁnal result with full data set was published in 2016 [1]. A
maximum likelihood analysis is performed to obtain the number of the signal events in the analysis window based on

Chapter 2 MEG and MEG II Experiment

28

Table 2.1: The detector performance of MEG and expected performance of MEG II [3].
Resolution

MEG

MEG II

Ee+ [keV] (momentum of e+ )

380

130

θe+ [mrad] (Angle of e+ )

9.4

5.3

ϕe+ [mrad] (Angle of e+ )

8.7

3.7

ze+ /ye+ [mm] (Vertex position of e+ )2.4/1.2

1.6/0.7

Eγ [%], w < 2 cm/w > 2 cm (Gamma energy)

2.4/1.7

1.1/1.0uγ , vγ , wγ [mm] (Gamma position)

5/5/6

2.6/2.2/5

te+ γ [ps] (Timing diﬀerence b/w e+ γ)

122

84

Trigger

99

99

γ

63

69

+

30

70

Eﬃciency(%)

eFig. 2.5: Event distributions for the 2009 – 2013 full dataset on the (Ee+ , Eγ )-plane with the selections of cos Θe+ γ < 0.99963 and |te+ γ | < 0.24 ns (left), and (cosΘe+ γ , te+ γ )-plane (right) with 51.0 < Eγ < 55.5 MeV and 52.4 < Ee+ < 55.0
MeV. The contours of the averaged signal PDFs (1σ, 1.64σ and 2σ) are superimposed [1].

the Probability Density Functions (PDFs) for signal, RMD, and accidental background events. Fig. 2.5 shows the event
distributions for the 2009 – 2013 full dataset on the (Ee+ , Eγ ) and (cosΘe+ γ , te+ γ ) planes. The contours of the averaged signal
PDFs are also shown. No signiﬁcant excess was found within the signal contours, and the new upper limit for the branchingratio of Br(µ+ → e+ γ) < 4.2 × 10−13 (90% C.L.) was set as shown in Fig. 2.6, which improved the world record by a factorof 30 from the one set by the MEGA experiment [47].
The continuation of the MEG experiment is not realistic to achieve the O(10−14 ) sensitivity. The single event sensitivityof the MEG experiment was 0.58 × 10−13 , while the upper limit of the branching ratio was 4.2 × 10−13 . These values meanthat the sensitivity of the MEG experiment was limited not by the statistics but by the number of the accidental backgrounds.
As shown in Fig. 2.6, the improvement of the upper limit in the MEG experiment got smaller and smaller as the DAQ time2.2 MEG Experiment29

Fig. 2.6: The branching ratio sensitivity as a function of the DAQ days in the MEG experiment [4].

passed during 2009 – 2013. Assuming that the contribution from the number of the backgrounds improves by a squareroot of the statistics, it will take O(100) years to achieve 10 times better sensitivity from the MEG experiment. In addition,
the MEG detectors were optimized for the MEG dedicated conditions (e.g. beam rate and experiment period). From theoperation point of view, e.g. rate tolerance and radiation hardness, it is not realistic to continue the MEG experiment.

2.2.3

Proposal of the MEG II Experiment

An upgrade experiment, MEG II experiment, was proposed [21] in 2013, aiming at a branching ratio of O(10−14 ) withthe twice intense muon beam. Table 2.1 shows the resolution and eﬃciencies achieved by MEG experiment and those
proposed for the MEG II upgrade. The positron reconstruction eﬃciency and resolution will be improved by a factorof ∼2. This proposed performance is required to suppress the backgrounds which determined the limitation in the MEG
experiment. The innovative positron spectrometer, which is composed of the highly segmented scintillation timing counter:pTC and ultra-low material drift chamber with large tracking volume: CDCH, was newly designed to achieve this goal.
Table 2.2 summarizes the list of systematic uncertainties in MEG experiment. Alignment of stopping target was the largest
uncertainty. Therefore, MEG II experiment will replace the stopping target system.

Chapter 2 MEG and MEG II Experiment

30

Table 2.2: The list of the systematic uncertainties considered in the physics analysis in the MEG experiment [4]. The
fractions of “All the other” are also shown in parentheses.
PDF parameters

Impact on sensitivity

Alignment of stopping target

13%

All the other<1%

Alignment of LXe detector - tracker(37%)

Eγ scale(23%)

Bias of center of teγ PDF(19%)

Ee bias(11%)

Normalization(7%)

Errors in event-by-event PDF

(3%)

COBRA
superconducting magnet

Liquid xenon photon detector(LXe)

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

Cylindrical drift chamber(CDCH)

Fig. 2.7: The overview of the MEG II experiment [3].

2.3

MEG II Experiment

The apparatus of the MEG II experiment (except for the positron spectrometer explained in the next section) is describedin this section [3].
The key points to reach O(10−14 ) sensitivity are the increased beam rate (Sec. 2.3.2), and the higher performance of thedetectors (Sec. 2.3.4, Sec. 2.3.5 and Sec. 2.4). In addition, the DAQ and trigger system (Sec. 2.3.6) are upgraded to cope

2.3 MEG II Experiment31
yx

Downstream(DS)z

Upstream(US)

Fig. 2.8: The global coordinate system of MEG II positron spectrometer.
y

US

DS

Wire

z

x

z
0 (center)Fig. 2.9: The local coordinate on a CDCH wire.
Fig. 2.10: The local coordinate of a pTC counter.

Fig. 2.12: The coordinate of the target ellipse.
Fig. 2.11: The dedicated coordinate of the LXe detector(u, v, w) [16].

with the higher number of readout channels and densities. The muon stopping target and the monitoring system (Sec. 2.3.3)
are also upgraded to decrease the systematic uncertainties.
Fig. 2.7 shows the overview of the MEG II experiment. The positive muon beam is stopped at the stopping target atthe center of the spectrometer magnet (Sec. 2.4.4). The positrons from the muon decays are measured by the new positron
spectrometer and gamma-rays by the LXe gamma-ray detector, which is also upgraded from the MEG experiment. RDC isa new detector for background rejection. The requested period for the MEG II physics run is 20 week/year and for 3 years.

2.3.1

Coordinate systems

In the MEG II global coordinate system, we deﬁne the z-axis along the muon beam axis with the origin at the center of the
COBRA. The y-axis is deﬁned as the direction from bottom to top to direction and x-axis is deﬁned as the rest direction in
the right-handed coordinate system. Fig. 2.8 shows the coordinate systems of positron spectrometer.
When we reconstruct a hit in a counter of the pTC or on a wire of the CDCH, positron variables are described in the local
coordinate system as deﬁned in Fig. 2.9 and Fig. 2.10. The local coordinate of the LXe detector and the target, which areChapter 2 MEG and MEG II Experiment32

Fig. 2.14: The large proton ring accelerator [17].
Fig. 2.13: The Cockcroft-Walton pre-accelerator [17].

shown in Fig. 2.11 and Fig. 2.12, respectively, are also used for the criteria in the track selection task.

2.3.2

Muon Beam LineAs described in the previous sections, an intense muon beam is necessary to accumulate Nsignal . The Naccidental ∝ R2µ indicatesthat a direct current (DC) muon beam is suitable instead of the pulsed muon beam. In addition, a positive muon beam should
be used to avoid the formation of the muonic atoms which deteriorates the simple two-body decay kinematics. Currently
the most intense DC muon beam in the world (∼ 108 µ+ /s) is available at Paul Scherrer Institut (PSI) in Switzerland.
The muon beam is produced at the proton cyclotron accelerator in the PSI. The protons from a hydrogen source areaccelerated up to 590 MeV with the combination of the Cockcroft-Walton pre-accelerator (870 keV), the 4-sector injector
2 cyclotron (72 MeV) and the large 8-sector ring cyclotron (590 MeV). Fig. 2.13 and Fig. 2.14 show the Cockcroft-Walton
pre-accelerator and the large proton ring accelerator, respectively. The proton beam (1.2 MW) is transported to the graphitetarget (the pion production target). The beam frequency is 50.7 MHz and the width of the beam bunch is 0.3 ns. Thisfrequency (∼20 ns interval) is short enough for the muon beam to be continuous compared with the pion lifetime (26 ns)
and muon lifetime (2.2 µs). The surface muons [48], which originate from the stopped pions near the target surface, arecollected and transported to the beamline (πE5) used by the MEG II experiment. The muons from the decays of the stopped
pions, π+ → µ+ + νµ , have a sharp momentum spectrum around 29.8 MeV/c and are ∼ 100% polarized*3 .
Fig. 2.15 shows the schematic view of the πE5 beamline and the MEG beam transport system with MEG detectors. The
production target is connected to the πE5 area by a quadrupole and hexapole channel in the direction of backward (165◦ ).
The muon beam is then transported through the beam transfer and contamination*4 removal components: quadrupole triplet(Triplet I), the Wien-ﬁlter (E × B ﬁeld separator), Triplet II, and a collimator system. Then, the muon beam goes throughthe Beam Transport Solenoid (BTS). BTS is a 2.8 m long iron-free superconducting solenoid to focus and transport themuon beam. The ﬁnal muon momentum is adjusted by a degrader system in the BTS and ﬁnally, the muon beam is spottedon the MEG II target with a stopping rate of 7 × 107 µ+ /s.

*3 The 100% polarized muons have several scientiﬁc merits: for the possibility of the measurement of angular distribution of µ → e + γ, which may

provide the crucial information of the new physics.
*4 The contamination comes from mainly positrons generated by a Michel decay or pair creation of a photon from π0 decay.

2.3 MEG II Experiment33

Fig. 2.15: The πE5 beam line [18].

Fig. 2.16: The MEG II scintillator target [3].

2.3.3

Target

The main requirements for the MEG II target are as follows:
1. High muon stopping eﬃciency.
2. Low material budget to avoid multiple scattering, photon conversion, annihilation in ﬂight (AIF), andbremsstrahlung.
3. Stable structure to reduce the systematic uncertainty.
4. Remotely movable structure for the insertion of the calibration targets.
For the MEG II target in the commissioning, a plastic scintillator target whose thickness is 174 µm was used. It wasplaced with the slant angle of 15.0◦ from the beam axis to achieve a longer eﬀective thickness for muons (requirement 1.)
and a shorter thickness for positrons (requirement 2.). The material is hard enough to avoid the deformation. The goal of
the target alignment precision is < 50 µm on the transverse direction and < 100 µm on the axial direction.
To monitor the target position, pattern dots are printed for the CCD camera monitoring as shown in Fig. 2.16. By CCD
camera monitoring of the patterned dots, we expect a ∼ 10 µm precision in the transverse coordinate and ∼ 100 µm in theaxial coordinate [3].
In addition, the small holes will be made for the tracking-based alignment as in MEG. The tracking-based alignment wasdone by checking the positron track distribution at the vertex and the deﬁcit of the distribution at the holes. Fig. 2.17 showsthe example of the distribution from the MEG data.
The additional advantage of the scintillator material is the possibility of non-destructive measurements of the beam

Chapter 2 MEG and MEG II Experiment34

Fig. 2.17: The distribution of positron reconstructed position at the target with 2011 MEG data [3].
Fig. 2.18: The perspective corrected and 2D gaussian ﬁtted
beam image viewed originally under 15◦ to the target plane
and taken in 2016 commissioning [3].

Fig. 2.19: The picture of the LXe photon detector [3].

intensity and proﬁle with a CCD camera and dedicated optical systems. Fig. 2.18 shows the beam image taken with the
CCD camera and optical system setup in the 2016 MEG II detector commissioning.

2.3.4

Liquid Xenon (LXe) photon Detector

The MEG II Liquid Xenon (LXe) photon detector is composed of ∼900 L LXe as a liquid scintillator and photo-sensors.
The LXe has the following advantages for precise photon measurement:• Fast timing response,• High stopping power,• Large light yield,

2.3 MEG II Experiment35

Fig. 2.21: A large area MPPC used in MEG II LXe photon
Fig. 2.20: The sketch of a large area VUV sensitive MPPC

detector [19].

used in MEG II LXe photon detector [19].
PMT(2-inch)MPPC(12×12mm2)Fig. 2.22: Example of scintillation light distribution detected by PMTs (left) and MPPCs (right) for a same simulated event[3].

• Uniformity of the scintillation response,• Radiation hardness.
On the other hand, it is expensive and a cryogenic system (∼165 K) is required for the detector operation. A major
challenge is to detect the LXe scintillation light, which is in the vacuum-ultraviolet (VUV) range (175±5 nm). VUVsensitive photo-sensors were developed in collaboration with Hamamatsu Photonics. In the MEG experiment, 846 2-inch
PMTs (HAMAMATSU R9869) were used as shown in Fig. 2.19. The biggest issue was the non-uniformity of the PMT
coverage in the inner face (photon entrance side). The collection eﬃciency strongly depended on the incident position due
to this non-uniformity especially at the shallow region, and this dependence deteriorated the energy and position resolution
in the MEG experiment. In MEG II, 216 PMTs on the inner face are replaced with 4092 SiPMs*5 .
A large area VUV enhanced MPPC*6 , shown in Fig. 2.20 (sketch) - Fig. 2.21 (picture), was developed. The detailed
studies and mass tests are summarized in Ref. [19]. As a result, a high photon detection eﬃciency (PDE) up to 21%, a highgain, a low dark count rate, and a good single photoelectron resolution were achieved.
Fig. 2.22 shows a comparison of event displays with the MPPC readout case and the PMT readout case for a same

*5 These replaced PMTs were re-used on the other face to replace the dead PMTs, and to further improve the uniformity of the readout by the

optimized PMT layout.
*6 Hamamatsu Photonics uses Multi-Pixel Photon Counter (MPPC) for their product name of SiPMs.

Chapter 2 MEG and MEG II Experiment36

Fig. 2.23: The schematic view of the RDC. The horizontal long plates in front are the plastic scintillator bars and the cubes
behind are the LYSO crystals [3].

simulated event. The imaging power is clearly improved by the higher granularity and uniform readout with MPPCs.

2.3.5

Radiative Decay Counter (RDC)

A gamma-ray from a RMD, which is a source of an accidental background event, can be identiﬁed by detecting a low
momentum positron from the same decay. The low momentum positrons are swept away quickly through the small radius
trajectory to either upstream (US) or downstream (DS), so the RDC is placed on the beam axis to detect those positrons andidentify the RMD events.
They measure the coincidence of the positron timing with the photon in the LXe detector, and tag the RMD events.
The energy measurement will help to separate the RMD positron and the accidental Michel positron whose energy is highenough to be distinguished.
DS-RDC

Fig. 2.23 shows the schematic view of the DS-RDC. DS-RDC is composed of the 12 plastic scintillation counters for thetiming measurement and the 76 LYSO crystals for the energy measurement. Fig. 2.24 shows the distribution of the timing
diﬀerence between the RDC and LXe detector. The peak in the red histogram corresponds to the RMD events, while theﬂat regions in both red and blue histograms correspond to the Michel events.
Fig. 2.25 shows the energy distribution at the RDC for RMD events with Eγ >48 MeV and Michel events. Typically theMichel positrons have higher energies and the energy measurement with LYSO crystals will help the identiﬁcation.
US-RDCThe high transparency for the muon beam and the high detection eﬃciency for the RMD positrons must be demonstrated
for a detector on the beam axis of the upstream side. In addition, the requirement for the radiation tolerance is severe under
the intense muon beam.
For US-RDC, ultra-low mass Resistive Plate Chamber (RPC) is newly designed [49]. The test of the US-RDC prototype
was conducted in December 2020 at PSI. Since the operation plan of US-RDC has not yet ﬁnalized, the contribution of the
US-RDC is not included for the analysis in this thesis.

2.3 MEG II Experiment37

Fig. 2.24: The expected (MC) distribution of the timing
diﬀerence between the RDC and LXe. Red line shows
the accidental background events and blue line shows
the signal events [3].

Fig. 2.25: The expected (MC) energy distribution at the
RDC for RMD events with Eγ >48 MeV (red) and forMichel events (blue) [3].

Fig. 2.26: The sketch of the single WaveDAQ crate [20]. The green boards are WDB, magenta DCB and blue TCB.
CMB is drawn on the right side. Arrows show connections in the backplane: red arrows for data transmission to backend
machines, blue for trigger serial links, orange to distribute back the trigger signal and green for hardware compensatedclock distribution, and brown shows low level access for slow control and conﬁguration.

2.3.6

Trigger and Data Acquisition (TDAQ) System

In the MEG II experiment waveform data is taken and stored for the oﬄine analysis. For the eﬃcient data accumulationand the limited space for the signiﬁcantly increased number of channels (∼9000 channels, which is ∼3 times larger than
MEG experiment), the new electronics, named Waveform Drs4 REadout Module Board (WaveDREAM Board, WDB) was
developed.

Chapter 2 MEG and MEG II Experiment38

MCX
TRG IN
Temperature sensors 1-Wire®

MCX
TRG OUT

previous channel
DAC

Attn.
:1,2,4

x10

Comp
C

PHY

Trigger

x10

x2

DRS4

+5V
+3.3V
+2.5V
+1.8V
+1.2V
-2.5V

ADC

XTAL
calibration

SiPM

next channel

PLL
(LMK)

RAM

FPGA

Input

... 2 x 8 channels ...

RJ45

PoE optional

x2

DRS4

DC

DC in
24 V

DC
power on

Attn.
:2

Input

DAC
DAC
offsetDAC

Shaper

24 V

RGB

BUS

SPI

ADC
SPI

DAC

HV Piggy-back
58-63V58-63V

5 V DAC

58 V

Comp
C

Trigger

Temp

PROM

CockroftWalton
TR BUS CLK

DC
+24V

DC

Osc.

En

HV
ON

LVDS

MCX
CLK INMCXCLK OUT

Fig. 2.27: The schematics of the WDB [3].

Fig. 2.28: The mechanism of the Domino Ring Sampler chip (DRS chip).

The WDB is inserted to the WaveDAQ crate with Data Concentrator Board (DCB) and Trigger Concentrator Board(TCB) in MEG II DAQ. Fig. 2.26 shows the single WaveDAQ crate. 16 boards (WDB) are connected to the 2 central slots(DCB and TCB) for the data and trigger processing, respectively. The power supply to the all boards and slow control areprovideed by the crate management board (CMB) [3, 20].
WaveDREAM Board (WDB)

A WDB is an integrated DAQ electronics device: signal ampliﬁer and shaper, high-voltage supply to the detectors, waveform digitizer, data transmission, and basic trigger functionalities are integrated on one board. Fig. 2.27 shows the schematics of the single WDB. A single WDB has 16 input channels, so the single crate has 256 readout channels at the maximum.
The ampliﬁer gain is adjustable in the range of 0.5–100. A waveform shaper is mounted and pole-zero cancellation can beapplied to the waveform. A WDB contains two DRS4 chips whose sampling speeds can be adjusted in the range of 0.5-5
GSPS (Giga Samples Per Second) with 900 MHz bandwidth. The DRS4 chips [50] are connected to 80 MSPS Analog-toDigital Convertors (ADCs). The scheme of the DRS chip is shown in Fig. 2.28. The voltage (amplitude) of the waveformis stored on 1024 capacitors as a charge by a logic wave propagating through the inverter domino chain (domino ring), and
it is read out to the ADC by a shift register when the trigger is recieved. The sampling speed is ﬂexible; 1.6 – 2.0 GSPS forpTC and 0.8 – 1.2 GSPS for the CDCH are used. This GSPS determines the timing window of one “event”: one sequential2.3 MEG II Experiment

Efficiency

39

1
MEG
MEG II expected

0.8

0.6

0.4

0.2

0
−20

−15

−10

−5

0

5

10

15

20
t e+γ (ns)Fig. 2.30: The comparison of the online te+ γ trigger seFig. 2.29: The online timing distribution of positrons inMC (black) ﬁtted with multiple gaussian function (red)[7].

lection eﬃciency of the MEG II expected (blue) timing
window and the MEG (red) timing window. The width(FWHM) is reduced from 20 ns (MEG) to 14 ns (MEG II)[3].

waveform by one trigger*7 . While the waveform is being sampled in the DRS4 chips, readout from sampling cells to the
ADC is running in parallel and digitized data is transferred to an FPGA in which the dedicated trigger logics are implemented using digitized data and fast comparator outputs. The HV to the detectors is generated in an attachment board (HVpiggy-back board), which has a 5V Digital-to-Analog Converter (DAC) and a Cockcroft-Walton voltage multiplier. The
readout scheme guarantees a data transfer dead time of ∼1 ms, which leads to a maximum DAQ rate of 100 Hz. Considering
the muon beam rate, realistic data size, and online selection eﬃciency, the maximum trigger rate of the MEG II experimentis about 10 Hz.
Data Concentrator Board (DCB) and Trigger Concentrator Board (TCB)

The central 2 slots are reserved for special boards, which are responsible for the crate-level functions and for multi-board
DAQ operation.
A DCB distributes the main reference clock and the trigger signal inside the crate. It is also responsible for the conﬁguration in the crate and for the communication to the DAQ machines via the Gigabit Ethernet interface.
A TCB receives and handles all the trigger information from the WDB and judges the event of interest.
Trigger

The trigger processing will reject the background record by almost 6 orders of magnitude, resulting in a DAQ rate of∼ 10Hz. Online event reconstructions, such as the momenta, relative timing and direction, are performed based on theinformation from pTC and LXe*8 . The necessary equation and lookup tables are implemented in the FPGA. The online
reconstruction (timing/energy) of gamma-rays are performed from a sum of waveforms in the LXe detector. The online*7 The deﬁnition of “pileup” is overlapping of triggered positrons/gamma-rays and background positrons/gamma-rays in a analysis window. If morethan one peak was found in one event (the timing window), the event can be counted as an event with pileups, as already explained in the ﬁrst
section of this chapter. The pileups by the background positrons/gamma-rays aﬀects the reconstruction of the triggered positrons/gamma-rays by
the baseline ﬂuctuation (if the backgrounds come before the triggered one) or the overlapping of the peak position (if the timing is too close to be
separated).
*8 Since the drift time of CDCH is too long (in the range of several ns to O(100) ns), information from CDCH cells cannot be used for the online
trigger. This makes the relative timing window wider since we cannot know the number of turns for positron track and obtain the TOF value frompTC to the vertex point.

Chapter 2 MEG and MEG II Experiment40

Fig. 2.31: The overview of the MEG (up) and MEG II (down) experiment [21]. The blue line shows the gamma ray and thered positron. The positron tracker volume (green region) was extended to the pTC interface, which increased the numberof CDCH hits for one track and improved the trajectory and timing integration (matching eﬃciency). The timing counter(light blue region) was segmentalized into small pixels.

timing of positrons is deﬁned from a pTC counter with the smallest |z| position. The CDCH is not used for the online trigger
due to its slow time response. The timing diﬀerences of positrons and gamma-rays at each channel are compared. Since
the positron go into the pTC region after several turns as illustrated in Fig. 2.7 (e+ reached at the pTC region at the second
turn in this ﬁgure) but the number of turns cannot be reconstructed online, the coincidence width must be much wider thanthe online timing resolution (∼450 ps). Fig. 2.29 shows the online timing distribution of positrons in the MC simulation.
The diﬀerence by ∼2.5 ns/turn can be observed thanks to the improvement of the online timing resolution from 2.5 ns(MEG) to 450 ps (MEG II). Fig. 2.30 shows the trigger selection eﬃciency as as function of the trigger timing window for
the MEG II and the MEG experiment. The coincidence width (FWHM) is reduced from 20 ns to 14 ns without eﬃciency
loss. In addition, the information on the opening angle between positrons and gamma-rays is available thanks to the highly
segmented design of the pTC and the LXe readout.

2.4

Positron Spectrometer

The trajectory and the timing of the positron from µ → eγ are measured by CDCH and pTC, respectively, in a gradientmagnetic ﬁeld generated by the spectrometer magnet named COnstant Bending RAdius magnet (COBRA). The requirement
for the positron spectrometer is to reconstruct positron trajectories and timing, and to achieve two times better resolution
and two times better eﬃciency under two times more intense muon beam. This requirement is achieved by the highly
segmented design of the pTC and the ultra-low mass CDCH with the large number of layers in the large tracking volume.

2.4.1

Concept of Upgrade from MEG

For the µ → eγ search, the positron measurement is crucial since the most dominant decay mode (Michel decay), µ → eνν,
emits positron around the signal energy.
The important requirements for the drift chamber are less material budget to avoid multiple scattering and very high

2.4 Positron Spectrometer

41

W = 50 mm

W = 40 mm

Fig. 2.32: The design of pTC detector [3].
Fig. 2.33: The picture of pTC detector.

Fig. 2.34: The backplanes on the pTC support structure [7].

Fig. 2.35: The signal lines of the backplane [7].

granularity to be tolerant to the intense muon beam. Based on these requirements, a high-granularity ultra-low mass
cylindrical stereo wire drift chamber has been considered.
The important requirement for the timing counter is a highly segmented and stacked design with small scintillators to
improve the overall timing resolution using multi-hit measurements from one positron track. SiPMs were chosen for thephoto-sensors of scintillation photons. This replacement solves the problem in MEG (PMT degradation) since SiPM isinsensitive to the magnetic ﬁeld. The time-oﬀset calibration and uniform performance of the counters are crucial since themultiple-hit information, which is one of the most important concept of MEG II timing measurement, is used to achieve thetarget resolution. Several prototypes were tested with diﬀerent scintillators and diﬀerent SiPMs [23], and ﬁnally, the designof the MEG II timing counter was ﬁxed [3].

2.4.2

Pixelated Timing Counter (pTC)

DesignFig. 2.32 shows a CAD view of the pTC detector, and Fig. 2.33 shows the constructed pTC detector. The MEG II pTC
is composed of 512 (256 for upstream and 256 for downstream) small scintillation counters. Each counter has 70 – 90
ps resolution with the double-side readout by 6 SiPMs connected in series at each side. The total capacitance becomesChapter 2 MEG and MEG II Experiment42

View from downstream

Side viewFig. 2.36: A simulated signal positron trajectory (blue line) and the pTC counters (yellow). The positron crossed the redcounters [3].

Fig. 2.37: (Left) The picture of single pTC counter. The picture of the two types of PCBs are also shown in right sketch [3].
(Right) The sketch of the counter design pattern. L-shape and mix-shape counters were designed to put counters on innerstep of the support structure.

smaller by the series connection, resulting in the faster output pulse and better timing pick up. The counters are mounted on
dedicated long (948 × 25 mm2 ) PCBs called backplanes placed on a semi-cylinder-shaped aluminum support structure. The
backplanes on the pTC support structure are shown in Fig. 2.34, and its drawing of the signal lines is shown in Fig. 2.35.
The signals from the pTC counters are transmitted to the WDB with co-axial cables (RG178).
One positron with ∼ 45 – 50 MeV momentum crosses eight counters on average. Fig. 2.36 shows an example of asimulated positron crossing the multiple pTC counters. The pTC achieves O(30 ps) timing resolution by using this multiple
hits information. The detailed reconstruction algorithms are described in Chap. 6.
Components of Single CounterFig. 2.37 is the picture of the design models of counters. The main components of a counter are a scintillator tile, 12 SiPMs
on two PCBs, an optical ﬁber and its support part, a reﬂector and a light shielding black sheet and connectors for backplane.
They are summarized in Table 2.3.
Fig. 2.39 shows the pTC counter layout. The scintillator size and the alignment of counters were optimized by using asimulation. From the mechanical constraint, the PCB has the two types: ﬂat-type and L-shaped type like the picture and thesketch. In total there are 4 design patterns on counters; ﬂat-PCBs with 4 cm height scintillator (mainly used and illustrated
with magenta in outer region of Fig. 2.39), L-shape PCBs with 4 cm (inner magenta) , L-PCB and ﬂat-PBC (Mixed-PCBs)
with 4 cm (yellow), and ﬂat-PCBs with 5 cm (light blue). Positrons will cross the scintillator plate at almost right angle. 5

2.4 Positron Spectrometer

43

Fig. 2.38: (Left) A mounted ﬂat-type counter on the backplane. (Right) Mounted L-shape counters on the inner step of the
support structure [7].

Table 2.3: The materials for a pTC counter
Component

Product

Note

Company

Scintillator

BC422

40 or 50 × 120 × 5mm3Saint-Gobain

SiPM

ASD-NUV3S-P High-Gain (MEG)

Used for main counters

AdvanSiD

SiPM 2

ASD-NUV3S-P

Used for spare counters. 40 or 50 µm pich

AdvanSiD

Reﬂector

ESR2 Film

32µm tickness, ≥ 98% reﬂection

3M

Tedlar25 µm tickness

DuPontLight Shielding

Table 2.4: The basic properties of BC-422 from the datasheet [5].
Property

ValuesLight Output (% Anthracene)

55

Rise Time [ns]0.35

Decay Time [ns]1.6

Pulse Width (FWHM) [ns]1.3

Bulk Light Attenuation Length [cm]8

cm height counters are used since the typical radius of the positron trajectory becomes larger around the light blue regionin Fig. 2.39. The Mixed-PCB counters and L-shaped PCBs are used due to the steps of the support structure. The othercounters are composed of 4 cm height scintillator and ﬂat-type PCBs. Fig. 2.38 shows the example of a mounted ﬂat-type
counter and mounted L-shape counters.
Scintillator

The rising part of the output waveform is crucial for timing measurement. The Saint-Gobain BC-422 scintillator whoserise time was ultra-fast (0.35 ns) was, therefore, chosen for pTC. The properties of BC-422 scintillator are summarized inTable 2.4.

Chapter 2 MEG and MEG II Experiment44

Fig. 2.39: The pTC counter map [22]. Counter region is ∼20 –110 along the beam axis (z-axis) for both downstream andupstream.

Table 2.5: The datasheet values ( provided by AdvanSiD [6]) of SiPMs used for the pTC ounter.
Type (Year)

SiPM

Pixel Pitch

Vbr (20 ◦ C)

VOV from Vbr# of Counters

Type-I (2014)

ASD-NUV3S-P High-Gain (MEG)

50 µm

24 ± 0.3 V+2 – +3.5∼448+2 – +6∼ 48+2 – +6∼16

Type-II (2015)

ASD-NUV3S-P

50 µm

26 ± 0.1*9 V

Type-III (2018)

ASD-NUV3S-P

40 µm

26 ± 0.1 V

SiPM

The studies of readout conﬁguration with SiPMs were conducted [23]. The series and parallel connection of SiPMs, which
are well known as the advantageous method to increase the sensor coverage, were studied in the lab test. Those tests
were carried out using SiPMs from diﬀerent vendors. The total capacitance of series-connected SiPMs is smaller thanthat of a single SiPM, which results in the narrower output and faster rise time, while the wider output was measured
with the parallel-connected SiPMs as shown in Fig. 2.40. The advantage on the rising part is especially crucial for thetiming measurement, and ﬁnally, the series connection of 6 SiPMs from the AdvanSiD company was chosen for the pTC
readout*10 . Currently, 3 types of SiPMs (Type-I, II, III), as shown in Table 2.5, are used for pTC counters depending on thepurchase period. Fig. 2.41 shows the timing resolution of single counter used until 2019.
Temperature and Humidity Control Systems

A stable detector operation is highly important for a long-term experiment. Especially, the relatively large temperaturedependence of the SiPM performances aﬀects the pTC timing resolution. A temperature control system is mandatory.
For pTC cooling, cooled water is circulated by a chiller machine (custom chill Model : CRAL300-230PE, 400W) throughpipes of pTC support structure as shown in Fig. 2.42. When the pTC is operated in low temperature, for example 10◦ C,*9 The Min value of Vbr is 24 V and The Max value is 28 V. 26 V is the typical value and ± 0.1 V is the 2 σ from the mean value in the same production

lot.
*10 In [23], the best timing resolution was obtained with the series connection of 3 SiPMs from the Hamamatsu Photonics. However, the AdvanSiD

SiPMs were more reasonable than those, which means the number of SiPMs in one series-connection readout can be increased. The increase of thecoverage was more crucial for the pTC performance than the performance of the single SiPM. Thus, the the series connection of 6 SiPMs from theAdvanSiD was adopted for the ﬁnal design.

2.4 Positron Spectrometer

45

Fig. 2.40: The diﬀerence of the pulse shape with diﬀerent connections of 3 SiPMs (3-SiPM parallel, single, and 3-SiPM
series) with BC422 with HPK SiPM (S10362-33-050C) [23].

Fig. 2.41: The counter resolution measured in the lab-test with 4 cm counters (pink-line) and 5 cm counters (blue-line),
which include type-I and type-II SiPMs [24]. The histograms ﬁlled with pink and blue show the resolution with type-III
SiPMs for 4 cm and 5 cm counters, respectively.

dry-air from the PSI compressed air line ﬂushes pTC to avoid the water condensation.
The pTC temperature and humidity are monitored with three thermal sensors and one humidity sensor on each backplane,
respectively. The sensor positions are shown in Fig. 2.43. The operation test of the temperature control is explained inSec. 3.4.4.
Laser-based Calibration System

To achieve the target performance of the pTC, the calibration of the time-oﬀset of each counter is crucial. Two complementary methods were developed for the timing calibration: one is called laser-based calibration and the other is track-based

Chapter 2 MEG and MEG II Experiment46

Fig. 2.42: The support structure viewed from the bottom side [7]. Cooling pipes and laser optical ﬁbers can be seen.
COBRA
BP00
BP01

DS pTC Support ・・Structure・
BP31

Cooled dry air

Temperature sensor: 1-Wire digital thermometer(DS28EA00)
Humidity: HIH4000

Fig. 2.43: The schematics of humidity and temperature sensor positions.

calibration. The details of the calibration algorithm are summarized in Chap. 6. In this subsection, the hardware of thelaser-based calibration system is brieﬂy explained.
The laser calibration system is shown in Fig. 2.44. The optical components selected based on the detailed studies [51]are summarized in Table A.1 in Appendix A. The optical length of these components were measured in advance. The
pulse laser light, generated by PLP-10 from HAMAMATSU, is divided by optical splitters and injected into the counters
simultaneously for a timing synchronization among counters. Since the laser power is not high enough to illuminate all(432) the counters simultaneously, an optical switch was installed to control the illumination to the counters.

2.4.3

Cylindrical Drift CHamber (CDCH)

DesignThe design of the CDCH is inspired by the wire chamber used in KLOE experiment [52]. The MEG II CDCH has a
2 m-long single volume with a cylindrical shape. The inner radius is 17 cm, and the outer 29 cm. Low mass materials
for the inner foil (aluminized Mylar foil) and outer support structure (carbon ﬁber) were used to lessen the eﬀects of themultiple scattering. The ﬁlled gas is ultra-low mass mixture of helium and isobutane in the ratio 90:10. Fig. 2.45 shows
the CDCH structure. The total radiation length for a positron track is ∼ 1.5 × 10−3 X0 in the MEG II CDCH, while that was∼ 2.0 × 10−3 X0 in the MEG drift chamber.

2.4 Positron Spectrometer

1×12

PhotodiodeOptical fibre(10 m)×8

*2

Photodiode signal

SYNC signal

1×8

OpticalSwitch×8→→Detector Hut

Optical splitter

×432

To USSplitter
1×8→

Laser Hut

pTC



To DS

Counter signal

Outside

1×8

×64

→

→

Optical fibre(2.5 m)

Laser
Head

DAQ electronics

(a)

1x2
Splitter*2

x 32

→

x4

Optical switch

Counter

Splitter Box→

PhotodiodeLaser
controller

Splitter
1×8

*3*2

→

1×2
Mode scrambler

→

Laser
head

47

Mode
Scrambler(b)

Fig. 2.44: (a) Schematic and (b) picture of the laser-based calibration system for the MEG II pTC (from [25]). The
individual components are described in the Table A.1.

JPS Annual Meeting 2018 (25aL401-3)

MITSUTAKA NAKAO  Page: 2/20

Fig. 2.45: The mechanical sketch of cylindrical drift chamber [3].

The long volume of the CDCH is installed in parallel to the muon beam inside the COBRA magnet and just inner area ofthe pTC. The layout of MEG II detectors is shown in Fig. 2.7 and Fig. 2.31. Since there is no large gap between the CDCH
tracking volume and the pTC, the matching eﬃciency and ﬂight time estimation are expected to be signiﬁcantly improved.
The CDCH adopts a stereo-wire conﬁguration with 9 layers for the precise z-determination. The stereo angle varies from◦

6 (inner most) to 8.5◦ (outer most), and wires in the continuous two layers were tilted in the opposite directions. Fig. 2.46
is the picture after the CDCH is fully wired.Due to the stereo angle tilting, not a cylindrical but a hyperbolic proﬁle is seen.
Wires

Generally, a wire chamber is composed of three kinds of wires:Chapter 2 MEG and MEG II Experiment48

Fig. 2.46: The picture of CDCH mounted all wires [3].

Table 2.6: The CDCH wires.
Diameter

Number of wires

Al (Ag-plated)

50 µm

768

Cathode Field Wires

Al (Ag-plated)

40 or 50 µm

7680 (40 µm) /1728 (50 µm)

Anode Sense Wires

W (Au-plated)

20 µm

1728

Wires

Material

Guard Field Wires• The guard ﬁeld wires shape the electric ﬁeld lines at the edge of the CDCH.
• The cathode ﬁeld wires deﬁne the drift cells and make its ground mesh.
• The anode sense wires collect the charge induced by the positrons (i.e. detect the ionization of the gas throughavalanche).
In total, 11904 wires are used to form 1728 drift cells (192 cells per layer) for the MEG II CDCH. The structure of layers
in the CDCH is shown in Fig. 2.47, and the materials and diameter of these wires are summarized in Table 2.6*11 . From the
R&D studies [26], wires made of 5056 Al alloy*12 (94.6% Al, 5.2% Mg, 0.1% Cr and 0.1% Mn) with diameters of 40 µm
and 50 µm were chosen for the ﬁeld and guard wires, respectively. The wire is silver-plated. The density is 3 g/cm3 and its
resistivity is 20 Ω/m. For the anodes, 20 µm pure-tungsten (W) wires with gold plate are used. The density is 19.25 g/cm3
and resistivity 170 Ω/m. The nominal wire tension is deﬁned as 50% of the wire elastic limit, +∼4 mm.
The drift cells have almost square shapes whose side length is from 5.8/6.7 mm (at the center/endplate in the innermost
layer) to 7.5/8.7 mm (in the outermost layer) as shown in Fig. 2.48, and its isochrone on the drift time in the cell is shown in
Fig. 2.49. The average drift velocity measured with a test setup and a monitoring chamber is ∼ 2 cm/µs, and the drift time isroughly in the range of 0 – 250 ns. The single-hit resolution in the cell is measured to be σr ∼110 µm in the prototype test
[54]. The higher granularity design will increase the number of hits per reconstructed track by a factor of four compared to
the MEG experiment.
The wiring process, which includes the monitoring of the wire position, the alignment, the mechanical tension, and thequality of soldering between the PCB and wires, was conducted by a wiring robot [55].
*11 The 10-layer design is illustrated in this ﬁgure, but we adopted the 9-layer design and the outermost layer was omitted for the real detector.
*12 From California Fine Wire (CFW) company [53]

2.4 Positron Spectrometer

49

Fig. 2.48: Drift cell conﬁguration of MEG II CDCH. Top: SimpliFig. 2.47: The layer structure in the CDCH [26]. ﬁed sketch of a single drift cell (an anode circle and cathode circles
are depicted). Bottom: schematic view of the wires in the CDCH
[26].

Fig. 2.49: Isochrones for a single 6 × 6 mm2 drift cell [26]. The vertical color is ns. The drift lines are curved and theisochrone map is distorted by the magnetic ﬁeld.

Gas

The CDCH uses a helium (He) based gas mixture. A small amount of isobutane (C4 H10 ) is added as a quencher to avoid
self-sustained discharge. The ratio of He:C4 H10 is 90:10. The advantage of He-based gas mixture is its large radiation
length (X0 ∼ 1300 m), which minimizes multiple scatterings of the positrons. The drawback of this gas mixture is the highhelium ionization potential of 24.6 eV, resulting in the small number of primary electron pairs, which potentially worsens
the spacial resolution.

Chapter 2 MEG and MEG II Experiment50

Fig. 2.50: Front-end electronics for CDCH [3].

Electronics

High speed signal processing is necessary for the better separation of single ionization clusters*13 , a better timing measurement at the two ends for z determination, and the cross-ﬁtting waveform analysis algorithm (Sec. 7.1). A high performance
8-channel frontend electronics (FE) was developed for CDCH as shown in Fig. 2.50. The CDCH FE output is diﬀerential
output (DIFF) to improve the noise immunity. The signal is transmitted to the dedicated WDB (diﬀerential readout) through5m customized twisted-pair cables (Amphenol Spectra Strip SkewClear).

2.4.4

COnstant Bending RAdius (COBRA) Magnet

The COBRA magnet based on a superconducting solenoid was developed in the MEG experiment for the eﬃcient µ → eγ
signal-like positron measurement [27], and is also used for MEG II experiment. The COBRA magnet generates a gradientmagnetic ﬁeld with 1.27 T at the center of the COBRA and 0.49 T at both ends. The layout of the COBRA magnet isshown in Fig. 2.51. The advantages of the COBRA gradient magnetic ﬁeld compared to the uniform ﬁeld are illustrated
in Fig. 2.52. The positrons with the same momentum have the same projected bending radius (i.e. the dependence on
the positron emission angle is small). The positrons with low-longitudinal momentum are swept away quickly and theunnecessary pileup can be avoided. Positrons with lower momentum have the smaller radius and do not reach the CDCH
and pTC, which improves the high rate tolerance of the spectrometer.
Hit Rate of Positron Spectrometer with COBRA magnetic ﬁeld

Due to the gradient magnetic ﬁeld, the inner layer of the CDCH has a higher rate (1.8 MHz for each cell under the MEG II
nominal beam intensity with the simulation) than the outer layers (0.8 MHz). The occupancy of the CDCH, which is theprobability to have a hit in a cell in 250 ns, is expected to be 35% (inner layer) - 22% (outer layer), which is 3 - 4 times
higher than the MEG experiment. As for the pTC, the rate itself is not so severe; less than 0.1 MHz. However, the same
positron sometimes (2-3% from simulation) comes back into the pTC region more than twice. The algorithm for those
events was developed and described in Chap. 6.

*13 One of the largest motivation of this fast electronics is for cluster-counting technique proposed in [56]. This algorithm will further improve theimpact parameter resolution, but currently it has not yet been implemented in the MEG II oﬃcial analysis.

2.4 Positron Spectrometer

51

Fig. 2.51: COBRA magnet [27].
Fig. 2.52: The concept of the COBRA gradient magnetic
ﬁeld [1]. (a) Positrons with the same momentum have thealmost same bending radius, even with the diﬀerent emission angles. (b) Positrons with low longitudinal momentum
are quickly swept away.

53

Chapter 3

Investigation of Radiation Damage for pTC
In the 2015 commissioning, an unexpected rapid current increase of pTC channels (∼0.5 µA increase after just two days ofirradiation) was observed, which was correlated with the beam irradiation. Fig. 3.1 shows a typical example of the current
increase.
From the average current increase under the 7 × 107 µ/s beam irradiation at 30 ◦ C with the over-voltage ∼18 V, the darkcurrent of each channel, a few µA before the exposure, is estimated to reach ∼100 µA after 3-year data taking period. The
eﬀects of the radiation damage in the pTC were investigated and mitigation strategies were studied, which are summarized
in this chapter. The full details on this topic are published in [31].

3.1

Radiation Damage on Series Connected SiPMs

The degradation of SiPMs due to the radiation damage is a major concern especially for high intensity experiments orlong-term experiments. Many studies on the radiation damage on SiPMs are reported as summarized in [57]. Nevertheless,the detailed studies on its eﬀects on the timing resolution of a scintillation counter and impacts to series connected SiPMs
have not been reported.
The series connection of multiple SiPMs shows some peculiar features. When n SiPMs with the identical electricalFig. 3.1: The pTC current of each channel (16 channels are shown with colored lines) in 2015 commissioning.

Chapter 3 Investigation of Radiation Damage for pTC

54

Table 3.1: Summary of the damage level of the SiPMs.
SiPM

Φeq [n1MeV /cm2 ]note#1 - #6#7 - #8#9 - #10#11 - #14

3 × 10
8.7 × 108
5.5 × 109
0 (or negligible)

Electron irradiation with 90 Sr step by step
Neutron irradiation at LENA
Neutron irradiation at LENA
Re-used from broken pTC counters9properties (breakdown voltage, dark current etc.) are connected in series, the total capacitance and the eﬀective charge
gain become 1n , while the eﬀective breakdown voltage, which is the voltage needed to apply the breakdown voltage toeach SiPM, becomes n times higher. A common current ﬂows through all the SiPMs connected in series, which results in
diﬀerent bias voltages for the individual SiPMs when the electrical properties of each SiPM are not identical.

3.2

Total Fluence

The estimated total ﬂuence during the MEG II DAQ full period (20 weeks × 3 years) is ∼ 8 × 1010 e+ /cm2 at the high-rate
region (∼100 kHz) and this is equivalent to Φeq ≈ 4 × 109 n1MeV /cm2 with the assumption of the eﬀective Non Ionizing
Energy Loss (NIEL) theory*1 [59].

3.3

Irradiation on SiPMs

The main goal of the lab tests is:• Study the radiation damage eﬀect on series connected SiPMs.
• Evaluate the performance degradation after the 3-year data taking.
• Establish the strategy to mitigate the deterioration.

3.3.1

SiPM Irradiation

SiPMs from AdvanSiD (ASD-NUV3S-P High-Gain (MEG), type-I) were used for the evaluation. The SiPMs were irradiated at the diﬀerent several dmage levels as summarized in Table 3.1. Six SiPMs (#1-#6) were irradiated with intenseelectrons from 37 MBq 90 Sr sources for 280 hours in total, which is equivalent to Φeq ≈ 3 × 109 n1MeV /cm2 . The irradiation
was separated into four steps, each 70 hours long, and no bias voltage was applied to the SiPMs during the irradiation.
The impact to the series connected SiPMs was evaluated with the diﬀerent set of SiPMs irradiated with electrons andneutrons. The details of SiPM patterns and characteristics are summarized in Appendix B*2 . Some characteristic phenomena by the series connection of diﬀerently damaged SiPMs were observed, and the dominant eﬀect was the current increase,which is described in this chapter. Another eﬀect by the hit position dependence is discussed in Sec. 6.5.6. In the appendix,
the irradiation test of ASD-NUV3S-P model (type-II) at the Beam Test Facility (BTF) is also summarized.

*1 Φeq is used for the comparison between the lab test in the following sections. Here the bulk damage, which is the silicon lattice defects and causes

the dark current increase, was focused. The impact of the surface damage, which generates the charges in dielectric parts of SiPMs, was not focusedsince the pTC absorbed dose of ∼ 20 Gy is small enough to be neglected by taking the result of Ref. [58] into account.
*2 The combination of 6 SiPMs are classiﬁed into four groups: Pattern-A - Pattern-D in this appendix. In this section, all of the SiPMs were irradiatedwith electrons equally and this combination corresponds to “Pattern-D”.

3.4 Eﬀect on pTC Performance by Dark Current Increase

3.4

55

Effect on pTC Performance by Dark Current Increase

The eﬀect of the dark current increase by the radiation damage was evaluated with SiPMs which were irradiated withelectrons step by step.

3.4.1

IV Curves for Each Damage Level

Figures 3.2a–e show the dark current Idark versus bias voltage Vbias (I-V curves) of each of the six electron-irradiated SiPMs(taken at 0.1 V steps), and Fig. 3.2f shows the breakdown voltages of SiPMs at each irradiation step. The breakdown voltage
Vbr is calculated from the maximum point in the second-derivative of the logarithm of Idark with three-point smoothing [60]and the systematic uncertainties are estimated from the change by diﬀerent-point smoothings. The signiﬁcant dark current
increase was observed after each irradiation step, but no signiﬁcant changes of the breakdown voltage and the IV-curve
shape were observed. Figs. 3.2g–h show the I-V curves when they are connected in series. When SiPMs were cooled from30◦ C to 10◦ C, the dark current increase by irradiation was mitigated.

3.4.2

Timing Measurement Setup

The deterioration of the timing resolution was evaluated using a test scintillation counter. Fig. 3.3 shows the test setup forthe timing measurement. A scintillator and 6 SiPMs connected in series are aligned with a special jig made by a 3D printer.
The electrical contacts with the SiPMs are made using spring probe pins so that the series circuit can be made each time
without soldering. The electrons from a 3.7 MBq 90 Sr source are injected to the center of the test counter. The trigger signal
is made by a small scintillation counter (a 5 × 5 × 5mm3 scintillator (BC422) readout by a SiPM (Hamamatsu Photonics
S10362-33-050C)), whose timing resolution is much better (σt ∼ 30 ps) than that of a single counter with one-side readout(σt ∼ 100 ps). The output signals were ampliﬁed and shaped through a two-staged voltage ampliﬁer with a pole-zerocancellation (PZC) ﬁlter. The schematics of the ampliﬁer is shown in Fig. 3.4. The signal waveforms were recorded using
the DRS4 chip at 1.6 GSPS. The temperature of the MEG II pTC is controlled by the chiller systems. The test counter is put
inside a thermal chamber and the measurements were performed at 30◦ C and 10◦ C, which correspond to the temperature in
the experimental area and the temperature achieved with the chiller system, respectively. For the timing pick up, the digitalconstant fraction method (CFD) was applied to the waveforms. The timing when the waveform reaches a certain fraction(CFD fraction) of the peak point is extracted.

3.4.3

Deterioration of Time Resolution

Fig. 3.5 shows the example of the waveforms after each irradiation step. Clear increase of the baseline ﬂuctuation by thedark noise was seen, but as for the signal height no signiﬁcant change was observed (0.15 - 0.16 V from the most-probablevalue of its Landau-like distribution). Fig. 3.6 shows the results of bias voltage scan at each electron irradiation step. As
explained above, the measurement was performed at 30◦ C and 10◦ C. The data were analyzed with a ﬁxed CFD fractionof 20%. The resolution ﬁrst improves with Vbias due to a higher gain and PDE, but at some voltage starts to deteriorate
due to increased dark counts. As the ﬂuence increases, the optimal voltage, where σt reaches the minimum, shifts to lower
voltages.
Fig. 3.7 shows the timing resolution at three applied voltages around the optimal resolutions in the bias scan. The CFD
fraction is optimized in steps of 10% from 10% to 60% for each dataset. As SiPMs are irradiated with more electrons
and the dark current (Idark ) increases, the measured timing resolution (σt ) becomes worse. The deterioration of the timing
resolution is due to an increase of the baseline ﬂuctuation caused by the dark noise: an increase of NRMS . The correlation

Chapter 3 Investigation of Radiation Damage for pTC

56

102

#1

#1

102

#2

10

#2

#3

#3

10

1

#4

I dark [µA]

I dark [µA]

#4
#5
#6

10−1
10−2

1

#5
#6

10−1
10−2

10−3
22

23

24

25
V bias [V]

26

27

10−3
22

28

23

(a) Before irradiation.

102

#1

102
10
I dark [µA]

I dark [µA]

27

28

#1

#3
#4

#5
#6

10−1
10−2

1

#5
#6

10−1
10−2

10−3
22

23

24

25
V bias [V]

26

27

10−3
22

28

(c) After 140 hours irradiation.

102

26

#2

#3
#4

1

25
V bias [V](b) After 70 hours irradiation.

#2

10

24

23

24

25
V bias [V]

26

27

28

(d) After 210 hours irradiation.
24.5

#1
#2

10

24.4

#3

V br [V]I dark [µA]

#4

1

#5
#6

24.3
#1

10−1

24.2

10−2

24.1

#2
#3

#5

10−3
22

23

24

25
V bias [V]

26

27

102

102

10

10

1
10−1

No irradiation
Φeq~7.5×108 cm−2
Φeq~1.5×109 cm−2
Φeq~2.3×109 cm−2
Φeq~3.0×109 cm−2

10−2

145

150

155
V bias [V]

160

#6

0

1
2
Φeq [109 cm−2]

3(f) Breakdown voltages of single SiPMs versus ﬂuence.

165(g) Six series-connected SiPMs at each irradiation step at 30◦ C.

I dark [µA]

I dark [µA]2428(e) After 280 hours irradiation.

10−3

#4

1
10−1

Φeq~7.5×108 cm−2
Φeq~1.5×109 cm−2
Φeq~2.3×109 cm−2
Φeq~3.0×109 cm−2

10−2
10−3

145

150

155
V bias [V]

160

165

(h) Six series-connected SiPMs at each irradiation step at 10◦ C.

Fig. 3.2: The I-V curves of the six electron-irradiated SiPMs. The I-V data of each SiPM were taken at 30◦ C (a–e), and thebreakdown voltages are plotted in (f). The I-V data of six series-connected SiPMs were taken at 30◦ C (g) and 10◦ C (h).

3.4 Eﬀect on pTC Performance by Dark Current Increase

57

Fig. 3.3: The timing resolution measurement setup for the radiation tolerance test.

100 pF

1.2 k

1.2 k

100 nF

100 nF+U+12 V
100 nF 1 mF

100 nF

100 nF

560
TCCH-80+

1.2 k

10 k

TCCH-80+OutIn
100 nF
50

SiPM chain

150
100 nF
10 k

P attenuator

100 nF

22 pF

100 nF

100 nF

MAR-6SM 10 k

MAR-6SM
0–2 k

Pole-zero cancellation

Fig. 3.4: The schematics of the ampliﬁer [23]. The pole-zero cancellation ﬁlter can be applied by tuning the adjustable
resistor in the circuit.

between Idark and NRMS , and that between NRMS and σt are also shown in Fig. 3.8 and Fig. 3.9.
The measurement with Vover ≈ 16 V after the full irradiation (the marker with the largest Idark in the same Vover in
Fig. 3.7) for 3-year data taking with a typical hit rate region (∼ 80 kHz) shows the expected deterioration of the pTC
counters*3 from the no-damaged measurement is 41% at 30 ◦ C. The deterioration can be suppressed to 13% at 10◦ C. When
50 ps timing resolution of gamma-ray measurement and 35 ps timing resolution of positron measurement are assumed, the
41% deterioration of the positron timing measurement at 30◦ C will worsen teγ from 61 ps to 70 ps, while at 10◦ C to 64
ps. In conclusion, operating the pTC at 10◦ C with the chiller system can be a reasonable solution to recover the timing
resolution.

3.4.4

Cooling System for pTC

In the 2017 commissioning, the temperature control (cooling) system with chiller for pTC was installed and tested. The
temperature and humidity were monitored by the sensors on the pTC backplanes as shown in Fig. 2.43. The goal of theoperation temperature was 10◦ C. Since the water condensation was a crucial problem at the low temperature in 2017, the*3 Note that the double-side readout is adopted for the pTC counters, and the absolute resolution becomesﬁgures.

√2 times better than the values in theChapter 3 Investigation of Radiation Damage for pTC
Amplitude [mV] Amplitude [mV] Amplitude [mV] Amplitude [mV] Amplitude [mV]

58
200
150
100

(a) Before: 2 µA

50
0
−50
200
150
100

(b) Φeq ~ 7.5×108 cm−2: 53 µA

50
0
−50
200
150
100

(c) Φeq ~ 1.5×109 cm−2: 94 µA

50
0
−50
200
150
100

(d) Φeq ~ 2.3×109 cm−2: 126 µA

50
0
−50
200
150
100

(e) Φeq ~ 3.0×109 cm−2: 155 µA

50
0
−50

−600

−400

−200

0

Time [ns]Fig. 3.5: The example of the waveform at each damage level.

operation temperature was 20◦ C in the 2017 commissioning.
In 2018, a ﬂowing system of cooled dry air with a heat exchanger and a chiller was prepared and tested. The temperature
was stable enough and the humidity became a safe level*4 . The whole system in the experimental area is shown in Fig. 3.10.
In 2019, the arrangement of air lines and water lines was improved, and the heat insulating materials were added for eﬃcientcooling and to avoid water condensation around the pipes. Fig. 3.11 shows the insulated pipes and the ﬂows of water anddry air.
Fig. 3.12 shows the monitored temperature and humidity on pTC in 2018 at 10◦ C setting. The humidity was in the safe
level (∼ 50%) and the temperature was very stable around 10◦ C.

*4 During the commissioning we set the safety threshold of the humidity for 70%.

3.4 Eﬀect on pTC Performance by Dark Current Increase

240

59

No irradiation, 30 °C

2408Φ eq~7.5× 10 cm −2 , 30°C
9220

Φ eq~1.5× 10 cm −2 , 30°C
9

Φ eq~3.0× 10

160

180
160

140

140

120

120
10

Φ eq~2.3× 109 cm −2 , 10°C

200

180

100
5

Φ eq~1.5× 109 cm −2 , 10°C

Φ eq~3.0× 109 cm −2 , 10°C

cm −2 , 30°C

σ t [ps]σ t [ps]

200

220

9

Φ eq~2.3× 10 cm −2 , 30°C

Φ eq~7.5× 108 cm −2 , 10°C

15
V over [V]

100
5

20

10

15
V over [V]

20

170

170

160

160

150

150

140

140

σ t [ps]σ t [ps]

Fig. 3.6: Timing resolution versus over-voltage at 30◦ C (left) and 10◦ C (right). The CFD fraction is 20%.

130
120

V over 11.1--11.6 V (30°C)
V over 13.6--14.1 V (30°C)

110
100
0

V over 16.1--16.6 V (30°C)

50100
I dark [µA]

130
120

V over 16.3--16.6 V (10°C)

110
100
0

150

V over 13.8--14.1 V (10°C)
V over 18.8--19.1 V (10°C)

50

100
I dark [µA]150

Fig. 3.7: The timing q
resolution with the diﬀerent damage level at the ﬁxed 3 applied voltage (157.5, 160 and 162.5 V). The

dashed curves σt =βIdark + σ20 are ﬁtted to the data.

1098
N RMS [mV]

7
6
5
4

Vbias = 162.5 V

3Vbias = 160.0 V

2

Vbias = 157.5 V

1
0
0

50

I dark [µA]

100

150

Fig. 3.8: qRelation between the dark current and the RMS noise at 30◦ C for three applied voltages. The dashed curves
NRMS =

αIdark + N02 are ﬁtted to the data.

Chapter 3 Investigation of Radiation Damage for pTC

60

170
160

σ t [ps]

150
140
130
120

V over 11.1--11.6 V (30°C)
V over 13.6--14.1 V (30°C)

110
100
0

V over 16.1--16.6 V (30°C)

2

4
6
N RMS [mV]8

10

Fig. 3.9: Relation
between the RMS noise and the timing resolution at 30◦ C for three applied voltages. The dashed curvesq
are σt =2γNRMS+ σ20 ﬁtted to the data.

Fig. 3.10: The system for pTC cooling. The pictures for a chiller, water pipes, a heat exchanger, air lines are also shown.

3.4 Eﬀect on pTC Performance by Dark Current Increase

Fig. 3.11: The picture of pTC for the low temperature operation.

Fig. 3.12: The temperature and humidity measured on the pTC sensors.

61

63

Chapter 4

Commissioning Runs from 2017 to 2019
In this chapter, the commissioning of the positron spectrometer performed between 2017 and 2019 is summarized.

4.1

Commissioning Overview

Main topics in each year are summarized below:• 2017: Test of the full pTC counters, performance evaluation with muon beam.
• 2018: First operation of the CDCH, preparation of the cooling system for pTC (stable 15◦ C operation).
• 2019: CDCH stability studies, stable 10◦ C operation of the pTC.

4.2

Status of Detectors

In 2017, the construction of the pTC counters was completed and the assembled detectors were installed in the experimental
area to be tested with beam. The mock-up CDCH was also installed, which was made of the same materials as the realdetector, 2 mm thick carbon ﬁber for the outer frame, 20 µm thick Mylar ﬁlm for the inner frame, and one sector of theanode wires and related electronics. The same gas mixture was used during 2017 commissioning. 2017 was the only year
in which both pTC (US / DS) were installed. However, up to 256 counters were readout at the same time due to the limited
number of the readout electronics. In 2017, the pTC was operated at 20◦ C and in 2018 and 2019, it was operated at 10◦ C.
The CDCH was delivered to PSI*1 and installed in 2018. In 2019, the design of the readout electronics for the CDCH was
ﬁxed and small number of the ﬁnal version WDB was installed. However, due to the instabilities of the CDCH, data taking
with the muon beam was not achieved. Instead, the data taking with cosmic rays was performed to obtain the waveform
data. The number of the readout channels for each detector during the commissioning 2017 – 2019 is summarized inTable 4.1.

4.3

DAQ for Positron SpectrometerIn this section, the DAQ status of the positron spectrometer is summarized.

4.3.1

Readout Channels

The readout channels assigned for pTC and CDCH in each year are summarized in this subsection.

*1 Considering the whole schedule of MEG II experiment, the wiring of the most outer layer (10-th layer) was omitted so that the construction can becompleted by the beam time in 2018. The eﬀect of losing one layer was an eﬃciency loss by roughly 10%, but this loss was found to be recoveredby the analysis reﬁnement and optimization.

Chapter 4 Commissioning Runs from 2017 to 201964

Table 4.1: The number of the maximum readout channels for pTC and CDCH each year.
pTC DAQ channels (counters)

CDCH cells

2017

512 (256)

N/A (mock-up CDCH)

2018

256 (128)96 (prototype WDB)

2019 Oct256 (128)96 (prototype WDB)

2019 Nov

256 (128)96 (prototype WDB) + 96 (ﬁnal version WDB)

30*φ

Year

10
0

496 480 464 448 432 416 400 384 368 352 336 320 304 288 272 256−10

498 482 466 450 434 418 402 386 370 354 338 322 306 290 274 258−20500 484 468 452 436 420 404 388 372 356 340 324 308 292 276 260

−30
−40
−50

1 17 33 49 65 81 97 113 129 145 161 177 193 209 225 241
2 18 34 50 66 82 98 114 130 146 162 178 194 210 226 242

499 483 467 451 435 419 403 387 371 355 339 323 307 291 275 259

3 19 35 51 67 83 99 115 131 147 163 179 195 211 227 243
4 20 36 52 68 84 100 116 132 148 164 180 196 212 228 244

501 485 469 453 437 421 405 389 373 357 341 325 309 293 277 261

5 21 37 53 69 85 101 117 133 149 165 181 197 213 229 245

502 486 470 454 438 422 406 390 374 358 342 326 310 294 278 262

6 22 38 54 70 86 102 118 134 150 166 182 198 214 230 246

503 487 471 455 439 423 407 391 375 359 343 327 311 295 279 263

7 23 39 55 71 87 103 119 135 151 167 183 199 215 231 247

504 488 472 456 440 424 408 392 376 360 344 328 312 296 280 264

8 24 40 56 72 88 104 120 136 152 168 184 200 216 232 248

505 489 473 457 441 425 409 393 377 361 345 329 313 297 281 265−60

506 490 474 458 442 426 410 394 378 362 346 330 314 298 282 266−70

508 492 476 460 444 428 412 396 380 364 348 332 316 300 284 268−80

510 494 478 462 446 430 414 398 382 366 350 334 318 302 286 270−90

0 16 32 48 64 80 96 112 128 144 160 176 192 208 224 240

497 481 465 449 433 417 401 385 369 353 337 321 305 289 273 257

9 25 41 57 73 89 105 121 137 153 169 185 201 217 233 249
10 26 42 58 74 90 106 122 138 154 170 186 202 218 234 250

507 491 475 459 443 427 411 395 379 363 347 331 315 299 283 267

11 27 43 59 75 91 107 123 139 155 171 187 203 219 235 251
12 28 44 60 76 92 108 124 140 156 172 188 204 220 236 252

509 493 477 461 445 429 413 397 381 365 349 333 317 301 285 269

13 29 45 61 77 93 109 125 141 157 173 189 205 221 237 253
14 30 46 62 78 94 110 126 142 158 174 190 206 222 238 254

511 495 479 463 447 431 415 399 383 367 351 335 319 303 287 271

−100

−50

15 31 47 63 79 95 111 127 143 159 175 191 207 223 239 255

0

50

100
z (cm)

Fig. 4.1: The pTC counter map with identiﬁcation number (0-511). In 2017, all of the counters (512) were tested, in 2018and 2019 128 counters were tested (# 128 - 255 in 2018 and # 304 - 431 in 2019). The colors of the counters show thecounter types (inner magenta: 4cm-L, yellow: 4cm-Mix, light blue: 5 cm-Flat, outer magenta: 4cm-Flat).

pTC Readout

In 2017, 512 WDB channels (for 256 counters) were assigned to the pTC, so the pTCs in the US and DS were tested
separately. In 2018 and 2019, 256 WDB channels were assigned at the maximum, so the half of DS counters (# 128 - 255
in Fig. 4.1) in 2018 and the half of US counters (# 304 - 431 in Fig. 4.1) in 2019 were read for the data taking for the
positron spectrometer. Fig. 4.1 shows the geometry net of pTC counters with the counter-identiﬁcation number (# 0-255
for DS counters and # 256-511 for US counters).
In 2018 the readout counters of the pTC were selected based on z-position dependence on the CDCH hit rate. However,
the reduction of gain at large z of CDCH was observed and the good positron tracks were less observed. In 2019, thecentral part of the upstream pTC counters were selected to maximize the number of the good positron tracks with the pTC
readout and the CDCH hits in the smaller z region. Considering the test of pTC sub-systems (laser, cooling and installationmaterials), the US pTC was installed in 2019 since the test of the sub-system for DS pTC was performed in 2018.
pTC Operation Voltage and Temperature

The operation voltage of the pTC counters was tuned to be +∼16 – 19 V from the breakdown voltage (equivalent to ∼ 4µA
dark current) for counters with type-I SiPMs, which gave the best timing resolution on average in the lab test. The counterswith type-II SiPMs had the wider operation range than the type-I SiPM counters, and the operation range was tuned to be∼22 – 23 V based on the results of the lab test. Since the cooling equipment (especially monitoring and humidity control
system) was not suﬃcient in 2017, the operation temperature was controlled to be 20◦ C.

4.3 DAQ for Positron Spectrometer

65

Fig. 4.2: The CDCH readout in 2018 commissioning [26]. Data acquisition was conducted

Fig. 4.3: The CDCH readout in 2019 commissioning [26]. Datawith the readout in S3 (L1-3) and S4 (L1-3).

acquisition was conducted mainly with the readout in S4 (L1 - 6).

In 2018, the cooling system was prepared and tested. The sensors for temperature and humidity were attached andmonitoring system was prepared in the experimental area. However, it was soon found that the simple wrapping with 20µm
PE ﬁlm was not suﬃcient for the sealing, and the air ﬂow was too weak to keep the safe humidity at 10◦ C. In addition, thewater condensation around the water pipe was found during operation. The safe temperature for the pTC was 15◦ C in 2018.
In 2019, the ﬂow rate of the dry air was increased by replacing the air tubes for the pTC and air pressures. The water
pipes were wrapped with the thermal insulation tubes and tapes. The wrapping of the pTC with the PE ﬁlm was also added
to increase the airtightness. The pTC was operated at 10◦ C stably during the commissioning period.
CDCH Readout

The fraction of the CDCH readout channels was ∼6% (96 wires) in 2018 and in the ﬁrst period of 2019, and ∼12% (192
wires) in the second period of 2019. The CDCH layer number was deﬁned as L1 – L9 from the outer to the inner layer.
The CDCH readout channels were divided into 12 sectors by every 16 channels. The sector number, S0 – S11, was deﬁned
counter-clockwise from the US-side view. The assigned readout cells for the 2018 and the 2019 commissioning (ﬁrst half)
are shown in Fig. 4.2 and Fig. 4.3. The additional 96 channels were assigned to S5, from L3 to L8.
In the ﬁrst half of 2019, two conﬁgurations were prepared for the CDCH data taking. One is called outer-conf, which
covers L1 – L6 in S4, and the other is inner-conf, which covers L4 – L6 and L8 – L9 in S4 and L7 in S5 (due to the FE
issue). In the second half of 2019, the ﬁnal version of WaveDREAM with the diﬀerential input*2 from the CDCH readout,
was ﬁnally installed and the readout channel increased from 96 to 96 (prototype) + 96 (ﬁnal type). The additional 96
channels were assigned to S5, from L3 to L8 with the outer-conf channels. In this thesis, the outer-conf was used for the
analysis of the cosmic-ray data. However, when the muon beam run was started, unexpected high current was observed inmany channels. The detector commissioning in 2019 was, therefore, ﬁnished without the enough muon beam data taking.
After the commissioning the detailed investigation for this abnormal current was conducted and the discharge problem wasfound.

*2 To use the prototype WDB (with single-end input), we had to convert the diﬀerential (DIFF) output from the CDCH to the single-end (SE) input

for the WDB. The DIFF-to-SE intermediate convertor was prepared and used in 2018 and 2019.

Chapter 4 Commissioning Runs from 2017 to 2019

66

CDCH Operation Voltage

The nominal HV value set for 2018 run with a gas mixture He : iC4 H10 = 90 : 10 were 800V on outer guards, 1480V on
L1 – L3, and 920V on L4 used as a guard layer*3 . The applied voltage was scanned in the range of 1460 – 1540 V for the
study of the gas gain and the stability check with several beam intensities (e.g. 6 × 106 , 1.34 × 107 , 3 × 107 , and 7 × 107 ).
The test with lighter gas mixture (He : iC4 H10 = 93 : 7) was also performed for the study of the gas gain [26].
After the 2018 commissioning, the extra wire stretching was performed to increase the cell stabilities. The nominal HV
setting in 2019 was 1480 – 1400 V in L1 – L9 every 10V step, i.e. 1480V for L1, 1470V for L2, ..., 1400V for L9, andguard wires were 700V with a gas mixture He : iC4 H10 = 90 : 10.

4.3.2

Triggers for Positron Spectrometer

Trigger Muon Beam

The single-counter trigger is mainly used for the DAQ of the positron spectrometer, i.e. if there are hits in the pTC counters
the waveform information from the DRS chips are recorded. Trigger rate was limited by the prototype data transfer system(around 3 – 5 Hz in 2017 and 5 – 6 Hz in 2018 - 2019 under the MEG II nominal intensity) , which will be improved to be
10 Hz in the future commissioning.
Trigger Cosmic Ray

The cosmic-ray counters (CRC), each of which is composed of a scintillation bar (4.0 × 4.0 × 79.6cm3 , Saint-Gobain
BC404*4 ) and two photo-multipliers (R5934 HAMAMATSU) at both ends. These components were reused from the MEG
timing counter. The cosmic ray tracks passing through the CDCH in the z-range of -40 cm – 40cm are triggered.
Other Triggers

In addition to the above triggers, a pedestal trigger, which is used for the study of the noise in the waveform baseline, anda laser trigger, which is used with the synchronization pulse from the laser controller for the laser-based calibration of thepTC (explained later), were used.
Synchronization between WDB

As described in Sec. 2.3.6, a main clock signal is distributed to each WDB from the ancillary board, and the PLL manages
the synchronization with the accuracy of ∼10 ps*5 . Then the synchronization is reﬁned in the oﬄine analysis by using
the sine waveforms from the PLL chips, resulting in 20 ps accuracy at 2 GSPS. The speciﬁc correction for the online
synchronization in 2018 – 2019 is summarized in Appendix C.

4.3.3

Muon Beam Rate

The data taking under the muon beam was conducted in the πE5 beamline at PSI. The muon beam rate was measured at
the center of COBRA for diﬀerent beam-line conﬁgurations using a dedicated set-up at the beginning of each year of beamtime and tuned by adjusting the beam slits. The muon stopping rate was calculated with the stopping eﬃciency in the MEG
II target of 85% evaluated with a MC study. The beam rate was lower than expected in 2017 due to the removal of a target*3 For CDCH operation, the HV working point for the gas gain 5 × 105 with He : iC4 H10 = 90 : 10 is expected as the nominal setting. The typical

HV values are around 1450 V with the +3.8 mm tension in 2018 as shown in [26], so the detailed analysis in the following chapter uses the datawith the applied voltage of 1460 V.
*4 https://www.crystals.saint-gobain.com/sites/imdf.crystals.com/files/documents/bc400-404-408-412-416-datasheet.pdf*5 The actual accuracy of the online synchronization is limited by the jitter in the DRS chips and it will be ∼60 ps.

4.3 DAQ for Positron Spectrometer67

in another line and a lower proton current (∼1380 - 1500µA, while 2200µA was nominal assumption). To recover this eﬀect
the muon beam was tuned to be 30% higher than the nominal setting, resulting in 5.6 − 6.1 × 107 µ/s. On the other hand,
the rate was higher in 2019 due to a problem with the beam blocker during the measurement, resulting in 10 - 20% higher
rate than 2018.

4.3.4

Data Size

In 2017, the pTC data was accumulated about 10 days with MEG II nominal intensity. The accumulated data was about
2,000,000 events (∼900,000 events for upstream and ∼1,300,000 events for downstream), which were used for the analysis
in the following chapter.
In 2018, the CDCH had many kinds of request related on the studies for the detector operation (current stability, gas gain
study, and so on). So the beam condition (beam instensity, cosmic rays, or pedestal) and the CDCH settings (HV scan, gastype) were changed many times. The accumulated data for each settings were not so large, (O(1000) events – O(100,000)
events) but suﬃcient to see the waveforms and S/N situation at each settings.
In 2019, the pTC and the CDCH data taking was performed about ∼20 days. In this period, the muon beam was changed
several times to study the gas gain, the stability of the detector, and so on. Due to the several instabilities, large noises, andreadout problems, suﬃcient data acquisition with the 2019 muon data was not completed, and the most of the period wasused to investigate the detector stabilities. The cosmic ray data was accumulated in the latter half of the period and analyzed
to understand the noise situation of the CDCH with the ﬁnal version electronics.

69

Chapter 5

Overview of Positron Analysis Flow
In this chapter, the overview of the positron analysis ﬂow in the MEG II experiment is described.

5.1

Data Flow

The MEG II analysis framework with experimental data or MC samples is summarized in Fig. 5.1. The online DAQ system
is based on Maximum Integrated Data Acquisition System (MIDAS) developed at PSI and TRIUMF [61]. Through the
MIDAS system the experimental apparatus is operated and the experimental information is stored in a compressed data
format. The oﬄine software for MEG II is based on ROOT-based Object oriented MIDAS Extension (ROME) [62], which
is developed in the MEG experiment and designed as a general purpose software for the experiment with the MIDAS
system. The key concept of ROME is to generate most of the codes of a project except the algorithm part. The experimental
framework is written in XML deﬁnition ﬁles compactly, and then ROME generates the speciﬁc class and framework out ofit.
For the analysis of experimental data, the ﬁrst step is the waveform analysis. Especially, noise reduction and clock
synchronization are performed to the experimental data (.mid.gz ﬁle in the ﬁgure) and .root ﬁles (called raw ﬁles) are
generated. This analysis part is separated from the other analysis chain since this part is applied to all the detectors andFig. 5.1: The overview of the MEG II analysis framework.

Chapter 5 Overview of Positron Analysis Flow70

not iterated so many times*1 . By using the information from the raw ﬁle, reconstruction algorithms are applied and thenecessary variables are extracted and stored in a .root ﬁle (called rec ﬁles).
For the analysis of simulation data, processes for event generation and event mixing are placed before the analysis of raw
ﬁle.

5.2

Event Generation

The event generation framework is summarized in the following subsections.

5.2.1

Simulation of Interactions

For the event generation and the simulation of the physics interactions with the detector materials, the software called gem4
is used. Gem4 is based on the GEANT4 [63] (version 4.10 [64]), which is a toolkit for the simulation of particle interaction
in matters written in C++. GEANT4 oﬀers comprehensive physics processes, for example electromagnetic, hadronic, andoptical processes over a wide energy range and with diﬀerent kinds of materials and elements.
Gem4 simulates kinematics of muon decay events (Michel, RMD, and µ+ → e+ γ) and interactions between the detectormaterials and particles from those decays. The information of positrons, for example, the trajectory, momentum, timing,
particle type, is recorded and used to evaluate the performance of the algorithms. This information is often called MC-truthor truth compared with the reconstructed information, and stored in the sev ﬁle (sub-events ﬁle).

5.2.2

Simulation of Detector Response

To simulate the detector response in a high rate environment, the µ+ → e+ γ signal decays and Michel decays are generated
separately with gem4, and then the Michel events are mixed into the µ+ → e+ γ events at the equivalent rate of 7 × 107
Hz. The triggered-timing region in the waveform is deﬁned by the signal decay and the background Michel positrons
are randomly distributed over the time according to Poisson distribution, i.e. simulated signal waveform with background
Michel positrons is counted as an “event”. The merged information ﬁle is called sim ﬁle, which contains the MC truth(kinematics at the vertex, incident point to the detectors, incident timing, positron sources - signal or Michel decay, andso on) for all of the positrons in events. The ionization process and its space-time relation in a CDCH cell is simulatedwith Garﬁeld++*2 . The response of the electronics is simulated with the SPICE software [65] and convoluted in the signal
waveform. The noises are added at the end of the waveform generation. Currently, the white noise with 2 mV as mean
amplitude, which was observed in the commissioning 2018, is added to the CDCH waveform simulation. As for the pTC
noise simulation, the parameters of the dark count rate, the probabilities of the secondary noises (cross talk, after pulse,
delayed cross talk), the recovery time of the SiPM were measured and implemented. The details of the measurement andthe parameters are reported in my master thesis [28]. The simulated waveform data are stored in the raw ﬁle in a sameformat as the real data.

5.3

Positron Reconstruction Chain

Fig. 5.2 shows the overview of the positron reconstruction chain, which consists of pTC analysis, CDCH analysis, andpTC-CDCH combined analysis. The goal of the pTC analysis is to obtain the positron crossing timing, and that of the*1 In addition to the time saving, this process can be used for the physics analysis such as blind analysis. MEG II adopts the blind analysis and thecollaborators must not access the MIDAS ﬁles.
*2 Garﬁeld/Garﬁeld++ is developed at CERN for the detailed detector simulation based on ionization measurement in gases and semiconductors,

https://garfield.web.cern.ch/help/ (Garﬁeld) and https://garfieldpp.web.cern.ch/garfieldpp/ for Garﬁeld++.

5.4 Updates from MEG II Oﬃcial Previous Studies

71

Fig. 5.2: The overview of the MEG II positron reconstruction algorithms.

Fig. 5.3: The ﬁxed combinations of counters used in [7] for the evaluation of the pTC resolution.

CDCH analysis is to obtain the “state” (i.e. best estimate of positron’s kinematic parameters and those covariance) vector
at the target. The pTC-CDCH combined analysis reconstructs “global tracks” from the pTC tracks and CDCH tracks. The
quality of global tracks were then carefully checked with several criteria in the track selection for the physics analysis.

5.4

Updates from MEG II Ofﬁcial Previous Studies

In this thesis, the data from 2017 is mainly used for the pTC analysis and obtained performances are compared with theprevious studies [7]. In the previous work, the timing resolution of the pTC was evaluated with “even-odd” analysis as thedetails are described in Sec. 6.4.1. The obtained resolution was 38.5 ps from the commissioning data in 2017 with the muon
beam of MEG II nominal intensity. However, even though 512 counters were operated, the evaluation was performed withthe limited combination of clusters as shown in Fig. 5.3 since there was no tracking information available due to missing
pTC tracking algorithms. Only clean positron events, i.e. positrons crossed at the center of the ﬁrst counter with the incident
angle of 90◦ and successive counters from the center of the ﬁrst counter (10 counters at the maximum), were selected forthe evaluation. In addition, the timing resolution obtained from the simulation with the same method was 31.0 ps in theprevious work, which is much better than the commissioning result. The deep understanding of the S/N was missing inprevious work and simulations were not properly tuned to reproduce basic characteristics of the pTC. In this thesis, themain improvements of the pTC driven by the author are summarized as follows:• Tracking algorithms were newly developed and the performance of the pTC was re-evaluated and demonstrated withthe tracking information. This work evaluated the performance of the pTC with full combinations, which includes

Chapter 5 Overview of Positron Analysis Flow

72

Table 5.1: Data mainly used in the following chapters.
Detectors

Year

Beam

pTC + Mock-up CDCH
pTC + CDCH
pTC + CDCH

2017
2018
2019

MEG II Nominal
Low Rate (1.34×107 µ+ /s) + MEG II Nominal
CosmicDescription
pTC performance evalation
CDCH waveform analysis with beam
CDCH waveform analysis with the ﬁnalized WDB

the systematic uncertainty from the individual counter diﬀerence.
• The systematic diﬀerence between the simulation and the commissioning was investigated. Especially, the hitposition dependence in a counter and the diﬀerence of the evaluation method were investigated in detail.
• The uncertainty of the calibration methods were investigated. The breakdown of the uncertainty on the laser-based
method was studied in detail. The track-based calibration method was established with newly developed tracking
algorithm.
• The cooling system for 10◦ C operation to mitigate the radiation damage eﬀect was prepared and the stable operation
was conﬁrmed in 2018 - 2019.
• The optimization methods for the operation voltage and the analysis parameter was developed in 2019.
The 2018 and 2019 data are mainly used for the CDCH waveform analysis. In [26] summarized the hardware statusof the CDCH until 2019, and the ﬁrst analysis on the gas gain, noise situation, waveform shape, and so on were studied.
However, due to the large low frequency noise from the intermediate convertor for the prototype electronics, it was very
diﬃcult to extract the information for the performance evaluation of the spectrometer. In this thesis, the main upgrade of
the CDCH analysis can be summarized as follows:• The algorithm for the CDCH waveform analysis was updated and global tracking algorithms were developed using
pTC and CDCH.
• Actual CDCH detector performance was taken into account. For example, S/N was found to be worse than the
expectation. This deterioration was included in the simulation and the realistic performance was evaluated using
newly developed algorithms.
The commissioning data used in this thesis in the following chapter is summarized in Table 5.1.

73

Chapter 6

Performance of the pTC
6.1

Goal of This Chapter

In this chapter, the analysis framework for the MEG II pTC was described. Then, the performance of the pTC was evaluatedwith the 2017 commissioning data.

6.2

Overview of Timing Reconstruction Algorithm

The goal of the pTC analysis is to obtain the positron crossing timing precisely from the counter hits. To achieve the target
performance of O(30) ps, the multiple-hit information from one single positron track is needed. The timing reconstruction
for the pTC is composed of the following algorithms:• Waveform Analysis,• Hit Reconstruction,• Clustering,• Standalone pTC Track Fitting (Tracking),• Calibration and Reﬁnement with Tracking Information.

6.3

Algorithms for pTC Analysis

In this section, the details of each algorithm for the pTC are described.

6.3.1

Waveform Analysis

Noise Reduction

Understanding the noise situation (signal-to-noise ratio, S/N) is crucial in the ﬁrst step of the analysis. Since the signal
cables, the readout electronics, and the detector components are gathered in the experimental area, unexpected noises areoften picked up. Some of the noises caused by other electronics are periodical, and such noise components can be subtracted
by making the template of the noise waveform. In the 2017 commissioning, the cross talk noise from the clock channel
was observed. Fig. 6.1 shows the sine waveform in the clock channel for the WDB synchronization. The template noise
waveform was made by summing up the pedestal data, and the example of the waveform is shown in Fig. 6.2. The resultsby the software noise reduction are shown in Fig. 6.3 and Fig. 6.4. The peak of the power spectrum around 100 MHz
vanished, and the mean RMS-noise was reduced from 6.5 mV to 5.4 mV.

Chapter 6 Performance of the pTC

74

Fig. 6.1: The sine waveform in the clock channel for the pTC WDB synchronization.

Fig. 6.2: The template noise extracted from the pedestal data taken in 2017 in the experimental area [28].

Signal Pulse Detection

Fig. 6.5 shows the example of the waveform from a single channel. To extract the timing information, the constant fraction
method (CFD) is used in the pTC analysis. The analysis ﬂow is as follows:
1. Pulse Search: a signal pulse whose height is over the threshold is searched.
2. Interpolation: The width of the waveform window and the sampling frequency are in the relation of trade-oﬀ. To
obtain the comparable timing resolution to the higher sampling frequency, cubic interpolation between the sampling
points is applied for the timing pickup*1 .
3. Timing Pickup by CFD: the timing is picked up at the threshold deﬁned as: (pulse peak) × (constant fraction (CF)value).

6.3.2

Hit Reconstruction

A timing coincidence, |t1 − t2 | < 20 ns, is then taken between both sides of a counter. Note that the timing of each counter
has an intrinsic time oﬀset, toﬀset , which is corrected in the calibration process. The reconstructed hit timing at each countercan be written as follows:tmeasured =t1 + t2− toﬀset .
2

(6.1)

The x-coordinate of the hit position in a counter is reconstructed based on the time diﬀerence between the two channels:
xhit =(t1 − t2 − ∆t)
veﬀ .
2

(6.2)

The eﬀective velocity veﬀ and the diﬀerence in the internal time oﬀset between both ends are obtained from the position
calibration.
*1 By cubic interpolation 2 GS/s (∼ 500 ns timing window) is enough to obtain the comparable resolution with 5GS/s (∼ 200 ns timing window) [23]

6.3 Algorithms for pTC Analysis

75

Fig. 6.3: The pedestal waveforms of the pTC (left black) and their amplitude of the power spectrum (right red) before / after the noise reduction

Fig. 6.4: The RMS-noise of each pTC
channel with pedestal data before / after thenoise reduction [28].

(up / down) [28].

Time pick up
by CFD

Threshold

Amplitude

Fig. 6.5: The extracted waveform from a pTC counter [29].

Position Calibration

To reconstruct the hit x-position (longitudinal direction) in a counter, the relative time oﬀset between two channels at theboth side of a scintillator (intra-time oﬀset) and the eﬀective velocity of the scintillation light in a scintillator must be known
beforehand. This is achieved by ﬁtting the histogram of the x-position with the trapezoid and gaussian convoluted function,
as shown in Fig. 6.6. The ﬁtting parameters are the center position, the oﬀset, and the length of the trapezoid function, andthe deviation of the convoluted gauss function which can be interpreted as the position resolution:f = trapezoid(center, length, oﬀset) ∗ gauss(σposition ).

(6.3)

Chapter 6 Performance of the pTC

76
MC Reconstructed hit distribution
in a 12cm-longcounter (id = 120)
spxhits.l {spxhits.pixelid==120}
300

Green: Original
Black: Averaged200
Blue: Trapezoid
150 Red: Convoluted

hcenter
45

h

slope

EntriesMean
Std Dev

250

offset4016003− 0.0601
3.704

35
30
25
20

length15100

Positionresolution

50
0
− 20

− 10

0

10

center

10
5
0

20

[cm]

− 0.2

0

hlengthhoffsetFig. 6.6: An example of the x-position
histogram of a counter. The green lineis the original histogram,
black after thehlength90
60
Entries500

Std Dev

0.305480
12.02 red line. The center
moving average, blue-dashed the trapezoid
function. The ﬁtting result is Meanshown withof the ﬁt result
50
70

60
corresponds to the relative oﬀset between
the two channels [30].

40

50

30

40

20

30
20

10

10 6.1: Parameters extracted from the position calibration.
Table
0

12

13

0

14

σcenterσLσposition

0.11 cm

0.27hslope
cm

1.1 cm

Eﬀective Velocity (data mean)

240

250

hslope12.4 40± 0.4 cm/ns

hsigmaEntriesMean
Std Dev

35
30

20

20

(cm)

10

0

300

15
250

10

length5200

0150 − 4center−6

50

Reconstructed hit distribution(After)hHit
Reconstructed hit position

Reconstructed hit position

Reconstructed
hit distribution
25(Before)
hHit

100

−10

20

(cm)

−2

0

30

250

20

200

10

150

0

40

300

10

0

1

1.2

100

−10
50

−20
0

60

500
− 2.988
0.8385

200

400

50

−20
0

0

Position ID

200

400

0

Position ID

Fig. 6.7: The position distributions of counters before/after the calibration [30].

The eﬀective velocity, veﬀ , and the eﬀective length, L ,can also be obtained from the length from the ﬁtting with MC. The
eﬀective velocity in data can be corrected by:veﬀ data =LMC
veﬀ MC .
Ldata

(6.4)

The extracted parameters are summarized in Table 6.1. The estimated uncertainty of 0.11 cm for the center alignment
satisﬁed our requirement for pTC counters (∼ 1 cm). Fig. 6.7 shows the position distributions of counters before/after thecalibration.
The position calibration is applied every year since 2017. Fig. 6.8 shows the diﬀerence of intra-time oﬀset between 2017and 2018 and examples of the two outliers: one is due to the bad ﬁtting and the other is actually shifted. The diﬀerence
between each year is rather small.
Energy Calibration

The energy deposit in a counter is calculated based on the pulse charge and an energy calibration factor C E . C E is extracted
by the peak position of the distribution of the geometric mean of the integrated charge from simulations:
CE = qE peakpeak

peak

Qch 1 · Qch 2

,

(6.5)

6.3 Algorithms for pTC Analysis

77

Fig. 6.8: The position calibration diﬀerence in 2017 and 2018, and the outlier examples.

Fig. 6.9: The deﬁnition of the geometrical order in pTC (left) and the distribution of the geometrical order from the ﬁrst hit
and timing from the ﬁrst hit [7].

peak

peak

where E peak is the most probable value of energy deposit, Qch 1 , Qch 2 are the most probable values of the reconstructedcharges.

6.3.3

Clustering

The reconstructed pTC hits are then grouped into a cluster. To separate the hits from diﬀerent particles, the geometricalorder is deﬁned as shown in Fig. 6.9. The reconstructed timing is projected on the geometrical order plane as shown in
Fig. 6.9 (geometrical order from the ﬁrst hit vs timing from the ﬁrst hit), and by ﬁtting the plot with a linear function andapplying the correction, the timing distribution of pTC hits on the projected plane was obtained. Then the projected hits
which have the close timing (±500 ps from a peak) are grouped into the clusters.
After several studies in the simulation, it was found that the ineﬃciency of the pTC clustering was mainly caused bypositrons with a small turning radius after scattering. Fig. 6.10 shows an example of this event. The positron passed
through the pTC counters in the orange region, and after a small turn, it soon came back into the pTC counters in the green
region. To separate these clusters, the new position criterion (±10 cm from a peak position) is also implemented as shownin the same plot. By removing or separating the counters with tail hits from the cluster, the cluster’s timing precision isrecovered. This position information can also be used to add the hits to the cluster as shown in Fig. 6.11. If the hits inChapter 6 Performance of the pTC

78

Projected timing distribution

Projected position distribution
Fig. 6.10: A typical tail event of pTC cluster. After crossing a ﬁrst cluster (orange), that positron loses the momentum bymaterial eﬀects and its turn radius becomes small, and it soon comes back to the pTC region (green).

Fig. 6.11: The hit addition to the cluster by using the projected hit position. The green counter in the left plot cannot be
assigned to the purple cluster only with the timing information, but it can be assigned to the purple cluster with the crosscheck of the timing information and the position information. The positron passed through under the counters in the middleof the cluster.

the cluster are not consistent between timing-based and position-based, the algorithm will test again with wider acceptance(e.g. ±700 ps in the plot).
The hit qualities in a cluster are also checked with other criteria, the energy deposit in a counter should be higher than
0.5 MeV and the longitudinal hit position from the center should be within ±(6 ± 5σposition ) ∼ ±11 cm, where σposition is
the resolution of the longitudinal position (local-x) reconstruction in a single counter (∼1.1 cm). An additional algorithm
to remove outlier hits from the cluster is implemented in the tracking process later.

6.3.4

Standalone pTC Track Fitting

To estimate the positron path length (and calculate the time of ﬂight between counters), a track ﬁtting process is performed.
Combining the hits in a cluster and reconstructing a positron track gives a better estimation of hit positions in a counter.
The standalone pTC track ﬁtting is developed for a pTC track ﬁtting without CDCH information. This algorithm enables
us to reconstruct a part of positron tracks even under the limited (or no) CDCH information which was the case for thecommissioning in 2017-2020. In addition, the independent tracks can be used for more reliable seeds in CDCH track
ﬁnding process than seeds from only CDCH hits (this seeding method is explained in Sec. 7.5.2) since the tracks provide
reliable information on the initial momenta and direction.
This algorithm is composed of three steps: the initial parameter estimation, the Kalman Filter (KF) ﬁtting (the details of

6.3 Algorithms for pTC Analysis

79
Red ＊: estimated R
Blue: Truth track
Pink ○: Hit positionr!"# position should be around here at this hit patternFig. 6.12: The schematics of the ylocal estimation algorithm (left) and its result (right).

the formulation is described in Appendix D), and the extrapolation to the CDCH. Using the extrapolated information fromthe pTC track will improve the track ﬁnding in the CDCH analysis thanks to the additional information on the track seed,
as shown in Appendix E.
Initial Parameter Estimation

The KF algorithm is a recursive algorithm, so the initial input (3D position and momentum) is crucial for the ﬁtting. Since
the counter thickness is only 5 mm, the center of the counter is used as the local-z coordinate of the hit. The transverse(local-x) direction is reconstructed by using the timing diﬀerence between both ends with ∼11 mm resolution. As for thelongitudinal direction (local-y), a dedicated algorithm was developed.
The concept of this algorithm is the classiﬁcation of the cluster patterns. Fig. 6.12 shows the schematics of this algorithm.
A single counter (shown red) is under the test, and 5 counter groups in front/behind that test counter in pTC geometricalorder is deﬁned. The hit or no-hit information in each group is recorded as the bit information and that 10-bit string
represents the cluster pattern. The distribution of the local-y hit position on the counter under test for each pattern is inadvance evaluated using a MC simulation and the mean and standard deviation are stored in a look-up table. The local-y hit
position is set to the mean value for the hit pattern.
Another unknown initial parameter is the momentum (direction) information. The absolute value of the momentum canbe estimated by the MEG II gradient magnetic ﬁeld: the positrons above 45 MeV can reach the pTC. This value is used forthe initial value of the KF calculation with a large initial uncertainty (∼8 MeV). The direction can be estimated by the ﬁrst
two counters in the cluster.
Kalman Filter (KF) Fitting

The pTC hit clusters are then ﬁtted with the KF algorithm. The KF is known as an eﬃcient recursive algorithm to obtain
the best estimate of a state vector*2 . In the GENFIT package, a generic toolkit for track reconstruction for experimentsin particle and nuclear physics [32], the KF algorithm and its extension algorithms like Deterministic Annealing Filter areavailable for the track ﬁtting. Fig. 6.13 illustrates the KF algorithm overview. The detailed formulation is explained inAppendix D, and here the concept is brieﬂy described. The key of the algorithm is to use both the estimation from thephysics model (the positron’s interaction among the materials with the gradient magnetic ﬁeld) and measurement from thedetectors. The KF starts from a certain state vector called seed. A seed state is important since it is the starting point of
the recursive steps and a wrong initial state results in a wrong estimation. The state vector at the next step (or plane) is*2 In this case, the state vector contains the positron trajectory information, i.e. position, momentum, timing and covariance among them.

Chapter 6 Performance of the pTC80

2. Extrapolate

1.Seed5. Iteration

Blue plane: Detector pBlue projection: Forwa
Purple projection: Bac
Red projection: Smoot・・・
4. Update
3. Search・・・

Fig. 6.13: The sketch of KF algorithm.

Blue plane: Detector planeBlue projection: Forward propagation
Purple projection: Backward propagation
Red projection: Smoothed track

ation

・

・・

Fig. 6.14: The reconstructed positron track by GENFIT.

estimated from the previous state and its physics models, for example the extrapolation from the previous plane to the next
plane. Then the estimated state and the measured state are combined with the factor called Kalman gain. After that the
updated (combined) state is used for the next estimation step and these steps are repeated. Fig. 6.14 shows the reconstructed
positron track in pTC region.

6.3.5

Timing Calibration

The timing calibration is the most crucial calibration for the analysis with the multiple counter hits. The reconstructed
positron crossing timing at each counter can be written as follows:
trec =

t1 + t2− toﬀset ,
2

(6.6)

where the ﬁrst term is the average of the timings measured at both ends of the counter and the second term is the time oﬀset
of the counter. The time oﬀset of the counter is deﬁned as:
toﬀset =l+ tSiPM + telec .
2veﬀ

(6.7)

6.3 Algorithms for pTC Analysis

81

Table 6.2: The summary of the uncertainties for the laser-based calibration.
Item

Uncertainty [ps]Reproducibility 4 cm/5cm counter11/3.0Measurement error (in lab test)

5.4

Statistics

1.0

Stability

8.8

Voltage correction

1.5

Time-walk correction

4.2

Waveform diﬀerence

4.3

Variation of transit time inside SiPMs

21

Total

27

The ﬁrst term is the correction for the propagation time in a scintillator, where l is the longitudinal length of the scintillator,
veﬀ is the eﬀective velocity of the light. telec is the signal transmission time in the electrical components (signal lines, cables
and DAQ electronics lines and so on), tSiPM is the oﬀset from the SiPM chain’s transit time.
Laser-based Calibration

The overview of the laser system and its concept are explained in Sec. 2.4.2. First, the time oﬀset from the laser-based
calibration is measured: the time oﬀset of each counter is calculated by using the measured timing and the reference timingfrom the laser synchronized pulse. The light source generates a pulse signal synchronized with the laser light emission
obs
time, which is used as the reference signal to calculate the toﬀset,
obs
toﬀset=t1 + t2− tSYNC ,2(6.8)

where tSYNC is the timing picked up by the laser synchronized pulse.
obs
Compared to toﬀset , toﬀset
includes the additional oﬀset from the laser components (optical ﬁber, connection point, andlaser light propagation), tlaser . This component is measured beforehand in the mass test process for the calibration system.
The uncertainty of the laser-based calibration was evaluated in 2019 [8], and Table 6.2 summarized the uncertainties forthe laser-based calibration measurement. The variations of the transit time inside the SiPMs are measured with the timing
measurement setup similar to Fig. 3.4.2: the hit timing of electrons from 90 Sr was measured and its mean timing (timecenter) was extracted, then the measurement was repeated for about 100 counters. The counter-by-counter variation of 21
ps, which includes the response of the SiPMs, is set as the upper limit of the variation of the transit time of SiPMs. The
reproducibility of the light injection (i.e. time center at a counter) was evaluated by repeating the timing measurement 10
times by extracting and inserting the ﬁber every time. The measurement error of the eﬀective optical length was calculated
from the test of optical components for counters (the 1×8 optical splitters, the 2.5 m optical ﬁbers, and the counter shownin Fig. 2.44). The stability, statistics, voltage correction, time-walk correction, waveform diﬀerence were studied with thedata taken in during the detector commissioning. Especially, the monitoring precision is shown in Fig. 6.15, which shows
the monitored time oﬀset of a counter during 2017 commissioning. The RMS of the time oﬀset monitored over a month
was 8.8 ps on average. The monitoring precision better than 10ps, which can be obtained with 30min data-taking, is goodenough for the detector operation.

Chapter 6 Performance of the pTC

82

relative time offset (ps)

RMS of monitored counters
5

40

0

5

20

(ps)

10

0
12/13

12/20

date

12/27

01/03

Fig. 6.15: The time oﬀset history of a counter in a month [8]. The histogram of the RMS of monitored counters is also
shown.

Fig. 6.16: The concept of track-based calibration.

Track-based Calibration

The concept of the track-based calibration is to obtain toﬀset by minimizing the squared diﬀerence (deﬁned as χ2 below)
between the measured timing and the calculated timing at each counter by using the information from a reconstructed trackin the pTC region. The algorithm ﬂow is as follows:
1. Track reconstruction: The reconstructed pTC hits are clustered, and then ﬁtted with Kalman Filter algorithm andpTC tracks are obtained.
2. Calculation of the χ2 : By using the reconstructed information χ2 deﬁned as below is calculated:
χ2 =

NX
Nhit
tracks X

(

i

=

j

NX
Nhit
tracks X(ijtmeasured − tcalculated 2)σﬁtti j − (ti0
+ T OFi j + ∆T j ) 2
)
σ

(6.9)

(6.10)

where Ntracks is the number of tracks from all events, Nhit is the number of hits (counters) in a track, σ is thetiming resolution, and tmeasured = ti j is the reconstructed timing at the j-th counter in the i-th track. tcalculated =
ﬁt
ﬁt
ti0
+ T OFi j + ∆T j is the calculated timing at the j-th counter by using the ﬁrst counter timing (ti0
) in the i-th track6.3 Algorithms for pTC Analysis

83

Fig. 6.17: The result of track-based calibration compared with the simulation random oﬀset. The standard deviation isestimated to be ∼13 ps.

Table 6.3: Comparison between two time calibration methods.
Item

Laser-Based

Track-Based

Position dependenceNo

DAQ time∼ 30 min.

∼2 daysBeam

not necessary

necessary

Coverage

84%

100%

Uncertainty

27 ps

13 ps

Strategy

Monitor Stability

Yes

Main Useobtained by ﬁtting, the ﬂight time between the ﬁrst counter and j-th counter (T OFi j ) in the i-th track and the intrinsic
time oﬀset of j-th counter (∆T j )*3 .
3. Minimization of χ2 : To obtain the best estimate of ∆T j , the χ2 is minimized by using the Millepede software[66],which is developed to solve the linear least squares problem with a simultaneous ﬁt of all global and local parameters
for eﬃcient and fast alignment and calibration of large detectors*4 .
Fig. 6.16 illustrates these steps. For the estimation of the calibration uncertainty, we used a simulation. The random
oﬀset (± 100ps) is generated and added to the counters*5 . Then the track reconstruction in pTC and the above track-based
calibration algorithm are performed. The result is compared with the generated oﬀset. A precision of ∼13ps was achieved
as shown in Fig. 6.17.
Strategy of Timing Calibration

Table 6.3 summarizes the comparison between the two methods. The basic strategy of the pTC time calibration is asfollows: the time oﬀset calculated from track-based calibration is mainly used, and its time-dependence during the datataking period is monitored by the laser-based calibration.

*3 tﬁt is the local parameter (minimized track by track) and ∆T j is the global parameter (common to all events) for ﬁtting.
i0*4 Software provided in [67] under the terms of the LGPLv2 license*5 When the time oﬀset is calculated with the commissioning data, the time oﬀsets from the laser-based calibration are used for the initial values,

whose precision is 27 ps, and ± 100ps random oﬀset is conservative enough for the evaluation of the algorithm.

Chapter 6 Performance of the pTC

84DS
Std Dev: 55 ps

40
30

40

US

30

Std Dev: 42 ps

20

20

10

10

0 200

0
(ps)

200

0

100

0
(ps)

100

200

Fig. 6.18: The consistency between two pTC timing calibration methods with 2017 commissioning data [8].

Fig. 6.19: The hit position dependence of the channel by channel time oﬀset after the correction of the time oﬀset in x
direction for 4 cm counters [24]. The left plot shows channel 1, and right plot shows channel 2.

Application to Commissioning Data

To evaluate the real precision of the pTC timing calibration, the consistency between these two methods was compared.
Fig. 6.18 shows the diﬀerence between the time oﬀset values from the laser calibration and those from the track-based
calibration. The estimated calibration precision was 42 ps for US pTC and 55 ps for DS pTC (48 ps on average). These
laser
track
values were worse than the estimated value from the simulation (σ(toﬀset) ⊕ σ(toﬀset) ∼ 30 ps), and it may have a moderateeﬀect on the pTC resolution. For example when 37 ps resolution was assumed with 9 counter hits, the eﬀect of thecalibration, whose uncertainties are random among counters, is 37 ⊕ √489 ≈ 40 ps conservatively.

6.3.6

Reﬁnement of the Timing Reconstruction

After the track reconstruction and calibrations, the timing reconstruction is reﬁned. The reﬁnement is classiﬁed into two
types: counter-level (inter-counter) for tracks and channel-level (intra-counter) for counters by using the energy deposit
dependence and the position dependence of the timing measurement. The full details of the reﬁnement are reported in [24].
These algorithms are applied to the 2017 commissioning data.

6.3 Algorithms for pTC Analysis

85

Fig. 6.20: The hit position dependence of the channel timing resolution (right) for 4 cm counters [24]. The left plot showschannel 1, and right plot shows channel 2.

Fig. 6.21: The relation between the energy deposit and the time oﬀset (left) and the timing resolution (right) [24].

Corrections (Channel-Level for Counters)
ch1
The channel by channel time oﬀset, toﬀset, at each (x, y) position in a counter is extracted as follows:lch1
toﬀset= tich1 − tave − T OF1i − 2

+ xi
,
veﬀ

(6.11)

where tich1 is the reconstructed timing at channel 1 of i-th counter, T OF1i is the ﬂight time between ﬁrst counter and the i-th
counter. Then the hit timing of the i-th counter is calculated with the weighted average of:

ti =

ch1
tich1 −toﬀset
tch2 −tch2+ i σ2 oﬀset
σ2ch1
ch2

1
+ σ12
σ2ch1
ch2

(6.12)The position dependence of the timing oﬀset and resolution in a counter after this correction for 4 cm counters are shownin Fig. 6.19 and Fig. 6.20, respectively.

Chapter 6 Performance of the pTC

86Fig. 6.22: The hit position dependence of the counter timing oﬀset (left) and the timing resolution [24].

Corrections (Counter-Level for Tracks)

There is a correlation between the energy deposit and the timing resolution / measured timing oﬀset (tcor oﬀset ) for eachcounter, as shown in Fig. 6.21. This dependence is corrected with the following formula:PN ti −T OF1i −ticor oﬀset
todd or teven =

i

σ2i

PN 1

,

(6.13)i σ2iwhere ti is the reconstructed timing at i-th counter (i is odd number for todd and even number for teven ), T OF1i is the ﬂight
time between ﬁrst counter and the i-th counter, σi is the relative weight of i-th hit in the track, ticor oﬀset is the energy-deposit
dependent oﬀset as shown in Fig. 6.21 and is extracted as the Gaussian mean of the following distribution:

tave is the track timing calculated from:ti − tave − T OF1i .

(6.14)

1 X(ti − t1 − T OF1i ).
N i(6.15)

N

tave =

Fig. 6.22 shows the relation between the hit position and the time oﬀset / timing resolution after the channel-level
correction. The hit position dependence is also used for the counter-level weighted average with the same formulation as
the energy deposit case.

6.4

Performance of pTC

In this section, the performance of the pTC is evaluated with the reconstruction algorithms explained in the previous
sections. The pTC-standalone tracking algorithm enabled us to evaluate the performance of the full pTC counters. The
development of the clustering algorithm, pTC tracking algorithm, and reﬁnement algorithm contributed to the performance
improvement of 15% from the previous work. In addition, the systematics of the counter hit position was newly discoveredand studied in detail.

6.4.1

Even-Odd Analysis

The timing resolution of the pTC was evaluated with the even-odd analysis in the commissioning. The concept of thisanalysis is to use the timing from the ieven -th hits and iodd -th hits as the reference timing of each other. This can be described6.4 Performance of pTC

87

Event time resolution [s]−1280 ×10

Event time resolution

70
60
50
40
30
20
10
0

4

6

8

10

12

14

Number of hits
Fig. 6.23: The timing resolution from even-odd analysis with 2017 commissioning data with the latest analysis.

as follows:1(todd − teven )
2
Neven
Nodd
1 X
1 1 X
(t2i − T OF1(2i) ))(t2i−1 − T OF1(2i−1) ) −= (2 Nodd i
Neven iσpTC (Nhit ) =X
1 X( (t2i−1 − T OF1(2i−1) ) −(t2i − T OF1(2i) )),
N i
i
N/2

=

(6.16)(6.17)

N/2(6.18)

recwhere ti is the reconstructed timing at i-th counter, T OF1i
is the reconstructed time of ﬂight from the ﬁrst counter to thei-th counter. N is the number of the pTC hits in the cluster (or track), Nodd = Neven = 12 N, note that N must be an evennumber.

6.4.2

Overall Timing Resolution

Fig. 6.23 shows the timing resolution of pTC tracks extracted by the even-odd analysis as a function of the number of hits.
The overall timing resolution of pTC was estimated by using the distribution of the number of pTC hits for signal positrons.
This distribution was obtained by using the MC, as shown in Fig. 6.24. The overall resolution is calculated as follows:
σpTC =N
max
X

P(Nhit ) × σpTC (Nhit ),(6.19)

Nhit

where Nhit is the number of pTC hits, P(Nhit ) is the probability for a signal positron crossing Nhit counters. σpTC (Nhit ) is theextracted resolution from the even-odd analysis as shown in Fig. 6.23 and ﬁtted with:s
σpTC (Nhit ) =σ21+ σ22 ,
Nhit

(6.20)

Chapter 6 Performance of the pTC

88

Probability

Number of pTC hits distribution

0.15

Mean

9.082

15

20

0.1

0.05

0
0

5

10

Number of hit pixels

Fig. 6.24: The probability distribution of the number of pTC hits for signal positrons.

Table 6.4: The pTC performance evaluation with the commissioning data: comparison of the updated studies and previous
studies.
Algorithm

σpTC

σTOF CDCH (MC)σe+ (Expected)

Previous [7]38.5 ps

14.8 ps

41.2 psUpdated34.3 ps

6.9 ps35.0 pswhere σ1 is equivalent to an averaged single-pixel resolution, whose contribution scales with the square root of the numberof counters ( √N1 )*6 . σ2 is the other contributions which do not scale with the number of hits*7 .
hit

The overall timing resolution was evaluated to be 34.3 ps with 2017 commissioning data. Combined with the ﬂight time
uncertainty of 7 ps inside the CDCH region (Sec. 7.5.3), the positron timing measurement on the target with a precision of
35.0 ps was obtained. The timing resolution was estimated 41.2ps in previous studies [7]. The improvement is summarizedin Table 6.4. 15% of improvement was achieved thanks to the new algorithms, i.e. the standalone pTC tracking, updateof the clustering, and the reﬁnement algorithms. The TOF calculation in CDCH is also optimized by using the KF ﬁtting
iteration, resulting in the improvement by a factor of two as described in Sec. 7.5.3. Now the overall timing resolution forµ → eγ measurement σte+ γ is calculated to be 68 ps with the assumption of σtγ = 58 ps. This value is much better than thedesign value of 84 ps and the MEG value of 122 ps.

6.5

Performance Studies Using MC Simulations

To verify the estimated performance of the pTC, the comparison of the evaluation methods with MC data was performed.
Table 6.5 summarizes the results of the resolution estimated by various methods in MC (even-odd or truth-based) and the*6 For example, the single counter resolution, the calibration precision, and the electronics jitter are contained in σ1 .
*7 For example, the multiple scattering, the secondary particle eﬀects, and the systematic time spread from the hit position dependence in counters arecontained in σ2 .

6.5 Performance Studies Using MC Simulations

89
RMS-noise

3

Entries

EntriesHeighth
EntriesMean
Std Dev

700

14218
0.2562
0.142

× 10

h

100

Entries5139108Mean

0.005054

Std Dev0.001294

80

600
500

60

400
300

40

200

20

100
0
0

0.2

0.4

0.6

0.8

1
[V]

0
0

0.002

0.004

0.006

0.008

0.01
[V]

Fig. 6.25: 2017 pTC amplitude.
Fig. 6.26: 2017 pTC RMS-noise .
HeightEntries

Entries

RMS-noise
h

3500
3000

Entries

59715

Mean

0.2083

Std Dev0.1202

h

4000
3500

Entries2048000

Mean

0.004797

Std Dev0.000957

3000

2500

2500
2000
2000
1500

1500

1000

1000

500
0
0

500
0.2

0.4

0.6

0.8

0
0

1
[V]

Fig. 6.27: pTC amplitude (MC).

0.002

0.004

0.006

0.008

0.01
[V]

Fig. 6.28: pTC RMS-noise (MC).

hit position dependence.

6.5.1

Tuning of S/N

As discussed in Sec. 3.4.3, the timing resolution of the pTC counter is predominantly aﬀected by the S/N. Fig. 6.25 andFig. 6.26 show the observed amplitude and RMS-noise of pTC waveforms, and Fig. 6.27 and Fig. 6.28 show the onesfor MC. The mean value of the height in the commissioning was higher than the MC mainly due to the diﬀerence of theoperation temperature and the over-voltage; the 2017 commissioning was performed at 20◦ C while the MC was tuned with
30◦C condition (this diﬀerence was equivalent to the over-voltage ∼ 1.2V). Also, the small amount of the counters with
type-II SiPMs had higher gain and lower noise.

6.5.2

Hit Rate

The hit rate of the pTC counters was calculated from the number of pulses outside the trigger timing (pedestal region). The
example of the timing distribution is shown in in Fig. 6.29. Assuming the Poisson distribution:
P(X = k) =Rk e−R,k!

(6.21)

then the expected value of the hit rate at each counter, R, can be calculated as follows:
R = −ln(

NPedestal),
NAll T(6.22)

Chapter 6 Performance of the pTC

90

Triggered Timing at Timing Counter [s]Fig. 6.29: The timing distribution of the pTC hits in 2018 data with the muon beam. Triggered events can be seen around410 ns – 430 ns. For the rate calculation, the ﬂat region (pedestal region) is used with the assumption of the Poisson
distribution.

where NPedestal is the number of the oﬀ-trigger timing events (no pulses in the trigger-timing region, k = 0), NAll is thetotal number of the events, and T is the timing window of the pedestal region. The comparison of the hit rate of eachcounter was already checked in the previous study [7], as shown in Fig. 6.30 with 2017 commissioning data. The hit rate isconsistent between the MC and the real data around |Z| <∼ 100. Hit rate around |Z| >∼ 100 is diﬀerent between real dataand simulations, which is considered due to the material diﬀerence between the mock-up CDCH (2017 commissioning)
and the CDCH (MC).
Fig. 6.31 shows the average hit rate of the counters at each z-position including the 2018 and the 2019 commissioning
data. As discussed above, there is discrepancy between the 2017 data and the MC. In contrast, the tendency (sharp droparound |Z| ∼ 100) is the same between the MC and the 2018 data since the CDCH material settings became consistent
between the real and the MC. Considering the beam rate diﬀerence between the 2017 and the 2018 (7 × 107 /6 × 107 ), we
can conclude that the hit rate is reproduced well by the MC simulations.

6.5.3

Tracking Quality

The tracking eﬃciency and the resolution were studied with MC and data. The tracking eﬃciency was estimated as follows:Eﬃciency =NFitted,NCand(6.23)

where NCand is the number of the candidate events for tracking (pTC clusters with 4 ≤ Nhits ≤ 14), and is the number ofthe ﬁtted events (ﬁtting converged with χ2 /dof ≤ 25). The extracted eﬃciency was 98.6% for the data in 2017 and 95.1%
for the MC. The estimated ylocal -position (described in Fig. 6.12) was also checked with MC. Fig. 6.32 shows the relation
between the resolution of the estimated position at the i-th counter. No signiﬁcant bias was observed in the estimation andthe resolution of ylocal -position was ∼8 mm.

6.5 Performance Studies Using MC Simulations

91

Table 6.5: The pTC performance evaluation with the commissioning data and MC.
σpTC (Even-Odd)

Data

6.5.4

σpTC (Truth-Based)

Commissioning

34.3 ps-

MC34.7 ps

37.4 ps

MC (position dep. + irradiation)

37.7 ps

42.6 ps

Position Dependence of Tracks

Fig. 6.33 and Fig. 6.34 show the timing resolution from even-odd analysis (6 – 10 hits) with 2017 commissioning data andMC at several |z| region, respectively. |z| of track is deﬁned as the mean position of the counters. Tracks in 40 cm ≤ |z| ≤ 75
cm have slightly worse resolution than the average (“all” in the ﬁgure) since 5 cm counters are mainly used in that region,
while tracks in 75 cm ≤ |z| have slightly better resolution than the average. The discrepancy between the data and MC is
within a few ps at the maximum. The comparison between MC and Data shows that the resolution of the data is very well
reproduced by the MC simulations, which veriﬁes the reliability of MC simulations.

6.5.5

Evaluation with MC Truth

In the MC, the precise evaluation of the reconstructed parameters is possible using “true” timing information (truth-based
method). The deviation of the following distribution is calculated:
hit
1 X
rec
true
((tirec − T OF1i
) − (titrue − T OF1i))
Nhit i(6.24)

hit
1 X(tcalc − t1true ),Nhit i 1(6.25)

N

σpTC (Nhit ) =

N

=

rec
where tirec is the reconstructed timing at i-th counter, titrue is the true (or reference) timing generated in MC. T OF1i
is thetrue
reconstructed time of ﬂight from the ﬁrst counter to the i-th counter, and T OF1i
is that of MC truth. t1calc is the calculated
rectiming at the ﬁrst counter by using tirec − T OF1i.

The obtained performance from the commissioning data and the MC data with the same method (even-odd) was consistent, while that from the even-odd for data and the truth-based method for MC was not as shown in Table 6.5. Ourinterpretation was that the even-odd analysis partially cancel out the systematics of the hit-position by subtracting theadjacent counters, resulting in the better timing resolution than the truth-based method.

6.5.6

Implementation of Systematics by Hit Position

The study on the systematics of timing measurement by the hit position in the counter was possible with the standalonepTC tracking (Sec. 6.3.4). The timing center is deﬁned as tch1 − tave − TOF, and its dependence on the hit position is shownin Fig. 6.35 with the 2017 commissioning data. To extract the dependence from the commissioning data, the correction (inSec. 6.3.6) was not applied here.
This eﬀect is implemented as the time oﬀset between adjacent SiPMs to reproduce the dependence of Fig. 6.35. As
a conclusion, 60 (4 cm counters)/75 ps (5 cm counters) time oﬀset between adjacent SiPMs are used to reproduce thedependence as shown in Fig. 6.36. The contribution to the pTC performance by this new systematics is estimated to be 2%.

Chapter 6 Performance of the pTC

92
Table 6.6: The pTC performance.
Items in Commissioning 2017

UpdatedObtained Performance from Even-Odd

34.3 ps

38.5 psFull combinations

Fixed combination

tracking (new)/clustering (2-3%)/reﬁnement (5%)-

Evaluation (8%)/Hit position (2-14%)

No systematics

37.0 ps-

47.6 ps-

Evaluation
New Algorithms (% : improvement)

Previous [7]New Systematics Studies
Systematics (% : deterioration)
With Systematics (At Commissioning 2017)◦

With Systematics (Full Radiation, 10 C)

Increase of Systematics by Radiation Damage

The eﬀect by the non-uniformed radiation damage after 3-year data taking is estimated by using the 6 damaged SiPMs
chain (comparable damage level to the MEG II expected dose) and damage-free new SiPMs chain. The damaged chain
was composed of; two electron irradiated SiPMs with the ﬂuence level of Φeq ≈ 3 × 109 n1MeV /cm2 (used in Chap. 3) and
four neutron irradiated SiPMs, two with the ﬂuence level of Φeq ≈ 8.7 × 108 n1MeV /cm2 samples and the other two withΦeq ≈ 5.5 × 109 n1MeV /cm2 ones. Fig. 6.37 shows the position dependence of the hit position with lab test setup (sameto Sec. 3.3.1). The detail of each pattern in the plot is explained in Appendix B, and the above pattern which should befocused here is “pattern C (reverse)”. Fig. 6.38 shows the position dependence of the damage-free SiPMs with lab test
setup. Comparing the dependence of Fig. 6.38 and Fig. 6.37, the factor for the position dependence of time center by theradiation damage can be extracted: ∼1.8, i.e. 60 (4 cm counters)/75 ps (5 cm counters) time oﬀset should be 108 / 135
ps. The simulated time center dependence at the edge is shown in Fig. 6.39, and the diﬀerence of the performance by thistime-oﬀset is summarized in Table 6.5. The eﬀect on the timing resolution from position dependence and irradiation isestimated to be 14%.

6.6

Performance of pTC

With the novel tracking algorithm in the pTC, performance evaluation with full counters and full combinations became
possible. 15% better than the previous value (from 38.5 ps to 34.3 ps) thanks to the new algorithms (especially clustering,
tracking, and reﬁnement) compared with the previous work in [7]. The MC was updated for the study of the systematics
from the evaluation method and the positron trajectory (i.e. hit position in pTC counters). The hit position dependence of thetime center was conﬁrmed both from the lab-test and the commissioning data. We found that the obtained performance fromthe even-odd could be 8% better than the true performance as shown in Table 6.5. Considering these updates, the conclusionof the pTC performance is summarized in Table 6.6. The performance with systematics, 37.0 ps, is calculated with thecorrection by the evaluation method (8%). The performance after the three-year running, 47.6 ps, is also shown, which is
calculated with the correction by the evaluation method, the position dependence (from 2% to 14% by the irradiation), andthe dark noise increase by the radiation damage (13%).

6.6 Performance of pTC

93

Fig. 6.30: Hit rates calculated with 2017 data (magenta) and MC (black) with MEG II nominal beam rate settings [7].
Larger discrepancy between the MC and the data was observed in the large |Z| region (position ∼200 - 256/∼450 - 512).

Chapter 6 Performance of the pTC

94

Fig. 6.31: Hit rates calculated with 2017, 2018, and 2019 data with MEG II nominal beam rate settings each year.

Fig. 6.32: The 2D scatter plot of the diﬀerence between the estimated position and the MC truth. The magenta line shows
the resolution, white square shows the mean of the distribution at each counter.

×10−1295

Event time resolution
×10−12All|z| < 40 cm

45

40 cm < |z| < 75 cm
75 cm < |z| < 95 cm

40

95 cm < |z|

35
30
25

Event time resolution [s]Event time resolution [s]6.6 Performance of pTC

Event time resolutionAll|z| < 40 cm

45

40 cm < |z| < 75 cm

40

75 cm < |z| < 95 cm
95 cm < |z|

35
30
25

6

7

8

9

10

Number of hits

Fig. 6.33: Timing resolution from even-odd analysis
with 2017 commissioning data at several |z| position of
tracks.

6

7

8

9

10

Number of hits

Fig. 6.34: Timing resolution from even-odd analysis
with MC at several |z| position of tracks.

Fig. 6.35: The y-dependence of the timing center in a

Fig. 6.36: The y-dependence of the timing center in acounter at the edge (xhit > 5 cm) with 2017 data [24].

counter at the edge (xhit > 5 cm) with MC to reproduce
the 2017 data [24].

Chapter 6 Performance of the pTC

96

−250
−300

µ t [ps]

−350
−400
−450
−500
−550
−600
−1.5

Pattern A (normal)

Pattern A (reverse)

Pattern B (normal)

Pattern B (reverse)

Pattern C (normal)

Pattern C (reverse)

−1

−0.5

0

0.5

1

1.5

y [cm]

Fig. 6.37: Position dependence of the time center in a

Fig. 6.38: The y-dependence of the timing center in acounter at x = −4.25 cm. The applied voltage was ﬁxed

counter at x = −4.25 cm [24].

◦to 162.5 V at 30 C [31].

Fig. 6.39: The y-dependence of the timing center in acounter at the edge (xhit > 5 cm) with 1.8 times increased
dependence, i.e. 108 (4 cm counters)/135 ps (5 cm counters) time oﬀset between adjacent SiPMs [24].

97

Chapter 7

CDCH Analysis
In this chapter, the waveform analysis of the MEG II CDCH is described. Then, the comparison between the commissioning
data in 2018 and the simulation is discussed. The CDCH tracking algorithms are explained based on the updated simulation.

7.1

Waveform Analysis of CDCH

When positrons pass through the CDCH cells, the noble gas particles in the mixture (He) are ionized and the electrons
move toward an anode wire and are then ampliﬁed by the avalanche process around an anode wire. The nominal gas gain
for MEG II CDCH is 5 × 105 *1 . The signal of CDCH is induced by those electrons. The average hit rate of CDCH cells(∼
1 MHz) is one order higher than pTC (∼ 100 kHz), and especially inner layers are more severe (∼ 1.8 MHz) due to thegradient magnetic ﬁeld. The number of ionization clusters is diﬀerent event by event, and signal height also diﬀers due tothe ﬂuctuation in the avalanche process and the space-charge eﬀect. The average cluster densities of the gases are NHe = 7.4/cm and NIso = 54 /cm. The slow drift velocity of the ionized clusters (∼ 2 cm/µs) limits the time resolution of the wiremeasurement. To reconstruct CDCH data in such severe conditions, a novel algorithm of the CDCH waveform analysis
was developed. The CDCH waveform analysis is mainly composed of two steps.

7.1.1

Signal Search

Signal pulses are searched for in a predeﬁned timing window (∼ 300 ns from the trigger timing, which is the maximum
drift time for a hit). The pulse search threshold is deﬁned from the RMS noise value calculated from the baseline region
and default value is 5 × NRMS . The pulse information such as the edge timing, the peak timing and so on is calculated fromthe sampling points of the waveform crossing the threshold and recorded for the next step.

7.1.2

Cross-Fitting

The idea of the cross-ﬁtting algorithm is to use the waveform from one wire end as the template of the waveform and to ﬁt
the waveform of the other end using template from one wire end. This procedure is expected to improve the signal ﬁnding
eﬃciency. In addition, the timing diﬀerence and height diﬀerence between both ends are used for the local-z reconstruction.
The shape of the signal waveforms obtained at the two ends is assumed to be the same except for the pulse amplitude
and the timing oﬀset. The χ2 to be minimized is deﬁned as below:Zχ =2( f (t) − c × g(t + τ))2
dt,
σ2

(7.1)

*1 The gas gain value can be tuned with the applied voltage, but the operation with too high applied voltage will result in the fast aging of the wirechamber, for example, loss of gain, loss of response uniformity, and electrical instability. The detailed study on the aging for MEG II CDCH isreported in [68].

Chapter 7 CDCH Analysis

98

ch1

ch2

Fig. 7.1: The example of the simulated CDCH waveforms and the cross-ﬁtting algorithm. The sky-blue horizontal line
shows the threshold for the signal ﬁnding, and the orange, green, magenta, and blue lines on the waveform shows the ﬁtted
results, respectively.

Fig. 7.2: The noise spectrum of the CDCH noise in 2018.

where g(t) is the ﬁt function (the waveform from one end), f (t) is the waveform from the other end, τ is the ﬁtting parameterfor the time diﬀerence. and c is also the ﬁtting parameter to scale the pulse amplitude. When a signal was found in one
end, the waveform was stored within a pulse packet range (-20 ns – +40 ns in a ﬁgure) and used for the χ2 calculation
with MINUIT*2 . Fig. 7.1 shows the example of the waveform from two ends of a wire. This cross-ﬁtting ﬁnds the CDCH
pulses with “OR” logic of the two ends. Under the severe S/N condition, this method drastically recovers the pulse ﬁnding
eﬃciency compared to the algorithms used in [7]. The eﬃciency of track reconstruction for signal positrons without pileups
is improved from 13% (27% for hit reconstruction) to 80% (69% for hit reconstruction) with the updated simulation.

7.2

Analysis of Low Rate Data

The algorithm for the CDCH waveform analysis applied to the commissioning data taken in 2018 (with 1.34 × 107 muonbeam) and 2019 (cosmic rays).

7.2.1

Noise Reduction

Fig. 7.2 shows the power spectrum of the periodical noises observed in 2018 in the experimental area, and the typical
waveforms taken in the 2018 commissioning are shown in Fig. 7.3. There were two major sources of the noises in the
CDCH as shown in Fig. 7.2: the low-frequency noise from the intermediate DIFF-to-SE converters which were used in the
prototype electronics in the 2018-2019 commissioning and the 50 MHz noise from the ground loop of the signal cables,
which might be related to the accelerator frequency (RF frequency). Fig. 7.4 shows the example of the 50 MHz strong
noise (black lines) observed in 2019. The red lines are the ﬁtted results with sine functions. The subtraction of 50 MHz*2 MINUIT in C++ implementation from ROOT reference guide [69].

7.2 Analysis of Low Rate Data

99

Fig. 7.3: The example of the CDCH waveform with the muon beam rate of 1.34 × 107 taken in 2018 commissioning.

Fig. 7.4: (Black) The observed 50 MHz noise in the 2019 commissioning. (Red) The template noise spectrum extracted
from the waveform themselves by the sine ﬁtting.

noise was not applied to the data taken in 2018, since the digital ﬁlter (described below) was suﬃcient to reduce the noisein 2018. The DIFF-to-SE intermediate converter will not be used in the future (the diﬀerential input is adopted for the ﬁnal
version of the WDB for CDCH), and the ground loop of the signal is solved after the commissioning, so these problems
will not be crucial for the future operation (the noise situation in 2020 is shown in Appendix F). As for the solution in 2018and 2019, the noise reduction by the digital ﬁlter was found to be eﬀective. Fig. 7.3 shows the comparison of the typical
waveforms before/after the software noise reduction. The digital ﬁlter was composed of two types of the moving averageﬁlter: a smoothing ﬁlter with 5 points, i.e. the 5 points including the target point are averaged, and a high-pass ﬁlter with
31 points, i.e. the average of the 31 points before the target point are subtracted from the target point. The high-pass ﬁlter
removed the low frequency large noise and the moving average ﬁlter reduced the RMS-noise from 2 mV to 1 mV at thepeak region of the distributions.

Chapter 7 CDCH Analysis

100

Amplitude
Entries

Entries

Amplitude
h

9000
8000

Entries

91471

Mean

0.01196

Std Dev0.01032

900

h

800

Entries

15662

Mean

0.01561

Std Dev0.01433

700

7000

600

6000

500

5000

400

4000
3000

300

2000

200

1000

100

0
0

0.02

0.04

0.06

0.08

0
0

0.1
[V]

(a) 2018 CDCH amplitude (1.34 ×
107 µ/s).

0.02

0.04

0.06

0.08

0.1
[V]

(b) 2019 CDCH amplitude (Cosmic). Red: Final Electronics,
Blue: Prototype only.

Fig. 7.5: The signal amplitude histograms from the commissioning data taken in 2018 and 2019.
RMS-noiseh3000

Entries

36658

Mean

0.0008973

Std Dev 0.0001229

Entries

Entries

RMS-noise

h
8000
7000

Entries

87890

Mean

0.001333

Std Dev 0.0001948

2500
6000
2000

5000

1500

4000
3000

1000
2000
500

0
0

1000

0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004[V](a) 2018 CDCH RMS-noise (1.34×
107 µ/s).

000.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004[V](b) 2019 CDCH RMS-noise (Cosmic). Red: Final Electronics,
Blue: Prototype only.

Fig. 7.6: The RMS-noise histograms from the commissioning data taken in 2018 and 2019. The dashed line shows the
RMS-noise calculated from the raw waveform and the solid line shows that after the noise subtraction by the moving
average ﬁlter.

7.2.2

Observed S/NAfter the noise reduction, the S/N of the CDCH waveform was extracted as shown in Fig. 7.5 and Fig. 7.6. The ﬁnal
version electronics (ﬁlled with red) seem to have slightly higher amplitude than the prototype (ﬁlled with blue) thanks to
the diﬀerential readout. As for the RMS-noise, the distribution before the noise reduction (dashed line) and that after thenoise reduction (solid line) are shown. The noise reduction algorithm signiﬁcantly reduced the RMS-noise of the CDCH. In
2018, the RMS-noise had a long tail at larger side due to the large low frequency noise. In 2019, the peak of the RMS-noise
became larger than 2018 due to the strong 50 MHz noise from the ground loops. The intrinsic component of the detector

7.3 Reproduction of Commissioning Data by MC Simulations

101

4500

Entries

4000

Amplitude3hEntries

Entries

RMS-noise
34712

Mean

0.7982

Std Dev

0.06246

3500

× 10

h

160

Entries

140

1657820Mean

0.0103

Std Dev0.006583

120

3000

100
2500

80
2000

60
1500

40

1000

20

500
0
0

0.5

1

1.5

2

2.5

3

3.5

0
0

4
[mV]

(a) CDCH RMS-noise (MC).

0.02

0.04

0.06

0.08

0.1
[V]

(b) CDCH amplitude (MC).

Fig. 7.7: The distributions of simulated RMS-noise (dashed line: before noise subtraction, solid line: after noise subtraction)and signal amplitude.

Table 7.1: The major updates of the CDCH waveform analysis after 2018 [7].
BeforeUpdateNote

Parametric

SPICE

S slightly decreased (∼ 2/3)

Amp Gain [mV/fC]

0.545

0.146

S decreased by a factor of 3.7

RMS-noise [mV]1

2

White-Gauss / 2020 noise spect (Appendix F)

Z-Dependence

None

Implemented

60% gain decrease at the edge

Per cluster

Per electron

Drift time ﬂuctuation for each electronSpace-Charge

None

Implemented

Described in the next subsection

Number of Layer

109∼10% eﬃciency drop

Settings
Pulse Shape

Diﬀusion

white noise (the peak region of the RMS-noise distribution in 2018) is extracted to be ∼ 2 mV before the noise subtractionand ∼ 1 mV after the noise subtraction. The S/N of the CDCH (S (10 mV) /N (1 mV) ≈ 10) was much worse comparedwith the pTC (S (200 mV) /N (5 mV) ≈ 40).

7.3

Reproduction of Commissioning Data by MC Simulations

In this section, the major updates of the simulation from previous studies [7] are summarized.

7.3.1

Update of Simulation

The major updates from previous studies [7] are summarized in Table 7.1. Fig. 7.7b and Fig. 7.7a show the simulated S/Nof the CDCH waveform. Fig. 7.8 shows the correlation of signal amplitudes at two ends before (left) and after (middle) the
updates. The correlation in the real data from 2018 commissioning is also shown in right of Fig. 7.8. The correlation seen
in real data is well reproduced by the updates of simulations (middle). The newly introduced SPICE-based signal shapecontributed to a slight decrease in the signal size. The amp-gain of the CDCH frontend was modiﬁed from the design value
to the actual value; the signal height became ∼1/3.7.
As for the noise simulation, two choices were prepared: one is to use the white Gaussia noise with 2 mV mean, the otherChapter 7 CDCH Analysis

102
Amplitude ch1:ch2

0.05

MC 7e7(updated)
0.04

35

h
Entries
Mean xMean y2000
0.01010.0101
Std Dev x 0.005896
Std Dev y 0.005907

0.045
0.035

0.03

[V]

[V]

Amplitude ch1:ch2

30
25
20

0.05

2018 data(Low int)
0.04

1846
0.010390.008965
Std Dev x 0.0064
Std Dev y 0.005915

0.035
0.03

0.02

15

0.02

0.015

10

0.015

0.01

5

0.005
0.01

0.02

0.03

0.04

0.05
[V]

0

35
30

20
15
10

0.01

5

0.005
0
0

40

25

0.025

0.025

0
0

h
Entries
Mean xMean y

0.045

0.01

0.02

0.03

0.04

0.05
[V]

0

Fig. 7.8: The scatter plots of the simulated signal amplitude at ch1 (x-axis) and ch2 (y-axis). Left plot is before the updateof the gain parameters, center plot is after the update, and right plot is from the commissioning data in 2018 (1.34×107 rate
at 1460V). Note that the scale of the axis is one-order diﬀerent between left plot and center/right plot.

is to use the noise spectrum observed during the commissioning. Since the diﬀerence of the two options was less than 1%
on the eﬃciency, as described in Appendix F, the ﬁrst option was used for the performance evaluation in the following
chapters.
Based on the results of the gas-gain measurement from the prototype [26], the z dependence (described as quadratic
function) was implemented. The diﬀusion was implemented per-electron level and each electron has its own drift time
ﬂuctuation due to diﬀusion. In addition, the space-charge eﬀect was implemented to simulate the high-rate environment in
the CDCH. The detail of the model was explained in the following subsection.

7.3.2

Space-Charge Effect for High Rate Environment

At the high gain in the CDCH, ions produced in the avalanche around the wire screen the electric ﬁeld, and reduce the gain
for electrons arriving later. This phenomenon is known as a “space-charge” eﬀect. To extend the MEG II simulation to thehigh rate environment, this eﬀect was newly implemented in 2019.
If a cluster produces a charge Q in an avalanche, a cluster arriving after a time ∆t < vr00 is aﬀected by the space charge:
QSC = Q0r0 − v0 ∆t
,
r0

(7.2)

with the assumption that the avalanche happens uniformly within the distance r0 , the avalanche has a lateral extension I0 ,and ions move out from the wire with a velocity v0 . Then the electric ﬁeld is reduced according to the following equation:
P SC
Q
E = E0 − i.
(7.3)
2πϵr0 l0
Finally, gain is decreased as follows:E

G = e E0

7.4

logG0

.

(7.4)

Comparison between MC and Commissioning Data at MEG II Beam Rate

Fig. 7.9a and Fig. 7.9b show the signal amplitude and the RMS-noise at each operation voltage in the 2018 commissioning
with the muon beam of the MEG II intensity. The MC waveforms have the consistent amplitudes around the peak region(0 - 0.03V) with the commissioning data, where operation voltage was around 1520 V and gas gain was ∼ 1 − −2 × 105[26]. The small discrepancy was seen in the region above 0.04 V, and the commissioning data had larger amplitudes thanthe MC.
As for the RMS-noise, the commissioning data in 2018 had the larger values than the MC due to the contribution from theintermediate converter and the ground loops, which will be disappeared in the future. In the MC, the contribution from these7.4 Comparison between MC and Commissioning Data at MEG II Beam Rate

103
RMS-Noise

1460 V h1
410

Entries

233968

Mean
1480
V

0.008948

Std Dev0.008396

1500 V

Entries

Entries

Amplitude1460 V h105

Entries

104

109.703e − 05

1520 V

103

1540 V3

0.000841

Std Dev

1500 V

1520 V

1670234

Mean
1480
V

MC

1540 V
MC

2

10
102

10
1

10
0

0.02

0.04

0.06

0.08

10−1
0

0.1
[V]

(a) The signal height with several operation voltages and thesimulation after the noise reduction under the MEG II nominal beam rate. The number of entries for the MC was scaled
to the number of the commissioning data at 1520 V.

0.0005 0.001 0.0015 0.002 0.0025 0.003[V](b) The RMS-noise with several operation voltages and thesimulation after the noise reduction under the MEG II nominal beam rate. The number of entries for the MC was scaled
to the number of the commissioning data at 1520 V.

EntriesFig. 7.9: The signal height and the RMS-noise under the MEG II nominal beam rate.

h41520 V

Entries
332246Mean
10.44
1520 V + MC Noise
Std Dev
7.441

104

MC

103

102
0

10

20

30

40

50
S/N

Fig. 7.10: S/N distributions from the commissioning data and the simulation. S from the commissioning data and N fromthe simulated mean (0.8 mV) is also shown.

equipment were removed and the 2 mV white noise was added instead. Fig. 7.10 shows the S/N of each waveform withthree patterns; S/N from the commissioning data (yellow), S/N from the simulation (brown), and S from the commissioning
data and N from the simulated mean, 0.8 mV (purple). Since the noise problems in CDCH were already ﬁxed, higher tailin the RMS-noise will disappear in the future. Therefore, consistency between MC and 1520V+MC noise shows that the
updated MC simulations are reliable enough. The S/N is one-order worse than the expectation in previous works [7].

Chapter 7 CDCH Analysis

104

7.5

CDCH Tracking Algorithms

In this section, the algorithms for the CDCH analysis after the waveform analysis, which are hit reconstruction, track
ﬁnding, and track ﬁtting, are described with MC. The goal of CDCH analysis is to reconstruct the positron tracks andestimate the state vector at the vertex on the stopping target. The state vector includes the kinematic variables related tothe µ → eγ search, i.e. position’s momentum (angle) and timing information. Also, the covariance between the variables iscalculated and used for the positron selection for physics analysis.

7.5.1

Hit Reconstruction

The CDCH hit reconstruction is performed based on the waveform analysis at the two ends.The important information of
the CDCH hit is the local-z position on the wire and its impact parameter (b)*3 . The target resolution of the z reconstruction
is 10 cm, and b estimation 110 µm. For the local-z reconstruction, two methods have been developed.
Charge Division

The conventional charge division method has been adopted for the reconstruction of the z-coordinate on the wire [70]. By
measuring the charge asymmetry between the two ends, the local-z can be measured as below:
Q

z=

up
−1 Z L
G Qdown( + ),Qup
G+1 ρ 2

(7.5)

Qdown

where the ﬁrst factor is the charge asymmetry calculated from the charges at both ends, the latter factor correspond to theeﬀective wire length. The input impedance of the readout preampliﬁer circuit is typically 360 Ω and the wire resistivity is
175 Ω/m. G is the gain ratio between the two ends, which must be calibrated with the data.
Time Difference

The arrival timing diﬀerence between the two ends can be used to determine the z position. This is called the timing
diﬀerence method. The local-z can be calculated as follows:z=(tup − tup oﬀset ) − (tdown − tdown oﬀset )
veﬀ ,
2

(7.6)

where the tup , tdown are the reconstructed timing at the two ends, veﬀ is the eﬀective velocity of the signal propagation on awire. tup oﬀset , tdown oﬀset are the timing oﬀset of the two ends.
Fig. 7.11 and Fig. 7.12 show the diﬀerence between the reconstructed z and the MC truth for the single Michel positron
and the Michel positron with pileup positrons at the MEG II nominal intensity of the muon beam, respectively. The
estimated resolutions of the core component (obtained ﬁtting with mean±1σ) are 3.2 cm from the time diﬀerence method
and 11.5 cm from the charge division method under the muon beam intensity expected in the MEG II. The consistency
between two methods, ztime diﬀ − zcharge div , is also shown in the plots. The width is 11.8 cm, and the mean value is slightly
shifted (∼ −1 cm, which is due to the bias in the charge division method). The time diﬀerence method is much more precise
than the charge division method and we use the z from time diﬀerence in the reconstruction procedure.

*3 The positron track information or assumption is needed to calculate the impact parameter b as described in Sec. 7.5.2. Even if the local-z and b are

obtained, there is still an ambiguity on whether a positron passed the left side of a wire or the right side. This ambiguity is iteratively solved in the
track ﬁtting process.

7.5 CDCH Tracking Algorithms

105

Fig. 7.11: The diﬀerence in z between the MC truth and the reconstruction (left: time diﬀerence, center: charge division).
The right histogram shows the consistency between the two methods under the MEG II expected muon decay rate (7 × 107 ).

Fig. 7.12: The diﬀerence in z between the MC truth and the measurement (left: time diﬀerence, center: charge division).
The right histogram shows the consistency between the two methods under the single Michel decay.

7.5.2

Track Finding

The nearby reconstructed hits are then clustered to reconstruct the positron track. This process is often called patternrecognition, or track ﬁnding in the ﬁeld of particle physics. For the track ﬁnding algorithm, there are two major categories:
one is the local following method and the other is the global following method. The concepts are summarized as follows:• Local Following: Starting from a reliable track seed, nearby hits are added step by step. For example, Kalman Filter
technique, local clustering.
• Global Following: All hits are treated equally and simultaneously at the process of clustering. For exmaple, Neural
Net, circle ﬁts.
In MEG II track ﬁnding, the local following algorithm based on the Kalman Filter technique is adopted. The algorithm
starts from making seeds, and then those seeds are prolongated to tracks. The algorithm and codes are partially based on
the Alice Oﬄine Project (AliRoot) [71] and are developed by the MEGII CDCH tracking project.
The basic procedure of the MEG II track ﬁnding is as following:• Calculate drift time for CDCH hits from the pTC clusters,• Construct possible seed tracks from the outer layers,• Extrapolate seed tracks,• Compute track qualities.

Chapter 7 CDCH Analysis

106

Fig. 7.13: The illustration of the CDCH seeding procedure. The blue and green circles show the drift circle, and the dashedlines are the candidate of the track (left-right for each circle). The yellow line shows the constructed track seed.

Fig. 7.13 shows the seeding procedure. To calculate the drift time and the impact parameter, the timing from pTC cluster
is mainly used as the reference timing, T 0 . The initial drift time is calculated as thit − T 0 *4 . The coordinate of pTC clusters
can be also used to ﬁlterate the initial CDCH hits for the seed to ∼1/4 of CDCH full volume. Since the wire measurement
is the 1-D measurement, it is impossible to know whether a positron passed through the left side or the right side of awire only from the wire measurement. To solve this “left-right” ambiguity, a part of track has to be assumed from thepossible patterns. The track seeds are mainly formed by two consecutive hit-pairs in two layers. The possible left-rightpatterns of the two hits are all checked in the same layer to estimate the direction, and the direction compatibility is checkedwith |∆cos(ϕ(direction) − ϕ(position))| < 0.2. The diﬀerence between the reconstructed z position and the stereo-crossing
z position, ∆z, is also used for the consistency check of the two pairs. The pre-determined criteria for z consistency is∆z2 < 9 ∗ 2 ∗ σ2z . σz can be optimized based on the data. In this thesis, ﬁxed value of 10 cm was implemented. The
reconstructed track seeds are then prolongated by the iteration of the extrapolation, hit addition and the Kalman Filter
ﬁtting. After the prolongation over a single turn, then the seeding and prolongation at the next turn region are tried.
The output of the pattern recognition has the many track candidates, including the ghost tracks. The quality factor, Q, isdeﬁned and calculated for each track candidate:
Q = ldense dmax + nhit + 0.2 nhit p(χ2 , ndof ),(7.7)

where ldense is the length (the number of the continuous layers) of the densest area of hits, dmax is the maximum density of
the hits, nhit is the number of hits in the candidate, p(χ2 , ndof ) is the probability value of the χ2 with the degree of freedom
ndof from the track ﬁtting. The ﬁrst term means that the more continuous tracks have higher weight, the second term means
the bigger tracks have the higher weight, and the third term means the tracks with the better χ2 have the higher weight. The*4 At the seeding level, the averaged drift velocity of ∼2.7 cm/µm is used for the calculation. The more precise b calculation is performed with the

pre-calculated table of time-xy relation (t-xy table), the incident angle, and the TOF correction by the track information after completing the patternrecognition.

7.5 CDCH Tracking Algorithms

SecondSegment(1.0 turn)

107

First Segment(0.5 turn)Third segment
before pTC region(1.5 turn)First Segment(0.5 turn)Third segment
before pTC region(1.5 turn)

SecondSegment(1.0 turn)Fig. 7.14: Event monitor with a simulated signal positron from the x-y projected view (left) and the 3-D monitor from the
top view (right).

factor 0.2 was manually tuned to maximize the reconstruction eﬃciency in the simulation. The tracks are removed fromthe output when they have 30% of hits who are already associated by the better quality track.

7.5.3

CDCH Track Fitting

In the ﬁnal step of CDCH analysis, the positron tracks are reconstructed by using the ﬁtting algorithms, and the best estimateof the state vector at the vertex is obtained. This task is composed of three steps: the DAF ﬁtting, the turn merge and theextrapolation.
The track ﬁtting of CDCH hits are performed with the DAF algorithm implemented in GENFIT. DAF (Deterministic
Annealing Filter) algorithm is an extension of the Kalman Filter (KF) technique with the re-weighted (assignment) measurement and the outlier hypothesis. The probabilities of the measurements, which are the “left” measurement and the“right” measurement on a wire measurement case, are assigned. Those measurements then compete each other during
the iteration process of the KF technique. The higher assignment measurement will survive the ﬁtting iteration, and thelower assignment measurement will be frozen out*5 . The sum of probabilities on a detector plane can be < 1, which means
the inconsistent measurement can have the small probability. Such inconsistent measurements can be removed. These
characteristics are suitable for the ﬁtting with wire measurements.
Then the ﬁtted tracks from diﬀerent turns are merged. The typical positron trajectory has 1.5 turns before entering pTC
as illustrated in Fig. 7.14, and crosses the CDCH active volume three times (leaves three track segments). To achieve thetarget resolution, these all segments must be merged for ﬁtting. This turn merge is based on the consistency of position
and timing between the state vectors extrapolated to the plane deﬁned at the center of the two segments. The turn merge
criteria should be wider than the resolution since the number of hits and the path length is not large enough with the only
single segment. For example, the momentum matching |∆p| < 5 MeV, the timing matching |∆t| < 20 ns, the position
matching |∆z| < 10 cm and |∆r| < 10 cm, the angle matching |∆θ| < 0.2 rad and |∆ϕ| < 0.2 (outer) or |∆ϕ| < 0.5 (inner)rad. If multiple tracks become the candidates for one segment, the χ2 values, which are calculated from the DAF ﬁttings
are compared and the best pair is accepted. After the ﬁtting again with full segments, the track state vector is extrapolatedby the Runge-Kutta algorithm to the stopping target to ﬁnd the vertex position. The ﬂight time from the vertex to the pTC*5 The DAF procedure can be considered as the thermodynamical approach since its assignment probability is the function of a parameter, T , which

can be considered as the temperature. The freezing out up to “hard” (T = 0) is equivalent to χ2 cut.

Chapter 7 CDCH Analysis

108

Target To pTCTime

1200

EntriesMean
Std Dev
p0
p1
p2
p3
p4
p5

1000
800
600

6724
2.985e −125.795e −11
1.694e −08 ± 3.625e −10
7.932e −12 ± 1.401e −13
6.938e −12 ± 1.526e −13
7.936e −09 ± 2.860e −10−2.275e −13 ± 1.289e −12
4.23e−11 ± 1.50e−12

400
200
0

−0.2

0

0.2

×10

−9

Time Difference from Truth [s]Fig. 7.15: The estimated ﬂight time precision (σTOF ≈ 6.9 ps) in the CDCH region with the simulation.

(i.e. inside the CDCH region) is calculated from the path length of the reconstructed track divided by the speed of light.
Fig. 7.15 shows the estimated ﬂight time precision, 6.9 ps, which is twice better than 14.8 ps from [7] since not only the
information from the forward propagation but also that from the backward propagation of the KF algorithm was utilized inthis thesis. The formulation of the KF algorithm is explained in detail in Appendix D.

109

Chapter 8

Performance of Positron Spectrometer
The pTC and CDCH algorithms were described in the previous chapters. In this chapter, the pTC and the CDCH combinedalgorithms, which are developed for the performance evaluation of the positron spectrometer, are described. The resolutionsof the positron spectrometer had not been evaluated with realistic MEG II conditions in previous studies [7]. In this thesis,
the performance of the positron spectrometer is evaluated based on the MEG II simulations tuned by the commissioning
data.

8.1

CDCH-pTC Combined Analysis for Global Tracking

The goal of the CDCH-pTC combined analysis is to reconstruct the global positron tracks and obtain the reﬁned information
at the vertex. This analysis is composed of two steps; the CDCH-pTC Matching and the pTC-CDCH Global Tracking.

8.1.1

CDCH-pTC Matching

The reconstructed positron track in CDCH is extrapolated to the pTC and associated with the pTC cluster, and then thepTC hits are re-ﬁtted by the DAF algorithm using the momentum information from the CDCH tracking. The state vector
from the CDCH track ﬁtting is extrapolated to the pTC clusters, and the matching between the extrapolated position andthe pTC counter position is tested. Fig. 8.1 shows the diﬀerence between the pTC hit position and the CDCH extrapolated
position. The criteria for the position diﬀerence is 5σ for the pTC local-x direction (i.e. xextrapolated − xcounter < 5.5 cm) andq
10 cm for the 3D distance (i.e. (xextrapolated − xcounter )2 + (yextrapolated − ycounter )2 + (zextrapolated − zcounter )2 ) < 10 cm) . The
diﬀerence between T 0 of the CDCH track and the pTC timing is also checked (± 15 ns timing window). The distribution
Timing Difference b/w pTC and CDCHy[cm]

Hit Position Difference in Counters

10

h
h

Entries
Mean xMean y4092
0.09669
0.6629
Std Dev x
3.442
Std Dev y
2.087

8
6
4
2

60
50

10

3

Entries

4092

Mean

8.903e − 10

Std Dev

1.838e − 09

102

40

0
−2

30

−4

20

−6
−8

10

−10
−10

0

−5

0

5

10
x[cm]

Fig. 8.1: The diﬀerence between the pTC hit position and the CDCH extrapolated position.

10

1
−20

−9

−10

0

×10
10
20
timing difference[s]Fig. 8.2: The timing diﬀerence between the pTC
clusters and the CDCH tracks. ±15 ns timing
window for the matching is applied.

Chapter 8 Performance of Positron Spectrometer

Entries

110

EntriesMean
Std Dev

2500

3280
1.209
0.4252

2000
1500
1000
500
0
0

2

4

Fig. 8.4: The propagation length from the CDCH

Number of Matched Cluters

Fig. 8.3: The number of matched cluters for one

region to the pTC counter which is illustrated in
the histogram: the length of the pink line is the

CDCH track.

propagation length, the black circle is the CDCH
outer foil, and yellow boxes are pTC counters.
The red histogram shows the after 5σ resolution
cut.

Y[cm]

Matched X-Y (4cm)

3

Entries
Mean xMean yStd Dev x
Std Dev y24238− 0.7477
1.457
3.124
0.8199

1

18
16
14
12
10

0

6
4

−2
−3

2

−5

0

0

5
X[cm]

Entries

8

−1

150

Entries

6852

Mean

66.19

Std Dev

23.84

Y[cm]

Matched X-Y (5cm)

3

Entries
Mean xMean yStd Dev x
Std Dev y22474− 0.4946
1.821
3.021
0.6626

1

14
12
10

100

8

0
6

−1

4

−2

2

−3

0

−5

0

5

50

X[cm]

Fig. 8.5: The distribution of (x, y) matched posi-

0
0

50

100

Matchd Z Position

tions in the counter local coordinate. Up: 4cm
counters (the counter region is ±6 cm for x and

Fig. 8.6: The matched |z|-position.

±2 cm for y), down: 5 cm counters (±6 cm for x
and ±2.5 cm for y).

of the timing diﬀerence after the matching is shown in Fig. 8.2. If the multiple CDCH tracks match with one pTC cluster,
the extrapolation lengths are compared since the large distance of the extrapolation increase the uncertainty, resulting in theworse path-length estimation. For example, Fig. 8.3 shows the number of the matching with pTC clusters for one CDCH
track. Fig. 8.4 shows the extrapolation length of CDCH tracks (black histogram). The tracks within the 5σ from the truth
are also shown (red histogram). Most of the good resolution tracks have shorter extrapolation length, since they have the8.1 CDCH-pTC Combined Analysis for Global Tracking

111
Imparct Parameter Resolution

Imparct Parameter Resolution

600
800
400

600
400

200

200
0
−0.05

0

0
−0.05

0.05

0

0.05

[cm]

[cm]

Fig. 8.7: The impact parameter resolutions with a simulated signal positron. The blue histogram was updated
to the red histogram by the pTC-CDCH track re-ﬁtting.
The resolution changed from 106 µm to 85 µm (thestandard deviation from 123 µm to 112 µm).

Fig. 8.8: The impact parameter resolutions with a simulated signal positron and 7 × 107 Michel positrons. The
blue histogram was updated to the red histogram by
the pTC-CDCH track re-ﬁtting. The resolution changed
from 111 µm to 84 µm (the standard deviation from 130µm to 114 µm).

track segment just before the pTC region as shown in Fig. 7.14. For these reasons, the pair with the shortest distance isselected. Fig. 8.5 shows the (x, y) distribution of the extrapolated CDCH tracks for matched positrons in the counter local
coordinate, and Fig. 8.6 shows that of the |z| matched position in the global coordinate. Since one positron crosses 8 – 9counters on average, the ﬁrst matched counter tends to have high y-position.

8.1.2

pTC-CDCH Global Track Reﬁnment

The positron track information in the CDCH and the timing information in the pTC are now available. The next step is thereﬁnement of the positron global tracks by utilizing both information.
Track Reﬁnement by pTC Timing

The timing information from the pTC is used for the re-calculation of the drift time. The accuracy of the timing at each
CDCH hits are not so good (∼ ns) before the reﬁnement. The positron crossing timing at each cell, T 0 , should be reﬁned
with the reconstructed pTC timing and CDCH TOF information. The drift time tdrift is calculated as follows:
tdrift = tCDCH Hit − (tpTC cluster − ∆T Path ),(8.1)

where tCDCH Hit is the measured time of the CDCH hit on the wire, tpTC − ∆T Path is the reﬁned T 0 with the pTC timing fromthe pTC cluster (tpTC cluster ) and the ﬂight time calculated by the path length from the pTC counter to the track point in the
hit cell (∆T Path ). Fig. 8.7 and Fig. 8.8 show the impact parameter resolution before (blue) / after (red) the reﬁnement*1 . The
impact of the reﬁnement is ∼20% improvement for σr .

*1 The reﬁnement is eﬀective when the track is combined with the correct cluster. When the track parameter is reﬁned with the wrong cluster, theimpact parameter resolution will be deteriorated. In principle, the matching criteria is severe enough to avoid the wrong matching of signal-likepositrons, however, this should be noted for the background analysis.

Chapter 8 Performance of Positron Spectrometer

112

Table 8.1: The timing resolution (calculated from the pTC performance in Table 6.6 and the path length estimation of the
CDCH in Fig. 7.15) at the vertex.
With CDCH Information from Simulation

UpdatedPrevious [7]

TOF Resolution in CDCH

6.9 ps

14.8 psResolution At Vertex (2017)37.6 ps44.1 ps (41.2 ps in [7])◦48.1 ps

55.4 ps◦59.8 ps

68.3 psResolution At Vertex (Full Radiation, 10 C)
Resolution At Vertex (Full Radiation, 30 C)

Timing Reconstruction by Global Tracking

The timing of the matched point of the tracks from the CDCH and the pTC (tpTC ) is calculated by using all the hit timings(ti , i = 1, 2, ... n) in the pTC track with the correction for TOF from the ﬁrst hit counter to the i-th hit counter (TOFi ):1
tpTC = Σni (ti − TOFi ).
n

(8.2)

The timing at the target is then calculated by using the ﬂight length from the target to the matched point (LCDCH ):tvertex = tpTC − LCDCH /c.

(8.3)

Table 8.1 summarized the timing resolution at the vertex (σt ) combined with the pTC resolution (σtpTC ) and the CDCH path
length estimation (σLCDCH /c ) as follows:
σt =

8.2

q
σ2tpTC + σ2LCDCH /c .

(8.4)

Positron Spectrometer Performance

The improvements of the positron reconstruction eﬃciency and the detector resolution are the crucial updates in the MEG
II experiment. In this section, criteria of the performance evaluation for the positron spectrometer is described.

8.2.1

Deﬁnition of Reconstruction Efﬁciency

The denominator of the eﬃciency is the total number of the events, where the gamma-ray from signal decay enters the LXedetector acceptance (|u| < 23.9 cm, |v| < 67.9 cm). The numerator of the eﬃciency is the number of the selected signal
events with the following conditions.

8.2.2

Global Track Selection

Most of the triggered events include more than one positron track due to high beam rate. The best candidate for the positron
track has to be selected. The selection task, which is the ﬁnal step of the global tracking chain, is composed of the following
components:• Track pre-selection,• pTC track selection,• Quality selection,• Track selection.

8.2 Positron Spectrometer Performance

113

Track pre-selection

In the actual physics analysis, the raw data size will be huge and a pre-selection will be applied to reduce the data size andcalculation time. The pre-selection criteria is summarized below:• Propagation to the pTC region and back-propagation to the target from CDCH tracks is succeeded,• 40 MeV < Prec < 65 MeV,
• -12 ns < δteγ < 12 ns,• -1 < cos(δθeγ ) < -0.9,
where Prec is the reconstructed momentum at the target, δteγ is the timing diﬀerence between a gamma-ray and a positron,δθeγ is the opening angle between a gamma-ray direction and a positron direction. The reconstruction and selection of the
gamma-ray in the triggered event is completed before the positron track pre-selection. The rate of high energy gamma-rays
are lower than that of high energy positrons, and a signal like gamma ray can be well separated from the pile up gammarays. Note that a pre-selection with too strong criteria will cause a selection bias and the criteria should be loose enoughcompared to the region of interest. For example, the µ → eγ blinding box of δteγ in MEG experiment was -1 ns < δteγ < 1
ns and timing sideband was -0.7 ns < δteγ ± 2 < 0.7 ns, which were determined by the detector resolution and the range ofthe likelihood analysis. Pre-selection should be much wider than these values. In addition, the momentum values from theMichel positrons will be used to extract the momentum resolution of the spectrometer, as described in Appendix G. The
wide range is needed for the pre-selection, and the above criteria was set in this thesis.
pTC Track Selection

The CDCH tracks can match more than one pTC cluster, so we should select the best pTC track (i.e. choose the best
positron timing measurement). The ﬁrst cluster, i.e. pTC cluster in the smallest |z| region, is selected. This is because thatthe latter clusters are more aﬀected by the scattering and energy loss from materials (ﬁrst pTC cluster, CDCH outer foil,
wires and so on). The resolution of the path length also becomes worse due to the large propagation length.
Quality Selection

The quality of the reconstructed CDCH track is checked. The “quality” does not depend on the event types (signal orMichel background events). In the KF ﬁtting, the χ2 /dof represents the quality of track ﬁtting. The following criteria arechecked in the quality selection:• NCDCH hit ≥ 9: require more than one hits per layer on average.
• 0 ≤ NCDCH turns ≤ 10: reject tracks with too many turns.
• σtrack< 1 MeV: reject the tail tracks.
P• σtrack< 30 mrad: reject the tail tracks.
ϕ• σtrack< 20 mrad: reject the tail tracks.
θwhere NCDCH hit is the number of the hits in the CDCH track, NCDCH turns is the number of turns on a CDCH track, σtrack
P ,σtrack, σtrack
are the square root of the corresponding diagonal component of the covariance matrix from a state vector ofϕθ
the starting point on the track.
Fig. 8.9 shows the number of positron tracks in each event (black), one after the track pre-selection (purple), and one
after the track quality selection (red). Most of the low quality tracks are rejected by up to the quality selection, and theevents which still have more than two tracks are only a few %.

Chapter 8 Performance of Positron Spectrometer

114

EntriesNumber of Tracks in an Event

4000

Entries

5470

Mean

1.077

Std Dev

0.4758

15

20

3000
2000
1000
0
0

5

10

Number of Tracks

Fig. 8.9: The number of positron tracks in each event with no selections (black), those with the track pre-selection (purple),and those with the track quality selection (red).

Track Selection

A track selection is applied on the qualiﬁed CDCH and pTC track pair to select the best track to be used in the physics
analysis. The track selection is composed of the following steps:
1. Target volume check2. Acceptance check3. Covariance check4. Ranking
All of the positron tracks used for the physics analysis must come from the target. The target ﬁducial area is deﬁned as
the ellipse:(y − yoﬀset )2 (z − zoﬀset )2+= 1.
ytargetztarget(8.5)

Where yoﬀset and zoﬀset are the oﬀset values for the target center position, ytarget and ztarget are the semi-minor and semi-majoraxes of the target ellipse. The reconstructed position, (yrec , zrec ), must be inside the target ﬁducial area.
The second step is to check whether the positron track is in the acceptance range or not. The positron acceptance for+µ → e+ γ search is deﬁned with the LXe detector acceptance (|u| < 23.9 cm and |v| < 67.9 cm). From the vertex position,
the state vector is extrapolated linearly opposite to the positron emission direction. When that state vector is inside theﬁducial volume at R = 64.84 cm, the event is accepted for physics analysis.
The third step is to check the values in the covariant matrix of the track at the vertex position. Since the tracking algorithm
adopts the KF technique and we have the covariance matrix on each track, the per-track error (per-error, σ′ ) can be deﬁned
as the diagonal components of the covariance matrix at the vertex point. If the per-error is large, that track is not used for thephysics analysis. Fig. 8.10 shows the distribution of each per-error. The per-error criteria is determined by the distributionof as follows:

8.2 Positron Spectrometer Performance115
Phi per error

Theta per error

103

P per error

Entries

7264

Entries

7264

Entries

7264

Mean

7.082

Mean

8.129

Mean

0.1128

Std Dev

9.777

Std Dev

11.37

Std Dev

0.1762

103

103

102

102

102

10

10

10

1
0

1
50

100

150

200

0

1
50

100

150

(mrad)

2

4(MeV)

Y per error
Entries

7264

Entries

7264

Mean

1.495

Mean

1.022

Std Dev

1.612

Std Dev

1.919

103

102

102

10

10

1
0

0

(mrad)Z per error

103

200

1
10

20

30

40

0

10

20

30

(mm)

40
(mm)

Fig. 8.10: The distribution of the per-errors of MEG II kinematic parameters.

• σ′P < 1 MeV• σ′ϕ < 30 mrad
• σ′θ < 20 mrad
• σ′z < 1 cm
• σ′y < 1 cm
The ﬁnal step is the ranking. Based on the ranking value (currently just the reduced χ2 value of each track), the best trackin an event is selected. The distribution of χ2 /dof is shown in Fig. 8.11. The distribution of tracks after the all selections
including the tail cut is also shown in the histogram ﬁlled with red.

8.2.3

Truth Check

The MEG II simulation ﬁle is made by mixing a single signal event and Michel events with the rate of 7×107 e+ /s. After the
track selection, the selected track is checked whether it is really a signal event or not by using the MC truth information.

8.2.4

Tail Cut

The track parameters (vertex, angle, and position) are checked by using the MC truth. If the reconstructed value is consistent
with the MC truth within 5σ, that event is used for the physics analysis. This 5σ region is deﬁned as Table 8.2.

Chapter 8 Performance of Positron Spectrometer116

χ2 of tracks
Entries

104

52818

Mean

1.104

Std Dev

0.6755

103
102
10
1
0

5

10

15

20

χ2/dofFig. 8.11: The distribution of the χ2 of tracks (black) and selected tracks with good quality (red, within 5σ tail cut).

Table 8.2: The criteria for the 5σ eﬃciency cut.

8.2.5

Variableσ

5σ

θ [mrad]

6.1

30.5

ϕ [mrad]

5.6

28.0

P [MeV]

0.09

0.45

z [mm]

1.5

7.5

y [mm]

0.76

3.8

t [ps]

40

200

Angle Correlation Correction

The correlation of the parameters, as shown in Fig. 8.12 in the signal region, is corrected. The correlation is obtained fromthe 2D plot of θ and ϕ, and the projected resolution of ϕ (σϕ ) is calculated with the slice of each θ. The weighted averagevalue of the σϕ with each slice is quoted. The projected σϕ is 4.9 mrad (σϕ without the correction was 6.2 mrad) with thepileup of 7×107 e+ /s.

8.2.6

Resolution and Efﬁciency

The resolutions and eﬃciency evaluated with the MC for ﬁve cases are summarized in Table 8.3. The four cases correspondto one signal in one event without backgrounds, and with muon rates at 3 × 107 , 5 × 107 , and 7 × 107 . The last case”Optimistic” assumes that the signal gain of the CDCH is recovered to the design value.
The diﬀerence between the MC truth and the reconstructed kinematics with the pileup of 7 × 107 e+ /s are shown in8.2 Positron Spectrometer Performance

117
Fitted value of σ φ

φ rec -φ[mrad]

0.182
0.02109
7.053 100
6.935

200

80

0

60

100

−20

40

50

20

−50

0

50

0

θ rec -θ MC [mrad]

26−3.72820.35
4.888 ± 0.078

rec

20

−40

EntriesMean
Std Devp0

MC4267 120σ φ -φEntries
Mean xMean yStd Dev x
Std Dev y40

MC[mrad]

Theta Phi Correlation

150

0
−50

0

50

θ rec -θ MC [mrad]Fig. 8.12: The relation between the θ and ϕ.

Table 8.3: The performance of the positron reconstruction under the several beam rates. The “optimistic” case uses the 3.7
times better S/N condition.
Variable

Signal Single

3 × 107

5 × 107

7 × 107

7 × 107 (Optimistic)

θ [mrad]

6.0

6.2

6.3

6.5

6.1

ϕ [mrad]

4.5

4.6

4.7

4.9

4.7

P [MeV]

79

82

86

91

84

z [mm]

1.5

1.6

1.5

1.7

1.5

y [mm]

0.7

0.7

0.8

0.8

0.7

t [ps]

40

42

42

41

41

Eﬃciency [%]

79.8

75.3

70.5

65.2

67.7

Fig. 8.13. The obtained reconstruction eﬃciency with the pileup of 7 × 107 e+ /s is 65.2%. Two times better eﬃciency
than that of the MEG experiment (30% with the pileup of 3 × 107 e+ /s) is obtained with the two times intense muon rate.
However, this value is slightly worse than the expected value in the design (70%). There is still room for the improvement
by studying cases of ineﬃciency events. As for the resolutions, the angular resolutions are 23 – 32% worse than expected
due to the worse reconstruction of the CDCH hits by the worse S/N, while the momentum resolution is 30% better due tothe improvement of the ﬁtting algorithms (the DAF ﬁtting with GENFIT, the turn merge algorithm, and so on). The resultswith 3.7 times higher gain for the CDCH is also shown in Table 8.3 as the “optimistic” scenario*2 , which is an optionalsetting for CDCH electronics prospected after the 2019 commissioning. Recovery of the resolutions, especially angle andmomentum resolutions, can be seen. The eﬃciency also slightly increased: 65% to 68%.

8.2.7

Breakdown of Inefﬁciency

Table 8.4 shows the breakdown of the ineﬃciency of the positron measurement. The breakdown study suggests that theineﬃciency is caused by the bad tracking quality: failure of turn merge of the CDCH tracks (“Quality Selection”) andtrack extrapolation from the CDCH region to the pTC region (“pTC-CDCH Matching”), and reconstruction of the signal*2 The optimistic scenario means the noise is constant (2 mV white noise) and simply S/N is improved by a factor of four.

Chapter 8 Performance of Positron Spectrometer

118
hTheta

103

hPhi

𝜎!

103

102

102

10

10

1

1

−100

− 50

0

50

100

10

1
− 50

103

𝜎%

hVertexZ

0

50

100

(mrad)

50

52

hVertexY

𝜎$

54

(MeV)

hT

𝜎&
102

102

102
10

10

10
1

1
− 20

103

𝜎#

102

−100

(mrad)

hP

𝜎"

1
− 10

0

10

20

− 20

Ztarget (mm)

−9

− 10

0

10

20

Ytarget (mm)

− 0.5

0

× 10
0.5

Fig. 8.13: The diﬀerence between the MC truth and the reconstructed kinematics with the pileup of 7 × 107 e+ /s. The redregion contains the eﬀective events after the tail cut. The tail cut will reduce the eﬃciency 10% (75.5% → 65.2%) at thisrate. The blue line shows the double-gaussian ﬁtting without tail cut, and the light blue shows the single gaussian ﬁtting
after the tail cut. The resolution is extracted from the σ of the latter ﬁtting.

Table 8.4: The breakdown of the ineﬃciency of the positron measurement with pileups of 7×107 Michel positrons.
Item
Within LXe AcceptanceWithin pTC Acceptance (pTC Hits)
Quality Selection
pTC-CDCH Matching
Pre-Selection
Selection
Tail CutEﬃciency [%]Single7 × 107

Main Reasons for Ineﬃciency at 7 × 107

100%
90.8%
88.5%
86.0%
85.6%
85.1%
79.8%
79.8±0.5%

100%
90.8%
83.6%
78.2%
77.9%
75.5%
65.2%
65.2±0.4%

Deﬁnition of denominator, 10000 events for this test in total
Scattered by CDCH materials, Annihilation
Small number of hits for one track (failure of turn merge)
Failure of propagation
Out of pre-selection window
Cut and selection based on signal kinematics
Lower tracking eﬃciency-

kinematics (“Tail Cut”).

8.2.8

Rate Dependence of pTC and CDCH Efﬁciencies

The rate dependence of the tracking (CDCH) and the timing reconstruction (pTC) eﬃciency for a signal positron is evaluated. The acceptance cuts are same to Table 8.4. The tracking eﬃciency includes the tail cuts for the kinematics except for
the timing, and the timing reconstruction includes the tail cut for the timing.
Table 8.5 shows the eﬃciency at each step; at CDCH tracking reconstruction, CDCH-pTC matching, and the pTC timing

8.2 Positron Spectrometer Performance

119

Table 8.5: The eﬃciency of CDCH tracking, CDCH-pTC matching, and pTC timing reconstruction under the beam of the
MEG II intensity.
Item

Eﬃciency at 7 × 107

Eﬃciency at Each Step

90.8%
69.6%
67.9%
65.7%

P(Acceptance|All) = 90.8
P(Tracking|Acceptance) = 76.7
P(Matching|Tracking) = 97.5
P(Timing|Matching) = 96.9

Within Acceptance
Tracking Rec.
CDCH-pTC Matching
Timing Rec.

Table 8.6: The rate dependence of CDCH tracking, CDCH-pTC matching, and pTC timing reconstruction eﬃciency.
Item
P(Tracking|Acceptance)
P(Matching|Tracking)P(Timing|Matching)

Signal Only

3 × 107

5 × 107

7 × 107

92.8
97.7
97.3

87.9
97.3
97.6

82.5
97.4
97.2

76.7
97.5
96.9

reconstruction, and Table 8.6 summarizes the rate dependence of those. The reconstruction eﬃciency of pTC clusters is
scarcely aﬀected by the increase of the beam rate, while that of CDCH tracks is signiﬁcantly aﬀected.
The maximum hit rate of the pTC counters is less than 100 kHz even at the MEG II nominal intensity. The S/N of thepTC waveform (≈ 40) is good enough to be detected. Sharp waveforms by the series connection of the SiPMs and stabilizedbaseline by the pole-zero cancellation also help the reconstruction at each counter. The contribution from the accidental
pileups in the pTC waveform (∼500 ns) is negligible. Most of 2% ineﬃciency of pTC clusters come from the scatteredparticles and secondary particles, which is diﬃcult to recover.
The deterioration of the CDCH tracking eﬃciency is due to the deterioration of CDCH hit reconstruction eﬃciency. At
high muon rate, space-charge eﬀects and pileup eﬀects are getting severe and cross-ﬁtting and hit reconstruction (explainedin Sec. 7.1 and Sec. 7.5.1, respectively) become more diﬃcult. The reconstruction eﬃciency of CDCH hits is aﬀected by∼10% as the beam rate increases, as shown in Fig. 8.14. The denominator of the hit eﬃciency is the total number of hits forthe signal positron, and the numerator is that of reconstructed hits. The z-position and timing criteria between the MC truth
and reconstructed hits, i.e. zMC − zrec < 30 cm and tMC − trec < 5 ns is applied to reject the low-quality or inconsistent hits.
Fig. 8.15 shows an example of an event that fails turn merge. If the turn merge fails, especially the merged segment isless than three, most of the tracks are rejected by the tail cut due to the less number of hits as shown in Fig. 8.16. The failureof the turn merge was caused by not optimized conditions for the turn merge and the propagation failure of each segment
due to the short tracking length (i.e. the number of CDCH hits in one segment is small). If we could solve the failure of theturn merge, the ineﬃciency from the propagation failure and the quality (∼8% at the maximum) might be recovered.

Chapter 8 Performance of Positron Spectrometer

120

100
95

Efficiency [%]

90
85
80
75
70
65
60
55
50
0

2

4
6
8
Beam Rate [10^7 µ / s]10

Fig. 8.14: The relation between the eﬃciency of the hit reconstruction by signal positrons and the beam rate.

Fig. 8.15: An example of an ineﬃciency event by turn merge failure from ± stereo view. The green-dot segment and theblue-dot segment were not merged.

121

Entries

Entries

8.2 Positron Spectrometer Performance

300

300

200

200

100

100

0
0

50

100

Number of Hits in a Track(a) MEG II nominal rate.

0
0

50

100

Number of Hits in a Track(b) Signal Only.

Fig. 8.16: Distribution of the number of hits in one signal track under the MEG II beam intensity before (black) and after(red) the tail cut. One track segment has ∼20 hits (ﬁrst peak), and these segments are merged to improve the quality of the
tracks.

123

Chapter 9

Projected Sensitivity of MEG II
Based on the results described in Chap. 8, the projected sensitivity of the MEG II experiment is calculated in this chapter.

9.1

Maximum Likelihood Fit

The MEG II collaboration employs the Maximum Likelihood Fit (ML-Fit) to estimate the number of µ+ → e+ γ events,
Nsig . The improved detector resolution in MEG II will give us better signal/background separation, and the improved
reconstruction eﬃciency will give us larger statistics. Based on the current best understanding on the detector performance,
the projected sensitivity of the MEG II experiment will be discussed.

9.1.1

Maximum Likelihood Function

The likelihood function, L(θ|X) where θ is the target parameters to be estimated and X is the obtained data set, can be
written as below:
L(θ|X) =Nobs
Yp(xi |θ),

(9.1)

i

where Nobs is the number of events observed in the experiment, p(xi |θ) is the probability density function of each event fora given set of parameters θ, and xi is the discriminant variables of the i-th event. The likelihood function can be extended[72] with the Poisson distribution of Nobs :obs
e−N N Nobs Yp(xi |θ),Nobs !
i

N

L(θ, N|X) =(9.2)

where N is the sum of the expected numbers of the three event types; the accidental background events (Nacc ), the RMD
events (NRMD ) and Nsig :N = Nsig + Nacc + NRMD .

(9.3)

So L(θ, N|X) can be written as L(Nsig , Nacc , NRMD |X). For simplicity we describe L(Nsig , Nacc , NRMD |X) as L.

9.1.2

Probability Density Function

To formulate the likelihood function, the probability density function (PDF) p(xi |Nsig , Nacc , NRMD ), hereafter denoted as p,
must be described properly. From the deﬁnition of PDF, there are relations below:p(sig) + p(acc) + p(RMD) = 1,

(9.4)

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

(9.5)

Chapter 9 Projected Sensitivity of MEG II

124

where p(sig), p(acc), p(RMD) is the PDF of a signal, accidental or RMD event, and p(sig|xi ), p(acc|xi ), p(RMD|xi ) is the
PDF of a signal, accidental or RMD event at the observation of xi . From the Beyes’ theorem, there is the relationship below:p(sig|xi ) =p(xi |sig)p(sig),p(xi )(9.6)

the same relation can be written on accidental and RMD events. The PDF can be written down as below:p(xi |Nsig , Nacc , NRMD ) = p(xi |sig)p(sig) + p(xi |acc)p(acc) + p(xi |RMD)p(RMD)(9.7)

The signal, accidental and RMD PDF are denoted as below:
S (xi ) = p(xi |sig), A(xi ) = p(xi |acc), R(xi ) = p(xi |RMD).

(9.8)

Then the event-by-event PDF function can be formulated as below:
p = S (xi )

Nsig
Nacc
NRMD
+ A(xi )+ R(xi )
.
N
N
N

(9.9)

Also, from the sideband of the signal box region, the Nacc and NRMD can be estimated and can be included in the likelihood
function as µacc and µRMD . In conclusion, the MEG II likelihood function can be written down:obs
e−N(Nacc − µacc )(NRMD − µRMD ) Y
exp(
)exp(
)
(S (xi )Nsig + A(xi )Nacc + R(xi )NRMD ),Nobs !
2σ2acc2σ2RMDi

N

L=(9.10)

where σacc , and σRMD are the uncertainties of the numbers of the accidental background events and the RMD events fromthe sideband of the signal box region.

9.1.3

Discriminant Variables

The discriminant variables for ML ﬁtting are described in x⃗i :x⃗i = (Eγ , Ee+ , te+ γ , Φe+ γ , Θe+ γ , trdc , Erdc ).

(9.11)

The analysis regions are summarized as follows:• Gamma energy: 48 < Eγ < 55 MeV,
• Positron energy: 52.2 < Ee+ < 53.5 MeV,• Time diﬀerence between gamma ray and positron |te+ γ | < 0.25 ns,• Relative angle of ﬂipped positron direction with reference to gamma direction: |Θeγ | < 40 mrad and |Φeγ | < 40 mrad.
This analysis region includes enough signal and background regions for the ﬁtting, and is wider than the signal region, e.g.
described in Sec. 2.1.2. The regions become narrower signiﬁcantly compared with MEG thanks to the improved resolutionsof the positron spectrometer*1 . The PDF functions S (xi ), A(xi ) and R(xi ) are calculated from the theoretical expectations
and the measured detector responses. For example, A(Ee+ ) is constructed from the measurement of the Michel spectrum,and S(Ee+ ) is constructed from the function of the energy resolution (PDFs are shown in Fig. 9.3 and Fig. 9.4 in the latter
section). S(te+ γ ) becomes the combination of the positron timing resolution and the gamma-ray timing resolution. The
resolution of te+ γ is calculated from the obtained resolutions in this thesis, but this value is measured by the peak of the
RMD events in the real experiment.

9.1 Maximum Likelihood Fit

125

Table 9.1: Default values for the sensitivity calculation of MEG II experiment.
Variables

9.1.4

ValuesRµ

7 × 107 µ/s

T

20 weeks / year × 3 year (84% live fraction)

Ω

10.8%

ϵγ

69 %

ϵe

70%

ϵs

91%

Nobs

1.01 × 1014 µ

Expected Number of Muon Decays

To estimate the probability of µ → e + γ, the estimation of the total number of the muon decay observed in the experiment(normalization factor, Nobs ) is needed. This can be calculated as follows:
Nobs = Rµ × T × Ω × ϵγ × ϵe × ϵ s ,(9.12)

the deﬁnition of each variable is the same in (2.1). For the MEG II sensitivity calculation, values summarized in Table 9.1
were used*2 .

9.1.5

Systematic Uncertainty

In the MEG experiment, the impact of systematic uncertainties on the sensitivity was small (less than 1%) except for theuncertainties for the target deformation, as shown in Table 2.2. As for the alignment of the target which had 13% impact on
the sensitivity, the dedicated systems (hard-material target, pattern dots, and camera system) are installed and it is expectedthat this uncertainty will decrease a lot. Therefore, this uncertainty is neglected in the estimation of MEG II sensitivity at
this moment. Even though muon intensity will be twice higher, other uncertainties related to the detector performances andreconstruction under high rate are assumed to be negligible in this sensitivity estimation.

9.1.6

Conﬁdence Interval and Sensitivity

The MLFit gives the best estimate of Nsig from a given dataset of an experiment. The best estimate of Br(µ → eγ) is thengiven as Nsig /Nobs . We adopt an asymptotic approach in [73] to calculate the conﬁdence interval of Nsig (or Br) at 90%
conﬁdence level in this thesis.*3
The “sensitivity” of an experiment is deﬁned here as the median of the upper limits of the conﬁdence intervals foran ensemble of “pseudo-experiments” with the null-signal hypothesis. The pseudo-experiment is a statistical dedicatedsimulation of the experiment to study the statistical behavior of the experiment. It is used in the sensitivity calculation
because the full simulation takes too much time and it is not realistic to use the full simulation for the statistical estimations.
It does not simulate the actual physics interaction, digitization of the detected information and so on, but generates the*1 The analysis region in the MEG experiment was as follows: 48 < E γ < 58 MeV, 50 < E + < 56 MeV, |t + | < 0.7 ns, |Θeγ | < 50 mrad and |Φeγ | <ee γ

75 mrad in [4].
*2 In the real experiment, the eﬃciencies and the stopping rate can be changed during the data taking. In the MEG experiment, the total number ofdecayed muons (normalization farctor) was calculated by two independent methods; counting the Michel positrons and the RMD events [1]. The
uncertainty of the total number of decayed muon was 3.5%.
*3 In the MEG experiment, a full frequentist approach was adopted.

Chapter 9 Projected Sensitivity of MEG II

Pseudo-experiments

126

60

50

40

30

20

10

0
0

2

4

6

8

10

12

14

16
18
20
Sensitivity[e-14]

Fig. 9.2: The distribution of the upper limits of seudoexperiments in the MEG experiment [4].

Fig. 9.1:

The distribution of the upper limits ofVerticaldashed line shows the search sensitivity from the me-

Nsig /Nobs at 90% C.L. for 3000 pseudo-experiments

dian calculation (5.3 × 10−13 ), and two arrows show thewith null-signal hypothesis. The obtained median isupper limits obtained from the timing sidebands.

medianNsig= 5.6, and the sensitivity is 6.0 × 10−14 .

Table 9.2: The number of background events obtained in the MEG experiment, and that expected in the MEG II experiment.
Variable

NACC

σNACC

NRMD

σNRMD

Nobs

MEG Data (Analysis Region) [4]7739.1

37.7

624.6

28.4

1.711×1013

MEG II Design [3]4793.6

28.6

57.2

5.7

1.01×1014

Previous work [7]3639.7

24.6

41.0

4.1

7.23×1013

Updated4746.3

28.1

53.4

5.3

9.43×1013

variables used for the discrimination of the event type*4 . The accidental background and the RMD background events are
generated including the statistical ﬂuctuations. Table 9.2 shows the examples of the generated number of events for thepseudo-experiments in the ﬁtting region. The projected sensitivity of the MEG II experiment was calculated from at leastO(1000) pseudo-experiments. Fig. 9.1 shows the distribution of the upper limits with updated parameters of the positron
spectrometer in this thesis. The median value is 6.0 × 10−14 . Fig. 9.2 shows that in the MEG [4], 5.3 × 10−13 (Nsig ≈ 9.1).
The total statistics in the MEG II experiment becomes 9.43×1013 /1.711×1013 ≈ 5.5 times larger than that in the MEG, while
the number of signal-like background events (Nsig in the null-hypothesis) becomes 9.1/5.6 ≈ 1.6 times smaller, resulting in
the net improvement of the sensitivity by a factor of 5.5 × 1.6 ≈ 9.

9.2

Comparison with MEG Experiment

The performance of the MEG positron spectrometer and the MEG II positron spectrometer (design values: Design column
and updated values: 7 × 107 column) are summarized in Table 9.3. The performance of the MEG II positron spectrometerat the halved rate (3.5 × 107 ) and with the additive gases to stabilize the CDCH (O2 addition) are also shown. The timing
resolution of “7 × 107 ” is calculated from the gamma-ray timing resolution (50 – 58 ps is expected, and here 55 ps [16] is*4 For example, some detector resolutions themselves are not used for the ML-Fit analysis, but that information is necessary to simulate the events inthe pseudo-experiment properly.

9.3 Comparison with MEG II Design Values

127

Table 9.3: The input parameters of the positron spectrometer for the likelihood analysis with several possible scenarios.
Variable

MEG

Design7 × 107

3.5 × 107 (Half rate scenario)

0.5% O2 addition to 7 × 107

θ [mrad]

9.4

5.3

6.5

6.2

6.7

ϕ [mrad]

8.7

3.7

4.9

4.7

4.6

P [keV]

380

130

91

82

95

z [mm]

2.4

1.6

1.7

1.6

1.8

y [mm]

1.2

0.7

0.8

0.8

0.8

teγ [ps]

122

84

70

69

70

Eﬃciency [%]

30

70

65.2

74.0

62.4

used) and the positron timing resolution (37.6 – 48.1 ps as shown in Table 8.1). The teγ is calculated to be 67 – 73 ps. Here70 ps is used for the input.

9.2.1

Extension of MEG Experiment

Before discussing the MEG II update, the extension of the MEG experiment is discussed. In the MEG ﬁnal result[1], thesingle event sensitivity was 0.58 × 10−13 while the upper limit sensitivity was 4.2 × 10−13 . This means that the sensitivity of
the MEG ﬁnal result was limited not by the statistics but by the number of the accidental backgrounds. The contribution to
the sensitivity from the background is improved by a square root of the statistics. With this assumption, three-year extensionof the MEG experiment will achieve ∼ 3 × 10−13 .

9.2.2

Several Upgrade Cases from MEG Experiment

The ﬁrst case is that the LXe detector performance is upgraded for MEG II [16], and that the position spectrometer performance and the timing resolution of teγ are assumed to be unchanged from the MEG performance. In this case, the sensitivity
after the three-year running will reach 2.2 × 10−13 . It is better than the simple MEG extension, however, it is still far fromthe sensitivity below O(10−14 ).
The second case is that the timing resolution is updated in addition to the LXe detector update, and the other resolutions
and the eﬃciency of the spectrometer are unchanged from the MEG. In this case, the the sensitivity after the three-year
running will reach 1.9 × 10−13 by the improvement from σteγ = 122 ps to 70 ps.
The third case is to consider the upgrade of CDCH performance. The projected sensitivity of 6.0 ×10−14 , which was
one order better than the MEG experiment, will be achieved thanks to the improved detector resolutions and eﬃciency of
the MEG II positron spectrometer. Considering the positron reconstruction eﬃciency was 30% in the MEG experiment,
the achieved 65% reconstruction eﬃciency is signiﬁcantly better. As for the resolution, improvement of the momentum
resolution is signiﬁcant by a factor of 4. The timing resolution, 70 ps, is also much better the MEG case (122 ps).

9.3

Comparison with MEG II Design Values

9.3.1

Sensitivity with Design Values

The sensitivity has been studied with updated performance of the LXe detector and RDC, but with the designed valuesof the positron spectrometer in Ref. [16]. The designed performance of the positron spectrometer is summarized again in
Table 9.3 (“Design”). The eﬀect of the US-RDC has not been taken into account. The branching ratio sensitivity of theChapter 9 Projected Sensitivity of MEG II

128

EPositron
Event

Event

EPositron
2200

1000

2000
1800

800

1600
1400

600

1200
1000

400

800
600

200

400
200
0
52

0
52.2

52.4

52.6

52.8

53

53.2

52.2 52.4 52.6 52.8 53 53.2 53.4 53.6 53.8 54[MeV]

Fig. 9.3: The generated signal event in the pseudoexperiments. Red histogram is made with the assumption of σ p = 93 keV and blue histogram σ p = 130 keV.

Fig. 9.4:

53.4
[MeV]

The generated background event in thepseudo-experiments. Red histogram is made with theassumption of σ p = 93 keV and blue histogram σ p =130 keV.

MEG II experiment is calculated to be (5.9 ± 0.1) × 10−14 .

9.3.2

Impact of Update

Momentum Resolution

The improvement of the momentum resolution (σ p ∼ 90 keV) is one of the largest changes from the design value (130keV). This improvement is due to the usage of GENFIT in the tracking algorithm and the improvement of the turn merge
algorithm. Fig. 9.3 and Fig. 9.4 shows the generated signal and background events for the pseudo-experiments, respectively,
with the momentum resolution 93 keV (red) or 130 keV (blue). The positron momentum measurement is especially important for the improvement of the signal/background separation. The detector acceptance at the low momentum region (45 –50 MeV) was also largely improved from the MEG experiment and the acceptance curve around the signal region became
ﬂat*5 . However, the impact on the sensitivity is almost negligible because the likelihood ﬁt is performed in a narrow pe+
range of 52.2-53.5 MeV. In conclusion, the expected improvement in the projected sensitivity by the update of the positron
momentum resolution is 9% from the design (5.4×10−14 when only the momentum resolution was updated).
Update of Angular Resolutions

The angular resolutions (6.5/4.9) became worse than the design values (5.3/3.7) due to the worse S/N of waveforms and thelower single-hit resolution of CDCH. The deterioration of the sensitivity by the angular resolutions is 8% from the design(6.4×10−14 when only the angular resolutions were updated).

9.4

Comparison with Previous Works

The comparison with previous work [7] is summarized Table 9.4. There are three points to be mentioned as the major
updates.

*5 The detail of the acceptance is described in Appendix G (Michel-Fit).

9.5 Possible Other Scenarios

129

Table 9.4: Summary of the contribution for the results in this thesis.
Update[7]This Thesis

Calculation of Resolution (CDCH)

MEG-based MC in 2013

MEG II updated MC

Calculation of Resolution (pTC)

From ﬁxed-pattern of data

From tracks of data

Eﬃciency (Initial Design Simulation)∼ 50% (56% at 10 layers)-

Eﬃciency (Updated Simulation)-65%

teγ (Without Radiation, σγ = 50 ps)

67 ps

63 ps

80 ps

75 ps

◦

teγ (Full Radiation at 10 C, σγ = 58 ps)
Projected Sensitivity−14

7.6×10

6.0×10−14• evaluation of the CDCH tracking resolution with the updated MEG II simulation while previous work used the MEG
simulation results,• evaluation of the positron reconstruction eﬃciency with the newly developed simulation and algorithms, while previous work used the initial MEG II design simulation,• updates of the pTC timing resolution and the detailed studies of the systematics and the radiation damage eﬀects,
which resulted in even better performance as in Table 9.4.
In [7] 56% of eﬃciency was obtained. However, this eﬃciency was based on the initial MEG II design simulation (i.e.
one-order better S/N for CDCH and 10 layers instead of 9 layers). The MEG II simulation was updated to be based on
the measured S/N and 9 layer conﬁguration of the CDCH in this thesis. When the algorithms used with the initial MEG II
design based MC is applied to the updated S/N conditions, the eﬃciency becomes much worse. If the cross-ﬁtting step isomitted from the current algorithm, the reconstruction eﬃciency became only 13% even without pileup case as explainedin Sec. 7.1. Without the all updates of the algorithms and with pileups, it will be less than 10%. Therefore, improvement to
65% with updated simulation is due to the reﬁnement algorithms of CDCH tracking, pTC tracking, and global tracking.
When we assume that 50% (or 56%) eﬃciency and 80 ps timing resolution in the previous study, the projected sensitivity
for three years becomes 8.2 × 10−14 (7.2 × 10−14 ), while that is 6.3×10−14 with 65% in this thesis. As for the timing
resolution, the timing resolution was improved from 67 ps to 63 ps without radiation damage and from 80 ps to 75 ps after
the 3-year irradiation at 10◦ C, which corresponds to the sensitivity from 5.9 - 6.3 × 10−14 to 5.7 - 6.1×10−14 at the 65%
eﬃciency.
In conclusion, the improvement from the previous work is 21% for three-year data taking.

9.5

Possible Other Scenarios

The projected sensitivity was updated based on the realistic conditions. Here, several possible updates are considered,
which will be achievable before the physics data taking starts.

9.5.1

Gain Improvement and Software Optimization

The CDCH FE pre-amp gain can be increased by a factor of four. Of course, the S/N does not increase simply by a factor offour since the electrical noise will also be increased. However, combined with the noise reduction algorithms, the single hitreconstruction may be signiﬁcantly improved. The study on the eﬀect of the diﬀerent gain on the performance is in progressusing commissioning data in 2020. As an example, the eﬃciency is 80%, which is the value of the “signal only” case andconsidered as the limit of the current reconstruction algorithms, the ﬁnal sensitivity will be improved to 5.2 × 10−14 .

Chapter 9 Projected Sensitivity of MEG II

Entries

130

300

250

200

150

100

50

0
0

2

4

6

8

10

12
14
16
18
20
90% C.L. upper limit of Nsig

Fig. 9.5: The distribution of the upper limits of Nsig at 90% C.L. for 3000 pseudo-experiments with null-signal hypothesis
medianat a half rate beam. The obtained median is Nsig
= 3.2.

9.5.2

Additive Gas Impact

In the 2020 commissioning, the additive gases, especially small fraction (0.5 – 2%) of O2 , were found to be eﬀective forthe stable CDCH operation. The detailed eﬀect of the additional gas is under study, but preliminary results suggest a slight
performance degradation by the change of waveform shape, number of the ionized electrons per track, and the gas-gain, assummarized in Table 9.3. The eﬀect on the projected sensitivity is ∼3%, which is not crucial.

9.5.3

New Detector Installation: CDCH II/US-RDC

All of the MEG II detectors were already installed in 2018, however, there will be other updates of the MEG II detector:
the new detector (US-RDC), and the new CDCH (CDCH-II).
The expected improvement by the US-RDC is roughly 2 – 9%, although the introduction of the US-RDC has not been
decided yet. The CDCH II may adopt thick cathode wires (for example, 60 µm) to mitigate the wire breaking problems,
which may result in slight (∼ 4%) degradation of the reconstruction eﬃciency. On the other hand, CDCH II can beassembled with 10-layer conﬁguration, which will improve the reconstruction eﬃciency roughly by 10% and result in the
better sensitivity.

9.5.4

Reduced Muon Stopping Rate

The MEG II data taking is supposed to be performed with the muon stopping rate of 7 × 107 , but it is likely that the rate will
be adjusted to maximize the sensitivity for the given detector performance. As already discussed, the PDE decrease of the
LXe VUV-MPPC can be a crucial problem at this beam rate. The running of the MEG II at a half rate (3.5 × 107 ) is underconsideration to mitigate the eﬀect of the PDE decrease.
An estimation of the sensitivity at the reduced beam rate has already been done in Ref. [16], but the better performanceof positron reconstruction at reduced rate has not been taken into account.
As described in the previous chapter, the positron spectrometer performance is largely aﬀected by the pileups. If thehalf rate is adopted, the eﬃciency will be improved from 65% to 74%, and the angular and momentum resolutions will
be improved by 5/4% (θ/ϕ) and 10%, respectively. Fig. 9.5 shows the distribution of the upper limits of Nsig , and Fig. 9.6

9.5 Possible Other Scenarios

131

Half Rate Event Distribution

Nominal Rate Event Distribution
h2
22
0.04976
0.05256
Std Dev x 0.001015
Std Dev y 0.0001752

0.05340.053

0.05280.053

0.05280.0526

0.05240.0524

0.049

0.05

0.051
0.052
0.053
Gamma [GeV]

0.054

0.055

0.056

72
0.04955
0.05253
Std Dev x 0.001331
Std Dev y 0.0001899

0.05320.0526

0.0522
0.048

Entries
Mean xMean y0.0534

Positron [GeV]

0.0532

Positron [GeV]h2

Entries
Mean xMean y0.0522
0.048

0.049

0.05

0.051
0.052
0.053
Gamma [GeV]

0.054

0.055

0.056

Fig. 9.6: The example event distribution within 1.64σ

Fig. 9.7: The example of event distribution within

angles, positions, and timing resolution at half rate

1.64σ angles, positions, and timing resolution at MEG

beam.

Nsig = 2.2 was obtained in this pseudo-

experiment.

II nominal beam.

Nsig = 7.4 was obtained in thispseudo-experiment.

shows the example of generated event distribution in the analysis region (with 1.64σ resolution cut). Compared with thenominal beam case, Fig. 9.1 and Fig. 9.7, the signiﬁcance of the signal/background separation will be improved. Including
the positron spectrometer update, the projected sensitivity with the half rate becomes (6.0 ± 0.1) ×10−14 which is 9% better
than the result in [16]. In addition to the reconstruction performance, there are other advantages on the hardware operation
by reducing the beam rate; less radiation damage on pTC, less wire aging for CDCH, and so on.
The expected sensitivity as a function of the running period at each beam rate is shown in Fig. 9.8. The up-to-dateestimation with the updates on the positron spectrometer performance achieved the projected sensitivity of 6.0 ×10−14 ,which is one-order better than the MEG experiment. As described in Sec. 1.5, the µ → eγ search with the sensitivity ofO(10−14 ) is an attractive probe for the new physics, especially SUSY-GUT theories with heavy right-handed neutrinos. The
results reported in this thesis extended the accessible parameter space around O(10 TeV), where it is diﬃcult to be accessedby the direct search experiment and has signiﬁcant impact on the BSM theories. The beam rate for the MEG II experimentwill be decided in the end of 2021 engineering run, considering all the detector conditions.

Chapter 9 Projected Sensitivity of MEG II

Branching Ratio Sensitivity

132

−13

10

0

1

2

3

4

5
6
DAQ YearFig. 9.8: The branching ratio sensitivity as a function of the DAQ years. (Black) With the updated resolutions under7 × 107 µ/s. (Red) With the updated resolutions under 3.5 × 107 µ/s.

133

Chapter 10

Conclusions
An innovative positron spectrometer has been developed for a µ+ → e+ γ search with a branching ratio sensitivity ofO(10−14 ) in the MEG II experiment. Commissioning of the detectors with the muon beam at PSI has been performed
over the past ﬁve years to demonstrate the detector performance and the stable operation. The pTC measures the positron
timing with a precision of 35.0 ps by using the multiple-hit information, which is 15% better than the previous studies.
The radiation damage to the pTC SiPMs has a signiﬁcant impact on the stable operation of pTC and the time resolution.
A detailed study of the eﬀect of radiation damage was conducted and new dedicated cooling system has been developed
to mitigate the deterioration of the pTC performance. Stable operation at 10◦ C was established, which mitigates the deterioration of the timing resolution by a factor of three. The MC simulations were developed based on the results from theanalysis of the commissioning data, for example, S/N tuned to the observed CDCH waveform (one-order decrease of the
S/N), new 9 layer conﬁguration of CDCH, and space-charge eﬀect of the CDCH. With the updated simulation, the eﬃciency of the positron spectrometer was evaluated to be 65%, which is twice better than the MEG (30%) and 9% better thanthe previous studies. The momentum resolution is 30% better than the design value thanks to the reﬁnement of the track
ﬁtting algorithm. The projected sensitivity of the MEG II experiment was evaluated based on the updated performance ofthe positron spectrometer, and we conclude that the MEG II experiment can reach a sensitivity of 6.0 × 10−14 in three yearsof data collection. The contribution to the sensitivity is 21% improvement from the previous studies, which extends theaccessible parameter space around O(10 TeV) energy scale in the new physics models. The engineering run for the MEG
II experiment will start with the full detectors and the full readout electronics in 2021, followed by the physics data-taking.

135

A

Laser components
The optical components for the laser calibration system (shown Fig. 2.44a) are summarized in Table A.1.

Picosecond Light Pulser PLP-10(HAMAMATSU
PHOTONICS
K.K.)
QMMJ-31-IRVIS-50/125-1HYWT2.5-SP(OZ OPTICS)
MMJ-33-IRVIS-50/125-3-10(OZ OPTICS)
ModCon Mode Controller(Arden PHOTONICS)FUSED-12-IRVIS-50/125-50/503S3S3S-3-0.25(OZ OPTICS)
MMC-18-A-EVEN-1-A-30CM-R-1(Lightel Technologies Inc.)
DET02AFC(THORLABS)
ﬁbre Optical Switch mol 1×12-50 µm(LEONI)

laser

optical switch

photodiode1×8 splitter

1×2 splittermode scrambler

optical ﬁbre (10 m)

optical ﬁbre (2.5 m)

Model(Manufacturer)

Item

Insertion loss < 2.0 dB for 5–16 output channels

400–1100 nm, bandwidh 1 GHz, rise time 1 ns

excess loss < 1.0 dB for 480–700 nm
FBT multi-mode coupler, insertion loss ≤ 11.5 dB

1

70
(+11)
1

1

(+129)
8(+6)
1

NA 0.2, 400–2000 nm, 1 mm jacket
GI multimode, core/clad 50/125 µm,
NA 0.2, 400–2000 nm
Insertion loss < 3 dB at 850 nm
FBT multi-mode coupler, 400–1600 nm,

432

1

Pieces(spares)High power GI multimode, core/clad 50/125 µm,

Wavelength 401 nm, pulse width 60 ps,
peak power 200 mW

Speciﬁcations

Table A.1: Optical components used in the laser calibration system [8]

[81]

[80]

[79]

[78]

[77]

[76]

[75]

[74]

Ref.

136
A Laser components

137

B

Radiation damage with differently damaged
SiPMs
In this chapter, the study of the radiation damage eﬀect with diﬀerently damaged SiPMs in series is summarized. The
full detail of this section is published in [31]. The position dependence and the eﬀect on the timing resolution are alreadydescribed in Sec. 6.5.6. Here, the information of the irradiation levels of the SiPMs, their alignment (pattern A–D), and the
IV-curves are shown and explained.
The radiation damage eﬀect with new type of SiPMs is also summarized (the detail is reported in [28]).

B.1 SiPMs Irradiation
Six SiPMs (#1-#6) were irradiated with intense electrons from 37 MBq 90 Sr sources for 280 hours in total, which isequivalent to Φeq ≈ 3 × 109 n1MeV /cm2 . The irradiation was separated into four steps, each 70 hours long, and no bias
voltage was applied to the SiPMs during the irradiation.
In addition, a set of SiPMs, which was irradiated with neutrons with kinetic energies ranging from 0.5 MeV to 16 MeV
using the reactor neutron facilities at the Laboratory of Applied Nuclear Energy (LENA) of the University of Pavia, wasprepared. Among them, two samples with Φeq ≈ 8.7 × 108 n1MeV /cm2 (#7, #8) and two with Φeq ≈ 5.5 × 109 n1MeV /cm2(#9, #10) were picked up for this study.

B.2 Patterns for SiPMs Connection
The speciﬁc concern on the series connection of SiPMs arises from the diﬀerence of the radiation damage levels dependingon the SiPM position in the counter. The diﬀerence is caused by the gradient magnetic ﬁeld of COBRA, and the hit rate ofa top part of a counter is ∼2 times larger than that of a bottom. Diﬀerent combinations of SiPMs were used for these tests
as summarized below:
Pattern A Two electron irradiated SiPMs (#1, #2 [or #5*1 ]) and four non irradiated SiPMs (#11 – #14).
Pattern B Four electron irradiated SiPMs (#1 – #4 [#5]) and two non irradiated SiPMs (#11, #13).
Pattern C Two electron irradiated SiPMs (#1, #2 [#5]) and four neutron irradiated SiPMs, two with the ﬂuence level ofΦeq ≈ 8.7 × 108 n1MeV /cm2 samples (#7, #8) and the other two with Φeq ≈ 5.5 × 109 n1MeV /cm2 ones (#9, #10).
Pattern D Six electron irradiated SiPMs (#1 – #6). The dose level is speciﬁed in the sentence or ﬁgures if necessary. If

omitted, the SiPMs after full irradiation (Φeq ≈ 3 × 109 n1MeV /cm2 ) are used for the measurement.
Pattern D is used to evaluate the radiation damage and current increase eﬀects on timing resolution step by step, as*1 SiPM #2 was broken during the measurement and was replaced with #5, which has the same damage level and the I-V characteristics as #2.

B Radiation damage with diﬀerently damaged SiPMs

138
1BUUFSO#/PSNBM

1BUUFSO$/PSNBM

1BUUFSO"
3FWFSTF

















































1BUUFSO"/PSNBM
4JHOBM3FBEPVU
1PTJUJWFZTJEF(SPVOE-JOF/FHBUJWFZTJEF

Fig. B.1: Schematic of SiPMs’ pattern A, pattern B, pattern C in normal order and pattern A in reverse order. The SiPMs
with highest dark currents are in black, those with lowest in white.

already described in this thesis. Pattern A and Pattern B are considered as extreme cases to highlight the eﬀects of theposition dependence of the irradiation, while pattern C simulates a gradient damage level closer to a realistic condition.
The SiPMs under test are located at the negative x side of the test counter; the signal is extracted from the positive yside, while the negative y side is connected to the ground line. The more highly-damaged SiPMs were located at larger yposition: this conﬁguration of SiPMs is called “normal order”. Data were taken also with SiPMs ordered in the opposite
way along the y direction: this conﬁguration is called “reverse order”. Figure B.1 illustrates the layout of each pattern*2 .

B.3 IV Curves for Each PatternFigures B.2–B.4 show the I-V curves of individual SiPMs used in patterns A, B, and C. Figures B.5 and B.6 show the I-V
curves in series measured at 30◦ C and 10◦ C, respectively. The breakdown voltages of patterns A and B turned out to be
shifted to values higher than that of pattern D. This “shift of the breakdown voltage” is one of the characteristic behaviors
for the series connection with diﬀerently damaged SiPMs.
When the I-V characteristics of series-connected SiPMs diﬀer, the applied voltage to each SiPM is automatically adjusted
to ﬂow a common current. As a consequence, the over-voltages for the six SiPMs diﬀer from one another; even when the
total applied voltage is below the breakdown voltage of the series-connected SiPMs, voltages applied to non-damaged
SiPMs may result to be higher than their breakdown voltages to ﬂow the same dark current as that of the damaged SiPMs
below the breakdown. This mechanism causes a breakdown voltage shift as illustrated in Figure B.7. Table B.1 summarized
the breakdown voltages of pattern A, pattern D, and the sum of the breakdown voltages of the single SiPM used for thosepatterns. A shift of ∼1.5 V is found between Pattern A and Pattern D, and this shift is not recovered by cooling.

B.4 New SiPM test
As explained in Sec. 2.4.2, ASD-NUV3S-P model is also used in addition to ASD-NUV3S-P High-Gain (MEG). The
radiation tolerance of this model is also checked with a beam test at Beam Test Facility (BTF) in Italy, Frascatti. The beam

*2 The pTC is designed with the readout from the larger radius side (i.e. negative y-side), which corresponds to the reverse order case in this study.

B.4 New SiPM test

102

139

#1

102

#2

#2

#5

10

#11
#12

1

I dark [µA]

I dark [µA]

10

#1

#13
#14

10−1
10−2

#3
#4
#5

1

#11
#13

10−1
10−2

10−3
22

23

24

25
V bias [V]

26

27

10−3
22

28

Fig. B.2: I-V curves of each SiPM used for pattern A.

23

24

25
V bias [V]

26

27

28

Fig. B.3: I-V curves of each SiPM used for pattern B

102

102

I dark [µA]

10
#1
#2

I dark [µA]

10

#5
#7
#8

1

1
Pattern A

10−1

Pattern B
Pattern C

10−2

#9

Pattern D

#10
−3

−1

10

10

145

150

155
V bias [V]

160

165

10−2

Fig. B.5: I-V curves of several patterns of series10−3
22

23

24

25
V bias [V]

26

27

28

connected SiPMs measured at 30◦ C.

Fig. B.4: I-V curves of each SiPM used for pattern C.

102

I dark [µA]10

%BNBHFE4J1.

1
Pattern A

10−1

Pattern B
Pattern C

−2

10

10−3

Pattern D

145

150

155
V bias [V]160/PSNBM4J1.
165

Fig. B.6: I-V curves of several patterns of series-

7CS 7CS 7* **

connected SiPMs measured at 10◦ C.
Fig. B.7: The explanation of breakdown voltage shiftarising from the diﬀerence in dark currents. If n SiPMs
have the same dark current I at the breakdown voltage Vbr , the breakdown voltage of the series-connected
SiPMs is expected to be n × Vbr . In pattern A, the breakdown voltage becomes 6 × Vbr + 4 × δVbr , and in pattern
B, 6 × Vbr + 2 × δVbr to accommodate the same current
I + δI at the breakdown voltage.

B Radiation damage with diﬀerently damaged SiPMs

140

Table B.1: Vbr values of Pattern A and Pattern D.
SiPM

Vbr (V)Sum of #1 - #6
Sum of #1, #2, #11 - #14
Pattern D (30◦ C)
Pattern A (30◦ C)
Pattern D (10◦ C)
Pattern A (10◦ C)

145.5 ± 0.2
145.7 ± 0.2
145.94 ± 0.05
147.51 ± 0.05
143.43 ± 0.05
144.89 ± 0.05

Fig. B.8: The irradiation test setup at BTF.

irradiation setup is shown in Fig. B.8. In this test, 24 type-II SiPMs (50 µm pitch) were irradiated. The calculated ﬂuence
was 1.1 × 1012 e+ /cm2 , which was roughly one order higher than the highest total dose expected in MEG II.
In spite of such a severe damage on SiPMs, the current level and the timing resolution measured were not bad, or evenbetter at 10◦ C than the type-I SiPMs as shown in Fig. B.9 and Fig. B.10. In conclusion, the radiation damage on ASDNUV3S-P models will not be a problem.

B.4 New SiPM test

141

Fig. B.9: The IV curves of the SiPMs after irradiation at 10◦ C and 30◦ C. The type-II SiPMs shown in ”New”.

Fig. B.10: The bias scan of the timing resolution of type-II SiPMs (shown as “New”) after irradiation at 10◦ C and 30◦ C.

143

C

Online Synchronization in 2018 - 2019
C.1 Analysis of Online Synchronization
The data quality on the synchronization were checked with 2018 - 2019 commissioning data, and the correction was applied
to the data.

C.1.1 Clock Analysis
The same 80 MHz sine waves are recorded at all the DRS chips to align the phase of diﬀerent DRS chips in the oﬄine
analysis.The start cell (cell-zero) of DRS is adjusted and aligned by ﬁtting the sine waves around the signal timing. The
DRS cell cycle is locked with the output signal (square wave with 1.95 MHz at 2GSPS case) of the phase-lock loop (PLL)in WaveDREAM board (see Fig. 2.27). The relationship among the clock signal, PLL output, and DRS cycle is illustrated
in Fig. C.1. For the evaluation of the timing synchronization, signals of the square pulses from a function generator (5 V
peak to peak divided into 8 channels with 1 MHz) were used as the input, and then the deviations of the timing diﬀerence
between two channels were checked. The online cell-zero adjustment jitter was ∼ 60 ps in the 2017 case, and combining
the oﬄine analysis the synchronization consistency became ∼ 20 ps at 2 GSPS.
Two problems on the online synchronization happened in 2018 and 2019: “12.5 ns jump” and “out-of-synchronization”.

C.1.2 12.5 ns Jump
Fig. C.2 shows the eﬀect of this 12.5 ns jump on the time-diﬀerence method of the CDCH hit reconstruction. There aresometimes 12.5 ns unphysical diﬀerences in the data from the diﬀerent chips. Fig. C.3 shows the time diﬀerence between
cell-zero chip id and the reference chip. It seemed that the synchronization sine wave was sampled at two diﬀerent clock
cycles and this cycle diﬀerence (1/80MHz ∼ 12.5 ns) caused the timing jump in the diﬀerent chips. In many cases, this12.5 ns jump happened only when the run started or ended (i.e. this jump was not observed during one run), so this jump iscorrected in the oﬄine analysis.
Main clock(80 MHz)PLL out(~1.95 MHz@ 2GSPS)1cell-01023

Domino 1 cycle

Fig. C.1: The relation among the clock, PLL and DRS cycle.

C Online Synchronization in 2018 - 2019

144

Fig. C.2: The reconstructed hit positions on CDCH wires (left) and the timing diﬀerence between both ends (right). Clearly
unphysical jump can be seen.
Trigger Cell Difference From the 1st chip

1 period(12.5 ns~15 cells)

LXe 1stLXe 4th CDCH/AUX

Fig. C.3: The cell-zero chip-id diﬀerence from the reference chip. If the synchronization completely works and no trigger

Start Cell Difference
From the 1st chipjitter, the diﬀerence should be zero.

Fig. C.4: Drift of the diﬀerence of the cell-zero from the reference chip during a run which caused the out-ofsynchronization problem. The cell-zero id of the chip drifted to the one direction.

C.1.3 Out-of-synchronization
In some runs, a drift of the cell-zero was observed as shown in Fig. C.4. It seemed that the sampling point of the synchronization signal failed to be ﬁxed, and the cell-zero continued to drift. The correction of these runs is much more diﬃcult
than the 12.5 ns jump since this drift happened suddenly during the same run and the numbers of drift cycles (12.5 ns ×
cycles) were not ﬁxed even among the runs with the same number of events. The runs with out-of-synchronization were
not used for the analysis. These jumps and drifts were modiﬁed in the ﬁnal version of electronics in 2019 latter half. The
problems of the jump and drift were solved.

145

D

Kalman Filter Algorithm
D.1 Kalman Filter Formalism
The Kalman Filter (KF) is a powerful algorithm to obtain the best estimation of the state, and used for the positron tracking
in the MEG II analysis. In this chapter, the schematics of the KF algorithm is described based on [32] and [82].
The states of the positron tracks at each point can be expressed by the ﬁve parameters (one for the momentum, two forthe direction, and two for the position) in GENFIT [32]:
"
⃗xk =

#T
q du dv,,, u, v ,|⃗p| dw dw

Fig. D.1: The coordinate system of the wire measurement in GENFIT [32].

(D.1)

D Kalman Filter Algorithm

146

where k is the index of the measurement (hit index in the track), ⃗xk is the state of k-th measurement, q is the particle charge,
p is the moentum. u, v, w is the coordinate system on the detector plane deﬁned in the GENFIT, as shown in Fig. D.1.
The k-th state of the positron track is estimated by using the information of the (k − 1)-th state:⃗xk = f k−1 (⃗xk−1 ) + w⃗ k−1 ,

(D.2)

where fk−1 is a transport matrix from the (k − 1)-th state to the k-th state, wk−1 is the white noise*1 . The measurement
state,⃗
mk , can be described with the projection matrix Hk :⃗ k = Hk ⃗xk + ⃗ϵk ,
m

(D.3)

where the ⃗ϵk is the measurement uncertainty. The contribution of the multiple scattering, bremsstrahlung, and the other⃗ k−1 .
stochastic processes are taken into account in w
The KF algorithm performs the two steps recursively; “prediction step” with the mathematical model and “update step”
with the measurement information. The schematics is described in Fig. 6.13. This recursive characteristics is suitable forthe particle tracking: the k-th state include all of the information up to the k − 1-th state.
The prediction step estimates the k-th state from the k − 1-th state which already include all of the information till thek − 1-th measurement and described as xk−1|k−1 . The predicted state, ⃗xk|k−1 , and its covariance, Ck|k−1 , are calculated asfollowing:⃗xk|k−1 = fk−1 (⃗xk−1|k−1 ),

(D.4)

T
Ck|k−1 = fk−1 Ck−1|k−1 fk−1
+ Qk−1 ,(D.5)⃗ k−1 .
where the Qk−1 is the covariance matrix of w
Then the predicted state is updated to ⃗xk|k and the covariance to Ck|k with the information of the k-th measurement:⃗xk|k = ⃗xk|k−1 + Kk m
⃗ k − Hk ⃗xk|k−1 ,(D.6)

Ck|k = [I − Kk Hk ] Ck|k−1 ,(D.7)

where Kk is the Kalman Gain matrix, which determines the best weight for the measurement and the prediction. The Kk is
described as following:hi−1
Kk = Ck|k−1 HTk Hk Ck|k−1 HTk + Vk ,(D.8)

where Vk is the covariance matrix of ⃗ϵk .
One more important information for the positron tracking is the calculation of χ2 for the track. The χ2 value at each point
after the update step, χ2k , can be calculated as following:Tχ2k = ⃗rk|k
R−1
rk|k .
k|k⃗(D.9)

The ⃗rk|k is the residual of the state vector after the k-th update step, Rk|k is that of the covariance matrix:⃗rk|k = m
⃗ k − Hk ⃗xk|k ,(D.10)

Rk|k = Vk − Hk Ck|k HTk .

(D.11)*1 The KF algorithm assumes the linear dynamic system, but the particle representation under the magnetic ﬁeld is not a linear system. In this case,the system equation is approximated by a linear function with the Taylor expansion. This extended algorithm to the non-linear system is called“Extended Kalman Filter”.

D.2 Deterministic Annealing Filter (DAF)147

The χ2 of the positron track is obtained by the sum of χ2k at each step.
After completing the iteration to the ﬁnal state, the KF performs the same iteration from the last state to the ﬁrst state(backward steps). This process is called the “smoothing step”. The weight for the smoothing step at k-th state, Ak , isdescribed as following:

Ak = Ck|k FTk C−1
k+1|k .

(D.12)

After the smoothing step, the state, covariance matrix, and residuals can be calculated as following, respectively:⃗xk|n = ⃗xk|k + Ak ⃗xk+1|n − ⃗xk+1|k ,(D.13)


Ck|n = Ck|k Ak Ck+1|n − Ck+1|k ATk ,(D.14)⃗rk|n = m
⃗ k − Hk ⃗xk|n ,(D.15)

Rk|n = Vk − Hk Ck|n HTk ,(D.16)

as described in [82].

D.2 Deterministic Annealing Filter (DAF)DAF is the extension of the KF algorithm to guard against the wrong measurement assignment in the same layer. For
exmaple, one CDCH hit has the two competing hits in the same (virtual) layer: a “left-measurement” and a “rightmeasurement” (one is the true measurement and the other is the wrong measurement). Here, the DAF algorithm is brieﬂy
described based on Ref. [83] and [33].
The concept of the DAF is to use the predicted residuals of the measurement for the re-weighted observations. The
prolongation part is actually identical to the KF case, but the assignment probabilities of all competing measurements canbe computed in every layer. Let us assume that there are nk measurements in the layer k, and their index is written with i,⃗ ik (i = 1, ... nk ). The prediction, ⃗xk|k−1 , is updated with the observation, m⃗ ik , with the assignment probability of pik :like m⃗xk|k = ⃗xk|k−1 + Kk

nk
X



⃗ k − Hk ⃗xk|k−1 .
pik m(D.17)

i=1

To allow the zero-weights of the measurements, the Kalman gain matrix has to be written in terms of inverse covariance (orweight matrix):

h
i−1
T −1
Kk = C−1
HTk + V−1k ,k|k−1 + pk Hk Vk Hk(D.18)

where pk is the sum of all weights pik . The covariance matrix of the updated state is given by:
h
i−1
T −1
Ck|k = C−1.
k|k−1 + pk Hk Vk Hk(D.19)∗
After the smoothing step, the prediction xk|nusing the all measurements except the ones at k-th layer can be obtained alongwith its covariance C∗k|n . By using this prediction and covariance matrix, the assignment probabilities of the measurements
can be computed as following:∗pik ∝ ϕ(⃗mik ; Hk ⃗xk|n, Vk + Hk C∗k|n HTk ).

(D.20)

D Kalman Filter Algorithm

148

Fig. D.2: Illustration of the probability assignment with deterministic annealing ﬁlter [33]. (a) The algorithm starts with hightemperature and all measurements (green circles) in the same layer have the similar weight. (b) At the lower temperature,
the measurements far from the estimate obtain the lower assignment probabilities. (c) Finally, the assignments are frozen
out.

where ϕ(measurement; mean, covariance) means the multivariate gaussian probability function. An even simpler formulacan be obtained if the covariance matrix after the smoothing step is neglected*2 :∗pik ∝ ϕ(⃗mik ; Hk ⃗xk|n, T Vk ) ≡ ϕik ,(D.21)

the Vk is replaced with T Vk , where T is the parameter to control the global optimization of the assignment probabilities
and called “temperature”. Practically, the weights are normalized as following:pik ∗ =ϕik
Λ(T, λ) +P nkj
j=0 ϕk

.

(D.22)

where λ is the parameter which deﬁnes the cut-oﬀ value*3 .
The meaning of the temperature is illustrated in Fig. D.2. The algorithm starts from the high temperature, resulting in thesimilar weights for all measurements. Then the update step is iterated at the lower temperature, and ﬁnally, the assignments
will be frozen out.

*2 This is natural approximation since the covariance with all the information in the track should have much smaller values than that of the single

measurement.
*3 At the very low temperature, this is equivalent to the χ2 cut.

149

E

Track Extrapolation from pTC to CDCH
In Sec. 6.3.4, it was written that the pTC-self tracking is composed of three steeps: the initial parameter estimation step,
the Kalman Filter (KF) ﬁtting step, and the extrapolation to the CDCH step. The ﬁnal step may be especially important toimprove the positron reconstruction eﬃciency by the additional track seeding in the track ﬁnding process. The detail of theextrapolation process and the hit ﬁnding test from the pTC to the CDCH with MC simulation is described in the following
section.

E.1

Extrapolation

The ﬁnal step of the pTC independent tracking task is extrapolating the track to the outer surface of the CDCH deﬁned
as a cylinder along the z-axis with R = 27 cm. In GENFIT package the Runge-Kutta algorithm including a full material
model is implemented. The extrapolation is performed step by step from the initial state obtained by the KF ﬁtting, withthe correction of the energy loss and the multiple scattering.
By extrapolating the state vector near the CDCH hits, the track ﬁnding in CDCH outer region becomes possible bychecking the consistency of the drift time, the phi-position, the position from the CDCH wire measurement and the stereo
crossing point of two layers. Fig. E.1 shows the example of the track ﬁtting results with pTC hits and CDCH outer (layer 1

Fig. E.1: A positron partial track reconstructed with pTC hits and CDCH hits (MC). Blue rectangular planes show pTC
hits, blue cylinders show drift circles of CDCH hits, and gray planes show CDCH hits.

150

E Track Extrapolation from pTC to CDCH– 4) hits.
This partial tracking algorithm is used to estimate the z-resolution on wires and the matching eﬃciency between the
CDCH and pTC with the commissioning data. One more important application of this extrapolated state is to be used as theseed state for CDCH track ﬁnding process. A partial track has much more information and reliability than a pTC cluster,these additional information will further improve the track ﬁnding quality and the reconstruction eﬃciency. This additional
seeding method is currently still under development.

151

F

Noise Spectrum from Commissioning 2020
In this section, the latest noise situation from the 2020 commissioning is used for the preliminary study.

F.1 Noise Spectrum and Noise Level
Fig. F.1 and Fig. F.2 shows the spectrum and the RMS-noise, respectively. In 2020, the higher gain FE cards (×2 and ×4
from the standard one) were also prepared and tested, but in this appendix, only the results with the standard FE cards wereshown. There still remains the 50 MHz noise and the unknown high frequency noise (300 MHz). As expected, the noise

Fig. F.1: The noise spectrum observed in 2020 with the standard FE card.

Entries

RMS-noise
2200
2000

h
Entries

25322

Mean

0.001093

Std Dev 9.836e − 05

1800
1600
1400
1200
1000
800
600
400
200
0
0

0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004[V]

Fig. F.2: The RMS-noise sin 2020 with the standard FE card. The muon rate is MEG II nominal (7 × 107 /s)

F Noise Spectrum from Commissioning 2020

152

Fig. F.3: The waveforms in the 2020 commissioning under the muon beam. (Left) before the noise subtraction, (right) after
the noise subtraction.

Table F.1: The positron reconstruction resolution under the several beam rates.
Variable

Signal Single

Signal Single+O2

Pile-up 7 × 107

Pile-up 7 × 107 +O2

θ [mrad]

6.0

6.2

6.7

6.7

ϕ [mrad]

5.5

5.9

6.7

6.2

P [MeV]

80

82

96

95

z [mm]

1.5

1.6

1.7

1.8

y [mm]

0.7

0.7

0.8

0.8

t [ps]

45

47

45

46

Eﬃciency [%]

80.0

77.5

64.6

62.5

level before the subtraction is ∼2 mV, and after the subtraction is ∼1 mV. The examples of the waveforms from the 2020
commissioning are shown in Fig. F.3. Clearly, the low frequency noise became smaller than the 2018 situation (Fig. 7.3).

F.2 Expected Performances
The expected performance of the positron spectrometer with the 2020 noise situation is summarized in Table F.1. The eﬀectof the additive gas (0.5% O2 ) is also summarized*1 .
The conclusion in Chap. 9 takes the additive gas eﬀect and the noise spectrum into account in “case-8”. Even with thelatest operation situation, 6 × 10−14 is still the reasonable goal.

*1 These values do not include the eﬀect of “angle correlation correction” and “pTC-CDCH track-selection”.

153

G

Performance Evaluated with Reconstructed
Kinematics
G.1

Performance Evaluated with Reconstructed Kinematics

The resolutions and eﬃciency of the positron reconstruction were evaluated by using the MC truth in Chap. 8. In this appendix, the performance of the positron spectrometer evaluated with the reconstructed variables under the actual condition,i.e. without MC truth information, will be described.
As for the evaluation of pTC timing resolution the even-odd analysis is used. Its concept and detail are already shown inthe sentences. In this chapter, the algorithms for the tracking evaluation, which could not be performed with the commissioning data due to the limited readout channels, are mainly summarized.

G.1.1

CDCH Tracking Resolution

For the evaluation of the tracking performance, two methods are inherited from the MEG experiment (evaluation with MEG
2013 data is shown in [4]): double turn analysis and Michel-Fit. Generally, the extracted resolutions and the resolutions
from MC truth do not completely agree with each other. The extracted values from the real data will be scaled by using thevalues from MC to obtain the detector performance.
Double Turn Analysis

To extract the energy resolution, angular resolution and position resolution of the track, double-turn analysis is used.
Double-turn analysis uses track segments for the positron with NTurn ≥ 2. An imaginary vertex plane is assumed between the ﬁrst turn and second turn. The ﬁrst turn segment and second turn segment are ﬁtted separately and each turnsegment is extrapolated to that plane. The diﬀerence in each variables (θ, ϕ, z, y, Ee ) between both turns is calculated
and ﬁtted with the double-gaussian function. Fig. G.1 shows the ﬁt result for each variable and Table G.1 summarized theextracted values.

Table G.1: The extracted and estimated resolutions for the detector.
Variable

MC (Signal)

7 × 107θ [mrad]

6.5

7.7

ϕ [mrad]

6.2

6.9

P [keV]91

118

z [mm]

1.7

1.6

y [mm]

0.8

0.85

G Performance Evaluated with Reconstructed Kinematics

154

Fig. G.1: The distributions of CDCH tracks between the ﬁrst turn and the second turn.

Table G.2: Comparison of the results from Michel-Fit with MEG II expected and MEG 2013 data.
Parameter

Michel Fit with 2013 data

Michel Fit with MEG II expected (MC)σcore [keV]

325

110

σtail [MeV]

1.91

2.28

fcore

0.852

0.911

µacceptance [MeV]

49

46.9

σacceptance [MeV]

2.5

2.4

Since the double turn analysis uses not typical 1.5-turn events but only 2(or more than 2)-turn events for the evaluation,
the extracted resolution may not agree with the results from MC truth completely. Though the double turn analysis algorithm
works ﬁne, further study to optimize the event selection criteria*1 is needed.
Michel-Fit

As for the momentum resolution, another method called “Michel-Fit” is also used. The theoretical energy spectrum fromparam

the Michel decay, S theo (Ee), is well known [41]. The reconstructed Michel energy spectrum, S rec (Eerec ), can be ﬁtted

with the following formula:param

S rec (Eerec ) = Σ(S theo × Facceptance )(Ee) ∗ Rresponse ,(G.1)*1 Currently the same event selection criteria to the signal case is applied for event selection except for the number of turns (NTurn ≥ 2) and the timing

coincidence (±12 ns) between the gamma ray.

G.1 Performance Evaluated with Reconstructed Kinematics

155
gAccepntanceFunc

Michel Edge [MeV]

600

400

EntriesMean
Std Dev
frac1
mean1
sigma1mean2
sigma2
mean_acc
sigma_acc

82476
49.32
2.438
0.9111 ± 0.0085−0.00944 ± 0.00447
0.1095 ± 0.0054−0.2165 ± 0.2018
2.282 ± 0.144
46.88 ± 0.02
2.424 ± 0.035

1
0.8
0.6
0.4
0.2

200

0

0
40

45

50

40

55

42

44

46

48

50

52

Fig. G.3: The acceptance function of MEG II (MC,Fig. G.2: Michel-Fit with the reconstructed energyblue) and MEG 2013 data (red) normalized at 52.8

spectrum (MC). The grey line shows the theoretical

MeV. The relative eﬃciency (normalized at 52.8 MeV)

Michel spectrum, the blue dashed line response func-

from the reconstructed tracks in the range of 43 – 53

tion, and the red line is the ﬁtting result.

MeV/2 MeV is also shown with cross marks.

100

Core Resolution [keV]

98
96
94
92
90
88
86
84
82
80
40

45
50
Momentum [MeV]55

Fig. G.4: The momentum dependence of the momentum resolution with Michel positrons.

where Facceptance is the acceptance function of the positron spectrometer, which describes the relative eﬃciency of thepositron spectrometer as a function of the positron momentum. Facceptance is deﬁned with an error function as follows:
param

Facceptance =1 + erf( Ee√2σ−µ )
2

.

(G.2)

Rresponse is the response function deﬁned with the double gaussian function:
Rresponse = fcore × gauscore + (1 − fcore ) × gaustail .
fcore is the fraction value for the core component of distribution.

(G.3)

G Performance Evaluated with Reconstructed Kinematics

156

Fig. G.2 shows an example of the Michel-Fit, and Table G.2 shows the values from the ﬁtting. Fig. G.3 shows theobtained acceptance functions in MEG II MC and MEG 2013 data. The relative reconstruction eﬃciency calculated fromthe reconstructed tracks and normalized at the signal energy bin (52 MeV) is also shown. The acceptance around the signal
region is clearly improved from the MEG experiment. The momentum resolution extracted from the Michel-Fit was worse
than the case of the evaluation with MC-truth. The same trend was obtained from the double turn analysis (118 keV). Thisdiﬀerence comes from the diﬀerence of the Michel events and the signal events, especially the diﬀerence of the momentumof positrons. Fig. G.4 shows the momentum dependence of the momentum resolution with Michel positrons. The MEG II
positron spectrometer is optimized for the detection of the signal-like (around 52.8 MeV) positrons. The resolution withlower-momentum Michel positrons becomes slightly worse than the signal positrons case. However, this dependence is too
small to explain the worse resolution extracted from the Michel-Fit. Other possibilities are the systematics from the track
selection for the Michel events and the intrinsic systematics of the method, but the reason of the worse resolution is notunderstood*2 .

*2 Actually, if this worse resolution comes from not a physics nor a software reason but just systematics of the methods, it is not a big problem; we

can just scale the parameter.

157

Acknowledgments
First of all, I would like to thank Prof. Toshinori Mori and Prof. Wataru Ootani for giving me a great opportunity to join
the MEG II experiment. I would like to thank all members of the MEG II pTC group, especially, Prof. Wataru Ootani, Dr.
Yusuke Uchiyama, Dr. P.W. Catttaneo, Dr. Matteo De Gerone, Dr. Miki Nishimura, Dr. Mitsutaka Nakao, Mr. Kosuke
Yanai, and Mr. Taku Yonemoto for working together. Prof. Wataru Ootani kindly supervised me and gave me lots ofadvices. I learned lots of things from Dr. Yusuke, not only the hardware and the software, but also the mind as a researcher.
Without his teaching, this work would not be completed. I would like to thank to all members of the MEG II positron
analysis group, especially, Dr. Francesco Renga, Dr. Cecilia Voena, Dr. Marco Chiappini, Mr. Mannuel Meucci, Dr.
Fedor V. Ignatov, Dr. William R. Molzon, Mr. Dylan Palo, and Mr. Patrick Schwendimann. I strongly wanted to join theengineering run for the positron spectrometer, however, I am sure that the MEG II positron analysis group will obtain thepromising and excellent results in 2021.
I would also like to express my great thanks to the collaborators, especially, Dr. Toshiyuki Iwamoto and Dr. Kei Ieki, who
supported not only my research but also my daily life in Switzerland, Dr. Miki Nishimura, Dr. Shiji Ogawa, Dr. Mitsutaka
Nakao, Mr. Satoru Kobayashi, Ms. Rina Onda, Mr. Kosuke Yanai, Mr. Kazuki Toyoda, who shared the wonderful time in
Switzerland. Especially, Dr. Nishimura Miki was always kind and helpful, Dr. Mitsutaka Nakao gave me lots of supports
and advices for the research life in the doctor course, and I worked on many pTC studies and tasks with Mr. Kosuke Yanai.
Finally, I would like to thank my family for their constant support and encouragement.

159

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