Master Thesis

Research on Long-term Operation and Analysis
Method of Positron Timing Counter in MEG II
Experiment(MEG II 実験陽電子タイミングカウンターの長期運用・解析手法に関する研究)

Kosuke Yanai
Supervisor: Prof. Wataru Ootani
Department of Physics, School of Science
The University of Tokyo2

Abstract
The MEG II experiment plans to search for new physics beyond the Standard Modelvia the charged-lepton-ﬂavor-violating µ → eγ decay. In order to achieve the target
sensitivity of 6 × 10−14 , all the detectors have been renewed from the preceding MEG
experiment to enhance each resolution by a factor of two. All the detector constructions
have now been completed, and the physics data will be taken as soon as the full electronics
are available.
The pixelated Timing Counter (pTC) in the MEG II experiment reduces the dominant
accidental background by detecting the emitted positrons with a high time resolution. It
consists of 512 pixels, each of which is composed of a 120 mm × (40 / 50) mm × 5 mm
plastic scintillator with six series-connected SiPMs at both ends. Each pixel has a time
resolution of 80–100 ps, and an overall resolution below 40 ps is expected to be achievedby a multiple-pixel-hit scheme. This thesis focuses on the long-term stable operation of
the pTC and its capability to achieve the expected performance in the long run.
The eﬀect of radiation damage to SiPMs on the pTC performance was studied indetail. It was newly found that intrinsic time oﬀsets exist between the series-connected
SiPMs, which can cause time ﬂuctuations depending on the hit position of the particle,
and consequently worsen the pTC resolution from the originally-expected value. It was
further found that this position dependence can be enhanced by a gradient radiation
damage to series-connected SiPMs as in the case of the MEG II pTC, which results in afurther ∼ 13 % degradation of the pTC resolution.
In order to compensate this eﬀect, two attempts were made. One was to develop
optimization schemes of the bias voltage to SiPMs and the constant fraction parameter inthe waveform analysis. The optimal values of these parameters shift with the increasing
dark noise level caused by radiation damage to SiPMs, and therefore, the maximum pTC
performance can be brought out by optimizing these parameters at each time point. The
latter optimization was veriﬁed to improve the pTC resolution by ∼ 3 %.
The other attempt was to improve the pTC resolution in the oﬄine analysis. A
method to directly correct for the position-dependent time ﬂuctuations was developed.
In addition, a completely new algorithm is introduced, which combines each channel or
hit time information with appropriate weights. The eﬀect of these analyses were evaluatedusing MC simulation.
Finally, an evaluation of the pTC resolution was performed to yield the value of∼ 38.4 ps, taking into account the newly-found position-dependent time ﬂuctuations.
Furthermore, an estimation of the deterioration of the pTC resolution was made, considering the eﬀect from radiation damage to SiPMs. The obtained value of ∼ 45.9 ps is
expected to be improved to ∼ 41.1 ps by the various attempts introduced in this thesis.
Thus, the required resolution of ≤ 46 ps is expected to be achieved even in the long term.

Contents
1 Introduction
1.1 Particle physics today . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Charged lepton ﬂavor violation . . . . . . . . . . . . . . . . . . . . . . . .
1.3 MEG II experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4 Pixelated timing counter . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.5 Structure of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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MEG II Experiment

2 Physics Motivation
2.1 The Standard Model and its limitations . . . . . . . . . . . . . . . . . . . .
2.1.1 Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.2 Limitations of the SM . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 BSM models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Grand Uniﬁed Theory . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.2 Supersymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.3 Seesaw mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Charged lepton ﬂavor violation . . . . . . . . . . . . . . . . . . . . . . . .
2.3.1 Possibility of charged lepton ﬂavor violation . . . . . . . . . . . . .
2.3.2 History of cLFV search . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 µ → eγ decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.1 Muon decay in the SM . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.2 µ → eγ in the SM . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.3 µ → eγ in BSM models . . . . . . . . . . . . . . . . . . . . . . . . .

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3 MEG II Experiment
3.1 Principle of µ → eγ search . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1 Signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.2 Backgrounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.3 Experimental requirements . . . . . . . . . . . . . . . . . . . . . . .
3.2 MEG experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.2 Beamline and target . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.3 Positron spectrometer . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.4 Liquid-xenon calorimeter . . . . . . . . . . . . . . . . . . . . . . . .
3.2.5 Data acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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3.3

MEG II experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 From MEG to MEG II . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.2 Beamline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.3 Muon stopping target . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.4 Cylindrical drift chamber . . . . . . . . . . . . . . . . . . . . . . . .
3.3.5 Pixelated timing counter . . . . . . . . . . . . . . . . . . . . . . . .
3.3.6 Liquid-xenon calorimeter . . . . . . . . . . . . . . . . . . . . . . . .
3.3.7 Radiative decay counter . . . . . . . . . . . . . . . . . . . . . . . .
3.3.8 Trigger and DAQ . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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4 Pixelated Timing Counter4.1 Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.1 Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.2 Upgrade concept . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.1 Overall design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.2 Single-pixel design . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.1 Waveform analysis . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.2 Hit reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.3 Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.4 Tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4.1 Energy calibration . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4.2 Position calibration . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4.3 Time calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5 Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5.1 Multiple-hit scheme . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5.2 Expected performance . . . . . . . . . . . . . . . . . . . . . . . . .
4.6 Slow control system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.6.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.6.2 Temperature control . . . . . . . . . . . . . . . . . . . . . . . . . .
4.6.3 Humidity control . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.7 Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.7.1 pER2015 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.7.2 pER2016 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.7.3 pER2017 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.7.4 pER2018 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.7.5 pER2019 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.8 Tasks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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61

Long-term Operation of pTC

5 New Pixel Assembly
63
5.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5.2 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

Contents

55.3

I-V measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.1 Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.2 Breakdown voltage . . . . . . . . . . . . . . . . . . . . . . . . . . .
Signal check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Pixel assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Bias voltage scan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Position scan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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6 Radiation Damage to SiPMs
6.1 Radiation damage to pTC SiPMs . . . . . . . . . . . . . . . . . . . . . . .
6.2 Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.1 SiPMs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.2 Pixel assembly setup . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.3 Overall setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.4 Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3 I-V characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4 Eﬀect on signal height . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4.1 Position dependence of pulse height . . . . . . . . . . . . . . . . . .
6.4.2 Interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.5 Eﬀect on time response . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.5.1 Position dependence of time center . . . . . . . . . . . . . . . . . .
6.5.2 Interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.5.3 Veriﬁcation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.6 Eﬀect on pTC performance . . . . . . . . . . . . . . . . . . . . . . . . . .
6.6.1 Eﬀect of cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.6.2 Eﬀect of intrinsic time oﬀsets . . . . . . . . . . . . . . . . . . . . .
6.6.3 Additional eﬀect of radiation damage . . . . . . . . . . . . . . . . .

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5.4
5.5
5.6
5.7
5.8

7 Optimization of Operation and Analysis Parameters
91
7.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
7.2 Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
7.2.1 SiPMs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
7.2.2 Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
7.3 Bias voltage optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
7.3.1 General idea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
7.3.2 Understanding of the time resolution . . . . . . . . . . . . . . . . . 93
7.3.3 Bias voltage dependence . . . . . . . . . . . . . . . . . . . . . . . . 95
7.3.4 Application to pER2019 data . . . . . . . . . . . . . . . . . . . . . 97
7.4 Constant fraction optimization . . . . . . . . . . . . . . . . . . . . . . . . . 98
7.4.1 General idea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
7.4.2 Dependence on the noise level . . . . . . . . . . . . . . . . . . . . . 99
7.4.3 Application to pER2019 data . . . . . . . . . . . . . . . . . . . . . 100

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III

Contents

Analysis Algorithm and Performance Evaluation of pTC103

8 Oﬀset Correction Algorithm
105
8.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
8.2 Simulated sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
8.3 Correction using MC values . . . . . . . . . . . . . . . . . . . . . . . . . . 106
8.3.1 Position dependence . . . . . . . . . . . . . . . . . . . . . . . . . . 106
8.3.2 Correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
8.4 Correction using reconstructed values . . . . . . . . . . . . . . . . . . . . . 109
8.4.1 Position resolutions . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
8.4.2 Position dependence . . . . . . . . . . . . . . . . . . . . . . . . . . 110
8.4.3 Correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
8.4.4 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
9 Weighted Mean Algorithm
113
9.1 General idea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
9.1.1 Using hit position information . . . . . . . . . . . . . . . . . . . . . 114
9.1.2 Using energy deposit information . . . . . . . . . . . . . . . . . . . 114
9.2 Simulated sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
9.3 Intra-pixel weight algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 115
9.3.1 Position dependence . . . . . . . . . . . . . . . . . . . . . . . . . . 115
9.3.2 Intra-pixel weighting . . . . . . . . . . . . . . . . . . . . . . . . . . 115
9.4 Inter-pixel weight algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 117
9.4.1 Energy deposit dependence . . . . . . . . . . . . . . . . . . . . . . 117
9.4.2 Inter-pixel weighting . . . . . . . . . . . . . . . . . . . . . . . . . . 118
9.4.3 Inter-pixel weighting using position information . . . . . . . . . . . 118
10 Evaluation of pTC Performance121
10.1 Evaluation method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
10.1.1 MC simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
10.1.2 Real data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
10.2 Evaluation of pTC resolution using data . . . . . . . . . . . . . . . . . . . 123
10.2.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
10.2.2 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
10.3 Application of new algorithms to data . . . . . . . . . . . . . . . . . . . . 124
10.3.1 Energy deposit inter-pixel weight algorithm . . . . . . . . . . . . . 124
10.3.2 Hit position intra-pixel weight algorithm . . . . . . . . . . . . . . . 125
10.3.3 Hit position inter-pixel weight algorithm . . . . . . . . . . . . . . . 126
10.4 pTC resolution evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
10.4.1 Problem with the even-odd analysis . . . . . . . . . . . . . . . . . . 127
10.4.2 Evaluation of pTC resolution . . . . . . . . . . . . . . . . . . . . . 128
10.4.3 Estimation of pTC resolution degradation . . . . . . . . . . . . . . 129

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IV

Summary and Prospect

7133

11 Summary and Prospect
135
11.1 Summary of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
11.1.1 Long-term operation of the pTC . . . . . . . . . . . . . . . . . . . . 135
11.1.2 Analysis method of the pTC . . . . . . . . . . . . . . . . . . . . . . 136
11.2 Future prospects and plans . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
11.2.1 Positron time resolution . . . . . . . . . . . . . . . . . . . . . . . . 136
11.2.2 Positron eﬃciency . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
11.2.3 Evaluation of pTC resolution . . . . . . . . . . . . . . . . . . . . . 137
Appendix
139
A
Radiation dose calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
B
Eﬀect of CF parameter on position dependence of time center . . . . . . . 139
Acknowledgements

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Chapter 1
Introduction
Here I introduce the overall picture of this thesis.

1.1

Particle physics today

Particle physics is a branch of physics that studies the nature and the interactions ofelementary particles which constitute the universe. The ultimate goal of this particularbranch of physics is to understand everything (that is to say all the elementary particles
and the fundamental forces) in the universe, in the simplest form. The Standard Model(SM) is probably the most beautiful and successful theory particle physicists have comeup with so far. It is a theory, developed in the latter half of the 20th century, describing
the three fundamental forces; the electromagnetic, the weak and the strong, as well asclassifying all known elementary particles. Furthermore, it has demonstrated great successes in predicting experimental results such as the existence of the Higgs boson, which
had been the last piece of the puzzle to complete the SM and was discovered at the Large
Hadron Collider (LHC) in 2012.
Although the SM is believed to be a self-consistent theory and has been successful inmany aspects, it is a common belief amongst particle physicists that the SM is not theultimate theory of everything they believe to exist. For one reason, it fails to incorporate any viable dark matter particle nor the fourth fundamental force, the gravitational
force. For another, it does not give any answers to the important questions the ultimate
theory ought to, such as the origin of the matter-antimatter asymmetry and the multiple generations of fermions. Nowadays, the SM is commonly regarded as a low-energy
approximation of a more general theory. That is why particle physicists, theorists andexperimentalists alike, are now searching for new physics beyond the Standard Model inthe high energy region as a hint for the desired ultimate theory.

1.2

Charged lepton ﬂavor violation

There are various ways in which one can search for new physics in the high energy
region. One way is to directly produce new particles using colliders, thus exploring physics
in O(1) TeV energy scales (“energy frontier”). On the other hand, “intensity frontier”
experiments attempt to observe interactions of BSM physics on SM particles via very
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Chapter 1. Introduction

precise measurements, thus enabling new physics search in O(≫ 10) TeV energy scales.
Indirect searches in intensity frontier experiments can be a powerful probe into highenergy physics because they do not require the new particle to be present in the ﬁnal
state. One potential observation target for such experiments is the charged lepton ﬂavor
violation (cLFV).
Conservation of lepton ﬂavor is incorporated in the SM, but it is not theoreticallyrequired. In fact, the historical non-observation of lepton-ﬂavor-violating processes led to
the notion of distinct lepton ﬂavors and their conservation. However, neutrino oscillation,
which is forbidden in the SM due to the assumption of massless neutrinos, was discoveredin 1998, meaning that lepton ﬂavor is violated in the neutral lepton sector. This gives riseto the possibility of lepton ﬂavor violation in the charged lepton sector too, making cLFV
search more important than ever before. Various experiments in search for rare decays ofcharged leptons are now ongoing.

1.3

MEG II experiment

The MEG II experiment is one such experiment which searches for the charged-leptonﬂavor-violating decay of muons, µ → eγ. The current most stringent upper limit on the
branching ratio of this particular decay is set by the MEG experiment, the forerunnerof the MEG II experiment, to be 4.2 × 10−13 (at 90% conﬁdence level). The MEG II
experiment aims to further enhance the sensitivity by one order of magnitude by making
full use of the high-intensity muon beam available at Paul Scherrer Institut. Sophisticateddetectors with high resolutions are necessary to cope with the high background rate insuch an extreme beam-rate condition.

1.4

Pixelated timing counter

The pixelated timing counter (pTC) is the positron timing detector for the µ+ → e+ γ
decay in the MEG II experiment. It consists of 512 small pixels and each pixel consists ofa 120 mm × (40 / 50) mm × 5 mm fast plastic scintillator with 6 series-connected SiPMs atboth ends. The pixelated design of the detector reduces pileup of positrons signiﬁcantly
and is expected to realize a time resolution below 40 ps by a multiple-pixel-hit scheme.
Furthermore, the fast time response of these pixels allow the pTC to be used as an online
timing trigger and enables an eﬀective reduction of the trigger rate and the data size.

1.5Structure of this thesis

This thesis is composed of four parts. The ﬁrst part is an introduction. The physics
motivation for the µ → eγ search is stated in chapter 2, and the overview of the MEG
II experiment, concentrating on the upgrade concepts from the MEG experiment, is described in chapter 3. In chapter 4, the pTC is introduced, which is the theme of thisthesis, along with all that has been achieved by the pTC group in the past years.
The second part concerns the long-term operation of the pTC. In chapter 5 are described the assembly procedure of spare pixels and their single-pixel performance. In

1.5. Structure of this thesis

3chapter 6, we discuss the eﬀect of radiation damage to SiPMs, especially a gradient damage to series-connected SiPMs, on the pTC performance. To put it simply, a newly-foundeﬀect was discovered to signiﬁcantly worsen the pTC resolution, and therefore, the restof this thesis focuses on various ways to recover the pTC resolution. In chapter 7 isintroduced the ﬁrst attempt to suppress the resolution deterioration; by optimizing theoperation and the analysis parameters.
The third part mainly involves the analysis method of the pTC. In chapter 8 and 9,
we discuss possible ways to improve the pTC resolution in the oﬄine analysis. Theireﬀects are evaluated using MC simulation. In chapter 10, an evaluation of the pTC
resolution is performed. In addition, the extent to which the resolution is expected todeteriorate in the three-year physics data taking is discussed, together with the impact of
the newly-developed algorithms and optimization schemes on the pTC resolution.
In the fourth and last part, I summarize the contents of this thesis. I conclude bystating some future tasks and prospects concerning the pTC towards the physics run.

Part I
MEG II Experiment5

Chapter 2
Physics Motivation
In this chapter is described the physics motivation for the µ → eγ search. This muon
decay is strictly forbidden in the SM, but predicted at observable branching ratios ofO(10−13 )–O(10−14 ) in many promising new physics models.

2.1

The Standard Model and its limitations

2.1.1

Standard ModelIn modern particle physics, the Standard Model (SM) has been the most successful
theory to describe the elementary particles and their interactions. Fig. 2.1 shows all theelementary particles and their classiﬁcation in the SM.
bosons

II

III

u

c

t

g

H

up

charm

top

gluon

Higgs

d

s

b

γ

down

strangebottomphotoneµτZelectron

muon

tauon

Z bosonν2
electronneutrino

ν3
muon
neutrinoν/
tauon
neutrinoW±
W bosonscalar bosons

Igauge bosons

leptons

quarksfermions

Figure 2.1: Elementary particles in the SM.

The SM postulates a local SU(3)C × SU(2)L × U(1)Y gauge symmetry and this gauge
symmetry gives rise to the three fundamental interactions. The SU(3)C corresponds tothe symmetry group of quantum chromodynamics (QCD) which describes the strong
interaction. The uniﬁed interaction of the electromagnetic and the weak, is incorporated
7

8

Chapter 2. Physics Motivationin the SM by interpreting the SU(2)L × U(1)Y as a group of gauge transformations underwhich the Lagrangian is invariant.
In a quantized gauge theory, gauge bosons are quanta of the gauge ﬁelds, which meansthat the SM has the same number of gauge bosons as the number of generators of thegauge ﬁeld. The SU(3)C symmetry group yields 8 generators, corresponding to gluons,
the SU(2)L symmetry group yields 3 generators which in essence corresponds to W and Z
bosons, and the U(1)Y symmetry group yields one generator, corresponding to photons.
Apart from these, the SM incorporates another scalar boson called the Higgs boson, whichis responsible for providing the mass for each particle via the Higgs mechanism.
The SM also incorporates 12 particles with 1/2 spin called fermions, and successfullyclassiﬁes them depending on how they interact. Quarks can interact via all three interactions whereas leptons only interact weakly or electromagnetically. Tab. 2.1 and Tab. 2.2
show the basic characteristics of the SM particles.
Table 2.1: Fermions in the SM [1].
Fermions (spin1/2)
Flavor
up
down
charm
strangetopbottomQuarksChargeMass [MeV/c2 ]+2/3
2.2+0.5−0.4−2/3
4.7+0.5−0.3
3+2/3(1.275+0.025−0.035 ) × 10
−2/3
95+9
−3
+2/3 (173.0 ± 0.4) × 103−2/3
4.18+0.04−0.03

Leptons
Flavor Charge
Mass [MeV/c2 ]e−10.5109989461 ± 0.0000000031
νe
0
0
µ
−1
105.6583745 ± 0.0000024
νµ
0
0
τ
−1
1776.86 ± 0.12ντ
00Table 2.2: Bosons in the SM [1].
BosonphotonW bosonZ boson
gluon

2.1.2

Gauge bosons (spin 1)
Scalar bosons (spin 0)
Force
Mass [GeV/c2 ] Boson Mass [GeV/c2 ]electromagnetic0
Higgs 125.18 ± 0.16
charged weak
80.379 ± 0.012
neutral weak
91.1876 ± 0.0021
strong0Limitations of the SM

Although the SM has successfully provided astonishingly accurate descriptions of phenomena in a wide range of energy scales, we also know that the SM is not the ultimate
theory of everything we believe to exist. For one thing, it contradicts with some of thelatest experimental results. One such example is the neutrino mass. Although the massof most elementary particles are free parameters in the SM, the neutrinos are assumed
to be massless as shown in Tab. 2.1. However, neutrino oscillation has been observed invarious experiments, indicating that neutrinos are indeed massive. This experimental fact

2.2. BSM models

9

obviously contradicts with the SM and proves that the SM does not correctly depict theuniverse.
For another, the SM has some gaping holes where it fails to give any explanation on
the observed phenomena. For instance, the SM does not contain any viable dark matterparticle, which means that the SM is only capable of explaining a small proportion of thematter in the universe. Nor does it state anything concerning the gravitational force.
Finally, the SM does not give any answers to the important questions we believe theultimate theory ought to; the origin of the matter-antimatter asymmetry and the multiple
generations of fermions, why the electric charge is quantized, and so on.
However, the fact that the SM accurately describes various phenomena at relatively
low energy regions suggests that it is a low-energy approximation of a more general theory.
Many promising models beyond the SM (BSM) have already been proposed and are underveriﬁcation by various experiments.

2.2

BSM models

Many theoretical models have already been proposed to incorporate experimental results the SM cannot explain, and also to naturally account for the questions the SM does
not give answers to. Here I will introduce some of them which seem promising steps
towards the theory of everything.

2.2.1

Grand Uniﬁed Theory

The SM covers three of the four fundamental forces, two of which are uniﬁed as theelectroweak force based on the SU(2)L × U(1)Y symmetry group. Although this wasan obvious success to understand the universe more simply, it still does not explain,
for instance, the reason for electric charge quantization, as the electromagnetic force ischaracterized by an abelian symmetry which allows arbitrary charge assignments.
However, the quantization of electric charge can be explained by postulating that thestrong interaction and the electroweak interaction are actually embedded in a uniﬁed interaction described by a single, larger simple symmetry group. The Grand Uniﬁed Theory(GUT) assumes just that. It states that the three fundamental interactions unify into asingle electronuclear interaction at a high energy scale (GUT scale) and is characterized
by one larger gauge symmetry having several force carriers but one uniﬁed coupling constant. This is depicted in Fig. 2.2. It shows how the three forces are uniﬁed in the GUT
energy scale of O(1016 ) GeV by assuming SUSY (c.f. 2.2.2) particles in O(1) TeV energy
scale.

10

Chapter 2. Physics Motivation

Inverse coupling constant 1/a

Gauge coupling constant evolution
60

U 1 electromagnetic force

50

40

1/ a1 (SM)1/ a1 (SUSY)

1/ a2 (SM)1/ a2 (SUSY)

1/ a3 (SM)1/ a3 (SUSY)

SU 2 weak force30

SU(3) strong force
20

GUT
10
2

4

6

8

10

12
14
16
Energy scale log (µ [GeV])
10

Figure 2.2: Evolution of the coupling constants in the SM and in the SUSY-GUT model.

2.2.2

Supersymmetry

Another promising theory is the supersymmetry (SUSY) [2]. The SM succeeded in
explaining the non-zero masses of particles by the Higgs mechanism, which was proven to
be correct by the discovery of the Higgs boson, but it fails to explain the mass scale. The
SM is an eﬀective ﬁeld theory that is expected work below a certain energy scale thatlies around O(1016 ) GeV (GUT scale) or O(1019 ) GeV (Planck scale). This means that
unlike the other SM particles whose masses are protected by gauge or chiral symmetries,
we would need some extremely unnatural ﬁne tuning between the bare Higgs mass andthe quadratic radiative corrections to achieve the observed Higgs mass which is 17 ordersof magnitude below the Planck scale.
The SUSY provides an elegant solution to this hierarchy problem. SUSY is a symmetry
which connects fermions and bosons, that is particles with half-integer spins and integer
spins. Their transformations are given by

Q|F ermion⟩ = |Boson⟩†

Q |Boson⟩ = |F ermion⟩

(2.1)
(2.2)

where Q is the SUSY generator. Applying these to the SM inevitably produces a supersymmetric partner for each SM particle as shown in Tab. 2.3. This seems to complicate
matters at ﬁrst glance, but these extra particles actually have the eﬀect of cancelling out
the contributions to the Higgs mass from the SM partners as shown in Fig. 2.3. Thus, thesupersymmetric SM is capable of naturally explaining the low mass of the Higgs boson.

2.2. BSM models

11

Table 2.3: Supersymmetric partners of SM particles.

SM particle typeFermionGauge boson
Scalar boson

SM particles
SUSY particles
Particle Spin Particle Spin
quark
1/2
squark0
lepton1/2slepton0
photon1
photino 1/2
W boson1
wino
1/2
Z boson
1
bino
1/2
gluon
1
gluino1/2
Higgs
0
Higgsino 1/2

t̃

t
H

H

H

(a) Radiative corrections to the Higgs massfrom top quark loop.

H(b) Radiative corrections to the Higgs massfrom stop quark loop.

Figure 2.3: One-loop corrections to the Higgs mass.
There are also other beneﬁts of assuming SUSY particles. For one, as already shown in
Fig. 2.2, a precise uniﬁcation of the gauge coupling constants can be achieved by assuming
the existence of SUSY particles in O(1) TeV energy scale. For another, it provides viablecandidates for dark matter as many supersymmetric models predict the lightest SUSY
particle to be stable, electrically neutral and to weakly interact with the SM particles.

2.2.3

Seesaw mechanism

Although the neutrino mass is strictly zero in the SM, neutrinos were found to bemassive by the discovery of neutrino oscillation. However, why neutrinos have a very
diﬀerent mass scale to the other fermions still remains an open question. The seesaw
mechanism can naturally account for the low mass of neutrinos by assuming two or more
additional right-handed neutrino ﬁelds inert under the electroweak interactions and theexistence of a large mass scale.
The neutrino Lagrangian in the most general form can be expressed as
Lν = −Ψiγ µ ∂µ Ψ − mD (ΨL ΨR + h.c.) −

mL c
mR c
(ΨR ΨL + h.c.) −(ΨL ΨR + h.c.)
2
2

(2.3)

where mD is the Dirac mass, mL , mR are the Majorana masses of left- and right-handed
neutrinos respectively, ΨL , ΨR are the Weyl spinors of left- and right-handed neutrinos
respectively, and Ψ = ΨL + ΨR . This equation can be simpliﬁed using two Majoranaﬁelds
ΨL + ΨcL
ΨR + ΨcR√√
N1 =, N2 =
(2.4)
2
2

12

Chapter 2. Physics Motivation

to beLν = −N 1 iγ µ ∂µ N1 − N 2 iγ µ ∂µ N2 − mD (N 1 N2 + N 2 N1 ) − mL N 1 N1 − mR N 2 N2
( )
(
) µ
N1
= N 1 , N 2 (iγ ∂µ + Mν )
(2.5)
,
N2
(

where
Mν =

mL mD
mD mR

)
(2.6)

is the mass matrix of neutrinos. The two ﬁelds obtained by the diagonalization of Eq. (2.6)
contain both L and R components and do not have ﬁxed chiralities. If we think within
the SM except for assuming the existence of right-handed neutrinos with a huge mass,
mL = 0, mD can roughly be the same as the masses of other fermions, and mR ≫ mD .
In this case the eigen solutions can be obtained as|ν ′ ⟩ ≃ |N1 ⟩ −mν ′ ≃ −

m2D
,
mR

mD
|N2 ⟩,
mR|N ⟩ ≃ |N2 ⟩ +

mD
|N1 ⟩
mR

mN ≃ mR

(2.7)
(2.8)

where |ν ′ ⟩ and |N ⟩ are the eigenvectors, and mν ′ and mN are their mass eigenvalues
respectively. The apparently negative mass, mν ′ , can be turned positive by setting |ν⟩ =γ 5 |ν ′ ⟩, in which casemν · mR = m2D(2.9)
holds. Eq. (2.9) eﬀectively depicts the seesaw mechanism, which explains the small observed neutrino mass, mν , by assuming the existence of right-handed neutrinos with alarge mass mR , which still remains to be discovered.

2.3

Charged lepton ﬂavor violation

2.3.1

Possibility of charged lepton ﬂavor violation

Not much is yet understood about the ﬂavors of fermionic elementary particles. We
know from observation that at least three generations of fermions exist, and that further
generations are disfavored by measurements. However, we are none the wiser about theorigin of multiple generations or why diﬀerent generations have such a large diﬀerence inthe mass scale.
Furthermore, ﬂavor mixing amongst generations is not well-understood. While theSM accounts for the ﬂavor mixing in the quark sector via the CKM matrix, it strictly
forbids ﬂavor mixing in the lepton sector. However, the ﬂavor conservation of leptons is
not theoretically required. In fact, the ﬂavor conservation in the charged lepton sector
derives from a non-observation of charged lepton ﬂavor violation (cLFV), and the ﬂavor
conservation in the neutral lepton sector simply derives from the assumption of masslessneutrinos.
In any case, neutrino oscillation was discovered proving that neutrinos can indeed
change their ﬂavor. This strongly hints the possibility of lepton ﬂavor violation (LFV)2.3. Charged lepton ﬂavor violation

13

in the charged lepton sector too, as lepton ﬂavor conservation was not required in theﬁrst place. In fact, many BSM models, including those introduced in 2.2, incorporate
cLFV processes at reasonably observable rates, and many experiments are now ongoingin search for these rare processes.

2.3.2

History of cLFV search

Since the discovery of muons in 1937, various searches for cLFV muon decays havebeen conducted. The ﬁrst result came in 1947 when Pontecorvo ﬁrst searched for theµ → eγ process using cosmic rays [3]. In the 1950s, the upper limits of cLFV branchingratios improved drastically through experiments using accelerators, and they have been
improving ever since. Fig. 2.4 shows the upper limits of the branching ratios for cLFV
processes set by experiments over the past century.

Figure 2.4: Experimental upper limits on cLFV muon decay channels [4].

In principle, the tau lepton would be the best object for the cLFV search, as it has
a stronger coupling to the new physics and possesses more cLFV channels (e.g. τ → eγ,
τ → µγ, τ → eee, etc). However, the current availability of muons in large quantities at
accelerators renders the muon cLFV searches more powerful. Thus, the following cLFVchannels, more often known as the golden channels, are being searched all around theworld:• µ → eγ
• µN → eN (muon conversion)• µ → eee
where N denotes an atomic nucleus. The current upper limits of these processes are set
by the MEG, the SINDRUM II, and the SINDRUM experiments to be 4.2 × 10−13 [5],7 × 10−13 [6], and 1 × 10−12 [7] respectively. The branching ratios of these three decays
depend sensitively on the new physics model. Therefore, it is very important to measure
the decay rate for each of these channels, even after the cLFV has been discovered in one
channel, to put further constraints on the possible models behind the process.

14

Chapter 2. Physics Motivation

2.4µ → eγ decay

2.4.1

Muon decay in the SM

Muon belongs to the second generation of charged leptons in the SM. Its physicalproperties are summarized in Tab. 2.4. It has a relatively long lifetime, which makes raremuon decay searches possible.
Table 2.4: Basic physical parameters of muon [1].
Parameter
Mass
Mean lifetime
Magnetic moment anomaly
Electric dipole moment

Value
105.6583745 ± 0.0000024 MeV(2.1969811 ± 0.0000022) × 10−6 s(11659209 ± 6) × 10−10(−0.1 ± 0.9) × 10−19 e cm

After its lifetime, a muon decays into other particles, which is summarized in Tab. 2.5.
These are the decay modes that can be the background in searching for cLFV muon
decays.
Table 2.5: Muon decay modes [1]. Ee and Eγ denote the energies of electron and photon
respectively. The decays from µ+ will be the charge conjugate of these modes.
Decay modeµ− → e− ν e νµµ− → e− ν e νµ γ−
µ → e− ν e νµ e+ e−

2.4.2

Branching ratio∼1(6.0 ± 0.5) × 10−8
(3.4 ± 0.4) × 10−5

Conditions
Ee > 45 MeV, Eγ > 40 MeV
Eγ > 14.5 MeVµ → eγ in the SM

The SM strictly prohibits LFV, and therefore the µ → eγ decay. However, by considering the already-discovered neutrino oscillation, we actually obtain a non-zero µ → eγ
branching ratio. A possible Feynman diagram is shown in Fig. 2.5. Here we follow thecalculations in [8].

γ

W

µ

e
νµ

νe

Figure 2.5: Possible µ → eγ decay considering neutrino oscillation in addition to the SM.

2.4. µ → eγ decay

15

Radiative decays of the generic lepton decay l1 → l2 + γ proceed through electromagnetic gauge-invariant transition amplitudes of the form
( 1 + γ5eGF ml1 − γ5 )M = √ 1 ϵµ q ν l2 (p2 )σµν DR+ DL
l1 (p1 )(2.10)
22
16 2π 2where q = p1 − p2 , σµν = 2i [γµ , γν ], and DR and DL are model-dependent transition dipole
moments. In the case of µ → eγ, mµ ≫ me holds, in which case the amplitude leads tothe decay rate
αG2F m5µ(|DR |2 + |DL |2 )(2.11)
Γ(µ → eγ) =22048π
and the branching ratio
3α(|DR |2 + |DL |2 )B(µ → eνµ ν e )32π
3α≃(|DR |2 + |DL |2 )(2.12)32π
as B(µ → eνµ νe ) ≃ 1. Considering neutrino oscillation in addition to the SM, DR andDL can be expressed as
B(µ → eγ) =1∆m2
sin 2θ13 sin θ23 e−iδ 2 32
3mW
DR = 0DL ≃(2.13)(2.14)

which leads to the ﬁnal branching ratio
sin2 2θ13
0.15−54∼ O(10 )B(µ → eγ) ≃ 10−54 ×(2.15)(2.16)

by applying θ13 ∼ 9◦ [9].
Thus, neutrino oscillation gives us a non-zero branching ratio of µ → eγ, but its value
is extremely suppressed by the fourth power of the mass ratio between the W boson andand neutrinos (see Eq. (2.13)). This means that we have almost no µ → eγ backgroundfrom the SM with neutrino oscillation, and that the observation of this process would bea clear proof of new physics beyond the SM.

2.4.3µ → eγ in BSM models

2.4.3.1

Model-independent approach

A model-independent Lagrangian for µ → eγ decay can be written as]
4GF [Lµ→eγ = − √ mµ AR µR σ µν eL Fµν + mµ AL µL σ µν eR Fµν + h.c.
2(2.17)

where AR and AL are the coupling constants corresponding to the right-handed process,µ → eR γ, and the left-handed process, µ → eL γ, respectively. The diﬀerential angular
distribution of µ → eγ can then be obtained from Eq. (2.17) as()
dB(µ → eγ)= 192π 2 |AR |2 (a − Pµ cos θe ) + |AL |2 (a + Pµ cos θe )d cos θe(2.18)

16

Chapter 2. Physics Motivation

where Pµ is the magnitude of the muon polarization, and θe is the angle between the muonpolarization and the positron momentum in the muon rest frame. AR and AL depend on
the new physics model, so once the µ → eγ decay is discovered, additional measurementsof the positron emission angle with respect to the polarized muon would further restrict
the BSM models.
2.4.3.2

SUSY

As explained in 2.2.2, the introduction of SUSY is one of the most prevailing extensionsof the SM. It naturally suppresses the divergence of the Higgs mass, and also provides
candidate particles for dark matter. Even the minimum SUSY extension of the SM(MSSM) incorporates huge degrees of freedom in the parameter space, and therefore it is
widely considered within the constraints to meet the phenomenological observations.
Within the MSSM, a muon is allowed to decay into a positron and a photon via a loopof neutralino and sleptons as shown in Fig. 2.6. These decays are made possible if theslepton mass matrix in the new physics model has oﬀ-diagonal elements. In these cases,
the decay rate is expected to be well within the experimentally observational level.

γ

∼
µ

~
e

µ

∼
µ
e

∼
χ0

γ

∼
τ
~
e

µ

e
∼
χ0

Figure 2.6: Examples of µ → eγ decay in the SUSY model.
2.4.3.3

SUSY seesaw

The seesaw mechanism is well-motivated as it naturally explains the small mass ofneutrinos with the assumption of right-handed Majorana neutrinos as explained in 2.2.3.
In the SUSY seesaw model, the right-handed neutrino supermultiplets, the Majorana
neutrino mass matrix and a new Yukawa coupling matrix are additionally included in the
lepton sector Lagrangian. As the Yukawa coupling matrix for electrons and neutrinos are
independent, oﬀ-diagonal elements arise in the left-handed slepton mass matrix as(m2l̃L )ij ≃ −MP1)(yν )∗ki (yν )kj m20 (3 + |A0 |2 ) ln(
28π
MR(2.19)

where yν is the Yukawa coupling matrix of neutrinos, m0 is the universal scalar mass, A0
is the universal trilinear coupling, MP is the Planck mass, and MR is the right-handed
neutrino mass [10]. In this model, only right handed neutrinos contribute to the decay,
meaning that the decay will have an angular distribution in the form of 1 − Pµ cos θe .
Fig. 2.7 shows the branching ratios of µ → eγ and τ → µγ expected in this model.
Considering the neutrino mixing angle θ13 ∼ 9◦ [9], the magenta region shows more orless the parameter region we still have to search.

2.4. µ → eγ decay

17

Figure 2.7: The branching ratio of µ → eγ against τ → µγ in the MSSM model with theseesaw mechanism. [11]. The current upper limit of the branching ratio of µ → eγ [5] isadded in blue to the original ﬁgure.

2.4.3.4

SUSY GUTThe SUSY GUT is also a well-motivated theory as it is capable of unifying the threegauge coupling constants via a larger symmetry group as explained in 2.2.1. The cLFV
source in the SUSY GUT is quite diﬀerent from that of the seesaw mechanism since itoriginates from oﬀ-diagonal elements in up quarks [12].
The smallest symmetry group satisfying this condition is SU(5), in which case oﬀdiagonal elements appear in the right-handed slepton mass matrix as(m2ẽR )ij = −MP3)(VR )i3 (VR )∗j3 |yu33 |2 m20 (3 + |A20 |) ln(
28π
MG(2.20)

where VR is a matrix to diagonalize the Yukawa coupling constant for leptons, yu is the
Yukawa coupling matrix of up quarks, and MG is the GUT scale [10]. Thus, the µ → eγ
decay is made possible via right-handed slepton sector.
There are even larger symmetry groups, such as SO(10), which satisfy the uniﬁcation
condition, and are therefore promising candidates for the SUSY GUT. Fig. 2.8 shows the
expected branching ratio of µ → eγ against stau mass predicted by the SU(10) SUSY
GUT.

18

Chapter 2. Physics Motivation

Figure 2.8: Branching ratio of µ → eγ against stau mass expected in the SO(10) SUSY
GUT [13]. The current upper limit of the branching ratio for µ → eγ [5] is added in blue
to the original ﬁgure.

2.4.3.5

Other models

Note that there are many other models which predict reasonably observable cLFV
processes, such as the SM with a fourth generation of quarks and leptons [14], and theRandall-Sundrum model [15]. Therefore, the µ → eγ search is an extremely promisingprobe for new physics beyond the SM. Both its discovery or its non-discovery at ultrahigh sensitivity would give us the means to put stringent restrictions on the new physics
model.

Chapter 3
MEG II Experiment
In this chapter, an overview of the MEG II experiment is given. After describing theprinciple of the µ → eγ search, the MEG experiment is introduced as a preceding work ofthe µ → eγ search, followed by a detailed explanation of the MEG II experiment focusing
on the upgrade concepts from the MEG experiment.

3.1

Principle of µ → eγ search

In experimental µ → eγ search, muons are stopped in a target and are made to
decay after their lifetime of O(10−6 s). The decay mode is identiﬁed by detecting the
decay products and reconstructing the decay event. Positive muons are used to avoid theformation of muonic atoms in the target which can complicate the decay kinematics.

3.1.1

SignalThe kinematics of the µ+ → e+ γ is a simple two-body decay. In the rest frameof the muon, the muon emits back to back a time-coincident pair of a mono-energetic
positron and a mono-energetic photon, as depicted in Fig. 3.1. Therefore, the signal canbe identiﬁed by four observables satisfying the following conditions:• Ee+ = Eγ = m2µ ≃ 52.8 MeV• te+ γ = 0• θe+ γ = 180◦
where Ee+ and Eγ are the energies of the positron and the photon respectively, mµ is therest mass of muon, te+ γ is the decay time diﬀerence between the positron and the photon,and θe+ γ is the opening angle between the positron and the photon.
1920

Chapter 3. MEG II Experiment

𝐞

𝛄

𝛍

Figure 3.1: A kinematic diagram of the µ → eγ decay.

The expected number of signals can be written in the form
Nsig = Rµ+ × T × Ω × B × ϵe+ × ϵγ × ϵs

(3.1)

where Rµ+ is the rate of muons stopping in the target, T is the total data acquisition time,Ω is the solid angle subtended by the positron and photon detectors, ϵe+ and ϵγ are thedetection eﬃciencies of the positron and the photon respectively, and ϵs is the eﬃciencyof the selection criteria. Each of the factors on the right hand side of Eq. (3.1) should be
maximized to achieve the highest possible sensitivity, except for B which is determinedby the BSM model.

3.1.2

Backgrounds

The background events in search for µ+ → e+ γ can be classiﬁed into two classes, thephysics background and the accidental background. Both are depicted in Fig. 3.2. Since
the kinematics of these background events are not exactly the same as that of signal
events, in principle, we can identify them by measuring the four observables, Ee+ , Eγ ,te+ γ , θe+ γ , with high precision.

𝐞

𝐞
𝛎𝐞
𝛄

𝛍
𝛎𝛍

(a) Physics background

𝛄
𝛍

𝛎𝐞
𝛎𝛍

(b) Accidental backgroundFigure 3.2: Kinematic diagrams of background events for the µ → eγ decay.
To discuss the expected number of background events, we introduce new quantities:
x = 2Ee+ /mµ and y = 2Eγ /mµ which are the energies of the positron and the photon

3.1. Principle of µ → eγ search21

respectively normalized to those of the signal, and z = θe+ γ − π. Using these quantities,
the search region of interest can be expressed as
(3.2a)
1 − δx ≤ x ≤ 1 + δx
 1 − δy ≤ y ≤ 1 + δy
(3.2b)
−δte+ γ ≤ te+ γ ≤ δte+ γ(3.2c)
0 ≤ z ≤ δz
(3.2d)
where the variables indicated with δ denote the range of the signal region for each corresponding observable.
3.1.2.1

Physics background

One type of background is the physics background. This occurs in a fraction ofradiative muon decays (RMDs), which is depicted in Fig. 3.2a and can be written asµ+ → e+ νe νµ γ. When the positron and the photon are emitted almost back to back,and little energy is carried out by the non-detectable neutrinos (i.e. x ≃ 1, y ≃ 1 andz ≃ 0), this decay mimics the signal and becomes a source of the physics background.
Therefore, the probability of a muon becoming a physics background in an experimentcan be obtained by integrating the RMD diﬀerential branching ratio dB(µ+ → e+ νe νµ γ)
over Eq. (3.2a), (3.2b) and (3.2d) as
Bphys =

dz

dy

dx
1−δx

∫ δz

∫ 1+δy∫ 1+δx1−δy0dB(µ+ → e+ νe νµ γ).
dxdydz(3.3)

Using this integrated value, the total expected number of physics background events
can be expressed as
Nphys = Rµ+ × T × Ω × Bphys × ϵe+phys

× ϵγphys(3.4)

where ϵe+ and ϵγphys are the detection eﬃciencies of background positrons and photons
physrespectively.
3.1.2.2

Accidental background

The other type of background is the accidental background, in which a positron and aphoton from independent sources mimic the signal and are detected as in Fig. 3.2b. The
positron in this background event comes from a Michel decay of a muon µ+ → e+ νe νµ ,whereas the photon comes either from an RMD or an annihilation-in-ﬂight (AIF) of apositron.
The fraction of Michel positrons entering the signal energy region, fe+ , can be obtainedby integrating the Michel positron energy spectrum, shown in Fig. 3.3, over Eq. (3.2a).
As the spectrum is almost ﬂat around the signal region (x ≃ 1),
fe+ ≃ 2(δx)
approximately holds.

(3.5)

22

Chapter 3. MEG II Experiment

The fraction of photons entering the signal energy region, on the other hand, is more
complicated, as it has contributions from both AIFs and RMDs. The AIF gamma spectrum depends on the material distribution in individual experiments, so here we focus
on the contribution from RMDs. This can be obtained in a similar way, by integrating
the RMD photon energy spectrum, shown in Fig. 3.4, over Eq. (3.2b). The fraction ofphotons entering the signal energy region can then be approximated to be
fγ ≃

(
)
α
(δy)2 ln(δy) + 7.33
2π

(3.6)

with the assumption of unpolarized muons. The detailed calculation can be found in [16].
The total number of expected accidental background events from RMD photons canthen be written in the form
Nacc(RMD) =Rµ+ × fe+ × Rµ+ × fγ ×(δz)2× 2(δte+ γ )4× T × Ω × ϵe+acc × ϵγacc(RMD)(3.7)

where ϵe+acc and ϵγacc(RMD) are the detection eﬃciencies of background positrons and photons
respectively. The quadratic term of δz comes from the necessity to take into account thesolid angle. By applying Eq. (3.5) and Eq. (3.6), the dependence of Nacc(RMD) on the
beam rate and the signal region of each observable can be shown to be
Nacc(RMD) ∝ (Rµ+ )2 × δx × (δy)2 × δte+ γ × (δz)2 .
Photon energy spectrum
Differential branching ratio

Differential branching ratio

Positron energy spectrum
1

0.8

0.6

0.4

0.2

0
0

1
10−1
10−2
10−3
10−4
10−5
10−6

0.2

0.4

0.6

0.8

1

0

Normalized positron energy x

Figure 3.3: Positron energy spectrum fromMichel decay

3.1.3

(3.8)

0.1 0.2

0.3 0.4 0.5

0.6 0.7

0.8 0.9

1

Normalized photon energy y

Figure 3.4: Photon energy spectrum from
RMD

Experimental requirements

The physical requirements to achieve ultra-high sensitivity for µ → eγ search can besummarized as maximizing Eq. (3.1) while minimizing Eq. (3.4) and Eq. (3.8). These inturn lead to the following experimental requirements.
Firstly, a high-intensity direct-current (DC) muon beam is required. High muon statistics is the ﬁrst step to increase the number of signals in Eq. (3.1). However, while thesignal increases linearly with the muon rate Rµ+ , the accidental background in Eq. (3.8) increases quadratically. Consequently, the overall muon intensity must be maximized while3.2. MEG experiment

23

minimizing the instantaneous muon intensity, which naturally results in the requirementof a high-intensity DC muon beam.
Secondly, the detectors must have high energy, time and position resolutions. Searching for such rare decays can only be achieved by an extreme reduction of the background.
The use of high-intensity muon beam incidentally causes the accidental background to be
dominant. Eq. (3.8) indicates that this can directly be suppressed by enhancing the resolution for each of the four observables. Eq. (3.3) indicates that the physics backgroundcan also be suppressed directly by high-resolution detectors.
While the two conditions stated above are the most crucial experimental requirementsfor µ → eγ search, there are also other important requirements such as the ones below:• Wide acceptance and high detection eﬃciency of each detector to earn the signal
statistics.
• Low material distribution around the target to minimize accidental AIF photons.
• Capability of each detector to cope with the high-rate environment (e.g. radiation
tolerance, high granularity to reduce pileup events, etc.).
• Fast electronics and trigger system.

3.2

MEG experiment

In this section the MEG experiment is introduced as a preceding work of the µ → eγ
search.

3.2.1

Overview

The MEG experiment searched for the µ → eγ decay from 2008 to 2013 and set
the current upper limit on the branching ratio, B(µ → eγ) < 4.2 × 10−13 (at 90 %conﬁdence level) [5]. The MEG experiment made use of the DC muon beam available at
PSI in Switzerland. Fig. 3.5 shows the overall picture of the detectors used in the MEG
experiment. Muons decay after stopping inside the target (3.2.2) and the decay products
are measured by the surrounding detectors; positrons, bent into spirals by the COBRA
magnet, are detected by the drift chamber and the timing counter (3.2.3), whereas photons
are detected by the liquid-xenon calorimeter (3.2.4). The data acquisition in each detector
is performed using Domino Ring Sampler chips (3.2.5).
The global coordinates in the MEG (and also MEG II) system are also depicted inFig. 3.5. The origin is set to the target center and the z axis corresponds to the beamaxis. Note also that the polar coordinates with respect to the z axis will also be referred
to in the following discussions.

24

Chapter 3. MEG II Experiment

Figure 3.5: An overall picture of the detectors in the MEG experiment [17].

3.2.2Beamline and target

The MEG experiment made use of the high-intensity DC muon beam available at
PSI. The muons originate from a proton beamline. Protons from a hydrogen source areaccelerated up to 590 MeV by a Cockcroft-Walton pre-accelerator and two cyclotrons.
These accelerated protons produce pions via nuclear interactions in a target, which thendecay into muons after being stopped in a target. The long lifetime of pions enables the
production of a DC muon beam from the originally periodic proton beam. More details
about the muon beamline at PSI are given in 3.3.2.
The muon stopping target used in the MEG experiment is shown in Fig. 3.6. It is
composed of a 205 µm-thick layer of polyethylene and polyester in an elliptical shapewith semi-major and semi-minor axes of 10 cm and 4 cm. The target was placed with aninclination of ∼ 20◦ with respect to the beam axis to maximize the muon stopping rate,
while minimizing the scattering of observable decay products within the target.

Figure 3.6: The muon stopping target in the MEG experiment mounted on a Rohacell
frame [5].

While the maximum muon beam rate available at PSI is ∼ 108 µ+ /s, the MEG experiment operated at a lower beam intensity. This is due to a limitation of the detector
performances. The consequential muon stopping rate at the target was 3 × 107 µ+ /s.

3.2. MEG experiment

3.2.3

25

Positron spectrometer

The positron spectrometer consists of three systems: the COBRA magnet, the drift
chamber (DCH) and the timing counter (TC). The COBRA magnet is responsible forthe trajectory of signal positrons, while the DCH and the TC reconstruct their track andtiming respectively.

3.2.3.1

COBRA magnet

The COBRA magnet, which stands for the COnstant Bending RAdius magnet, is asuperconducting solenoid developed specially for the MEG experiment [18]. It surrounds
the target region completely, and also the DCH and the TC. It has a gradient magnetic
ﬁeld along z; 1.27 T at the center and 0.49 T at both ends. This gradient magnetic ﬁeld
is capable of leading the signal-like positrons (i.e. with energy of half the muon mass) to
the DCH and the TC detector region, regardless of the positron emission angle. It is also
capable of sweeping the positron outwards, to reduce pileup in the DCH and the TC.
These characteristics are schematized in Fig. 3.7.

DCH
COBRA

TC

(a)

(b)

Figure 3.7: A schematic view of the COBRA magnet showing (a) the weak dependence ofthe bending radius on the positron emission angle and (b) how it sweeps positrons awayfrom the central region [17]. The labels in blue are added to the original ﬁgure.

3.2.3.2

Drift Chamber

The DCH is mainly responsible for providing the precise track of positrons [19]. It
consists of 16 trapezoidal modules lined along ϕ direction as in Fig. 3.8. Each module
consists of two detector planes with wires stretching parallel to the beam, and these twoplanes are staggered by half a drift cell to resolve the left-right position ambiguity as
shown in Fig. 3.9, and determine the positron position in x-y plane. The z position is
obtained by the charge division method and a method called the vernier pad method
which is depicted in Fig. 3.10; the cathode foils are divided into two sub-cathodes, andthe induced charge on each 5 cm zig-zag shaped pad provides the z coordinate.

26

Chapter 3. MEG II Experiment

Figure 3.9: A schematic view of the drift
cell structure [17].

Figure 3.8: The design of the MEG DCH[20]. Only a fraction of the modules are
depicted.

Figure 3.10: A schematic view of thevernier pad method [17].

The DCH must be of low material to minimize the multiple scattering of positrons
and also the creation of accidental AIF photons. That is why each module is ﬁlled witha low-density gas mixture of He and C2 H6 with the proportion of 1 : 1, and the support
structure is also made of low-mass carbon ﬁber. With this design, the average amount of
DCH material intercepted by a positron track is suppressed to 2 × 10−3 X0 .
3.2.3.3

Timing counter

The TC is responsible for providing the precise timing of positrons [21]. Its design isshown in Fig. 3.11. 15 scintillation counters, each 80 cm long and lined along ϕ direction,
are placed below the DCH both upstream and downstream of the target. Each scintillation
counter consists of a fast plastic scintillator (Saint-Gobain BC-404 [22]) and ﬁne-meshphotomultiplier tubes (PMTs) (R5924 from Hamamatsu Photonics [23]) at both ends.
The position information can also be obtained; the hit counter gives the ϕ position, while
the time diﬀerence between the two channels in a counter gives the z position. Placed
on top of the scintillation counters and perpendicular to the beam are scintillation ﬁbers
read out by avalanche photodiodes (APDs) (S8664-55 from Hamamatsu Photonics [24]).
This can enhance the time resolution as well as improve the z position reconstruction.

Figure 3.11: The design of the MEG TC [17].

3.2. MEG experiment

3.2.4

27

Liquid-xenon calorimeter

The liquid-xenon (LXe) calorimeter is solely responsible for the energy, time and position reconstruction of photons [25]. Its design is depicted in Fig. 3.12. It has a C-shaped
structure ﬁtting the outer radius of the COBRA magnet and has the ﬁducial volume of∼ 800 L. It is ﬁlled with LXe, and its inner walls are covered with 846 PMTs (R9869 from
Hamamatsu Photonics). It is a homogeneous calorimeter capable of fully containing theshower induced by signal photons, thus enabling the photon energy reconstruction. The
fast time response of LXe allows a precise time reconstruction, and the photon direction
can be inferred from the direction of the line between the reconstructed photon interaction
vertex and the intercept of the positron trajectory at the muon stopping target.

Figure 3.12: A schematic view of the MEG LXe calorimeter from the downstream side
(left), and the top side (right) [17].

3.2.5

Data acquisition

The data acquisition (DAQ) system is dedicated to recording the signals from all thedetectors in the experiment. The MEG experiment as a high-precision and high-rate
experiment requires a signiﬁcant precision and speed of the electronics, as well as theavailability of raw waveforms for oﬄine pileup reduction. This was achieved in the MEG
experiment using high-speed waveform digitizers called Domino Ring Sampler 4 (DRS4)
chips [26]. The chain of inverters in a ring, called the domino wave circuit, samples thesignals. The sampled voltage information is kept in 1024 capacitors, which once triggered,is read out one by one by shift registers. The ﬂexible sampling speed was ﬁxed to 1.6 giga
samples per second (GSPS) for the LXe calorimeter and the TC, and 0.8 GSPS for theDCH, which has less stringent timing requirements. A schematic view of the inverter chain
and a functional block diagram of the DRS4 chip are shown in Fig. 3.13 and Fig. 3.14
respectively.

28

Chapter 3. MEG II Experiment

Figure 3.13: A simpliﬁed schematics of theinverter chain in the DRS4 chip [26].
Figure 3.14: A functional block diagram of
the DRS4 chip [26].

3.3

MEG II experiment

The MEG II experiment is an upgraded experiment of the MEG experiment, aiming
to search for the µ → eγ decay with one order higher sensitivity. Depicted in Fig. 3.15
is the overall picture of the MEG II experiment. Positron events are reconstructed by
the cylindrical drift chamber and the pixelated timing counter, while photon events arereconstructed by the LXe calorimeter. Although the COBRA magnet used to control
the positron tracks is retained from the MEG experiment, the radiative decay counter is
newly installed. In this chapter, we discuss the necessary requirements for an upgrade,and the actual upgrades in each subsystem.

Figure 3.15: A schematic overview of the MEG II experiment [27].

3.3. MEG II experiment

3.3.1

29

From MEG to MEG II

As discussed in 3.1.3, the physical requirements to achieve a high sensitivity in µ → eγ
search is to maximize the number of signals given by Eq. (3.1) and to minimize thenumber of background events which are partly given by Eq. (3.4) and Eq. (3.8). The only
realistic way to increase the number of signals is to increase the detection eﬃciency or
the beam intensity. To achieve the former, the detector designs must be renewed. The
latter is possible by utilizing the full beam available at PSI, but as explained in 3.1.3,
the detector resolutions must be enhanced signiﬁcantly to reduce the correspondinglyincreased background.
This is exactly the concept of the MEG II experiment. It aims for one order higher
sensitivity in the µ → eγ search by• Utilizing the maximum muon beam available at PSI.
• A signiﬁcant improvement in each detector performance.
By detector performance, I mean increasing the detection eﬃciency to maximize thesignal statistics, and enhancing the resolutions to minimize the background. Summarizedin Tab. 3.1 and Tab. 3.2 respectively are the eﬃciencies and resolutions expected in the
MEG II experiment compared to those achieved in the MEG experiment. The details ofthese variables will be discussed in the following subsections.
Table 3.1: The trigger and detection eﬃciencies achieved in the MEG experiment andexpected in the MEG II experiment [27].
Eﬃciency type
Trigger eﬃciency
Positron detection eﬃciency
Photon detection eﬃciency

Eﬃciency in MEG
99 %
30 %
63 %

Eﬃciency in MEG II
99 %
70 %
69 %

Table 3.2: The resolutions achieved in the MEG experiment and expected in the MEG II
experiment [5].
Observable
Positron energy Ee+
Positron emission angle θe+Positron emission angle ϕe+Normalized photon energy 2Eγ /mµ(w < 2 cm)/(w > 2 cm)
Photon conversion position uγ /vγ /wγTime diﬀerence te+ γ

Resolution in MEG
380 keV
9.4 mrad8.7 mradResolution in MEG II
130 keV
5.3 mrad3.7 mrad2.4 %/1.7 %

1.1 %/1.0 %5 mm/5 mm/6 mm
122 ps

2.6 mm/2.2 mm/5 mm
84 ps

30

Chapter 3. MEG II Experiment

3.3.2

Beamline

The muon beam in the MEG II experiment originates from protons and are produced
through three stages at PSI. Fig. 3.16 shows an overview of the PSI proton accelerator[28].

Figure 3.16: An overview of the PSI high-intensity proton accelerator complex [28].

3.3.2.1

Muon production

The ﬁrst stage is the acceleration of protons, which is also performed in three steps.
Protons from a hydrogen source are ﬁrst accelerated up to 870 keV by a Cockcroft-Walton
pre-accelerator shown in Fig. 3.17. The pre-accelerated protons are injected into an
isochronous cyclotron called Injector II, which is equipped with two main radiofrequency(RF) cavities operating at ∼ 400 kV, and two third-harmonic cavities operated at 30 kV[29]. This ﬁrst cyclotron accelerates the proton up to 72 MeV and delivers 2.4 mA beam
to the second cyclotron. The second cyclotron is the main cyclotron composed of fourmain RF cavities and eight magnets as shown in Fig. 3.18. The main cavities operate in acontinuous wave mode at a frequency of 50.6 MHz and produce the ﬁnal 590 MeV proton
beam with a periodic 19.75 ns beam microstructure.

Figure 3.17: The CockcroftWalton pre-accelerator [30].

Figure 3.18: The 590 MeV ring cyclotron [30].

3.3. MEG II experiment

31

The second stage is the production of pions which are the source of muons. The
accelerated proton beam is directed onto a 40 mm-thick graphite target called target E,
after having passed through another 5 mm-thick target called target M. Here, protons
impinging on the target produce Delta baryons, which then quickly decay into pions.
These reactions can be written as below:+p + p → p + n + π
p + n → n + n + π+p + p → d + π+.

(3.9a)(3.9b)(3.9c)The third and last stage is the production of muons. The pions produced in thetarget subsequently produce muons via π + → µ+ νµ decay. Pions have a mean lifetime of∼ 2.6 × 10−8 s. The relatively long lifetime of pions enables the production of an eﬀective
DC muon beam from the originally-periodic proton beam.
3.3.2.2

Muon beam in the MEG II experiment

While there are several beamlines stretching from target E as shown in Fig. 3.16, the
MEG II experiment will be conducted in the πE5 area, where the highest-intensity muon
beam is available. The πE5 beamline utilizes surface muons [31], which means that they
originate from pions stopped in a thin region from the target surface. Surface muons
have momenta of ∼ 28 MeV/c, and can be stopped in a very thin target, thus reducing
unnecessary backgrounds.
These surface muons are delivered through a transport system to the muon stopping
target in the MEG II detectors. The transport system consists of a ﬁrst quadruple triplet
magnet, a cross-ﬁeld separator (Wien-ﬁlter), a second quadruple triplet magnet and abeam transport solenoid (BTS) as shown in Fig. 3.19. The magnets and the Wien-ﬁlter
are capable of separating the muon beam from positron contaminations, and the BTS
performs the ﬁnal muon momentum adjustment. Thus, together with the muon stopping
target to be explained in 3.3.3, a muon stopping rate of 7 × 107 µ+ /s is realized, which ismore than twice that in the MEG experiment.

Figure 3.19: A schematic view of the πE5 channel and the beam transport system in the
MEG II experiment [17].

32

3.3.3

Chapter 3. MEG II Experiment

Muon stopping target

The muon stopping target contains two contradictory requirements; one is to maximize
the muon stopping rate, and the other is to reduce the target material in order to minimize
the multiple scattering of emitted positrons and the production or background photons
from positron bremsstrahlung or AIF. In the MEG II experiment, these requirements are
realized by a 130 µm-thick scintillating polyvinyl toluene (PVT) foil shown in Fig. 3.20,
which is capable of stopping ∼ 84 % of the muons. The use of a scintillating material alsoenables a monitoring of the beam intensity and proﬁle by capturing the scintillation lightwith a CCD camera. It is placed at a slanting angle of 15◦ with respect to the beam to
reduce the multiple scattering of positrons and the production of background photons.
In the MEG experiment, a severe deformation of the target foil was found, which could
not be monitored. A lack of information on the precise target position and shape led
to a signiﬁcant systematic uncertainty in the positron angle measurement. This eﬀect is
expected to be compensated in the MEG II experiment by a photogrammetric monitoringof the dots printed on the target foil (see Fig. 3.20) by a CCD camera.

Figure 3.20: The muon stopping target in the MEG II experiment[27]. Optical markings
are printed on the scintillator target.

3.3.4

Cylindrical drift chamber

In the MEG experiment, the eﬃciency and resolutions on the positron side was signiﬁcantly worse than the designed values. This was mainly due to a low performance of
the DCH as a positron tracker. The tracking ineﬃciency derived mainly from a trackmatching ineﬃciency between the DCH and the TC, caused by the frontend electronics
boards and the mechanical support of the DCH intercepting a large fraction of the positron
tracks on their paths to the TC. The low position resolution arose from a generally-low
amplitude of the induced signals on the cathodes, resulting in a poor z reconstruction.
There were also some operational instabilities limiting the number of DCH planes duringsome of the data-taking periods.
To overcome these issues in the MEG II experiment, a completely-new, low-mass,
single-volume, high-granularity, full-stereo cylindrical drift chamber was designed [32]. A
picture of the constructed CDCH is shown in Fig. 3.21. It is composed of 11904 wires
in total, the details of which are summarized in Tab. 3.3. The sense wires stretch over 9
layers. Each layer has a stereo angle ranging from ∼ 6◦ to ∼ 8◦ with two continuous layers
having stereo angles of opposite signs. The drift cells are almost square, their size ranging
from ∼ 6.6 mm in the most inner layer to ∼ 8.7 mm in the most outer layer. The wholechamber is ﬁlled with a low-density gas mixture of He and C4 H10 with the proportion of
90 : 10.

3.3. MEG II experiment

33(a) An overview.

(b) An enlarged view of the endcap.

Figure 3.21: The MEG II CDCH [27].

Table 3.3: The wire conﬁguration in the MEG II CDCH. The number of each wire isexpressed as (number of wires per plane)×(number of planes).
Wire type
DiameterMaterial
Number of wires
Sense wire
20 µm
Gold-plated W 192 × 9 = 1728
Field wire (anode plane)
40 µm
Silver-plated Al 192 × 9 = 1728
Field wire (cathode plane)
40 µm
Silver-plated Al 384 × 29 = 7680
Guard wire
50 µm
Silver-plated Al
192 × 4 = 768

The positron tracking ineﬃciency in the MEG experiment is solved by the use of
single-volume chamber and eliminating any material between the CDCH and the pTC.
The use of low-density gas also helps to reduce the multiple scattering of positrons and thegeneration of background photons; the equivalent radiation length per positron track turnis as small as 1.58 × 10−3 X0 . The highly-granular drift cell design enables operation in ahigh-rate environment whilst enhancing the position resolution in the positron tracking.
The double readout of the wires with the techniques of time propagation diﬀerence andof charge division and the stereo conﬁguration of the CDCH is expected to improve thez resolution considerably. Thus, the MEG II CDCH is expected to achieve the higheﬃciency and resolutions in Tab. 3.1 and Tab. 3.2.

3.3.5

Pixelated timing counter

The te+ γ resolution in the MEG experiment was strictly limited by the positron time
resolution, which was a factor of two worse than the designed value. This was partly due
to a large uncertainty in the track length from the DCH, and partly due to a mediocre
performance of the TC. The TC resolution was mainly limited by a large variation in the
optical photon path lengths originating from the large scintillator size, and the degradationof PMT performance in the COBRA magnetic ﬁeld.
Both these problems can be solved by the use of silicon photomultipliers (SiPMs);
small silicon detectors with single-photon counting capability. The use of such small
photo sensors enables us to utilize a highly-segmented scintillator design, which not only
enhances the time resolution but also enables operation in a high-rate environment without

34

Chapter 3. MEG II Experimentsigniﬁcant pileups. SiPMs are also known to be robust to magnetic ﬁelds, ensuring a stableperformance of the detector over the data-taking periods.
A picture of the constructed MEG II pTC is shown in Fig. 3.23, in comparison to the
MEG TC in Fig. 3.22. It is composed of 512 small ultra-fast scintillator tiles with SiPM
readout on both ends. All the pixels are laid to be perpendicular to the signal positron
track, so as to minimize multiple scattering. This highly-pixelated design of the detector
realizes excellent time resolution below 40 ps by a multiple-pixel-hit scheme, and also
provides eﬃcient online positron time and position information for the signal triggering.
The details of this detector will be discussed further in chapter 4.

Figure 3.22: The MEG TC [33].

3.3.6

Figure 3.23: The MEG II pTC.

Liquid-xenon calorimeter

While the foreseen photon detection eﬃciency and position resolution were achieved in
the MEG experiment, the achieved energy resolution was ∼ 40 % worse than the designed
value. This led to twice the number of backgrounds (c.f. Eq. (3.8)), strongly limiting thephysics reach of the MEG experiment. The low energy resolution was mainly due to a
position dependence of the light collection eﬃciency caused by a non-uniformity of the
PMT coverage, especially on the inner face.
The upgrade concept of the LXe calorimeter, therefore, is to eliminate this nonuniformity by replacing the inner 216 PMTs with smaller SiPMs, and also by modifying the layout of PMTs on the lateral faces [34]. Large-area multi-pixel photon counters(MPPCs), sensitive to vacuum-ultraviolet (VUV) scintillation light, was specially developed in corporation with Hamamatsu Photonics for this purpose [35]. The ﬁrst upgrade
point is depicted in Fig. 3.24, which shows the inner walls of the LXe calorimeter in the
MEG and MEG II experiment, whilst Fig. 3.26 compares the event display for the same
Monte-Carlo (MC) event. The highly-granular design clearly achieves an excellent position resolution of photons, and also a high energy resolution arising from the uniform
readout. The second upgrade concept is depicted in Fig. 3.25, which illustrates a viewof the detector in an r-z section. The inner face is extended, which reduces the energy
leakage for events near the lateral walls and increases the detection eﬃciency by ∼ 10 %.

3.3. MEG II experiment35

Figure 3.24: Inner walls of the LXe calorimeter inthe MEG (left) and MEG II (right) detector.

(a) Event display in the MEG LXe calorimeter

Figure 3.25: MEG (left) and MEG
II (right) layout of the PMTs
viewed in an r-z section [27].

(b) Event display in the MEG II LXe detector

Figure 3.26: A comparison of the same MC event in the MEG and MEG II LXe calorimeter[27]. The capability of the new detector to distinguish diﬀerent photons is depicted.

3.3.7

Radiative decay counter

3.3.7.1

Concept of RDC

The radiative decay counter (RDC) is an additional detector in the MEG II experiment. It is a unique detector solely for reducing the background, not by enhancing theresolution of the relevant physical quantities, but by identifying particular background
events. Thanks to the low-density CDCH, the dominant background in the MEG II experiment is the accidental background whose photon comes from RMDs. A fraction ofthese events can be identiﬁed by tagging the low-energy positros from the RMDs. These
positrons follow an almost helical trajectory with a small radius along the beamline. The
RDC is placed on the beam axis and detects these low-energy positrons to identify accidental background events. In principle, the RDC can be placed both upstream anddownstream of the target to maximize the identiﬁcation of accidental background events.
Fig. 3.27 shows a schematic view of the identiﬁcation of an accidental background eventwith the downstream RDC (DS-RDC).
There are two potential observables to distinguish an accidental RMD event with the
RDC; one is the positron time with respect to the photon detected in the LXe calorimeter,
and the other is the positron energy. The helical trajectory paths of low-energy RMD
positrons diﬀer little event by event, yielding an almost ﬁxed positron time with respect
to the RMD photon detected in the LXe calorimeter. As background Michel positrons

36

Chapter 3. MEG II Experiment

have a random time distribution, this time diﬀerence can be used to identify accidental
RMD events. This is depicted in Fig. 3.28. In addition, as the RDC detects low-energy
RMD positrons, the energy information can also be used to distinguish them from therelatively high-energy Michel positrons.

Figure 3.27: A schematic view of the identiﬁcationof an accidental background event with the DS-RDC[27].

3.3.7.2

Figure 3.28: Simulated time differences between the positron detection in the RDC and thephoton detection in the LXecalorimeter for accidental background events (red) and signal
events(blue) [27].

Downstream RDC

The downstream RDC (DS-RDC) has already been designed and developed. It consistsof two parts; a timing detector in front for the positron timing measurement, and acalorimeter attached to its back for the positron energy measurement. Both must havepixelated designs to cope with pileups.
The timing detector is composed of 12 diﬀerently-sized plastic scintillators (BC-418
from Saint-Gobain [36]) with SiPM (MPPC S13360-3050PE from Hamamatsu Photonics[37]) readout; its design is shown in Fig. 3.29. The use of fast plastic scintillators realizes ahigh time resolution, whilst the use of SiPMs enables operation in the COBRA magnetic
ﬁeld.
The calorimeter, on the other hand, is made of 76 LYSO crystals (from Shanghai
Institute of Ceramics) with SiPM (MPPC S12572-025 from Hamamatsu Photonics [38])readout; its design is shown in Fig. 3.30. LYSO crystals with a high light yield anda short decay constant are suitable for the positron energy measurement in a high-rateenvironment. LYSO also has intrinsic radioactivity, which can be used for a self energy
calibration. Again, the use of SiPMs enables operation in the COBRA magnetic ﬁeld.

3.3. MEG II experiment

Figure 3.29: The design of the timing detector of the DS-RDC [27].

3.3.7.3

37

Figure 3.30: The calorimeter of the DSRDC [27]. SiPMs are attached to LYSO
crystals with springs.

Upstream RDC

While the DS-RDC distinguishes accidental background events from both the positron
time and energy, the energy information is not available for the upstream RDC (US-RDC),
as it must not degrade the muon beam energy. Therefore, the US-RDC must be capable ofidentifying background events from the positron timing measurement alone, and it mustalso be of little material so as not to aﬀect the beam. Other harsh requirements also exist,
such as radiation hardness of the detector, and a high time resolution to distinguish RMD
positron signals immersed in the muon beam background.
Various detectors have already been tested, such as scintillating ﬁbers, a diamonddetector, a silicon detector, etc., but none satisﬁed all the necessary requirements. A gas
detector is now being developed as a promising candidate [39]. It is a resistive plate chamber (RPC) with multi layers; its design is schematically shown in Fig. 3.31. A single-layer
RPC consists of two highly-resistive plates, charged positive and negative respectively,
separated by a gas volume. Charged particles are detected by the ampliﬁcation of theionized electron in the electric gaseous ﬁeld. The use of diamond-like carbon (DLC) for
resistive plates, can localize the electrical discharge, enabling high-rate detection of particles. The multi-layer structure can enhance the time resolution by reducing the thicknessof each layer, while maintaining a high overall eﬃciency [40].

-HV

gas
resistive plate
insulator
resistive plate+HV

readout pad

Figure 3.31: A schematic view of a multi-layer RPC.

38

Chapter 3. MEG II Experiment

3.3.8

Trigger and DAQ

The MEG II detectors meet the requirement to operate at a high-rate environment
generally by a ﬁner readout or a segmented design of the detectors. This has led toan almost tripling of the readout channels with respect to the MEG experiment, whilst
an eﬃcient oﬄine pileup reconstruction and rejection requires the availability of raw
waveforms. Thus, the DAQ waveform digitizer has to provide state-of-the-art time andcharge resolution and a sampling speed in the GSPS range.
In addition, the general replacement of PMTs with SiPMs require electronic signal
ampliﬁcation as SiPMs have a lower internal gain compared to PMTs. The use of SiPMs
in LXe prevents us from placing preampliﬁers next to the SiPMs due to cooling problems.
Thus, the new electronics must also incorporate a ﬂexible ampliﬁcation scheme for small
signals.
3.3.8.1

WaveDREAM board

The requirements for the electronics are met by the development of WaveDREAMboards (WDBs) [41]. A WDB has the functionalities of DAQ, basic trigger, high voltage (HV) application and signal ampliﬁcation all integrated into a single compact board.
Fig. 3.32 shows a schematic view of the WDB. It contains an ampliﬁer capable of ampliﬁcation in the range from 0.5 to 100, as well as a waveform shaper through a programmablepole-zero cancellation. One WDB incorporates two DRS4 chips, which digitize the waveform with a maximum sampling speed of 5 GSPS. The DRS4 chips are connected toanalog-to-digital converters (ADCs), which transmit the signal to a ﬁeld-programmablegate array (FPGA) capable of treating trigger algorithms. The HVs for SiPMs can also
be generated in the WDB by a Cockcroft-Walton (CW) voltage multiplier. A simple 5 V
digital-to-analog converter (DAC) is mounted to apply diﬀerent HV to each channel witha high precision.

Figure 3.32: A schematic view of the WDB [27].

16 of these WDBs, each containing 16 channels, can be stored in a WaveDAQ crate,

3.3. MEG II experiment

39

together with a crate management board (CMB), a data concentrator board (DCB) anda trigger concentrator board (TCB). A picture of a single WDB and a sketch of the
WaveDAQ crate are shown in Fig. 3.33 and Fig. 3.34 respectively. CMBs supply power toall the boards in the crate, and also manage the slow control system. DCBs are responsible
for the conﬁguration of all boards inside the crate, the distribution of the master clock andthe trigger signals, the readout of waveform data, and the interface to the global DAQ
computers. TCBs are in charge of online data processing for triggering, which gather
information from lower level trigger boards to perform online reconstruction of the decay
product observables. The trigger in the MEG II experiment will be discussed in moredetail in 3.3.8.2.

Figure 3.33: A WDB without a
HV module [41].

3.3.8.2

Figure 3.34: A sketch of a WaveDAQ crate with
16 WDBs (green), a DCB (magenta), a TCB (blue)
and a CMB on the right [41].

Trigger

The trigger in the MEG II experiment is required to collect µ+ → eγ-like eventswith a high eﬃciency by suppressing the backgrounds by almost six orders of magnitude,
resulting in an DAQ rate of 10 Hz. This also leads to a substantial reduction in the data
size. The slow response of the CDCH makes it impossible to use its information for online
triggering. Therefore, the reconstructed information from the pTC on the positron sideand the LXe calorimeter on the photon side are used for the online triggering. Hence, theobservables used for the online triggering are Eγ , te+ γ and θe+ γ .
Eγ is reconstructed online by summing the amplitudes of MPPC signals and PMT
signals, after having corrected for the gain, the quantum eﬃciency (QE), etc. of each photosensor. An event is triggered when the reconstructed Eγ is above a certain threshold.
te+ γ is reconstructed from the online time of the LXe calorimeter and the pTC, which
are extracted by sampling the WDB discriminator output at 800 MHz and intercepting
the ﬁrst sample over the threshold. The positron detection time is extracted from a single
pixel placed at the most inner z of all hit pixels. However, the unavailability of thepositron track information from the CDCH at trigger level makes the correction of the
propagation time from the target diﬃcult. An estimation of the positron time of ﬂight(TOF) can be made from the correlation between the triggered pixel ID and the TOF (seeFig. 3.35), but this depends on the number of positron turns, so the trigger time window
must be kept relatively wide.
Lastly, θe+ γ direction match is performed by using a lookup table (LUT). Grouping4 × 4 MPPCs in the LXe calorimeter as a single patch, the ID of the patch with the40

Chapter 3. MEG II Experimenthighest signal has a strong correlation with the pixel ID of the ﬁrst hit pTC pixel for
signal events as shown in Fig. 3.36. This information is summarized in the online LUT,
to which the trigger can refer in order to estimate θe+ γ .

Figure 3.35: The TOF of positrons as afunction of pTC pixel ID [42]. A clear correlation between the TOF and number ofturns is seen.

Figure 3.36: The LUT used for the θe+ γ
direction matching [42].

Chapter 4
Pixelated Timing Counter
The MEG II pTC provides the precise decay time of muons and eﬃcient trigger information on the positron side. In this chapter is described the concept and the design of thepTC to satisfy these requirements, along with its basic operation, analysis and calibration
procedures. In the end, the remaining tasks concerning the pTC towards the physics run
are introduced.

4.1

Concept

4.1.1

Requirements

The role of the pTC in the MEG II experiment is to reduce the number of background
events by a precise reconstruction of the decay time of muons and to provide eﬃcient trigger information on the positron side. Therefore, the parameters that must be maximized
are as follows:• The positron time resolution at the vertex point, σte+ .
• The positron tracking eﬃciency ϵe+ .
• The online positron time and emission angle resolution.
The te+ γ resolution at the vertex point is given by√
σte+ γ = (σte+ )2 + (σtγ )2√( σlCDCH)+
2 + (σ )2=( e)2 + (σtpTC
)
tγ
e+
c

(4.1)

where σte+ is the positron time resolution, σtγ is the photon time resolution, σlCDCH
ise+

the CDCH positron track length uncertainty, c is the speed of light, and σtpTC
is thee+pTC positron time resolution. The photon time resolution using the LXe calorimeter is
expected to be 50–70 ps from MC studies. Adopting a conservative value of σtγ ∼ 70 ps andconsidering the contribution from the CDCH track length uncertainty, σlCDCH/c ∼ 6 ps,e+in order to achieve the expected te+ γ resolution of 84 ps at the vertex (c.f. Tab. 3.2), therequired pTC positron time resolution is calculated to be ∼ 46 ps.
41

42

Chapter 4. Pixelated Timing Counter

In addition, to achieve one order higher sensitivity than the MEG experiment, arealistic goal for the tracking eﬃciency is ϵe+ ≥ 70 %. The MEG II pTC is also required
to be tolerant to a high-rate condition with the planned beam intensity increase.

4.1.2

Upgrade concept

The MEG TC together with the DCH tried to achieve lower but similar goals, but
resulted in an unexpectedly poor result as summarized in Tab. 3.1 and Tab. 3.2. The low
positron tracking eﬃciency was due to the material between the DCH and the TC, while
the time resolution was strictly limited by the large scintillator size, the PMT performancedegradation in the COBRA magnetic ﬁeld, poor time calibration between scintillator bars,
and pileup eﬀects.
The MEG II pTC overcomes such limitations by a highly-segmented detector design.
The 30 plastic scintillator bars of the MEG TC are replaced by 512 smaller scintillator tiles
in the new conﬁguration, which is made possible by the use of SiPMs as photo sensors.
This new design of the pTC has various advantages over the previous one:
• A high single-pixel time resolution can be achieved for the small scintillator size.
• The multiple-pixel-hit scheme signiﬁcantly improves the overall time resolution.
• A high online emission angle resolution can be achieved for its segmented design.
• A ﬂexible detector layout enables maximization of the detection and tracking eﬃciencies.
• A stable detector performance is possible as SiPMs are unaﬀected by magnetic ﬁelds.
• Pileup becomes negligible due to the segmented design.
The most important point of these, concerning the pTC resolution, is the second point;
the multiple-pixel-hit scheme (c.f. 4.5.1). The new design allows signal positrons to hit
an average of ∼ 9 pTC pixels as shown in Fig. 4.1. As the timing measurement in eachpixel
√ is independent of each other, in principle, the overall resolution should improve with
1/ Nhit , with the number of hit pixels, Nhit . This multiple-pixel-hit scheme signiﬁcantly
improves the pTC time resolution from the single-pixel time resolution, and the overall
resolution goal of 46 ps is expected to be achieved.

Figure 4.1: An example of a hit pattern by a simulated signal positron.

4.2. Design

43

On the other hand, the most important point, concerning the positron eﬃciency is
the third point. No material is placed between the CDCH and the pTC, and the pTC isplaced just below the CDCH to allow positrons to be tracked up to just before the pTC.
Hence, the eﬃciency goal of 70 % is also expected to be made possible with a suitable
tracking algorithm.

4.2

Design4.2.1

Overall design

The pTC consists of two semi-cylindrical super-modules, which are mirror-symmetricto each other and placed both upstream (US) and downstream (DS) of the target between
the CDCH and the COBRA. Fig. 4.2 shows the design of the DS super-module. Eachsuper-module is composed of 256 scintillation counters (or pixels) described in 4.2.2; 16
pixels align in z direction at 5.5 cm intervals, while 16 lines are cylindrically arranged at
10.3◦ intervals, alternately staggered by half a pixel. All the pixels are tilted at 45◦ tobe perpendicular to the signal positron trajectories. This overall design covers 23.0 cm <|z| < 116.7 cm in the longitudinal direction and −165.8◦ < ϕ < 5.2◦ in the azimuthal
direction, which fully covers the signal positron acceptance when the photon points to the
LXe calorimeter.
The signals are read out through the backplanes (BPs); 32 BPs align in ϕ direction ineach super-module, and a common BP is used for channels in the same ϕ. All the pixels
are ﬁxed onto these BPs, which lead the signals from SiPMs to higher |z| and allow them
to be read out through coaxial cables (RG-178 from Radiall [43]) and by the WDBs. Thisis shown in Fig. 4.3.

Figure 4.2: CAD design of the DS pTC
super-module [27].

4.2.2

Figure 4.3: The pTC with cables prolonged
from the BPs.

Single-pixel design

A single pixel is composed of a plastic scintillator with six series-connected SiPMs atboth sides as shown in Fig. 4.4. The scintillation light produced by a charged particle
penetrating the scintillator is detected by the SiPMs on both sides. The SiPMs are
soldered onto specially-made print circuit boards (PCBs), and are glued to the scintillator
using optical cement (BC600). Some pixels have a hole and a support structure at the44

Chapter 4. Pixelated Timing Counterbottom to insert an optical ﬁber used for time calibration between pixels (see 4.4.3).
The scintillator is wrapped with a reﬂective ﬁlm (ESR from 3M), and afterwards withRa polyvinyl ﬂuoride ﬁlm (Tedlar⃝[44]) together with the support structure for lightshielding. A list of materials used for the pTC pixel assembly is shown in Tab. 4.1.

120 mmplastic
scintillator

50 mm

40 mm

seriesconnected
SiPMs

ESR

optical fiber

Figure 4.4: Single pTC pixels. One (left) is wrapped with an ESR, while the other (right)
has an optical ﬁber inserted.

Table 4.1: Major materials used for pTC pixel assembly.
Material
Product
Scintillator
BC-422 [36]SiPM
ASD-NUV3S-P High-Gain
Reﬂector
ESR
R
Light shielder
Tedlar⃝4.2.2.1

Manufacturer ReferenceSaint-Gobain[36]
AdvanSiD
3M
DuPont[44]

Plastic scintillator

The main requirements for the scintillator material are a high light yield and a fasttime response to achieve a high pixel time resolution. Thus, ultra-fast plastic scintillators,
BC-422 from Saint-Gobain [36], are chosen. All the scintillator tiles have the same length(L = 120 mm) and thickness (T = 5 mm), while the width is either W = 40 mm or
W = 50 mm depending on where the pixel is placed as already shown in Fig.4.2. Although
there are some geometrical restrictions, the size of the pixels are generally optimized tomaximize the acceptance and the resolution.
4.2.2.2

The principle of SiPMs

SiPMs are photo sensors made up of multi-pixel avalanche photodiodes (APDs) working in Geiger modes. By applying a reverse bias voltage, charge carriers generated by
the absorption of photons are accelerated, trigger avalanches in the gain region, and thus
multiply the signal. Fig. 4.5 shows a schematic view of the structure and the working
principle of SiPMs.

4.2. Design

45

Figure 4.5: Schematic view of how a SiPM works [45].

Here, some basic parameters which characterize SiPMs are introduced.
• Breakdown voltage and overvoltage
A SiPM needs a certain magnitude of reverse bias voltage for the produced charge
carriers to cause an avalanche. This voltage is called the breakdown voltage and a
SiPM must be operated above this voltage. The operational characteristic of SiPMs
are determined by the overvoltage deﬁned as
Vov = V − Vbd(4.2)

where V is the applied bias voltage and Vbd is the breakdown voltage. The breakdown voltage of SiPMs is known to have a strong dependence on the temperature.
• GainSiPMs have high gains in the range of ∼ 105 –106 . It is deﬁned by the output charge
from a single photoelectron and is known to be proportional to the overvoltage as
G=

Q
∝ Vov
q

(4.3)

where G is the gain, Q is the output charge from an electron, and q is the electron
charge.
• Photon detection eﬃciency
The photon detection eﬃciency (PDE) is the probability of a photon entering the
SiPM to cause an avalanche. This factor has a positive correlation with the overvoltage.
• Dark noise
A dark pulse is a pulse generated not by a photon, but by the thermal excitation ofan electron or via tunneling eﬀect. This is quantize by the dark count rate (DCR),
which is the number of dark pulses in a second. The dark noise a generic term for
the SiPM noise from pulses that are not generated by photons. This dark noise is
known to have a strong correlation with the overvoltage and the temperature. In
addition, radiation damage to SiPMs can signiﬁcantly increase the amount of darknoise as later explained (see 4.7.1).

46

Chapter 4. Pixelated Timing Counter• Crosstalk
A crosstalk (CT) is caused when accelerated carriers in the high ﬁeld region emit
photons, which initiate a secondary avalanche in a neighboring microcell. A CT
occurs in correlation with another pulse, and is therefore called a correlated noise.
The CT probability increases with the overvoltage.

• Afterpulse
An afterpulse (AP) is another type of the correlated noise. It occurs when charge
carriers get trapped in crystal defects during an avalanche, and cause a delayed
avalanche. Delayed CTs can also cause afterpulsing. The AP probability also increases with the overvoltage.

4.2.2.3

SiPMs in the pTC

The time resolution of scintillation counters strongly depend on the photon statistics.
Higher photon statistics can be obtained either by increasing the SiPM coverage of thescintillator, or by using SiPMs with higher PDE. After testing various combinations of
SiPMs, the combination of six 3 mm × 3 mm ASD-NUV3S-P SiPMs from AdvanSiD waschosen. The AdvanSiD SiPMs used for the pTC can be classiﬁed into three types according
to when they were manufactured. This is summarized in Tab. 4.2. Type I SiPMs are usedin most pixels, but ∼ 40 pixels consist of type II SiPMs. Type III SiPMs are newly used
for the spare pixels introduced in chapter 6.

Table 4.2: SiPMs used for the pTC.
Type
SiPM
I
ASD-NUV3S-P High-Gain
II
ASD-NUV3S-P
III
ASD-NUV3S-P [46]

Cell size
50µm × 50 µm
50µm × 50 µm
40µm × 40 µm

These SiPMs can be connected either in parallel or in series. It was found that parallel connection of SiPMs can increase the signal rise time and the width, leading to adegradation in the time resolution, while a sharper pulse can be obtained using seriesconnection [47]. This arises from the small capacitance in the series connection. These
results are depicted in Fig. 4.6 and Fig. 4.7.

4.3. Analysis

47

Figure 4.6: Waveforms obtained using parallel connection (top) and series connection(bottom) of SiPMs[47]. The waveforms areshaped using pole-zero cancellation.

4.3

Figure 4.7: A comparison of the overvoltage dependence of the time resolution using parallel and series connection of SiPMs[47].

AnalysisFig. 4.8 shows the reconstruction procedure of positrons. On the pTC side, ﬁrst,
an analysis of the waveforms obtained by the WDBs is performed. Second, pixel hits
are reconstructed from the two channels in each pixel. Third, the hits which belong
to the same positron track are grouped together into a cluster; this procedure is called
the clustering. Fourth, the hits in the same cluster are combined into a single positron
track. Finally, a matching between the pTC track and the CDCH track is performed
to create one ﬁnal positron track, and the positron momentum, time and emission angle
are reconstructed. Methods for matching the pTC and the CDCH information are still
under development, so I introduce the analysis procedures from the waveform analysis tothe pTC tracking in this section. One thing to note is that the pTC tracking requires
a certain minimum number of hits. When the number of the pTC hits is below thisthreshold, the pTC tracking is skipped and the pTC cluster information and the CDCH
track information are combined.
• Energy calibration• Position calibration• Time calibration

pTC analysis
Waveform
analysis

Hit
reconstruction

Clustering

Tracking
Positronreconstruction

initial time
Wavefrom
analysis

Hit
reconstruction

Trackfinding

Tracking

CDCH analysis

Figure 4.8: The analysis ﬂow of the positron reconstruction.

48

4.3.1

Chapter 4. Pixelated Timing Counter

Waveform analysis

To obtain the signal arrival time from the waveform, the constant fraction (CF) method
is used, in which the time the waveform reaches a certain fraction of the peak pointis extracted. Setting a ﬁxed threshold can potentially cause time walks depending on
the signal size, but this method always yields the same time as long as the waveformcharacteristic does not change. Hence, a better time resolution can be obtained using thismethod.

4.3.2

Hit reconstruction

The pixel hit time, thit , and the horizontal hit position, xhit , are reconstructed in the
hit reconstruction stage. The local coordinates in a pixel are deﬁned in Fig.4.9.

Channel 1𝑡!"# [s]𝑦hit point(𝑡"$% , 𝑥"$% , 𝑦"$% )𝑧𝑥Channel 2𝑡!"& [s]Figure 4.9: Deﬁnition of the local coordinates in a pixel.

4.3.2.1

Hit time

The time we measure with the two channels deviate from the true pixel hit time by the
propagation time of the scintillation light to each channel, plus some time oﬀset intrinsic
to each channel. Thus, the two measured times can be written as
δt
)
(4.4)
2
δt
(4.5)
tch2 = thit + ∆tch2 + (toﬀset + )2
where the subscripts ch1 and ch2 correspond to the two readout channels, thit is the true
pixel hit time, ∆t is the propagation time of the scintillation light to each channel, toﬀset isthe intrinsic pixel time oﬀset, and δt satisﬁes δt = tch2 − tch1 when xhit = 0. The intrinsic
time oﬀset of each channel is incorporated in toﬀset ∓ δt2 .
From Eq. (4.4) and Eq. (4.5), the hit time can be reconstructed astch1 = thit + ∆tch1 + (toﬀset −tch1 + tch2 ∆tch1 + ∆tch2−− toﬀset2
2
L
tch1 + tch2−
− toﬀset=2
2veﬀ

thit =(4.6)

4.3. Analysis

49

where L(= 12 cm) is the length of a pixel, and veﬀ is the eﬀective velocity of the scintillation
light, which is assumed to be uniform throughout each pixel. In truth, L/2veﬀ + toﬀset
is obtained beforehand in the time calibration between pixels (see 4.4.3). Therefore, we
do not actually have to consider the propagation time of the scintillation light in the hit
time reconstruction, but obtain consistent hit times independent of xhit .

4.3.2.2

Hit position

The horizontal hit position in a pixel can be obtained by the time diﬀerence of the twochannels. The propagation time of the scintillation light to each channel can be writtenasL+ xhit2L−xhit.
∆tch2 = 22

∆tch1 = 2

(4.7)
(4.8)

By taking the diﬀerence between Eq. (4.7) and Eq. (4.8) and using Eq. (4.4) and Eq. (4.5),
the hit position can be obtained as(∆tch1 − ∆tch2 )veﬀ
2
tch1 − tch2 + δt
=
veﬀ .
2

xhit =(4.9)

The eﬀective velocity of the scintillation light in each pixel, veﬀ , and the relative time oﬀset
of the two channels, δt, must, therefore, be obtained beforehand. These are obtained in
the position calibration (see 4.4.2).

4.3.3

Clustering

In the clustering process, the reconstructed hits belonging to the same positron track
are grouped together. To do this, an index called the geometry ID is deﬁned as in Fig. 4.10
according to the order the positron track penetrates. Using this, each pixel hit time andx hit position are projected to the pixel with the youngest geometry ID (i.e. the assumed
ﬁrst-hit pixel). A typical TOF between adjacent pixels is used for the former projection,
and a typical positron penetration angle is used for the latter. Thus, the hits with close
projected hit times and projected hit positions are grouped together into a single cluster.

50

Chapter 4. Pixelated Timing Counter
1

3
5

2
4

positrontrack

Figure 4.10: Deﬁnition of the geometry ID for clustering.

4.3.4

Tracking

The last stage of the pTC analysis is the reconstruction of a track from the hits in thesame cluster. This procedure can be divided into two steps; the former is the estimation of
the initial values for the track ﬁt, and the latter is the actual track ﬁt with the estimatedparameters.

4.3.4.1

Parameter estimation

In order to colligate the hits into a single track, an estimation of a couple of quantities
must be made in advance. First, a reasonable initial value of the positron momentum isneeded, as it largely aﬀects the positron trajectory. However, the positron acceptance ofthe pTC is strictly limited to those with momentum close to the signal positron; positrons
with low momentum seldom reach the pTC due to the COBRA magnetic ﬁeld. Therefore,a typical value of 45 MeV is suﬃcient as the initial value.
Another necessary parameter is the local y position in each pixel hit. xhit is alreadyestimated with ∼ 11 mm precision in the hit reconstruction as explained in 4.3.2.2. zhit
does not need to be estimated as each pixel is only 5 mm thick, and the mean value of
2.5 mm can be used. In some way yhit must also be estimated to create a track.
This is realized by making use of the hit pattern in a cluster. The “hit” or “non-hit”
in n pixels with consecutive geometry IDs can be converted into an n-bit information. In
this way, all the cluster hit patterns can be listed up. Using MC simulation to obtain the
averaged true y hit position for each hit in each cluster hit pattern, yhit can be estimatedwith ∼ 8 mm precision. In truth, the hit pattern of ﬁve pixels in front and back of the
pixel under estimation is used to estimate yhit . This method is schematically depicted inFig. 4.11.

4.4. Calibration

51
forward pixels

0

0

0

0

backward pixels

11

pixel under estimation

1

1

0

0

positron trajectory

Hit pattern: 00001|11100

Figure 4.11: A schematic diagram of yhit estimation from the cluster hit pattern.

4.3.4.2

Tracking

The pTC positron track is reconstructed using the Kalman Filter (KF) technique.
Fig. 4.12 shows a schematic view of how the KF works. It is an eﬃcient recursive algorithm
to estimate the state vector and its covariance matrix based on the previous states, andcan be used to estimate time-changing variables from discrete values with errors. In otherwords, the KF technique enables us to choose the most likely track from all the possible
tracks, taking into account of the hit position error of each hit. In addition to the KF
technique, an algorithm called the Deterministic Annealing Filter (DAF) is implemented,
which is an extension of the KF and allows us to exclude any outlier hits from the track.
Fig. 4.13 shows a graphic view of a reconstructed positron track in a MC event using
the pTC tracking. You can see how the KF technique creates a continuous track fromthe discrete hit information. A GENFIT package is used for the calculation.

2. extrapolate

5. iterate

1. seed3. search
4. update

Figure 4.12: A schematic diagram of theprinciple of the KF.

4.4

Figure 4.13: A graphic view of a reconstructed pTC track [48].

Calibration

There are various quantities that must be calibrated to analyze the pTC data. HereI brieﬂy introduce some of them which are relevant to the coming discussions.

4.4.1

Energy calibration

The energy deposited in a pixel by a positron is reconstructed from the pulse charge.
In the waveform analysis, the collected charge is calculated by the integration of the
waveform. The charge-to-energy conversion factor can then be obtained by ﬁtting the52

Chapter 4. Pixelated Timing Counterreconstructed charge distribution to the energy deposit distribution obtained using MC
simulation. To be more speciﬁc, the energy calibration factor CE is obtained as
E peak1
CE = √peak
peak
Qch1 · Qch2

(4.10)

peak
where E peak is the peak in the MC energy deposit distribution, and Qpeak
ch1 and Qch2 are thepeaks of the reconstructed charge in the two channels. This conversion factor is obtainedfor each pixel and retained for the analysis.

4.4.2

Position calibration

In order to reconstruct the hit position in each pixel as explained in 4.3.2.2, the relative
time oﬀset of the two channels and the eﬀective velocity of the scintillation light must be
calibrated. To do this, the reconstructed hit position distribution in each pixel as shownin Fig. 4.14 is used. The horizontal length essentially demonstrates the eﬀective light
velocity, while the center position of the distribution shows the time oﬀset between thetwo channels. The xhit position resolution of each pixel can also be obtained from thestandard deviation of the convoluted Gaussian.

Figure 4.14: An example of the reconstructed xhit distribution in a pixel. The black histogram shows the position distribution after taking the moving average from the original
distribution(green). This is ﬁtted with a Gaussian-convoluted trapezoid (red) [49].

4.4.3Time calibration

The MEG TC performance was partly limited by the inaccuracy of the time calibration
between the TC bars. A more precise inter-pixel time calibration is required for the MEG
II pTC with a higher time resolution and much more components. Two complementary
methods have already been developed to achieve the required time calibration precision
between pixels. The characteristics and the performance of each method is summarizedin Tab. 4.3.
1

It was found in past studies that a geometrical mean of the two charges gives a better reconstruction
than an arithmetic mean.

4.4. Calibration

53

Table 4.3: A comparison of the two time calibration methods.
MethodNumber of pixels
Uncertainty
Major advantage

4.4.3.1

Laser calibration
432
24 ps
No beam needed

Michel calibration
512∼ 10 ps
High coverage and precision

Laser calibration

One is a time calibration method using laser light. As was shown in Fig. 4.4, most pixels have a laser ﬁber inserted into the scintillator, from which a laser light can be injected.2
Fig. 4.15 shows the overall picture of the laser system (PLP-10 from Hamamatsu Photonics [50] is used for the light source). The laser light is divided using optical splitters andcan be injected into 432 of the 512 pixels. By illuminating multiple pixels simultaneously,
a time synchronization between pixels is possible. The optical lengths of the laser systemcomponents are measured in advance. Using this method, a time calibration accuracy of
24 ps was already demonstrated in the pre-engineering run in 2016 (pER2016) [51]. The
laser system can also be used for a signal check or other various DAQs without the muon
beam.

Figure 4.15: A schematic overview of the laser system.

4.4.3.2

Michel calibration

The other method is based on the positron tracks using the muon beam, and is commonly called the “Michel calibration”. Since the positron TOF between pixels can beobtained from the positron track, the inter-pixel time oﬀsets can be calibrated using
multiple-hit events. The Michel calibration minimizes the χ2 deﬁned as
2

χ =

Nhit
N∑
event ∑
i=1

2

( tij − (ti1 + T OFi1j + ∆Tj ) )2σ
j=1

(4.11)

Pixels positioned in the most inner z do not have the laser ﬁber inserted due to geometrical restrictions.

54

Chapter 4. Pixelated Timing Counter

where Nevent is the number of events, Nhit is the number of pixel hits in a track, tij is thereconstructed hit time of the j-th hit in the i-th event, ti1 is the estimated hit time of
the ﬁrst-hit pixel, and T OFi1j is the estimated TOF from the ﬁrst-hit pixel to the j-th
hit in the i-th event. Here, ∆Tj is the intrinsic time oﬀset of the j-th hit pixel, and theparameter to be calibrated. In MC simulation, 6 ps precision can be obtained.
The Michel calibration was performed with the fully constructed pTC in the pER2017.
The diﬀerence between the time oﬀsets obtained in the two methods is plotted in Fig. 4.16,
in which a standard deviation of ∼ 50 ps is seen. From this result,√ the uncertainty of thetime calibration for an arbitrary pixel is estimated to be 50 ps/ 2 ∼ 35 ps.

Figure 4.16: Diﬀerence between the time oﬀsets obtained in the Michel and the laser
calibration method [52].

4.5

Performance

4.5.1

Multiple-hit scheme

The pTC time resolution has greatly improved from the MEG TC for its segmented
design. First, the small size of each pixel greatly reduces the variation of the optical path
lengths of the scintillation light, which results in a high single-pixel time resolution. The
time resolution strongly depends on the noise condition, but a mean resolution of ∼ 72 ps
and ∼ 81 ps are obtained for 4 cm and 5 cm pixels respectively in lab tests.
√
Second, the positron time resolution improves by a factor, 1/ Nhit , with the numberof hit pixels, Nhit . Fig. 4.17 is a preliminary result showing a distribution of the number ofhit pixels for signal positrons using MC simulation, and Fig. 4.18 shows the pTC resolution
as a function of the number of hit pixels. A typical signal positron hits ∼ 9 pixels, so theoverall pTC resolution can be estimated as roughly 1/3 of the single-pixel resolution.

4.6. Slow control system

55

Figure 4.17: Distribution of the number ofhit pixels for signal positrons in MC simulation [47].

4.5.2

Figure 4.18: The overall pTC resolution as
a function of the number of hit pixels [47].

Expected performance

To get a more precise estimate of the pTC resolution, some additional eﬀects, like theuncertainty of the inter-pixel time calibration must be taken into account. Indeed, a moreaccurate resolution of the pTC for a Nhit -hit event can be written in the form√
σt+e (Nhit ) =222
σsingle+ σinter−pixel+ σelec2+ σconst
Nhit(4.12)

where σsingle is the intrinsic resolution of a single pixel, σinter−pixel is the uncertainty of theinter-pixel time calibration, σelec is the uncertainty from the electronics
jitter, and σconst√
is the uncertainty from other eﬀects that does not scale with 1/ Nhit , such as the eﬀect
from the multiple scattering of positrons.
A rough estimation of the pTC resolution has already been made in [51] using the
pER2016 data. It assumes the single-pixel resolution of 93 ps, which also includes theelectronics jitter and the uncertainty of the inter-pixel calibration to be 39 ps by comparing
the consistency between the laser and the Michel calibration. In addition, making a roughestimation of σconst ∼ 10 ps and using a typical value of 9 pixel hits, the overall pTC
resolution is roughly evaluated to be√
σt+e ∼

4.6(93 ps)2 + (39 ps)2
+ (10 ps)2 ≃ 35 ps.
9(4.13)

Slow control system

The slow control system enables the monitoring and the controlling of the physicalquantities that change slowly over time during operation, such as the temperature and thehumidity. The pTC is actually planned to be operated in a cooled and dried condition,
so here, I introduce the temperature and humidity control system for the pTC.

56

Chapter 4. Pixelated Timing Counter

4.6.1

Motivation

4.6.1.1

Radiation damage to SiPMs

As brieﬂy mentioned in 4.2.2.2, radiation damage to SiPMs can signiﬁcantly increase
the amount of dark noise. There are two types of radiation damage; one is bulk damage
to Si from non-ionizing energy loss (NIEL) of energetic particles, and the other is surface
damage to SiO2 from ionizing energy loss (IEL) of charged particles such as electrons.
The former can potentially create lattice defects, which give rise to new energy levels in
the Si band gap and increase the thermal excitation of electrons. The latter can cause
charge accumulation in the oxide, again creating new energy levels. The latter eﬀect isalready known to be negligible in our case [53], and therefore, the dominant damage for
the MEG II pTC is the former. The precise dose level is estimated to be equivalent to∼ 5 × 109 /cm2 1 MeV neutrons in the three-year physics run. The details of the dose
calculation are given in Appendix A.
The problem with the increase of dark noise is that it can degrade the time resolutionof the pTC. A basic study on the eﬀect of radiation damage to SiPMs on the pTC
performance has already been conducted [54]. In this study, SiPMs were irradiated with
an electron source in several steps to a level comparable to the MEG II pTC damagelevel, and the single-pixel time resolution was measured at each damage level. From thisstudy, a resolution deterioration of ∼ 30 % is expected at the temperature of 30 ◦ C.

4.6.1.2

Eﬀect of cooling

As mentioned in 4.2.2.2, the DCR of SiPMs has a strong dependence on the temperature. This means that the dark noise can be suppressed by cooling the SiPMs andthus reducing the thermal excitation of electrons. The eﬀect of cooling SiPMs on thepTC performance was also studied in [54], and the results are shown in Fig. 4.19. The
increase of dark noise with radiation damage is apparent from the current increase, andthe eﬀectiveness of cooling is apparent from comparing the two plots. The conclusion wasthat the ∼ 30 % degradation of the pTC resolution at 30 ◦ C can be suppressed to ∼ 5 %by cooling the SiPMs to 10 ◦ C.

4.6. Slow control system

57(a) Measurement at 30 ◦ C(b) Measurement at 10 ◦ C

Figure 4.19: The single-pixel time resolution as a function of the readout current [54].
Diﬀerent points in the same color show measurements at diﬀerent damage levels.

4.6.2

Temperature control

From the study described above, the pTC is planned to be operated in a 10 ◦ C cooled
condition. A basic cooling system has already been developed [54]. Water chillers (SH1501000 from LabTech [55]) are used to deliver cooled water to the copper pipes attachedto the backside of the support structure. This is schematically depicted in Fig. 4.20.
The water cools the entire support structure including the BPs. As each pixel is ﬁxed
onto the BP using a thermal link and thermal paste to enhance the thermal conductivity,
the SiPMs should also be suﬃciently cooled with this system. Numerous thermometers(DS28EA00 from Maxim Integrated [56]) are mounted on the BPs for monitoring, andthe temperature stability at 10 ◦ C has already been conﬁrmed.
support structure

dry airpixel

heat
exchangerBPcooled dry air

waterchillercooled water

Figure 4.20: A schematic view of the pTC cooling system.

4.6.3

Humidity control

The humidity must also be controlled as the cooled operation can potentially cause
water condensation in the pTC, which we do not want both from the material and the

58

Chapter 4. Pixelated Timing Counterelectronic stability point of view. The humidity control system has also been developed[54], and is also demonstrated in Fig. 4.20. It makes use of the dry air available at PSI;
the dry air is cooled down by the cooled water at the heat exchanger and is ﬂushed into
the pTC through pipes mounted around the support structure. There are also several
hygrometers (HIH-4000 Series from Honeywell [57]) attached to the BPs to monitor thehumidity. The stability of the humidity control system at 10 ◦ C condition has alreadybeen achieved by covering the pTC with a thin plastic foil to keep the dry air in.

4.7

Operation

The construction of the pTC started in 2015, and since then, several pERs have alreadybeen performed to demonstrate the performance of the pTC. Tab. 4.4 summarizes thenumber of readout channels, together with the major update in each year. In this section,
I summarize what has already been achieved by the pTC group in the past years.
Table 4.4: A summary of the past pERs.
Year Number of channels
Readout region
2015
256
1/2 DS (middle ϕ)2016
256
1/2 DS (middle ϕ)2017
512
DS and US
2018256
1/2 DS (latter z)
2019
256
1/2 US (middle z)

4.7.1

Major update
1/4 detector constructed
Laser system developed
Full detector constructed
Cooling system developed
Advance in positron analysis

pER2015

The construction of the pTC started in 2015, and 128 DS pixels had been integrated
onto a prototype support structure by the pER2015. The basic method of the pixel
assembly, as well as the pTC insertion and extraction system were established this year.
In addition, a ﬁrst test of the laser system was performed with 8 pixels. However, theanalysis of the data was strictly limited by some issues on the DAQ side.

4.7.2

pER2016

There were two major updates in the pER2016 from the hardware point of view.
First, the ﬁnal support structure was constructed and all of the 256 DS pixels were
integrated. Second, the laser calibration was performed with 40 pixels. DAQ issues in theprevious year were ﬁxed and the calibration and the data analysis were made possible.
The eﬀectiveness of the multiple-hit scheme was demonstrated using the pTC clustering
analysis.

4.7.3

pER2017

The construction of the full detector was ﬁnished in 2017, and although the numberof readout electronics was limited, all channels were read out by dividing the DAQ period

4.8. Tasks

59

in two, one for the DS and one for the US pTC. The laser calibration was also performed
with the full system, demonstrating ∼ 35 ps inter-pixel time calibration precision together
with the Michel calibration. For the data analysis, a ﬁrst realistic evaluation of the overallpTC resolution was performed using ﬁxed geometrical combinations of pixels in clusters,
yielding the value of ∼ 38.5 ps.

4.7.4

pER2018

The full cooling system was established in 2018, and its general eﬀect and its stability
were demonstrated in the pER2018. There was also another big update on the softwareside; the pTC tracking algorithm (c.f. 4.3.4) was developed. This allows us to get a better
evaluation of the pTC resolution, as well as improve the pTC-CDCH positron matchingquality.
Concerning the positron spectrometer as a whole, the construction of the CDCH wascompleted and it was installed for the ﬁrst time. Although the CDCH showed very
diﬀerent behaviors to that of the MC CDCH (e.g. low gain, instability of the baseline,etc.), a combined analysis of the CDCH and the pTC was ﬁnally made possible.

4.7.5

pER2019

Further understanding of the detector and advances on the software side were achievedin the pER2019, which are the topics of this thesis. In addition, a basic combined tracking
algorithm of the pTC and the CDCH was developed, which is beyond the scope of thisthesis.

4.8

Tasks

As explained above, the hardware system of the pTC has already been constructed,
and the standard calibration methods and analysis algorithms have also been established.
However, there still remain some issues that must be solved.
One concerns the stable operation of the pTC. Our group has faced a malfunctioningof some channels in the past. Although the cause was investigated and some countermeasures were taken, we cannot deny the possibility of a similar malfunctioning occurring in
the future, in which case we expect to partly lose the eﬃciency and the resolution. In
preparation for such accidents, the construction of spare pixels is essential. By doing so,even if we encounter some unexpected failure of some pixels, we would be able to replacethem immediately and maintain the expected pTC performance.
Another remaining task is a detailed study on the eﬀect of radiation damage to SiPMs.
Although a basic study on the general eﬀect of radiation damage to SiPMs has been
conducted, no study has been performed to see its eﬀect on SiPMs connected in series.
This is a fundamental but essential study that must be done to get a precise understandingof our detector.
These topics are covered in chapter 5 and chapter 6 respectively. The rest of this thesis
demonstrates various attempts to maintain the high pTC performance in the long run.

Part II
Long-term Operation of pTC

61

Chapter 5
New Pixel Assembly
18 new pixels were assembled as spares. In this chapter, I describe the assembly procedure and the various tests at each assembly step. In the end, the single-pixel performanceof the newly-assembled pixels are given.

5.1

BackgroundThe series connection of SiPMs have the advantage of sharper signal waveforms. However, from the viewpoint of the long-term detector operation, there is a risk that a malfunctioning of a single SiPM can result in a dead channel. Such a case has already been
confronted in the past, where the anode and the cathode of a SiPM suddenly became
electrically disconnected.
Another known case of malfunctioning is the detachment of SiPMs from the scintillator
tile as depicted in Fig. 5.1a. It is assumed to be caused by a mechanical stress on the
SiPM array arising from a mismatch between the channel interval of the pixel and that of
the support structure. A countermeasure for this problem has already been taken; a tiny
scratch is created to the scintillator, and additional optical cement is put between some
SiPMs to reinforce the adhesiveness. This is depicted in Fig. 5.1b.
original
cementscratchadditional
cementdetachment

(a)

(b)

Figure 5.1: A schematic drawing of (a) the detachment problem and (b) the countermeasure against it.
Although we expect the detachment problem to have been solved by the reinforcement,
we do not know the cause for the former problem, and we cannot deny the possibility of63

64

Chapter 5. New Pixel Assembly

some dead channels appearing in the three-year physics run. A dead channel degrades the
single-pixel resolution, and also makes impossible the hit time and position reconstructionin the pixel. Therefore, to maintain the pTC performance, it is necessary to constructspare pixels, to which we can swap the pixel with a dead channel if any such case arises.

5.2

Overview

18 new pixels were assembled: nine 4 cm pixels and nine 5 cm pixels. The assembly
procedure is shown in Fig. 5.2. First, the SiPMs were soldered onto PCBs in groups of six.
Second, the SiPM arrays were glued onto scintillator tiles cut into the standard size, andthus the pixels were constructed. Lastly, the scintillators were wrapped with reﬂective
foils and then with polyvinyl ﬂuoride ﬁlms for light-shielding.
There were also some measurements to be performed at each assembly stage. After thesoldering process, a current-voltage (I-V) measurement of each SiPM array was performed
to obtain the breakdown voltage. A signal check using an LED light was also performed
to see the signal size of each SiPM array. After the pixel assembly, measurements using
a 90 Sr radiation source were performed. The bias voltage was scanned ﬁrst for each pixel
to determine the operation voltage. Lastly, a hit position scan was performed to evaluate
the ﬁnal single-pixel performance of each pixel.
SiPM

PCB

Scintillator

Soldering

Cutting
Hole making

SiPM array• IV measurement• Signal check
Adhesion
Pixel
Reflector wrapping• Bias voltage scan
• Position scanLight shielding

Figure 5.2: The procedures for a pixel assembly.

5.3

I-V measurement

5.3.1

Measurement

After the soldering process, I-V measurements were performed for the SiPM arrays,
in which the behavior of the current ﬂow with respect to the applied bias voltage wasmeasured. The breakdown voltage of a SiPM array can be obtained from the obtained
I-V curve. The I-V measurement is particularly important for the new pixels as the5.3. I-V measurement

65

constituting SiPMs (type III in Tab. 4.2) are diﬀerent from the ones used in old pixels(type I or II), and have diﬀerent I-V characteristics. The new SiPMs soldered onto PCBs
are shown in Fig. 5.3.
The setup for the I-V measurement is schematically shown in Fig. 5.4. The PCBs
were placed in a thermal chamber kept at 30 ◦ C, and both the HV application and thecurrent readout were performed using a picoammeter (6487 picoammeter from Keithley[58]). The data was taken in 0.1 V steps and all the 36 SiPM arrays were measured.
Thermal chamber (30 ℃)
PC

SiPM array

Figure 5.4: A schematic drawing of the I-V measurement
setup.

Figure 5.3: A picture of new
SiPMs soldered onto PCBs.

5.3.2

Picoammeter

Breakdown voltage

Fig. 5.5 shows the obtained I-V curves of all 36 SiPM arrays. One SiPM array (O24F)
shows a strange I-V curve, but similar I-V characteristics are seen in all the others. The
apparent breakdown voltage of ∼ 160 V is relatively high compared to old SiPM arrays(type I and II), whose breakdown voltages are typically ∼ 145 V at the same temperature.

Current [µA]

IV curves of new SiPM arrays

10

1

10−1

10−2
150

160

170

O21A

O21B

O21C

O21D

O21E

O21F

O22A

O22B

O22C

O22D

O22E

O22F

O23A

O23B

O23C

O23D

O23E

O23F

O24A

O24B

O24C

O24D

O24E

O24F

O25A

O25B

O25C

O25D

O25E

O25F

O26A

O26B

O26C

O26D

O26E

O26F

180

190

200
Voltage [V]Figure 5.5: I-V curves of new SiPM arrays.

The breakdown voltage of each SiPM array was obtained in the following procedures:

66

Chapter 5. New Pixel Assembly
1. Take the moving average of the I-V curve using ﬁve points to suppress the measurement error.
2. Calculate the second derivative of the curve.
3. Take the moving average of the curve again.
4. Fit the peak with a quadratic function.

Fig. 5.6 shows the result at each analysis step for a typical channel. The breakdown voltage
in this method is deﬁned as the axis of the ﬁtted quadratic function. The obtained values
are shown in Fig. 5.7. The variation of the breakdown voltages is very small except for
O24F previously mentioned.

moving average

2!" differential

Figure 5.6: The procedure to calculate the breakdown voltage from the raw I-V curve(left). The middle shows the curve after taking the moving average, and the right shows
the curve after taking the second derivative and then the moving average again.

Number of SiPM arrays

Distribution of breakdown voltage
hist

8
7
6

Entries

36

Mean

161

Std Dev0.574254
3
2
1
0
160 160.5 161 161.5 162 162.5 163 163.5 164 164.5 165

Breakdown voltage [V]Figure 5.7: Distribution of the obtained breakdown voltages.

5.4

Signal check

After the I-V measurement, the signal check of each SiPM array was performed using
an LED light source. The measurement setup is shown in Fig. 5.8 and Fig. 5.9. The SiPM
arrays were again placed in a thermal chamber kept at 30 ◦ C. The HV to the SiPMs wereapplied using the same picoammeter, and the voltage was set to +18 V of the obtained

5.4. Signal check67

breakdown voltage1 . The signals were ampliﬁed using an ampliﬁer developed at PSI. For
the DAQ, a DRS Evaluation Board was used, which was also developed at PSI and works
in the same way as the WDBs.

Thermal chamber (30 ℃)
LED

PicoammeterPC

SiPM array

PSI amp

DRS board

Figure 5.8: A schematic drawing of the signal check setup.

LED light

SiPM arrays

Figure 5.9: The SiPM arrays ﬁxed onto a support structure with an LED light.

The result is shown in Fig. 5.10. The amount of light injected into each SiPM array depends on the PCB position in the support structure, so this eﬀect is corrected oﬄine. The
signal can be seen in all SiPM arrays, including the one with a strange I-V characteristic,
with ∼ 10 % deviation in the observed signal size.

1

The breakdown voltage of the SiPM array with a strange I-V characteristic (O24F) was assumed to
be a typical value of 161 V, and the overvoltage was set to 179 V.

68

Chapter 5. New Pixel Assembly

Number of SiPM arrays

Relative Gain of SiPM arrays
histResult

4
3.5
3

Entries36

Mean

0.2985

Std Dev0.02046

2.5
2
1.5
1
0.5
0
0.2

0.25

0.3

0.35

0.4

Signal height [V]Figure 5.10: Distribution of the obtained mean signal height.

5.5

Pixel assembly

After the basic tests of the SiPM arrays, the pixels were assembled one by one. First,
the optical cement (BC600) was evacuated and heated to remove any void in the material.
Second, using a jig shown in Fig. 5.11, the SiPM arrays were glued onto both sides of thescintillator tiles. In this procedure, SiPM arrays with close breakdown voltages obtainedin 5.3.2 were chosen as pairs and used in the same pixel. The procedure to strengthen theconnection (c.f. 5.1) was also taken. After the SiPM-array attachment, each scintillator
was wrapped with a reﬂective foil (ESR from 3M). Afterwards, each pixel was wrappedRwith a polyvinyl ﬂuoride ﬁlm (Tedlar⃝[44]) and a black tape for light shielding and theassembly was completed. The assembly procedure is shown in Fig. 5.11.
SiPM attachment

Reflector wrapping

Light shielding

Figure 5.11: The pixel assembly procedure.

5.6

Bias voltage scan

The bias voltage scan is necessary to determine the operation voltage of SiPMs. The
setup for the measurement is shown in Fig. 5.12. Electrons from a 90 Sr radiation source
were injected to the center of the pixel and to a trigger counter below it. The trigger
counter is composed of a 5 mm × 5 mm × 5 mm plastic scintillator wrapped with Teﬂon

5.6. Bias voltage scan69

and a SiPM (S10362-33-050C from Hamamatsu Photonics [59]) for readout. The twochannels of the pixel and the trigger counter were read out using PSI ampliﬁers and a DRS
Evaluation Board. The HV to each channel was supplied from diﬀerent picoammeters.
Thermal chamber (30 ℃)
!"

Sr

ch 1

ch 2

pixel

Picoammeter

PC

PSI amp

DRS board

triggercounterch 3

Figure 5.12: A schematic drawing of the bias voltage scan setup. Two PSI ampliﬁers andtwo picoammeters are omitted in the drawing.

The bias voltage scan was performed in steps of 0.5 V for ﬁve of the newly assembled
pixels. The resulting single-pixel resolution is plotted as a function of the overvoltage in
Fig. 5.13. The single-pixel resolution for each pixel is obtained from the distribution of
tch1 + tch2t=
− ttrigger(5.1)
2
where tch1 and tch2 are the signal times obtained in the two channels, and ttrigger is the time
obtained by the trigger counter. The standard deviation of this t distribution, correctedby the ∼ 30 ps resolution of the trigger counter is deﬁned as the single-pixel resolution.
Fig. 5.13 indicates that an optimal overvoltage from the time resolution viewpoint lies
somewhere around ∼ 25 V for all pixels. This is because the signal-to-noise ratio (S/N)
largely aﬀects the time resolution and both the signal and noise level are dependent on
the overvoltage. From this result, all new pixels will be operated at the overvoltage of
24 V, which corresponds to 4 V overvoltage for each SiPM.
Time resolution [s]−90.1 ×10

Bias voltage scan result

0.095
0.09

Pixel 556

Pixel 557

Pixel 559

Pixel 560

Pixel 558

0.085
0.08
0.075
0.07
0.065
0.06
0.055
0.05

10

20

30

40

Overvoltage [V]Figure 5.13: Overvoltage dependence of the single-pixel resolutions.

70

Chapter 5. New Pixel Assembly

5.7

Position scanThe ﬁnal single-pixel resolutions were determined by performing position scans at thedetermined bias voltage. While the bias voltage scan was performed for only a part of the
pixels, the position scan was performed for all new pixels. The measurement setup was
almost exactly the same as the bias voltage scan. The only diﬀerence was that the pixel
was mounted on a stage mover, and could be moved in local x direction.
The position scan was performed at three points of x = −4.25 cm, 0 cm, 4.25 cm with
a ﬁxed y = 0 cm. The results are shown in Fig. 5.14. High resolutions are achieved
independent of the hit position, and 4 cm pixels yield higher performance than 5 cm ones
as expected. The resolution at the center position is deﬁned as the ﬁnal single-pixel
resolution of each pixel.

Position scan result

0.095
0.09
0.085

Pixel 556

Pixel 557

Pixel 558

Pixel 559

Pixel 560

Pixel 561

Pixel 562

Pixel 563

Pixel 564

0.08
0.075

0.1 ×10
0.095
0.09
0.085

0.065

0.065

0.06

0.06
−2

0

2

4

6

Pixel 566

Pixel 567

Pixel 568

Pixel 569

Pixel 570

Pixel 571

Pixel 572

Pixel 573

0.075
0.07

−4

Pixel 565

0.08

0.07

0.055
−6

Position scan result−9Time resolution [s]Time resolution [s]−90.1 ×10

0.055
−6

−4

−2

0

2

x [cm](a) 4 cm pixels

46x [cm](b) 5 cm pixels

Figure 5.14: x hit position dependence of the single-pixel resolutions.

The distribution of the obtained single-pixel resolutions are shown in Fig. 5.15, together with those of old pixels. It is obvious that the new pixels have a higher time
resolution than the old ones. This is due to a higher gain and a lower noise level in the
new SiPMs.

5.8. Conclusion

71

Figure 5.15: Distribution of the single-pixel resolutions. The color-ﬁlled histograms represent the new pixels, while the non-ﬁlled ones represent the old ones.

5.8

Conclusion

The original purpose of the new pixel assembly was to retain the new pixels as spares,
to which we can replace any broken ones. However, as the new pixels showed better
performance than the old ones, we decided to install the new ones in the pTC and keep
the replaced ones as spares. Indeed 16 of these new pixels were installed in the US pTC
and successfully operated in the pER2019.

Chapter 6
Radiation Damage to SiPMs
Measurements were performed to understand the eﬀect of radiation damage to SiPMs
on the time response of scintillation counters. Discussed in this chapter, are the results
obtained in lab tests and their interpretations. In the last section, the impact of the
newly-found eﬀect on the pTC performance is evaluated.

6.1

Radiation damage to pTC SiPMs

Many studies on the general eﬀect of radiation damage to SiPMs have been carriedout in the past. The most prominent known eﬀect is the increase of dark noise, which candirectly deteriorate the time resolution of scintillation counters. However, as mentioned
before, we already know that this can be suppressed to some extent by lowering thetemperature of SiPMs.
In the case of the MEG II pTC, a linear increase of the current level due to the darknoise increase was observed in the past pERs. A simple extrapolation indicates that theoriginally ∼ 10 µA current level can reach ∼ 100 µA in the three-year physics run. Thisis consistent with a past study [54], in which SiPMs were irradiated to the radiation level
expected in the MEG II pTC in the three years and yielded a current level of ∼ 100 µA.
This study demonstrated that the deterioration of the pTC resolution due to the darknoise increase can be suppressed to ∼ 5 % by operating the detector at 10 ◦ C.
However, in the MEG II pTC case, there may be other eﬀects of radiation damage
other than the simple dark noise increase. One factor comes from the fact that thepTC utilizes a series connection of SiPMs, which is unique and has not been studied indetail before. Another comes from the gradation of the damage level within the seriesconnection. Fig. 6.1 shows the positron hit dose dependence on the radial length in thepTC. It is apparent that SiPMs at higher local y receive more radiation damage than theones at lower y. Such a special case has never been investigated before, and an additional
study is essential in order to know the potential eﬀects.
73

74

Chapter 6. Radiation Damage to SiPMs

Figure 6.1: r dependence of the positron hit dose [54]. The number of positrons with eachcurvature radius is calculated using MC simulation.

6.2

Measurement

The aim of this study, therefore, was to investigate how radiation damage to seriesconnected SiPMs aﬀect the pixel performance, especially when the radiation damage levelis not uniform. To test this, we prepared SiPMs with diﬀerent damage levels, and themeasurement setup was designed to be ﬂexible to be able to change the array of SiPMs
and test various damage patterns. The details of the setup is explained in this section.

6.2.1

SiPMs

SiPMs with four damage types were prepared for this measurement; one was completely free from damage, another was irradiated with electrons, and the other two were
irradiated with neutrons but to diﬀerent levels. The electron irradiation was performed in
the lab with a 37 MBq 90 Sr source and a collimator, and the ﬁnal dose level was evaluatedto be equivalent to ∼ 3 × 109 /cm2 1 MeV neutrons. On the other hand, the neutronirradiated samples were irradiated using reactor neutron facilities at the Laboratory ofApplied Nuclear Energy (LENA) of University of Pavia. The dose levels were evaluatedto be equivalent to ∼ 8.7 × 108 /cm2 and ∼ 5.5 × 109 /cm2 1 MeV neutrons respectively.
This is summarized in Tab. 6.1. Note that the dose level expected in the pTC in three
years is ∼ 5 × 109 /cm2 1 MeV neutrons at the highest point. For the details of the dose
calculation, see Appendix A.

6.2. Measurement

75

Table 6.1: A list of SiPMs used in the measurement.
SiPM type
a.
b.
c.
d.

Damage type
Dose level equivalent to 1 MeV neutrons
Non-damaged
0
Neutron-damaged∼ 8.7 × 108 /cm2
Electron-damaged∼ 3 × 109 /cm2
Neutron-damaged∼ 5.5 × 109 /cm2

Using these SiPMs, three types of SiPM arrays were created for the following measurements, each imitating the non-uniform damage pattern in a diﬀerent way. The damage
patterns are summarized in Fig. 6.2. The damage pattern C imitates the most realistic
case, where the six SiPMs have gradient damage levels in sets of two. On the other hand,the damage pattern A and B are the extreme cases where two (four) of the SiPMs aredamaged and four (two) are not at all.

Non-damaged
Pattern A
Pattern B
Pattern C
higher damage

Non-damaged SiPM
Neutron-irradiated SiPM
(8.7×10' n* +,- /cm1 )Electron-irradiated SiPM
(3×103 n* +,- /cm1 )Neutron-irradiated SiPM
(5.5×103 n* +,- /cm1 )Figure 6.2: The damage pattern of SiPM arrays used for the measurements.

6.2.2

Pixel assembly setup

In order to test SiPM arrays with diﬀerent damage patterns, the setup had to be
ﬂexible to allow an easy replacement of the SiPMs. This was realized by the parts shownin Fig. 6.3a and the assembly structure shown in Fig. 6.3b. The parts were designed using
computer-aided design (CAD) and produced using a plastic 3D printer.
The scintillator plate was pinched between the two parts labeled 1. SiPMs were placedin the dimples in part 2 and stuck to both sides of the scintillator using optical grease.
The two parts were ﬁxed using screws. Part 3 with twelve spring test probe pins was ﬁxed
onto part 2 in such a way that the probe pins attached the electrodes of SiPMs throughthe holes in part 2 and created a series-connected circuit of SiPMs. The attachment ofprobe pins to the SiPMs can be seen in Fig. 6.4. By adopting this design, the SiPMs
could be replaced simply by removing part 2 and part 3 temporarily.

76

Chapter 6. Radiation Damage to SiPMs

Part 2

Part 1
Part 3(a) The parts used in the assembly setup.

(b) The assembled structure with the scintillator plate in the middle.

Figure 6.3: A CAD design of the pixel assembly structure.

Figure 6.4: The assembled setup.

6.2.3

Overall setup

The overall setup was almost the same as the one used for the position scan in 5.7. The
same 90 Sr source was used, the thermal chamber was set to ∼ 30 ◦ C, and the triggering
was performed by the same trigger counter. The SiPM array to be tested was placed inchannel one, whereas channel two was used as a reference with non-damaged SiPMs. The
only additional requirement was the capability to scan the position in y direction to see
the eﬀect of non-uniform radiation damage.
This was realized by the setup depicted in Fig. 6.5. The position of the radiation source
was ﬁxed, so the pixel had to move in y direction. As the moving stage was capable ofposition scanning only in x direction, two aluminium bars were ﬁxed onto the moving
stage with screws. These bars had a number of screw holes at 5 mm intervals, making yposition scanning possible.

6.3. I-V characteristics

77
𝑥

Moving stage

Moving stage

hit position

hit position𝑦Figure 6.5: A schematic diagram of y position scanning.

6.2.4

Measurement

In order to clearly distinguish the eﬀect of radiation damage to SiPMs from othereﬀects, each damage pattern was tested with two conﬁgurations; one with the standard
array of SiPMs, in which the SiPMs at higher y have higher damage, and the other withthe reversed order of SiPMs. The diﬀerence in the two results can then be assumed
to be caused by the unbalanced radiation damage to SiPMs. In addition, a completely
damage-free array of SiPMs was also tested as a control experiment.
For each of these seven conﬁgurations, a position scan was performed both in x andy direction. x position scan was performed using the moving stage, while y position scan
was performed by shifting the aluminium bars.
Besides that, I-V measurements were performed for each SiPM used in the measurement and for the series-connected SiPM array of each damage pattern, as the I-V characteristic reﬂects the damage level most eﬀectively. The measurement setup used for the I-V
measurement was exactly the same as that used in the new pixel measurement (c.f. 5.3).

6.3

I-V characteristics

The obtained I-V curves for each of the used SiPMs are depicted in Fig. 6.6. The I-V
characteristics are clearly diﬀerent according to the damage level of SiPMs; the ones withmore damage show higher noise levels.

78

Chapter 6. Radiation Damage to SiPMs

10

SiPM1

SiPM2

SiPM3

SiPM4

SiPM5

SiPM6

1

10

2

10

SiPM1

SiPM2

SiPM3

SiPM4

SiPM5

SiPM6

I-V curve of each SiPM

Current [µA]

10

I-V curve of each SiPM

Current [µA]

Current [µA]

I-V curve of each SiPM
2

1

10

2

10

10−1

10−1

10−2

10−2

10−2

23

24

25

26

27

28

10−3
22

23

24

25

Voltage [V]

26

27

28

SiPM2

SiPM3

SiPM4

SiPM5

SiPM6

1

10−1

10−3
22

SiPM1

10−3
22

23

24

25

Voltage [V](a) Pattern A

26

27

28

Voltage [V](b) Pattern B(c) Pattern C

Figure 6.6: I-V curves of SiPMs used in each damage pattern at 30 ◦ C. SiPMs with lessdamage are labeled with younger numbers.
The I-V curves of the SiPM arrays with each damage pattern are shown in Fig. 6.7.
From this, the overall damage level in each pattern can be extracted; pattern C has thehighest damage, pattern B the second highest, and pattern A the lowest.

Current [µA]

I-V curve of each SiPM array
102

Pattern A
Pattern B

10

Pattern C

1

10−1

10−2

145

150

155

160

165

Voltage [V]Figure 6.7: I-V curves of SiPM arrays with each damage pattern.

6.4

Eﬀect on signal height

The eﬀect of radiation damage on the signal height was checked. The pulse heightin the following discussions are obtained by ﬁtting the pulse height distribution witha Landau function convoluted with a Gaussian, and extracting the peak of the ﬁtted
function.

6.4.1

Position dependence of pulse heightFig. 6.8 shows y hit position dependence of the pulse height when the hit point isclose to the damaged channel (x = −4.25 cm) for each damage pattern. A similar and6.4. Eﬀect on signal height79

clear position dependence is seen in all damage patterns, and the behavior is opposite
for the standard and the reversed conﬁguration. This clearly implies that this position
dependence is a result of the gradient damage to SiPMs.
Pulse height v.s. y

0.2
0.18
0.16
0.14

0.2
0.18
0.16
0.14

0.12
0.1

0.12
standard
−1

−0.5

0.22
0.2
0.18
0.16
0.14
0.12

standard

0.1

reverse
0.08−1.5

Pulse height v.s. y

0.22

Pulse height [V]Pulse height [V]Pulse height [V]Pulse height v.s. y
0.22

standard

0.1

reverse
0

0.5

1

0.08
−1.5

1.5

−1

−0.5

reverse00.5

y [cm]

1

1.5

0.08
−1.5

−1

−0.5

0

0.5

y [cm](a) Pattern A

11.5y [cm](b) Pattern B(c) Pattern C

Figure 6.8: y hit position dependence of the pulse height at x = −4.25 cm in each damage pattern. The red and blue markers correspond to the standard and the reversed
conﬁguration respectively.
Fig. 6.9 shows the same position dependence for pattern A, but when the hit point isfarther away from the damaged channel. The position dependence becomes less prominent
as the hit point shifts farther away. Similar results are seen in other damage patterns.
Pulse height v.s. y

Pulse height [V]Pulse height [V]Pulse height v.s. y
0.22
0.2
0.18
0.16
0.14

0.2
0.18
0.16
0.14

0.12
0.1

0.22

0.12
standard

0.1

reverse
0.08
−1.5

−1

−0.5

standard
reverse

0

0.5

1

1.5

0.08
−1.5

−1

−0.5

0

0.5

y [cm](a) x = −3 cm

11.5

y [cm](b) x = 0 cm

Figure 6.9: y hit position dependence of the pulse height in pattern A at diﬀerent x.

6.4.2

Interpretation

The general drop in the signal height as the hit point shifts farther away can be
explained by a decrease in the scintillation light collection eﬃciency. This must also betrue in y direction; that is more scintillation light is collected by SiPMs placed closer tothe hit point. Therefore, it naturally follows that the SiPM closest to the hit point must
produce the dominant signal. Combining this speculation with the position dependence

80

Chapter 6. Radiation Damage to SiPMs

result in Fig. 6.8, it is concluded that SiPMs with less damage produce larger signals thanthe ones with more damage.
This is caused by a variation in the SiPM gains. In a series connection of SiPMs, thebias voltage to each SiPM is applied in such a way that a common current ﬂows through all
SiPMs. Therefore, the applied voltage to each SiPM depend on the I-V characteristics ofthe constituting SiPMs. This eﬀect is schematically depicted in Fig. 6.10. The diﬀerencein I-V characteristics causes overvoltage variation, and therefore gain variation amongst
SiPMs. This interpretation explains the general position dependence, as well as thesmaller position dependence in pattern C arising from a smaller damage diﬀerence.

Current [µA]

I-V curve of each SiPM

102
10

SiPM1

SiPM2

SiPM3

SiPM4

SiPM5

SiPM6

common currrent

1

damaged10-1

nondamaged

10-2
10-322

23

24

25

26

27
28
Voltage [V]Figure 6.10: A schematic view of how the overvoltage variation among series-connected
SiPMs is produced. I-V curves of SiPMs in pattern A are used.

6.5

Eﬀect on time response

In a similar way, the eﬀect of the radiation damage on the time response was checked,
as this is most important for the pTC operation. The time center in this section is deﬁned
as the Gaussian mean of the tch1 −ttrigger distribution. The constant fraction (CF) method
is used in the analysis with the fraction set to 20 %.

6.5.1

Position dependence of time center

Fig. 6.11 shows y hit position dependence of the time center at x = −4.25 cm foreach damage pattern. A similar and clear position dependence is seen in all damage
patterns. This time, however, the two conﬁgurations yield similar results. This implies
the existence of some intrinsic position dependence of the time center independent of theradiation damage.

6.5. Eﬀect on time response
Time center v.s. y−0.25 ×10

−0.3

−0.35

−0.5
−1.5

−0.25 ×10

−0.3

−0.35

−0.4
−0.45

Time center v.s. y−9Time center [s]−9Time center [s]Time center [s]−0.25 ×10

81

−1

−0.5

0

0.5

1

−0.45

standard
reverse

−0.5
−1.5

1.5

−0.3

−0.4

−0.45

reverseTime center v.s. y

−0.35

−0.4
standard

−9

−1

−0.5

0

0.5

y [cm]

1

1.5

−0.5
−1.5

standard
reverse
−1

−0.5

0

0.5

y [cm](a) Pattern A(b) Pattern B

11.5y [cm](c) Pattern C

Figure 6.11: y hit position dependence of the time center at x = −4.25 cm in each damage
pattern.

Time center [s]Fig. 6.12 shows the same position dependence using SiPMs without any damage. An
intrinsic position dependence is clearly seen. However, the results in each damage pattern
in Fig. 6.11 show signiﬁcant deviations from this result, suggesting that some additionaleﬀect is caused by the radiation damage. This additional eﬀect seems to enhance theposition dependence in the reversed conﬁguration more than in the standard conﬁguration.

−0.25

×10

Time center v.s. y

−9

−0.3

−0.35

−0.4

−0.45

−0.5

−1

−0.5

0

0.5

1

y [cm]

Figure 6.12: y hit position dependence of the time center at x = −4.25 cm for a SiPM
array with damage-free SiPMs.

Fig. 6.13 shows the same position dependence for pattern A, but at diﬀerent x. The
position dependence becomes less prominent as the hit point shifts away from the channel.
Similar results are seen in other damage patterns.

82

Chapter 6. Radiation Damage to SiPMs−9

Time center v.s. yTime center [s]Time center [s]−0.15 ×10
−0.2

−0.25
−0.3
−0.35
−0.4
−1.5

0.1 ×10−9Time center v.s. y

0.05
0

−0.05
−0.1

standard
reverse
−1

−0.5

0

0.5

1

1.5

−0.15
−1.5

standard
reverse
−1

−0.5

0

0.5

y [cm](a) x = −3 cm

11.5

y [cm](b) x = 0 cm

Figure 6.13: y hit position dependence of the time center in pattern A at diﬀerent x.

6.5.2

Interpretation

First, the intrinsic position dependence is assumed to be caused by a ﬁnite propagation
time of the scintillation light through the scintillator and the electronic signal through the
SiPM array. In our measurement setup, the readout is in +y direction, so this accounts
for the general position dependence that the signals from higher y hit are detected earlier
than those from lower y hit.
The additional eﬀect from radiation damage is more complex. In fact, the time center
behavior is determined mainly by the following four factors:• The distribution of photons to each SiPM.
• The gain of each SiPM.
• The time response of each SiPM.
• The signal propagation speed in the SiPM array.
This is because the CF method utilizes both the leading edge of the pulse, which isdetermined by the fastest fraction of the signal, and the pulse peak, which is determined
more or less by the sum of signals from all SiPMs. Assuming a ﬁnite signal propagation
speed, the rising part of the signal is likely to be produced by a few SiPMs closest to thereadout. However, the non-uniform radiation damage can complicate matters by creating
an overvoltage variation amongst the SiPMs, which can aﬀect both the gain and the time
response of SiPMs.
The mechanism to cause a gain variation was discussed in 6.4.2. The time response ofa SiPM also has an overvoltage dependence. This dependence was checked by performing
a bias voltage scan with the same setup. The result is shown in Fig. 6.14. Both damaged
and non-damaged SiPMs show faster time response with higher overvoltage, although itsaturates at some point. This can be explained by the charge collection speed in SiPMs;
charge carriers in Si can be collected faster in a stronger electric ﬁeld. Thus, SiPMs withless damage, and therefore higher overvoltage, show a faster time response than the ones
with more damage.

Time center [s]6.5. Eﬀect on time response
×10−9

83
Time center v.s. overvoltage−0.18

Non-damaged−0.2

Electron-irradiated

−0.22
−0.24
−0.26
−0.28
−0.3
0

5

10

15

Overvoltage [V]Figure 6.14: Overvoltage dependence of the time center. The green and cyan markers
correspond to a SiPM array of four non-damaged and four type c SiPMs respectively. The
number of SiPMs is set to four for technical reasons.

Due to this complex mechanism, which incorporates some parameters impossible tomeasure directly, a quantitative explanation for each pattern is not possible. However, thegeneral diﬀerence between the standard and the reversed conﬁguration can be explained
as follows. When the hit point is at higher y, the rising part of the pulse is dominantly
produced by the SiPMs closest to the readout (i.e. at higher y). These SiPMs yield smallerand slower signals in the standard conﬁguration, and thus a larger time center is obtainedwith respect to the reversed conﬁguration. The diﬀerence is smaller in pattern C as thedamage diﬀerence is smaller.
On the other hand, when the hit point is at lower y, little scintillation light is collectedby the SiPMs closest to the readout, and the signals from successive SiPMs are needed
to generate the minimum signal fraction in the CF method. This weakens the eﬀectof the gradient radiation damage, because, for instance, the damage level of the middle
two SiPMs are the same in the two conﬁgurations. Thus, similar time center values are
obtained in the two conﬁgurations.

6.5.3

Veriﬁcation

The interpretation given above can be veriﬁed by performing a scan of the CF threshold used in the waveform analysis. If the above interpretation is correct, the position
dependence should be sensitive to the CF threshold, and diﬀerent position dependences
should appear in the CF scan. Diﬀerent behaviors should also be observed in the two
conﬁgurations.
Fig. 6.15 and Fig. 6.16 show the same data as in Fig. 6.11, and Fig. 6.17 shows thesame data as in Fig. 6.12, but analyzed with diﬀerent CF values. In all damage patterns,
including the one using a non-damaged SiPM array, the position dependence becomes lessprominent as the CF value is raised. In addition to this, the standard conﬁguration ineach damage pattern show a somewhat reversed position dependence at higher CF values.

Chapter 6. Radiation Damage to SiPMs−9

Time center v.s. y

0.25
0.2
0.15
0.1

0.3 ×10−9Time center v.s. yTime center [s]0.3 ×10

Time center [s]Time center [s]

84

0.25
0.2
0.15
0.1

standard
reverse

0.05
−1.5

−1

0.3 ×10

−9

0.25
0.2
0.15
0.1

standard

standard

reverse

−0.5

0

0.5

1

0.05
−1.5

1.5

Time center v.s. y

−1

−0.5

reverse00.5

y [cm]

1

0.05
−1.5

1.5

−1

−0.5

0

0.5

y [cm](a) Pattern A

11.5y [cm](b) Pattern B(c) Pattern C−9Time center v.s. y

0.75
0.7
0.65
0.6

0.8 ×10

Time center v.s. y

0.75
0.7

0.8

0.6

standard
−1

×10

−9

0.7

0.65

standard

standard

0.6

reverse

−0.5

0

0.5

1

0.55
−1.5

1.5

Time center v.s. y

0.75

0.65

reverse
0.55
−1.5

−9

Time center [s]0.8 ×10

Time center [s]Time center [s]Figure 6.15: y hit position dependence of the time center at x = −4.25 cm in each damage
pattern. The CF threshold is set to 50 %.

−1

−0.5

reverse00.5

y [cm]

1

0.55
−1.5

1.5

−1

−0.5

0

0.5

y [cm](a) Pattern A

11.5y [cm](b) Pattern B(c) Pattern C

0.3 ×10−9Time center v.s. yTime center [s]Time center [s]Figure 6.16: y hit position dependence of the time center at x = −4.25 cm in each damage
pattern. The CF threshold is set to 80 %.

0.25
0.2
0.15
0.1

0.65 ×10−9Time center v.s. y

0.6
0.55
0.5

0.05
0.45
0
−0.05

−1

−0.5

0

0.5

1

y [cm](a) 50 % threshold

0.4

−1

−0.5

0

0.5

1

y [cm](b) 80 % threshold

Figure 6.17: y hit position dependence of the time center at x = −4.25 cm for nondamaged SiPMs using diﬀerent CF thresholds.

6.6. Eﬀect on pTC performance

85

These behaviors can be explained by the low gain and the slow response of damaged
SiPMs. In order to create a large fraction of the peak pulse, signals of latter SiPMs
are needed in addition to the former ones. This eﬀect should be more prominent in thestandard conﬁguration as the SiPMs closer to the readout have lower gain and slower
time response. Therefore, even if the hit position is at higher y, the dominant signal canonly be carried through the SiPMs at lower y. This causes the signals from higher y hit
to be delayed than or comparable to those from lower y hit.

6.6

Eﬀect on pTC performance

The intrinsic position-dependent time oﬀsets found in this study, arises from a ﬁnite
signal propagation time in the SiPM array. This eﬀect had never been considered before,
and therefore it was not implemented in MC simulations to evaluate the pTC resolution.
Considering this eﬀect, the single-pixel resolution is expected to worsen.
Furthermore, non-uniform damage to SiPMs were found to create additional positiondependent time ﬂuctuations. The readout of the pTC pixels are in −y direction, whereas
the damage is higher at higher y. This corresponds to the reversed conﬁguration in theabove study, which means that position-dependent time oﬀsets can be enhanced severely.
This is expected to further worsen the pTC resolution.

6.6.1

Eﬀect of cooling

One thing to note is that the eﬀect of radiation damage found in this study cannot
be suppressed by cooling the SiPMs. Operation at a lower temperature can reduce thedark noise, but the damage diﬀerence itself does not change. Therefore, the overvoltage
variation of SiPMs in a series connection remains, and the position-dependent time oﬀsets
are unaﬀected.
Fig. 6.18 shows the I-V curves of SiPMs used in each damage pattern measured at◦
10 C. Although the dark noise is reduced from the measurement at 30 ◦ C (see Fig. 6.6),
the diﬀerences in the I-V characteristics between diﬀerently-damaged SiPMs are retained.

10

SiPM1

SiPM2

SiPM3

SiPM4

SiPM5

SiPM6

1

102
10

SiPM1

SiPM2

SiPM3

SiPM4

SiPM5

SiPM6

I-V curve of each SiPM

Current [µA]102

I-V curve of each SiPM

Current [µA]

Current [µA]

I-V curve of each SiPM

1

102
10

10−1

10−1

10−2

10−2

10−2

23

24

25

26

27

28

Voltage [V](a) Pattern A

10−3
22

23

24

25

26

27

28

Voltage [V](b) Pattern B

SiPM2

SiPM3

SiPM4

SiPM5

SiPM6

1

10−1

10−3
22

SiPM1

10−3
22

23

24

25

26

27

28

Voltage [V](c) Pattern C

Figure 6.18: I-V curves of SiPMs used in each damage pattern at 10 ◦ C. SiPMs with lessdamage are labeled with younger numbers.

86

6.6.2

Chapter 6. Radiation Damage to SiPMs

Eﬀect of intrinsic time oﬀsets

A MC simulation study was performed to see the eﬀect of the intrinsic time oﬀsets
between SiPMs arising from the signal propagation time in the SiPM array. In MC
simulation, the scintillation photons are tracked using Geant4 and the signal of each
SiPM is formed by adding up the single photon waveforms at each photon arrival time.
In the original MC setup, all the SiPM signals in a series connection were added up
simultaneously. In this study, however, a ﬁxed time oﬀset was set between adjacent
SiPMs when adding the signals from each SiPM. As this time oﬀset cannot be measured
directly, it must be estimated from the position dependence of the time center.

6.6.2.1

Reproduction of data

First, the y hit position dependence of the time center in the pTC was checked using
the pER2017 data; the pER2017 data was chosen for its maximum number of readout
channels (c.f. Tab. 4.4). The pTC tracking was used to exploit the position information.
Shown in Fig. 6.19 is the y hit position dependence of the time center in channel 1 foredge hits (xhit < −5 cm). The reconstructed hit position from the pTC tracking is usedboth to select edge hits, and to estimate y. The time center for each channel using thepTC data is deﬁned as the Gaussian mean of

tch1
ihit − tave − T OF1ihit(6.1a)

tch2
ihit − tave − T OF1ihit(6.1b)

ch2
distribution respectively, where tch1
ihit and tihit are the signal detection times of the ihit -th
hit pixel in the two channels, and T OF1ihit is the TOF from the ﬁrst to the ihit -th hit
pixel, andhit
1 ∑tave =(ti − t1 − T OF1ihit ),Nhit i =1 hit

N

(6.2)

hit

where Nhit is the number of hit pixels in a track, and tihit is the reconstructed hit timeof the ihit -th hit pixel in a track. A general inclination is clearly seen, conﬁrming theexistence of intrinsic time oﬀsets between SiPMs. The sign of the inclination is diﬀerent
from that of the lab test result because the direction of the readout is opposite in thepTC. A similar position dependence in seen in channel 2 for xhit > 5 cm hits.

6.6. Eﬀect on pTC performance87

tch1-tave-TOF [s]−9−0.2 ×10−0.25

Time center v.s. y

4cm pixel
5cm pixel

−0.3

−0.35
−0.4

−0.45
−0.5
−0.55
−0.6
−0.65
−0.7

−2

−1

0

1

2

Reconstructed y [cm]Figure 6.19: y hit position dependence of the time center for edge hits (xhit < −5 cm) inchannel 1 using the pER2017 data. Hits for 4 cm and 5 cm pixels are analyzed separately,and shown in red and blue markers respectively.

Second, various MC-simulated datasets were produced, but with diﬀerent time oﬀsets
between adjacent SiPMs. By performing the same analysis as above, the one that reproduces the y hit position dependence best contains the most plausible time oﬀset. The
input time oﬀset should be diﬀerent for 4 cm and 5 cm pixels as the circuit lengths diﬀer,
so the time oﬀset in 5 cm pixels is ﬁxed to be 5/4 of those in 4 cm pixels. Fig. 6.20 shows
the position dependence obtained using MC simulation but with diﬀerent time oﬀsets between SiPMs. The position dependence becomes more prominent as the input time oﬀsets
are increased. Comparing these with Fig. 6.19, Fig. 6.20b best reproduces the data. As
a conclusion, ∼ 60 / 75 ps time oﬀsets roughly exist between adjacent SiPMs in 4 / 5 cm
pixels.
−94cm pixel−0.25

5cm pixel−0.3−0.2 ×10

−0.35

−0.3

Time center v.s. y−9tch1-tave-TOF [s]−0.25Time center v.s. ytch1-tave-TOF [s]tch1-tave-TOF [s]−9−0.2 ×10

4cm pixel−0.25

5cm pixel

−0.35

−0.4

−0.45

−0.2 ×10
−0.3

−0.45

−0.4

−0.5

−0.5

−0.55

−0.55

−0.6

−0.6

−0.6

−0.65

−0.65

−0.65

−1

0

1

2

−0.7

−2

Reconstructed y [cm](a) 40 / 50 ps

5cm pixel

−0.45

−0.5

−2

4cm pixel

−0.35

−0.4

−0.55

−0.7

Time center v.s. y

−1

0

1

2

Reconstructed y [cm](b) 60 / 75 ps

−0.7

−2

−1

0

1

2

Reconstructed y [cm](c) 80 / 100 ps

Figure 6.20: y hit position dependence of the time center for edge hits (xhit < −5 cm) inchannel 1 using MC-simulated data. The input time oﬀsets between adjacent SiPMs in 4
/ 5 cm pixels are denoted in each subcaption.
6.6.2.2

Eﬀect on pTC resolution

The eﬀect of the intrinsic time oﬀsets between SiPMs on the pTC resolution was evaluated using MC simulation. First, the pTC resolution for events with each number of hit

88Chapter 6. Radiation Damage to SiPMs

pixels was obtained using MC datasets with no and the intrinsic time oﬀsets implemented.
The result is shown in Fig. 6.21. The event time resolution for Nhit -hit events is obtained
from the standard deviation of
hit
( rec
)
1 ∑
rec
MC
(tihit − tMC
ihit ) − (T OF1ihit − T OF1ihit )Nhit i =1

N

hit

hit
1 ∑
=
(trec − T OF1irechit − tMC
1 )Nhit i =1 ihit

N

(6.3)

hit

MC
distribution where trec
ihit and tihit are the reconstructed and MC-true hit time respectivelyof the ihit -th hit pixel, and T OF1irechit and T OF1iMC
are the reconstructed and the MC-truehit
TOF from the ﬁrst to the ihit -th hit pixel. The pTC resolution is clearly deteriorated
by the existence of time oﬀsets between SiPMs. Note that adding diﬀerent time oﬀsets
for 4 cm and 5 cm can create a systematic time oﬀset between the two. However, thiseﬀect is removed oﬄine when working out each resolution, as this systematic time oﬀset
is expected to be removed by the inter-pixel time calibration.

Event time resolution

Event time resolution [s]−90.1 ×10w/o time offset

0.09
0.08

w/ intrinsic time offset

0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
0

2

4

6

8

10

12

14

Number of hits

Figure 6.21: The pTC resolution for events with each number of hit pixels. MC datasetswith 0 ps and 60 / 75 ps time oﬀsets between SiPMs are used to obtain the red and blue
plots respectively.

In order to compute the overall pTC resolution, the obtained resolution for eachnumber-of-hit events must be summed up considering the probability of each numberof-hit events as was shown in Fig. 4.17. Calculating the appropriate weighted sum ofthese resolutions yield 38.1 ps and 38.7 ps respectively for the datasets with no and the
intrinsic time oﬀsets. In conclusion, the pTC resolution worsens by ∼ 2 % from theoriginally-expected value by considering the intrinsic time oﬀsets between SiPMs.

6.6.3

Additional eﬀect of radiation damage

The enhanced position dependence of the time center caused by a gradient radiation
damage to SiPMs, is expected to further degrade the pTC resolution. However, the exacteﬀect of the radiation damage is not easy to simulate, as it requires a precise evaluation

6.6. Eﬀect on pTC performance89of the gradient damage level in each pixel, the overvoltage variation amongst SiPMs, the
SiPM time response dependence on the overvoltage, etc. Therefore, we do not simulate
the exact eﬀect of the gradient damage, but imitate this eﬀect by increasing the time
oﬀset between SiPMs.
First, we assume that the reversed conﬁguration of pattern C in the previous study
embodies a typical pTC channel after three years of data-taking. As the damage levelin pattern C is comparable to the most damaged channel expected in the pTC, thisassumption should be conservative enough. As the position dependence of the time centerin a non-damaged sample (c.f. Fig. 6.12) is enhanced by a factor of ∼ 1.8 in the reversed
conﬁguration of pattern C (c.f. Fig. 6.11c), it should be reasonable to set the time oﬀsets
in the MC simulation to be 1.8 of the original; namely 108 ps for 4 cm pixels and 135 ps
for 5 cm pixels.
Fig. 6.22 shows the y hit position dependence of the time center for edge hits usinga MC-simulated dataset with the enhanced time oﬀsets implemented. The analysis procedure is exactly the same as that used to obtain the results in Fig. 6.20. The position
dependence of the time center is clearly enhanced.
Calculating the pTC resolution for events with each number of hit pixels gives themagenta plots in Fig. 6.23. The enhanced time oﬀsets clearly cause a further deteriorationof the pTC resolution. By calculating the weighted sum of these resolutions, the overallpTC resolution is obtained to be 44.4 ps.
Event time resolution−9−0.2 ×10

−0.25
−0.3

Time center v.s. y

Event time resolution [s]tch1-tave-TOF [s]−94cm pixel
5cm pixel

−0.35
−0.4

−0.45
−0.5
−0.55
−0.6

w/o time offset

0.09
0.08

w/ intrinsic time offset

0.07

w/ enhanced time offset

0.06
0.05
0.04
0.03
0.02
0.01

−0.65
−0.7

0.1 ×10

−2

−1

0
0
0

1

2

Reconstructed y [cm]Figure 6.22: y hit position dependence ofthe time center for edge hits (xhit < −5 cm)
in channel 1 using MC-simulated data with108 / 135 ps time oﬀsets implemented between adjacent SiPMs in 4 / 5 cm pixels.

2

4

6

8

10

12

14

Number of hits

Figure 6.23: The pTC resolution for eventswith each number of hit pixels. The MCdatasets with 0 ps, 60 / 75 ps and 108 /135 ps time oﬀsets between SiPMs are used
to obtain the red, blue and magenta plots
respectively.

Although the pTC resolution obtained here is rather conservative, as it assumes the
maximum damage in all pixels, it is clear that a non-uniform radiation damage to SiPMs
can signiﬁcantly degrade the pTC resolution. The intrinsic time oﬀsets, which had notbeen considered before, worsens the pTC resolution by ∼ 2 % from the expected, and the
additional eﬀect from radiation damage to SiPMs can cause a further ∼ 13 % deteriorationof the pTC resolution. Therefore, in order to achieve the target performance, it is essential
to bring out the maximum pTC resolution possible both from the hardware and software

90
point of views.

Chapter 6. Radiation Damage to SiPMs

Chapter 7
Optimization of Operation andAnalysis Parameters
The degradation of the pTC resolution due to radiation damage to SiPMs must be
recovered somehow to achieve the target performance. This can partly be realized by
optimizing the operation and analysis parameters. In this chapter is introduced newschemes to optimize the bias voltage applied to SiPMs and the CF parameter in theanalysis.

7.1

Motivation

The conventional way to optimize the bias voltage and the CF parameter is to performa scan of these parameters and ﬁnd the value which yields the best time resolution. Ideally,
the beam data should be used, but obtaining each channel time resolution with reasonablestatistics requires a huge amount of beam data, and performing a scan on the hardware
side is not realistic. Therefore, the beam data is only used for the CF scan, and the bias
voltage scan is performed using the laser system (c.f. Fig 4.15).
However, optimizing the bias voltage using the laser data can cause some bias. We
know that the optimal values of both the bias voltage and the CF parameter depend
sensitively on the signal-to-noise ratio (S/N). This means that if the laser signal is considerably diﬀerent from that of the signal positron, then this scheme does not give thetrue optimal value. One motivation here was to optimize the bias voltage with respect tothe signal positron by somehow converting the laser bias voltage scan result.
Another motivation was to optimize the two parameters at each time point. As alreadymentioned, the optimal values of both these parameters depend on the S/N. This meansthat the optimal points are expected to shift as the dark noise is increased by the radiation
damage to SiPMs. In the conventional method, a time-by-time optimization is possible
for the CF parameter, but not for the bias voltage as the laser data is needed at eachtime point. Therefore, by developing a scheme to optimize the two parameters at eachtime point, we would always be able to bring out the maximal pTC resolution.
The last idea for improvement was to optimize these parameters for each channel
independently. In the conventional method, the overvoltage or the CF value which yields
the best average resolution of all channels was chosen as the optimal. However, thespeed of the dark noise increase should diﬀer from channel to channel, as the radiation91

92

Chapter 7. Optimization of Operation and Analysis Parameters

damage to SiPMs depend on the global pixel position. Therefore, considering the longterm operation, a channel-by-channel optimization of both these parameters should givea better resolution.
The aim of this study, therefore, was to develop ﬁxed channel-by-channel HV and
CF optimization schemes with respect to the signal positrons, which would require no
dedicated DAQ, but determine the optimal values solely from the observed noise level ata particular time. The maximal pTC resolution can then be extracted at each time point
both from the hardware and software side.

7.2

Measurement

7.2.1

SiPMs

The SiPMs used in this study were the type c SiPMs in Tab. 6.1. The irradiation ofelectrons to these SiPMs were conducted in the lab in four steps. The dose level at each
irradiation step is summarized in Tab. 7.1.
Table 7.1: Dose level of type c SiPMs at each irradiation step.
Damage step
Step 0
Step 1
Step 2
Step 3
Step 4

7.2.2

Hours of electron irradiation Dose level equivalent to 1 MeV neutrons
0 hours
0 /cm270 hours
7.5 × 108 /cm2
140 hours
1.5 × 109 /cm2
210 hours
2.25 × 109 /cm2
280 hours
3 × 109 /cm2

Measurement

A bias voltage scan was performed at each irradiation step. The measurement setup
used for the bias voltage scan was the same as the one used in chapter 6 except for
the SiPM array. While SiPMs with diﬀerent damage levels were used in the previous
measurement, the bias voltage scan here was performed using six SiPMs at the same
irradiation step (i.e. with the same damage level). This is because our interest was in the
total dark noise increase, and the diﬀerence in the behavior of each SiPM was irrelevant.
The other parts of the setup were exactly the same as in chapter 6; the pixel assembly
setup, the radiation source, and the trigger counter are all the same. The bias voltage
scan was performed with the thermal chamber set both to 10 ◦ C and 30 ◦ C, except atdamage step 0 where the measurement was only performed at 30 ◦ C.

7.3

Bias voltage optimization

7.3.1

General idea

We know empirically that the time resolution has a strong correlation with the S/N.
In fact, that is why an optimal bias voltage exists from the time resolution viewpoint.

7.3. Bias voltage optimization

93

S/N

noise RMS

signal heightThe signal of SiPMs increase almost linearly with the overvoltage, as the gain has a linear
correlation with the overvoltage1 . On the other hand, although the electronics noise is
expected to be constant, the SiPM noise increases drastically with the overvoltage. As
a consequence, the S/N is maximized at a particular bias voltage, and an optimal bias
voltage is produced.
Another factor that aﬀects the S/N, apart from the overvoltage, is the radiation damage to SiPMs. This is not expected to aﬀect the signal size, but the dark noise is increased,so the S/N changes accordingly. Thus, the optimal overvoltage is expected to shift lower
with the accumulation of radiation damage, as schematically shown in Fig. 7.1.

dark noise
dark noiseelectronics
noise

overvoltage

overvoltage

overvoltage

Figure 7.1: A schematic view of the how the optimal bias voltage is determined. The redlines show the case with higher radiation damage with respect to the blue lines.

The idea for the new HV optimization scheme is as follows. We assume that thetime resolution is maximized when the S/N is maximized. If we know the overvoltage
dependence of both the signal and the noise, then the bias voltage at which the maximum
S/N is given can be calculated mathematically. However, as already mentioned, the noise
curve in Fig. 7.1 shifts over time. Therefore, in order to realize this scheme, we must
be capable of predicting the noise curve at a particular time from the observed noiselevel, assuming that the electronics noise is stable. This is, in principle, possible if thenoise curve can be expressed by a simple function with only one degree of freedom. The
feasibility of this scheme was checked in this study, using the bias voltage scan data at
diﬀerent irradiation steps.

7.3.2

Understanding of the time resolution

In order to conﬁrm our understanding of the time resolution, its correlation to various
parameters was checked. Fig. 7.2 shows the relation between the S/N and the time resolution. The S/N here is deﬁned as the mean of the (pulse height)/(noise root mean square(RMS)) distribution. As expected, setups with higher S/N yield better time resolutions.
1

The PDE also has an overvoltage dependence but it is saturated in the operation region.

94

Chapter 7. Optimization of Operation and Analysis Parameters

Time resolution [s]−90.24 ×10

Time resolution v.s. S/N
Step 0
Step 2
Step 40.22

Step 1
Step 3

0.2
0.18
0.16
0.14
0.12
0.1
0

20

40

60

80

S/N

Figure 7.2: Relation between the S/N and the time resolution. The bias voltage scandata at 30 ◦ C with diﬀerent damage levels is used.

In addition, it was found that the noise-to-signal ratio (N/S), which is deﬁned here as
the inverse of the S/N, has a linear and much clearer correlation with the time resolution.
This is shown in Fig. 7.3a. However, the distribution in Fig. 7.3a is relatively broad,suggesting some other eﬀect on the time resolution other than the N/S.
This can be understood by checking the bias voltage dependence of this result as shownin Fig. 7.3b. It is clear that the plots at each bias voltage is in a clear linear correlation,and that a better time resolution is achieved at higher bias voltages if the N/S is ﬁxed.
This can be speculated to be the caused by less deviation in the SiPM charge collection
time at higher overvoltages.

0.22Time resolution v.s. N/S

Step 0
Step 2
Step 4−9Time resolution [s]Time resolution [s]−90.24 ×10

Step 1
Step 3

0.2
0.18
0.16

0.22

0.16

0.12

0.12
0.04

0.06

0.08

0.1

N/S

(a) Diﬀerent marker colors represent diﬀerent
damage levels.

155.0 [V]160.0 [V]165.0 [V]

0.18

0.14

0.02

157.5 [V]162.5 [V]167.5 [V]

0.2

0.14

0.1
0

Time resolution v.s. N/S

0.24 ×10152.5 [V]

0.1
0

0.02

0.04

0.06

0.08

0.1

N/S

(b) Diﬀerent marker colors represent diﬀerent
bias voltages.

Figure 7.3: Relation between the N/S and the time resolution. The bias voltage scandata at 30 ◦ C with diﬀerent damage levels is used.
Thus, the time resolution of a pixel is assumed to be determined by two factors; theovervoltage, which sets some intrinsic time resolutions of SiPMs, and the N/S, which
linearly worsens the time resolution from the intrinsic value. However, in the actual pTC
in the πE5 area, the noise level is generally larger than the lab environment, so the time

7.3. Bias voltage optimization95

resolution is expected to be dominated by the N/S factor. Therefore, we can neglect
the overvoltage-dependent factor and simply search for the bias voltage which yields theminimal N/S.

7.3.3

Bias voltage dependenceFirst, the overvoltage dependence of the signal height was checked, which is shown in
Fig. 7.4. As expected, the signal increases linearly with the overvoltage, and the radiation
damage to SiPMs does not aﬀect the signal size. Although the SiPMs are equally damaged
in this measurement, this is expected hold true for the non-uniform damage case too, as
the total bias voltage to SiPMs does not change.

Step 1
Step 3

Pulse height v.s. bias voltage

Pulse height [V]Pulse height [V]Pulse height v.s. bias voltage
0.25

Step 2
Step 4

0.2

0.15

0.25

0.2

0.1

0.05

0.05
155

160

165

Step 1
Step 3

0.15

0.1

150

Step 0
Step 2
Step 4150

155

Bias voltage [V]

160

165

Bias voltage [V](a) 10 ◦ C(b) 30 ◦ C

Figure 7.4: Bias voltage dependence of the signal height at diﬀerent damage levels.
Next, the overvoltage dependence of the noise RMS was checked, which is shown in
Fig. 7.5. The general dependence on the overvoltage and the damage level is as was
assumed in Fig. 7.1. Our goal is to ﬁnd a function that ﬁts the plots of all damage steps
by changing a single parameter, and then the whole noise curve can be estimated fromthe observed noise level at a particular applied voltage.

9

Step 1
Step 3Noise RMS v.s. bias voltage

Noise RMS [mV]Noise RMS [mV]Noise RMS v.s. bias voltage
10

Step 2
Step 4

8
7
6
5

10
9
8
6
5
4

3

3

2

2

1

1

0
150

0
150

160

165

Bias voltage [V](a) 10 ◦ C

Step 1
Step 37

4

155

Step 0
Step 2
Step 4

155

160

165

Bias voltage [V](b) 30 ◦ C

Figure 7.5: Bias voltage dependence of the noise RMS at diﬀerent damage levels.

96

Chapter 7. Optimization of Operation and Analysis Parameters

Assuming, that the noise is composed of two components, namely the electronics noise
and the SiPM noise, then the noise RMS should be expressed as the square root of thesquared sum of these two;√2
2
N = NSiPM+ Nelec(7.1)
where N is the observed noise RMS, and NSiPM and Nelec are the noise deriving from the
SiPMs and the electronics respectively. Nelec is a constant which does not change withthe bias voltage, whereas NSiPM must be an increasing function of the overvoltage and is
expected to converge to zero at the breakdown voltage.
Several such functions were tested, and it was found that at 10 ◦ C, which is the operation temperature of the pTC, a cubic function depicts the SiPM noise very well:
NSiPM = C × (V − Vbd )3(7.2)

where C is a constant that changes with the damage level, V is the applied voltage, and
Vbd is the breakdown voltage of the SiPM array. This is shown in Fig. 7.6. Although Nelec
was a free parameter in the ﬁt, it diﬀered very little in the four steps. This diﬀerence isassumed to derive simply from the diﬀerence in the noise situation in each measurement.
In any case, the diﬀerence is negligibly small (∼ 0.3 mV), and assuming the Nelec to beconstant should not be a problem.

Noise RMS [mV]Noise RMS v.s. bias voltage
109

Step 1
Step 3

Step 2
Step 4

8
7
6
5
4
3
2
1
0
150

155

160

165

Bias voltage [V]Figure 7.6: Bias √voltage dependence of the noise RMS at diﬀerent damage levels at 10 ◦ C
2ﬁtted with N = C 2 (V − Vbd )6 + Nelec
where Vbd is ﬁxed. Each ﬁt function corresponds
to the markers of the same color.

In this strategy, therefore, only C changes with the damage level, and the other parameters do not change over time. Thus, once Vbd and Nelec are obtained, the noise RMS
at an arbitrary bias voltage can be obtained simply from the observed noise level. This,in principle, allows a channel-by-channel optimization of the pTC bias voltage at any
damage level.

7.3. Bias voltage optimization

97

7.3.4

Application to pER2019 data

7.3.4.1

Optimization procedure

To apply the optimization scheme to the pTC, a bias voltage scan data of 256 channels
was obtained using the laser system. The bias voltage scan was performed in steps of 0.5 V
from −15 V to +1 V of the nominal HV in the pER2019.
The procedures for the bias voltage optimization for each channel is as follows:
1. Perform an I-V measurement and obtain the breakdown voltage.
2. Using the obtained breakdown voltage, ﬁt the bias voltage v.s. noise RMS relation
with the function discussed above.
3. Obtain the dependence of the signal height on the bias voltage during the laser bias
voltage scan.
4. Check the signal size in the beam data at a particular bias voltage, and convert thebias voltage dependence of the signal height to meet the beam data.
5. From the two functions, calculate the bias voltage that minimizes the N/S factor.
In this way, the optimal bias voltage can be obtained independently of the laser signal
size. The I-V measurement for all channels can be performed simultaneously using the
WDBs.
Fig. 7.7 shows the relation between the bias voltage and the signal height for sometypical channels obtained in the bias voltage scan. They are clearly ﬁtted well with linear
functions. Fig. 7.8 shows the relation between the bias voltage and the noise RMS for thesame channels, ﬁtted with the function discussed above. The cubic function in Eq. (7.2)
seems to depict the bias voltage dependence of the SiPM noise in the pTC very eﬀectively.

0.12
0.11
0.1

0.24

Channel 289

Signal height [V]0.13

Channel 206

Signal height [V]Channel 141

Signal height [V]Signal height [V]Channel 108
0.14

0.32

0.22
0.2

0.3
0.28

0.26

0.18

0.24
0.22

0.16

0.24
0.22
0.2
0.18
0.16

0.2

0.09
0.14

0.18

0.12

0.16

0.08
−10

−8

−6

−4

−2

Bias voltage [V]

−10

−8

−6

−4

−2

Bias voltage [V]

0.14
0.12
−10 −8−6−4−2

Bias voltage [V]

−10

−8

−6

−4

Bias voltage [V]Figure 7.7: Bias voltage dependence of the signal height for some typical channels in thepTC bias voltage scan using the laser system. The horizontal axis is taken with respect
to the nominal HV in the pER2019. Each plot is ﬁtted with a linear function.

Chapter 7. Optimization of Operation and Analysis Parameters

4.5
4.4
4.3
4.2
4.1
4
−10 −8 −6 −4 −2

5.2

Channel 206

5.1
5
4.9

2.85
2.8
2.75
2.7
2.65

4.8

2.6
2.55

4.7

2.5
2.45

4.6

Bias voltage [V]Channel 289

Noise RMS [mV]Channel 141

Noise RMS [mV]Noise RMS [mV]Channel 108

Noise RMS [mV]98

Bias voltage [V]

5.8
5.7
5.6
5.5
5.4
5.3
5.2

2.4
−10 −8 −6 −4 −2

5.9−10 −8 −6 −4 −20Bias voltage [V]−10 −8−6−4−2

Bias voltage [V]Figure 7.8: Bias voltage dependence of the noise RMS for some typical channels in thepTC bias voltage scan using the laser system. The horizontal axis is taken with respect
to the nominal HV in the pER2019. Each plot is ﬁtted with the function discussed in thetext.

7.3.4.2

Eﬀect on pTC resolution

In order to verify the eﬀect of this optimization scheme, the pTC time resolution before
and after this optimization must be checked. This has not been performed yet, as we have
had any DAQ time with the muon beam after this scheme was developed. Therefore, theveriﬁcation of this optimization method will be left for future studies, although we expect
it to be eﬀective.

7.4

Constant fraction optimization

7.4.1

General idea

If the waveform is always the same or only diﬀerent in the voltage scale, then the
CF method should always give the same timing. In reality, however, both the leadingedge and the peak point ﬂuctuate event by event, as they are determined by a complex
combination of the number of scintillation photons, their optical paths, the time responseof SiPMs, the baseline ﬂuctuation, and so on.
However, an optimal CF value exists which gives the best time resolution. This isdetermined by the balance between the time ﬂuctuation of the leading edge and thepeak point. This eﬀect is schematically shown in Fig. 7.9. When the noise level is low,
the ﬂuctuation of the baseline is small enough, and therefore, the time ﬂuctuation of theleading edge is kept small. However, the peak time is aﬀected by a number of probabilistic
factors and the ﬂuctuation is relatively large. Therefore, a lower CF threshold gives abetter time resolution. On the other hand, when the noise level is high, the ﬂuctuationof the baseline becomes large. This leads to a comparable or larger time ﬂuctuation of
the leading edge with respect to the peak time, and a higher CF value is preferred. This
explains how the optimal CF value depends sensitively on the S/N.

7.4. Constant fraction optimization

99

peak

peak

optimal CF
optimal CF

baselinebaseline

Low noise caseHigh noise case

Figure 7.9: A schematic drawing showing the concept of the CF optimization.

7.4.2

Dependence on the noise level

A CF scan was performed in steps of 0.05 from 0.15 to 0.6 for the data at each bias
voltage in each damage step. Fig. 7.10 shows the dependence of the time resolution on
both the bias voltage and the CF value. The optimal CF clearly shifts higher as thedamage level increases, conﬁrming our understanding of the CF method.

×10−9

6055
Co 50
ns4540ta 35
nt 3025
fra20
c 15

tio
n

160

165

e [V]

ltag
ias vo155B(a) Damage step 0

Bias & CF scan result

×10−9Time resolution [s]

0.18
0.17
0.16
0.15
0.14
0.13
0.12

Bias & CF scan result

Time resolution [s]Time resolution [s]Bias & CF scan result

0.21
0.2
0.19
0.18
0.17
0.16
0.15
6055
Co 50
ns4540ta 35
nt 3025
fra20
c 15

tio

n

165

[V]
ltage
ias vo160

155B(b) Damage step 2

×10−9
0.24
0.23
0.22
0.21
0.2
0.19
0.18
0.17
0.16
6055
Co 50
ns4540ta 35
nt 3025
fra20
c 15

tio

n

165

[V]
ltage
ias vo160

155B(c) Damage step 4

Figure 7.10: Bias voltage and CF dependence of the time resolution at 30 ◦ C at diﬀerent
damage levels. The magenta markers show the optimal CF values at each bias voltage.

If our understanding is correct, the optimal CF value should depend sensitively on
the S/N. To conﬁrm this, the correlation between the optimal CF value and various
parameters was checked. In fact, it was found to have a moderately clear, linear correlation
with the N/S as demonstrated in Fig. 7.11.

100

Chapter 7. Optimization of Operation and Analysis Parameters

60

Step 1
Step 3

Optimal CF v.s. N/S

Optimal CF value

Optimal CF value

Optimal CF v.s. N/S
70

Step 2
Step 4

50
40
30

70
60

40
30
20

10

10
0.02

0.04

0.06

0.08

0.1

Step 1
Step 3

50

20

0
0

Step 0
Step 2
Step 4

0
0

0.02

0.04

0.06

(a) 10 ◦ C

0.08

0.1

Mean N/S

Mean N/S(b) 30 ◦ C

Figure 7.11: Relation between the N/S and the optimal CF value at diﬀerent temperatures.
Using this correlation, it is possible to optimize the CF value channel by channel fromthe observed noise RMS at a particular time and the typical signal height. It is also
obvious from Fig. 7.10 that such an optimization is important in order to suppress theresolution degradation due to the dark noise increase.

7.4.3

Application to pER2019 data

7.4.3.1

Optimization procedure

To apply the optimization scheme to the pTC, the same laser bias voltage scan data as
in 7.3.4 is used. The reason for using the bias voltage scan data is that it yields a varietyof N/S values and its correlation with the optimal CF value should be seen clearly.
The procedures for the CF optimization for each channel is as follows:
1. Perform a CF scan to the bias voltage scan data.
2. Obtain the CF value which yields the best time resolution for each data point.
3. Fit the N/S v.s. optimal CF relation with a linear function.
4. Obtain a typical N/S using the beam data.
5. Calculate the corresponding optimal CF using the linear function.
In this way, the optimal CF value can be obtained independently of the laser signal size.
Fig. 7.12 shows the correlation between the N/S and the optimal CF in the obtainedlaser data for some typical channels. The linear correlations can be seen clearly, andthe correlation seems to diﬀer from channel to channel, indicating that a channel-bychannel optimization is eﬀective even without considering the radiation damage eﬀect.
Although the reason for the channel-by-channel diﬀerence has not been investigated yet,
it is assumed to be caused by the diﬀerence in the SiPM characteristics, such as the risetime and the correlated noise probability. In any case, the linear function for each channel
was obtained.

7.4. Constant fraction optimization
Channel 227

50

60
50

Channel 229

70

Optimal CF

60

Channel 228

70

Optimal CF

70

Optimal CF

Optimal CF

Channel 226

101

60
50

70
60
50

40

40

40

40

30

30

30

30

20

20

20

20

10

10

10

10

0
0 0.020.040.060.08 0.1 0.12

0
0 0.020.040.060.08 0.1 0.12

0
0 0.020.040.060.08 0.1 0.12

0
0 0.020.040.060.08 0.1 0.12

N/S

N/S

N/S

N/S

Figure 7.12: N/S dependence of the optimal CF value for some typical channels using
pTC bias voltage scan data using the laser system.

Next, using the pER2019 beam data, a typical N/S factor was obtained for eachchannel. Combining these with the obtained linear functions, the optimal CF was calculated for each channel. The distribution of the obtained optimal CF values are shownin Fig. 7.13. The distribution is broad, indicating the eﬀectiveness of channel-by-channel
optimization. Note that this method can yield optimal values larger than 1, in which case
the CF value should be set to 1.
Number of channels

Optimal CF distribution
hist

22
20
18
16

Entries251

Mean0.4792

Std Dev

0.1271

14
12
10
8
6
4
2
0
0

0.2

0.4

0.6

0.8

1

1.2

Optimal CF

Figure 7.13: Distribution of the obtained optimal CF values. The number of entries issmaller than the 256 readout channels due to the existence of some dead channels.

7.4.3.2

Eﬀect on pTC resolution

In order to verify the eﬀect of this optimization scheme, the time resolutions of eachpixel before and after the optimization were compared. The same beam data used toobtain the N/S factors is used. To obtain the time resolution of each pixel the 2-hit
analysis method was used, in which the time resolution is obtained from the hit time
diﬀerence distribution in ﬁxed combinations of adjacent pixels.
Fig. 7.14 shows the obtained time resolution of each pixel before and after the optimization. Pixels with ID from 304 to 432 were read out in the pER2019, but theresolutions for the ﬁrst 16 pixels are not shown, as they do not have the coupling pixels
for the 2-hit analysis. The CF parameter before the optimization was set to 20 % for all

102

Chapter 7. Optimization of Operation and Analysis Parameters

Time resolution [s]channels, which was a value obtained in the pER2017 using the conventional optimization
scheme in steps of 10 %. The average time resolution is improved by ∼ 3 %, and thus, theeﬀectiveness of this optimization scheme is veriﬁed.
0.2 ×10

TC pixel resolution−9

All set to 0.2

0.18
After optimization

0.16
0.14
0.12
0.1
0.08
0.06
320

340

360

380

400

420

Pixel number

Figure 7.14: Time resolution of each pixel obtained using the 2-hit analysis method before(red) and after (blue) the optimization.

One thing to note is that the optimization scheme was found not to work for pixels
with type II and type III SiPMs in Tab. 4.2. That is, the time resolutions obtained withthe 2-hit analysis method was worse after the optimization than before. Therefore, theCF values for these pixels are set to the original 20 % for these pixels to obtain Fig. 7.14.
The reason for this is unknown, but the only possible explanation is that some systematic
diﬀerence exists between the laser and beam data which aﬀects the new SiPMs more.

Part III
Analysis Algorithm and Performance
Evaluation of pTC103

Chapter 8
Oﬀset Correction Algorithm
In this chapter is introduced a method to correct the position dependence of the time
center in the oﬄine analysis. The method and the eﬀect of the correction on the pTC
resolution is discussed using MC simulation.

8.1

Motivation

It was found that the intrinsic time oﬀsets between SiPMs worsen the pTC resolutionby ∼ 2 %, and that a further ∼ 13 % degradation is expected by the non-uniform radiation damage to SiPMs which essentially enhances these time oﬀsets. As this cannot be
suppressed by cooling or any other hardware measures, this must be compensated on thesoftware side.
The most obvious and direct way to compensate this eﬀect is to correct the positiondependent time oﬀsets in the oﬄine analysis. The hit position information is available
from the CDCH (or pTC) tracking, and therefore, the position dependence can be calculated. Using the obtained dependence, the oﬀset can be subtracted depending on eachreconstructed hit position.

8.2

Simulated sample

In order to study this eﬀect, MC-simulated data is used. One motivation for using MC
simulation rather than the actual data is that an arbitrary time oﬀset can be implemented
between the SiPMs. Another is that the CDCH track information is available in the MC,
whereas it is not in the real data due to a limited number of readout channels.
Three datasets, each with ∼ 450, 000 signal positron events, were produced using MC
simulation. In each dataset is implemented the intrinsic time oﬀsets (60 / 75 ps), theenhanced time oﬀsets (108 / 135 ps), and no time oﬀsets (0 / 0 ps) between adjacent
SiPMs in 4 / 5 cm pixels. The main purpose of this study was to check the feasibilityof the correction, and therefore the Michel positron background is not included in thesimulation.
105

106

Chapter 8. Oﬀset Correction Algorithm

8.3

Correction using MC values

8.3.1

Position dependence

Fig. 8.1 shows the MC hit position dependence of the time center for each channel
for 4 cm pixels using the dataset with the intrinsic time oﬀsets. The time center for eachchannel using MC data is deﬁned as the Gaussian mean ofMC
tch1
ihit − tihit(8.1a)

MC
tch2
ihit − tihit(8.1b)

ch2
distribution respectively, where tch1
ihit and tihit are the signal detection times of the ihit -th
hit pixel in the two channels, and tMC
ihit is the MC-true hit time of the ihit -th hit pixel. The
propagation time of the scintillation light in x direction dominates the time oﬀset, but
for edge hits close to the readout channel, clear position dependences in y direction canalso be seen. Slightly enhanced but similar dependences are seen in 5 cm pixels.

Time center v.s. x v.s. y×10−9

tch2-tMC [s]tch1-tMC [s]Time center v.s. x v.s. y

0.4
0.2
0
−0.2
−0.4
−0.6
1.5

M 10.5C −00.5
2 4
y [ −1
cm −1.5
−2 0
−
4
[cm]
] −2 −6
MC x

×10−9
0.4
0.2
0
−0.2
−0.4
−0.6
1.5

M 10.5C −00.5
2 4
y [ −1
cm −1.5
−2 0
−
4
[cm]
] −2 −6MC x(a) Channel 1(b) Channel 2

Figure 8.1: MC hit position dependence of the time center for 4 cm pixels with intrinsic
time oﬀsets.
Fig. 8.2 shows the same position dependence of the time center after correcting theoﬀset in x direction using the MC-true x hit position. That is, the Gaussian means of
L
+ xMC
ihit
MC
ch1
2
tihit − tihit −
veﬀ
L
− xMC
ihit
MC
2
tch2
−
t
−
ihit
ihit
veﬀ

(8.2a)(8.2b)

distributions at each MC hit position are plotted respectively, where L(= 12 cm) is thelength of the pTC pixel, xMC
ihit is the MC x hit position in the pixel for the ihit -th hit, andveﬀ is the eﬀective velocity of the scintillation light. A clearer y position dependence ofthe time center can be seen compared to Fig. 8.1. As the time oﬀset in x direction is taken
into account in the original hit reconstruction, these are the additional time oﬀsets thatmust be corrected in the oﬄine analysis. Similar dependences are seen in 5 cm pixels.

8.3. Correction using MC values

107

×10−9

Time center v.s. x v.s. ytch2-tMC-(L/2-xMC)/v [s]tch1-tMC-(L/2+xMC)/v [s]Time center v.s. x v.s. y

×10−9

0.1
0.05
0
−0.05
−0.1
−0.15

0.1
0.05
0
−0.05
−0.1
−0.15
1.5
M 10.5C −00.5
4y [ −1
0 2
cm −1.5−2[cm]] −2 −6 −4
MC x

1.5
M 10.5C −00.5
4y [ −1
0 2
cm −1.5−2[cm]] −2 −6 −4MC x(a) Channel 1(b) Channel 2

Figure 8.2: MC hit position dependence of the time center for 4 cm pixels with intrinsic
time oﬀsets after correcting the oﬀset in x direction.
The same position dependence of the time center for 4 cm pixels but using the datasetwith the enhanced time oﬀsets is shown in Fig. 8.3. The time oﬀsets are clearly enhanced.

×10−9
0.2
0.1
0
−0.1
−0.2
1.5
M 10.5C −00.5
4y [ −1
0 2
cm −1.5−2[cm]] −2 −6 −4MC x(a) Channel 1

Time center v.s. x v.s. ytch2-tMC-(L/2-xMC)/v [s]tch1-tMC-(L/2+xMC)/v [s]Time center v.s. x v.s. y

×10−9
0.2
0.1
0
−0.1
−0.2
1.5
M 10.5C −00.5
4y [ −1
0 2
cm −1.5−2[cm]] −2 −6 −4MC x(b) Channel 2

Figure 8.3: MC hit position dependence of the time center for 4 cm pixels with enhanced
time oﬀsets after correcting the oﬀset in x direction.

8.3.2

Correction

The degradation of the pTC resolution in the enhanced time oﬀset case occurs via two
mechanisms:• The bluntening of the waveform.
• The position dependence of the time center.
The former leads to larger ﬂuctuations in the time obtained in each channel in the waveform analysis. The latter worsens each pixel hit time, as large time ﬂuctuations occur
according to the hit position of the particle.

108

Chapter 8. Oﬀset Correction Algorithm

There is no way to cancel out the former eﬀect, as we cannot separate the signals
from each SiPM. The degradation caused by the latter eﬀect is the one we can wipe out
with our correction. The maximal extent to which we can recover the resolution can bechecked by performing the correction using MC truth values for the hit positions. It isalso possible from this correction to distinguish the eﬀect of the two mechanisms on thepTC resolution.
Using the position dependence obtained above, the signal detection time in each channel was corrected according to the MC hit position in a pixel. After the oﬀset correction,
the obtained time of the two channels are combined to reconstruct the hit time, which
are further combined to obtain the overall positron time. Thus, the pTC resolution forevents with each number of hit pixels was obtained both with and without the oﬄine
oﬀset correction, which are shown in Fig. 8.4. Eq. 6.3 is used to obtain each resolution.
The correction is clearly eﬀective, especially in the case of the enhanced time oﬀsets.

Event time resolution
w/o correction

0.09
0.08

w/ correction

0.07
0.06
0.05
0.04
0.03

0.1 ×10
0.08
0.06
0.05
0.04
0.03

0.01

0.01
4

6

8

10

12

14

Number of hits(a) Intrinsic time oﬀset

w/ correction

0.07

0.02

2

w/o correction

0.09

0.02
0
0

Event time resolution−9

Event time resolution [s]Event time resolution [s]−90.1 ×10

0
0

2

4

6

8

10

12

14

Number of hits(b) Enhanced time oﬀset

Figure 8.4: The pTC resolution for events with each number of hit pixels for diﬀerent
datasets. The blue and red markers correspond to with and without the oﬀset correction
using MC values respectively.

Using these resolutions, the overall pTC resolution was calculated for each dataset.
The result is summarized in Tab. 8.1. The correction also works for the dataset withno time oﬀsets, as some small position dependence exists. The degradation of the pTC
resolution after the correction indicates the eﬀect from the waveform bluntening. Thisis, however, relatively small compared to the overall degradation, suggesting that thedegradation caused by the position dependence of the time center is indeed dominant.
Looking at the bright side, however, this means that the pTC resolution can be recovered
to a large extent if we have enough position resolution to eﬀectively perform the oﬀset
correction.

8.4. Correction using reconstructed values

109

Table 8.1: The eﬀect of the oﬄine time oﬀset correction using MC hit positions in eachdataset.
Time oﬀset

pTC resolution
Without correction With correction
38.1 ps
37.6 ps
38.7 ps
38.2 ps44.4 ps
40.9 ps

No time oﬀset
Intrinsic time oﬀset
Enhanced time oﬀset

8.4

Correction using reconstructed values

8.4.1

Position resolutions

The correction using MC values turned out to be highly eﬀective. However, thisassumes an inﬁnite hit position resolution, and the actual extent to which we can recover
the time resolution is likely to be limited by the x and y position resolutions of thereconstructed hit point.
Fig. 8.5 and Fig. 8.6 show the x and y resolution respectively obtained in the two
tracking methods. The horizontal axis shows the hit index, which is the number of thehit pixel in a track counting from the ﬁrst. The MC dataset with no time oﬀsets is used,and each resolution is obtained from the standard deviation of the distribution of the hit
position diﬀerence between the reconstructed and the MC truth.
The x hit position resolution in the CDCH tracking is worse for hits at higher hit
indices due to multiple scattering. This is not the case in y direction, as y estimation in
the pTC tracking is used as initial values for the CDCH track ﬁt and the y estimation
is better for hits at higher hit indices. In any case, averaged resolutions of ∼ 5 mm and∼ 6 mm are achieved for x and y position respectively using the CDCH tracking. The
pTC tracking yields slightly worse position resolutions.
y position resolutiony resolution [cm]x resolution [cm]x position resolution
1
0.9
0.8
0.7
0.6
0.5
0.4

0.9
0.8
0.7
0.6
0.5
0.4

0.3

0.3

CDCH tracking

0.2

CDCH tracking

0.2

pTC tracking

0.1
0
0

1

5

10

pTC tracking

0.1
15

Hit index

Figure 8.5: x resolution at each hit index in
the CDCH tracking and the pTC tracking.

0
0

5

10

15

Hit index

Figure 8.6: y resolution at each hit index in
the CDCH tracking and the pTC tracking.

110

Chapter 8. Oﬀset Correction Algorithm

8.4.2

Position dependence

The hit position dependence of the time center using reconstructed hit positions isshown in Fig. 8.7. The time oﬀset in x direction is corrected beforehand. In explicit
forms, the Gaussian means ofL+ xrecihit
ch1
rectihit − tave − T OF1ihit − 2
veﬀ
L− xrec
ihit
rec
2
tch2
−
t
−
T
OF
−
ave
ihit
1ihit
veﬀ

(8.3a)(8.3b)

distributions at each reconstructed hit position are plotted respectively, where T OF1irechit
is the reconstructed TOF from the ﬁrst to the ihit -th hit pixel, xrec
ihit is the reconstructed
x hit position in the pixel for the ihit -th hit, andhit
1 ∑tave =(trec − t1 − T OF1irechit ),Nhit i =1 ihit

N

(8.4)

hit

where Nhit is the number of hit pixels in a track, and trec
ihit is the reconstructed hit time of
the ihit -th hit pixel in a track. Similar dependences are seen in 5 cm pixels.

tch1-tave-TOFrec-(L/2+xrec)/v [s]

0.25
0.2
0.15
0.1
0.05
0
−0.05
−0.1

×10−9

Time center v.s. x v.s. ytch2-tave-TOFrec-(L/2-xrec)/v [s]Time center v.s. x v.s. y

0.15
0.1
0.05
0
−0.05
−0.1

1.5
Re 10.5
co −00.5
2 4
ns −1
tru −1.5
−2 0
m]
−
4
cte −2 −6
d x [cdy
tructe
s
n
o
c
[cmRe
]

(a) Channel 1

×10−9

1.5
Re 10.5
co −00.5
2 4
ns −1
tru −1.5
−2 0
m]
−
4
cte −2 −6
d x [cdy
tructe
s
n
o
c
[cmRe
]

(b) Channel 2

Figure 8.7: Hit position dependence of the time center for 4 cm pixels with intrinsic time
oﬀsets after correcting the oﬀsets in x direction.
Due to a ﬁnite position resolution, the position dependence obtained using reconstructed values are less prominent than the one obtained using MC values. There also
seems to be some position reconstruction bias, which causes the strange behavior at thecorners. In any case, the correction can be performed using the observed position dependence.

8.4.3

Correction

Using the position dependence obtained with reconstructed variables, the oﬀset correction was performed. The pTC resolution for events with each number of hit pixels

8.4. Correction using reconstructed values

111

was obtained using Eq. 6.3, both for the intrinsic and the enhanced time oﬀset case. The
results are summarized in Fig. 8.8. The correction using reconstructed variables seems to
be capable of recovering the pTC resolution to some extent, though not as eﬀectively as
the correction using MC values.
Event time resolution
w/o correction

0.09
0.08

w/ correction

0.07
0.06
0.05
0.04
0.03

0.1 ×10
0.08
0.06
0.05
0.04
0.03

0.01

0.01
4

6

8

10

12

14

Number of hits(a) Intrinsic time oﬀset

w/ correction

0.07

0.02

2

w/o correction

0.09

0.02
0
0

Event time resolution−9

Event time resolution [s]Event time resolution [s]−90.1 ×10

0
0

2

4

6

8

10

12

14

Number of hits(b) Enhanced time oﬀset

Figure 8.8: The pTC resolution for events with each number of hit pixels for diﬀerent
datasets. The blue and red markers correspond to with and without the oﬀset correction
using reconstructed values respectively.
Using these resolutions, the overall pTC resolution was calculated for each dataset.
The obtained resolutions were 38.3 ps and 42.8 ps for the dataset with the intrinsic andthe enhanced time oﬀsets respectively. Comparing these values with the ones obtained in
Tab. 8.1 using MC hit positions, it is clear that the eﬀect of the correction is limited by
the hit position resolution in the CDCH tracking. This is consistent with the fact thatthe correction works less for events with larger number of hits in Fig. 8.8, as the position
resolution is worse for hits at higher hit indices. In any case, the oﬀset correction canrecover the pTC resolution to some extent, and the signiﬁcance of the correction increases
with the integrated radiation damage.

8.4.4

Implementation

In the above study, an averaged position dependence of all pixels was used for thecorrection. However, this strategy is not wise when it comes to applying to the pTC datain the long run. The amount of radiation damage diﬀers from channel to channel, andtherefore, the position dependence in each pixel is also expected to diﬀer.
Fig. 8.9 shows the global z dependence of the positron hit rate in pTC pixels. The
hit rate clearly diﬀers with z, and so the radiation damage in each channel depends
strongly on the z position of the pixel. Therefore it is best to divide the pTC into several
sectors according to the expected radiation damage to SiPMs, and the averaged position
dependence within each sector should be used for the oﬀset correction. The details of thesector division and other implementations will be left for future study, as it requires adetailed understanding of the radiation damage at each global point.

112

Chapter 8. Oﬀset Correction Algorithm

Figure 8.9: Global z dependence of the positron hit rate in pTC pixels using MC simulation and the pER2017 data [60]. Outliers at z ∼ 75 cm come from noisy DAQ channels.

Chapter 9
Weighted Mean Algorithm
In this chapter, I introduce further ideas to improve the pTC resolution in the oﬄine
analysis. The general ideas and methods are discussed, and their eﬀects are evaluatedusing MC simulation.

9.1

General idea

The positron time measured by the pTC is obtained in three steps. First, the channel
times in pixels with hits are obtained in the waveform analysis using the CF method.
Second, the time information of the two channels in each pixel are combined to reconstruct
the hit time of the pixel. Lastly, the pixel hit times are again combined to reconstruct
the overall positron time.
In the original pTC analysis, the time information at the same step is treated equally.
For instance, the hit time is obtained as the simple mean of the CF times of the twochannels, and the positron time is obtained more or less as the simple mean of all thehit times in a track corrected by each TOF. However, the physical process of the signal
induction does not necessarily give equivalent information to each channel, or each hit.
In fact, a better time reconstruction should be possible by inﬂicting appropriate weights
to each time information. This is depicted in Fig. 9.1.
𝑡%&'

𝑡'"#$

𝑡%&!
t %&'

𝑡!"#$

𝑡%&!

𝑡%&'

𝑡) *

𝑡("#$

𝑡%&!

intra-pixel weightinter-pixel weight

Figure 9.1: A schematic view of the pTC analysis and the weighted mean algorithm.

113

114

9.1.1

Chapter 9. Weighted Mean Algorithm

Using hit position information

One idea is to make use of the hit position information in the hit reconstruction.
When the positron hit position in a pixel is oﬀ-center in x direction, the arrival timeof scintillation photons should deviate less for the channel closer to the hit point thanthe one farther from the hit point. This causes the closer channel to have a better time
resolution than the other. Therefore, the hit time should be reconstructed better by anappropriate weighted mean of the two channel times. The hit position can be obtainedwith reasonable resolution using the CDCH tracking. This weighted mean algorithm of
the two channels is hereon called the hit position intra-pixel weight algorithm.
One thing to note is that any position-dependent time oﬀsets should be eliminatedbefore taking the weighted mean, or else the oﬀset will be enhanced. This should bepossible by applying the time oﬀset correction explained in chapter 8 before the intrapixel weight algorithm.

9.1.2

Using energy deposit information

Another idea is to make use of the energy deposit information in each pixel in thepositron time reconstruction. The energy loss process of a charged particle in a matter isprobabilistic, which means that the energy deposit of positrons in each pixel ﬂuctuates hit
by hit. When the energy deposit in a pixel is large, more scintillation light is produced in
the pixel. Therefore, from the photon statistics point of view, the hits with more energy
deposits should have better resolutions than the hits with smaller energy deposits. Thus,
the positron time should be reconstructed better by an appropriate weighted mean ofeach hit time. The energy deposit in each pixel can be obtained from the pulse charge
in the two channels (c.f. 4.4.1). This weighted mean algorithm of the hits in a track ishereon called the energy deposit inter-pixel weight algorithm.
Like in the case of the hit position intra-pixel weight algorithm, any unnecessary time
oﬀsets should be eliminated before taking the weighted mean. We already know frompast studies that some time walk exists which depend on the energy deposit (i.e. thepulse height) [60]. Correcting these time walk eﬀects should further enhance the pTC
resolution.

9.2

Simulated sample

In order to study the eﬀect of these new algorithms, again, MC simulated data isused. The datasets used for this study are the same as those used in chapter 8. The hit
position intra-pixel weight algorithm is tested using the datasets with the intrinsic (60 /75 ps) and the enhanced (108 / 135 ps) time oﬀsets between SiPMs. On the other hand,the energy deposit inter-pixel algorithm using the energy deposit information is tested
using the dataset with no time oﬀsets, in order to neglect any unnecessary eﬀects fromthe position dependence.

9.3. Intra-pixel weight algorithm

115

9.3

Intra-pixel weight algorithm

9.3.1

Position dependence

In order to conﬁrm that the assumptions for the intra-pixel weight algorithm are correct, the x hit position dependence of the channel time resolution was checked. Fig. 9.2
shows the result for both 4 cm and 5 cm pixels with intrinsic time oﬀsets. These dependences were obtained essentially in the same way as in 8.4.2 (c.f. Eq. (8.3a) and (8.3b)).
As assumed, the time resolution for hits closer to the readout channel is generally better
than the hits farther away, and the dependence is more prominent when the time oﬀset
correction explained in chapter 8 is applied. A similar position dependence is found in
the enhanced time oﬀset case.
Time resolution v.s. x

0.16
0.14
0.12
0.1
0.08
0.06

ch1 (before correction)ch1 (after correction)ch2 (before correction)ch2 (after correction)−50Time resolution v.s. x−9Channel time resolution [s]Channel time resolution [s]

−9

×10

×10
0.16
0.14
0.12
0.1
0.08
0.06

ch1 (before correction)ch1 (after correction)ch2 (before correction)ch2 (after correction)−55Reconstructed x [cm](a) 4 cm pixels

05Reconstructed x [cm](b) 5 cm pixels

Figure 9.2: x hit position dependence of the channel time resolution. The red and blue
makers show the position dependence before and after the time oﬀset correction respectively.

9.3.2

Intra-pixel weighting

The channel time resolution at each hit position in Fig. 9.2 can be used as the weights
to reconstruct each hit time from the two channel times. In an explicit form, the hit timeis reconstructed as follows in the intra-pixel weight algorithm:
thit =

t −tch2
tch1 −tch1
oﬀset+ ch2σ2 oﬀset
2
σch1
ch2
1
1
+
2
2
σch1
σch2

(9.1)

ch2
where tch1 and tch2 are the signal detection times, tch1
oﬀset and toﬀset are the positiondependent time oﬀsets, and σch1 and σch2 are the relative weights of each channel.
The eﬀect of the intra-pixel weight algorithm is shown in Fig. 9.3. The pixel time
resolution clearly improves, especially for edge hits as the eﬀect of weighting becomesprominent. A similar improvement is found in the dataset with the enhanced time oﬀsets.
The resolution worsens only at point x ∼ −6 cm, which is probably due to some bias in
the time oﬀset correction arising from a poor position resolution. This will be neglected,
however, as this is negligible compared to the overall resolution improvement.

116

Chapter 9. Weighted Mean Algorithm
Time resolution v.s. x

Time resolution v.s. x

−9

0.13

Simple mean

0.12

Weighted mean

Pixel time resolution [s]Pixel time resolution [s]

−9

×10

0.11
0.1
0.09
0.08

×10
0.13

Simple mean

0.12

Weighted mean

0.11
0.1
0.09
0.08

−5

0

−5

5

0

Reconstructed x [cm]5

Reconstructed x [cm](a) 4 cm pixels(b) 5 cm pixels

Figure 9.3: A comparison of the hit time resolution using the simple-mean and the hit
position intra-pixel weight algorithm at each x hit position.

The pTC resolution for each number-of-hit events using the intra-pixel weight algorithm is shown in Fig. 9.4. Each resolution was obtained using Eq. (6.3). The newalgorithm is clearly eﬀective.

Event time resolution

0.09

Simple mean

0.08

Weighted mean

0.07
0.06
0.05
0.04
0.03

0.1 ×10
0.09

Simple mean

0.08

Weighted mean

0.07
0.06
0.05
0.04
0.03

0.02

0.02

0.01

0.01

0
0

2

4

6

8

10

12

14

Number of hits(a) Intrinsic time oﬀset

Event time resolution−9

Event time resolution [s]Event time resolution [s]−90.1 ×10

0
0

2

4

6

8

10

12

14

Number of hits(b) Enhanced time oﬀset

Figure 9.4: The pTC resolution for events with each number of hit pixels for diﬀerent
datasets. The blue and red markers correspond to the result using the simple-mean andthe hit position intra-pixel weight algorithm respectively.

The overall pTC resolution using the original and the hit position intra-pixel weightalgorithm are summarized in Tab. 9.1. The pTC resolution improves by ∼ 4.4 % in thedataset with the intrinsic time oﬀsets, and by ∼ 5.1 % in the dataset with the enhanced
time oﬀsets. The algorithm works better for the latter as the position dependence is more
prominent.

9.4. Inter-pixel weight algorithm

117

Table 9.1: The eﬀect of the hit position intra-pixel weight algorithm in each dataset.
Time oﬀset
Intrinsic time oﬀset
Enhanced time oﬀset

pTC resolution
Simple-mean algorithm Intra-pixel weight algorithm
38.7 ps37.0 ps44.4 ps
42.1 ps

9.4

Inter-pixel weight algorithm

9.4.1

Energy deposit dependence

In order to conﬁrm that the assumptions for the energy deposit inter-pixel weightalgorithm are correct, the energy deposit dependence of the pixel time oﬀset and theresolution were checked, which are shown in Fig. 9.5 and Fig. 9.6 respectively. These wereobtained respectively as the Gaussian mean and standard deviation ofrec
trec
ihit − tave − T OF1ihit(9.2)

distribution1 , where trec
ihit is the reconstructed hit time of the ihit -th hit pixel in a track,tave is deﬁned in the same was as in Eq. (6.2), and T OF1irechit is the TOF from the ﬁrst to
the ihit -th hit pixel.

Pixel time resolution [s]Pixel time offset [s]Timeoffset v.s. energy deposit−9

0.1 ×104cm pixels
5cm pixels

0.08
0.06
0.04
0.02
0
−0.02
−0.04

Time
resolution v.s. energy deposit−90.25 ×10

4cm pixels
5cm pixels

0.2
0.15
0.1
0.05

−0.06
−0.08
0

1

2

3

4

5

Reconstructed energy deposit [MeV]

Figure 9.5: Energy deposit dependence ofthe pixel time oﬀset.

0
0

1

2

3

4

5

Reconstructed energy deposit [MeV]

Figure 9.6: Energy deposit dependence ofthe pixel time resolution.

As already stated, some time walk eﬀect depending on the energy deposit is clearlyseen in Fig. 9.5. The energy deposit dependence of the pixel time resolution in Fig. 9.6
is more or less as we assumed; the resolution generally improves with increasing energy
deposit. The expected dependence is slightly deformed by the pileup eﬀect of secondary
particles at high energy deposit region.
1

In truth, the distribution was found to contain tail events arising from pile up of secondary particles.
Therefore, the distribution is ﬁtted with a double Gaussian, and the narrower distribution is used toobtain the mean and the standard deviation.

118

9.4.2

Chapter 9. Weighted Mean Algorithm

Inter-pixel weighting

In any case, the inter-pixel weighting can be performed using the observed energy
deposit dependence. The pTC positron time is reconstructed as follows in the inter-pixel
weight algorithm:
ihit
rec∑Nhit trec
ihit −T OF1ihit −toﬀset
t

e+

σi2

ihit =1

∑Nhit

=

hit

(9.3)

1

ihit =1 σi2hit

where Nhit is the number of hit pixels in a track, thit
ihit is the reconstructed hit time of therecihit -th hit pixel, T OF1ihit is the reconstructed TOF from the ﬁrst to the ihit -th hit pixel,
hit
tioﬀsetis the energy-deposit-dependent time oﬀset of the ihit -th hit pixel, and σihit is therelative weight of the ihit -th hit in a track.
Again, the pTC resolution for each number-of-hit events using the energy depositinter-pixel weight algorithm was obtained using Eq. (6.3) as shown in Fig. 9.7. The
algorithm is reasonably eﬀective. The overall pTC resolution obtained from this result
improves by ∼ 2.9 % from 38.1 ps to 37.0 ps using the energy deposit inter-pixel weightalgorithm. Note that these values are diﬀerent from the ones in 9.3 as no time oﬀsets are
implemented between SiPMs in the used MC dataset.
Event time resolution

Event time resolution [s]−90.1 ×10
0.09

Simple mean

0.08

Weighted mean

0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
0

2

4

6

8

10

12

14

Number of hits

Figure 9.7: The pTC resolution for events with each number of hit pixels. The blue
and red markers correspond to the result using the simple-mean and the energy depositinter-pixel weight algorithm respectively.

9.4.3

Inter-pixel weighting using position information

The original idea of the inter-pixel weight algorithm was to exploit the energy deposit
information. However, it can also be performed by using the hit position information.
This algorithm is hereon called the hit position inter-pixel weight algorithm.
Fig. 9.8 and Fig. 9.9 show the position dependence of the pixel time oﬀset and theresolution respectively after the intra-pixel weight algorithm for 4 cm pixels with the
intrinsic time oﬀsets. These dependences were obtained essentially in the same way as in
9.4.1 (c.f. Eq. (9.2)). Although the hit position dependence of the pixel time oﬀset been
removed by the hit position intra-pixel weight algorithm, some position dependence of9.4. Inter-pixel weight algorithm

119

the pixel time resolution is found. The resolution seems to be better for edge hits in x
direction. This position dependence can be further used when combining the hit times toobtain the overall positron time. Similar dependences were found in 5 cm pixels and inboth types of pixels in the dataset with the enhanced time oﬀsets.

1

×10−12

0.5
0
−0.5
−1
−1.5
1.5

Re 10.5
co −00.5
2 4
ns − 1tru −1.5
−2 0
−
4
[cm]
−
2
−6
cte
cted x
u
r
dy
t
s
on
[cmRec]Figure 9.8: Hit position dependence ofthe pixel time oﬀset after the intra-pixel
weight algorithm for 4 cm pixels with intrinsic time oﬀsets.

Time resolution v.s. x v.s. y

Pixel time resolution [s]Pixel time offset [s]Time offset v.s. x v.s. y

×10−9
0.16
0.15
0.14
0.13
0.12
0.11
0.1
0.09
0.08
1.5

Re 10.5
co −00.5
2 4
ns −1
tru −1.5
−2 0
−
4
[cm]
−
2
−6
cte
cted x
u
r
t
dy
s
on
[cmRec]Figure 9.9: Hit position dependence of the
pixel time resolution after the intra-pixel
weight algorithm for 4 cm pixels with intrinsic time oﬀsets.

The overall pTC resolution after the hit position inter-pixel weighting was obtainedin the same way as previously described. The resolution is further enhanced to 36.9 psin the case of intrinsic time oﬀsets, and to 41.7 ps in the case of enhanced time oﬀsets(c.f. Tab. 9.1). Together with the intra-pixel weight algorithm, the pTC resolution improves by ∼ 4.6 % and ∼ 5.9 % in each case.

Chapter 10
Evaluation of pTC Performance
In this last chapter, an evaluation of the pTC performance is performed using the
pER2017 data. An estimate of the deterioration of the pTC resolution in the three-year
physics run is made, and the ﬁnal resolution considering the eﬀects of the various methods
introduced in this thesis is also given.

10.1

Evaluation method

The methods to evaluate the pTC resolution using MC simulation and the real data
are diﬀerent and are introduced here. The MC evaluation method is the one alreadyadopted in the past chapters.

10.1.1

MC simulation

The pTC resolution using MC simulation can be evaluated rather easily. First, thetime resolution for each number-of-hit events is obtained. The time resolution for an
Nhit -hit event is obtained from the standard deviation of the
hit
( rec
)
1 ∑
rec
MC
te+ (Nhit ) =(tihit − tMC
ihit ) − (T OF1ihit − T OF1ihit )Nhit i =1

N

hit

=

Nhit
∑

1
rec
MC
(trec
ihit − T OF1ihit − t1 )Nhit i(10.1)

hitMC
distribution, where trec
ihit and tihit are the reconstructed and MC-true hit time respectively
are the reconstructed and the MC-trueof the ihit -th hit pixel, and T OF1irechit and T OF1iMC
hit
TOF from the ﬁrst to the ihit -th hit pixel. Thus, a plot as shown in Fig. 10.1 can beobtained.
This is then ﬁtted with√
σ12(10.2)
σte+ (Nhit ) =
+ σ22
Nhit

where σ1 comes from the single-pixel resolution, the inter-pixel calibration√ precision, theelectronics jitter, etc., and the other eﬀects that do not scale with 1/ Nhit are incorporated in σ2 (c.f. Eq. (4.12)). The resolution for each number-of-hit events is calculated
121

122

Chapter 10. Evaluation of pTC Performancefrom the ﬁtted curve. The overall pTC resolution is obtained by the weighted sum ofthese values with the probability of each number of hits. Fig. 10.2 shows the probability
distribution of the number of pTC hits using the latest positron analysis algorithm. This
distribution is used to evaluate the pTC resolution in this thesis.
Event time resolution
Number of pTC hits distribution

Probability

Event time resolution [s]−90.1 ×10
0.09

0.15

0.08
0.07
0.06

Mean

9.082

15

20

0.1

0.05
0.04
0.03

0.05

0.02
0.01
0
0

2

4

6

8

Figure 10.1: The pTC resolution for eventswith each number of hit pixels using MC
data ﬁtted with the function in Eq. (10.2).
The MC data without time oﬀsets between
SiPMs is used.

10.1.2

0
0

10
12
14
Number of hits

5

10

Number of hit pixels

Figure 10.2: Probability distribution of thenumber of pTC hit pixels after various
selection criteria in the positron analysis.
This is obtained using MC data.

Real data

Using MC simulation, the pTC resolution was evaluated simply by comparing thereconstructed hit time and TOF with the MC-true ones. However, this method cannot
be applied to the real data. In order to evaluate the pTC resolution in the real data, weuse a method called the “even-odd analysis”.
The idea is to use one pixel hit time as a reference of another pixel hit time, as wehave no absolute reference time in the real data. The pTC hits in a track are groupedalternately into “odd” and “even” hits by the order of the pixels traversed by the positron.
The pTC resolution for Nodd odd hits and Neven even hits (Nodd = Neven ) can then be
obtained as the standard deviation of the)1(
todd (Nodd ) − teven (Neven )
2
Nodd
Neven
)
1( 1 ∑
1 ∑=(t2ihit −1 − T OF1(2ihit −1) ) −(t2ihit − T OF1(2ihit ) )2 Nodd i
Neven itodd−even (Nhit ) =

hit

=

N
odd
∑

1 (
Nhit ihit(t2ihit −1 − T OF1(2ihit −1) ) −

hit

N
even
∑

(t2ihit − T OF1(2ihit ) ))(10.3)

ihit

distribution where Nhit = Nodd + Neven , tihit is the reconstructed hit time of the ihit -th
hit pixel, and T OFij is the TOF from the i-th to the j-th hit pixel. The TOF can be
estimated from the CDCH tracking.

10.2. Evaluation of pTC resolution using data

123

This can then be ﬁtted with the function in Eq. (10.2), to obtain the time resolution foreach number-of-hit events. To obtain the overall pTC resolution, the same number-of-hit
distribution as in Fig. 10.2 is used.

10.2

Evaluation of pTC resolution using data

10.2.1Data

The pER2017 data was used to evaluate the pTC resolution. In the pER2017, thenumber of readout channels of 512 was maximum so far, and both the DS and US sectors
were read out in turn (c.f. Tab. 4.4). ∼ 1, 000, 000 events were taken with each sector,
which is more than enough to evaluate the pTC performance. One thing to note is that
the CDCH was not installed in the pER2017, and therefore, the CDCH track information
is not available. The evaluation is carried out using the pTC track information.

10.2.2

Evaluation

The even-odd analysis was applied to the pER2017 data using the pTC tracking, andthe pTC resolution for each number-of-hit events is shown in Fig. 10.3. Fitting the plot
with Eq. (10.2) yielded the values of σ1 ≃ 100.8 ps and σ2 =≃ 0 ps. Using the ﬁtted curve,
the overall pTC resolution of ∼ 36.0 ps was computed.
Event time resolution

Event time resolution [s]−90.1 ×10
0.09
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
0

2

4

6

8

10
12
14
Number of hits

Figure 10.3: The pTC resolution for events with each number of hit pixels using the
pER2017 data ﬁtted with the function in Eq. (10.2).

The pTC resolution evaluation using the pER2017 data had already been performedin the past to be ∼ 38.5 ps [60]. However the pTC tracking algorithm had not beendeveloped then, and therefore, the time resolution was obtained using ﬁxed combinationsof pixel hits in the pTC clusters. Using the pTC tracking, we now have less bias in
the positron track selection, better estimation of the TOFs, and consequently, a better
estimation of the pTC resolution. Note that the positron analysis algorithm has also been
updated since the previous work to enhance the positron eﬃciency.

124

Chapter 10. Evaluation of pTC Performance

10.3

Application of new algorithms to data

The new algorithms introduced in chapter 9 were applied to the pER2017 data. The
eﬀect of each algorithm when applied to the data is shown below.

10.3.1

Energy deposit inter-pixel weight algorithm

The energy deposit inter-pixel weight algorithm was applied to the pER2017 data.
In order to apply the algorithm to the even-odd analysis, the inter-pixel weighting was
performed within even hits and odd hits. That is,
hit∑Nodd tihit −T OF1ihit −tioﬀset



2
ihit
σi


hit

t
(N
)
=
∑
odd
odd

N
even
1


ihit
σ2






teven (Neven ) =(10.4a)ihit∑Neven tihit −T OF1ihit −toﬀset
oﬀset
ihit

σi2

∑Nevenhit(10.4b)

1
σi2

ihit

hit

in Eq. (10.3) are used.
Fig. 10.4 and Fig. 10.5 show the energy deposit dependence of the pixel time oﬀset
and the resolution. These dependences were obtained in the same was as in chapter 9(c.f. Eq. (9.2)). Although, the energy deposit dependence of the pixel time resolution
is similar to the one obtained using MC simulation, the dependence of the time oﬀset
is clearly diﬀerent. One possible cause for this diﬀerence is the existence of background
Michel positrons, but the exact reason is unknown. The eﬀect of the energy depositinter-pixel weight algorithm using these values is shown in Fig. 10.6. The overall pTC
resolution improves from ∼ 36.0 ps to ∼ 34.6 ps with the new algorithm.
Time offset v.s. energy deposit

4cm pixels
5cm pixels

0.08
0.06
0.04
0.02
0

−0.02
−0.04

Time resolution v.s. energy deposit−9

Pixel time resolution [s]Pixel time offset [s]−90.1 ×100.25 ×10

4cm pixels
5cm pixels

0.2
0.15
0.1
0.05

−0.06
−0.08
0

1

2
3
4
5
Reconstructed energy deposit [MeV]

Figure 10.4: Energy deposit dependence ofthe pixel time oﬀset.

0
0

1

2
3
4
5
Reconstructed energy deposit [MeV]

Figure 10.5: Energy deposit dependence ofthe pixel time resolution.

10.3. Application of new algorithms to data
Event time resolution−9

Event time resolution [s]125

0.1 ×10

Simple mean

0.09
0.08

Weighted mean

0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
0

2

4

6

8

10
12
14
Number of hits

Figure 10.6: The pTC resolution for events with each number of hit pixels. The blue
and red markers correspond to the result using the simple-mean and the energy depositinter-pixel weight algorithm respectively.

10.3.2

Hit position intra-pixel weight algorithm

The hit position intra-pixel weight algorithm together with the time oﬀset correction
was applied to data. Fig. 10.7 and Fig. 10.8 show the hit position dependence of thechannel time oﬀset and the resolution respectively for 4 cm pixels. These dependenceswere obtained in the same way is in chapter 9 (c.f. Eq. (8.3a) and Eq. (8.3b)). The
dependences are somewhat blurred by the lower position resolution of the pTC tracking,but the time oﬀset in y direction and higher resolutions at hit points closer to the readout
channel are seen. Similar dependences are seen in 5 cm pixels.

0.3
0.25
0.2
0.15
0.1
0.05
0
−0.05
−0.1

×10−9

1.5
Re 10.5
co −00.5
2 4
ns −1
tru −1.5
−2 0
m]
−
4
cte −2 −6
d x [c
ructe
dy
t
s
n
o
[cmRec](a) Channel 1

Time offset v.s. x v.s. y

Channel time offset [s]Channel time offset [s]Time offset v.s. x v.s. y

×10−9
0.1
0.05
0
−0.05
−0.1
1.5
Re 10.5
co −00.5
2 4
ns −1
tru −1.5
−2 0
m]
−
4
cte −2 −6
d x [c
ructe
dy
t
s
n
o
[cmRec](b) Channel 2

Figure 10.7: Hit position dependence of the channel time oﬀset for 4 cm pixels after
correcting the oﬀsets in x direction. The pTC tracking is used to obtain the hit position.

Chapter 10. Evaluation of pTC Performance
Time resolution v.s. x v.s. yTime resolution v.s. x v.s. y

×10−9

×10−9

0.28
0.26
0.24
0.22
0.2
0.18
0.16
0.14
0.12
1.5
Re 10.5
co −00.5
4
ns −1
0 2
tru −1.5−
2[cm]
cte −2 −6 −4cted x
u
r
dy
t
s
on
[cmRec]Channel time resolution [s]Channel time resolution [s]

126

0.22
0.2
0.18
0.16
0.14
0.12
0.1
1.5

Re 10.5
co −00.5
4
ns −1
0 2
tru −1.5−
2[cm]
cte −2 −6 −4cted x
u
r
dy
t
s
on
[cmRec](a) Channel 1(b) Channel 2

Figure 10.8: Hit position dependence of the channel time resolution for 4 cm pixels. The
pTC tracking is used to obtain the hit position.
The intra-pixel weighting was performed in the same way as in chapter 9 (c.f. Eq. (9.1)),
and its eﬀect was evaluated. The overall pTC resolution improves from 36.0 ps to 35.6 pswith the new algorithm.

10.3.3Hit position inter-pixel weight algorithm

The hit position inter-pixel weight algorithm was applied to data in addition to theintra-pixel weight algorithm. Fig. 10.9 and Fig. 10.10 show the hit position dependenceof the pixel time oﬀset and the resolution. Again, the position dependence is somewhat
blurred by the low position resolution.

12
10
8
6
4
2
0
−2
−4

×10−12

1.5
Re 10.5
co −00.5
2 4
ns − 1tru −1.5
−2 0
m]
−
4
cte −2 −6
d x [c
ructe
dy
t
s
n
o
[cmRec]Figure 10.9: Hit position dependence of the
pixel time oﬀset.

Time resolution v.s. x v.s. y

Pixel time resolution [s]Pixel time offset [s]Time offset v.s. x v.s. y

×10−9
0.17
0.16
0.15
0.14
0.13
0.12
0.11
0.1
0.09
0.08
1.5
Re 10.5
co −00.5
ns −1
tru −1.5−2
ct −2 −6 −4

ed
y

0

u
onstr

[cmRec]2

4cm]
ed x [

ct

Figure 10.10: Hit position dependence ofthe pixel time resolution.

The eﬀect of the hit position inter-pixel weight algorithm in addition to the intra-pixel
weight algorithm is shown in Fig. 10.11. The overall pTC resolution further improves to35.4 ps by applying the two algorithms. The application of the algorithm to the even-odd
analysis was performed using Eq. (10.4a) and (10.4b).

10.4. pTC resolution evaluation

127
Event time resolution

Event time resolution [s]−90.1 ×10
0.09

Simple mean

0.08

Weighted mean

0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
0

2

4

6

8

10

12

14

Number of hits

Figure 10.11: The pTC resolution for events with each number of hit pixels. Red andblue markers show the result using the simple mean and both the hit position intra- andinter-pixel weight algorithm respectively.

10.4

pTC resolution evaluation

10.4.1

Problem with the even-odd analysis

The eﬀect of the new algorithms on the pTC resolution when applied to the pER2017
data is summarized in Tab. 10.1. On the other hand, the eﬀect of the algorithms in MC
simulation is summarized in Tab. 10.2. Comparing the two results, the energy depositinter-pixel weight algorithm yields comparable results in the two cases, while a signiﬁcantdiﬀerence can be seen in the eﬀect of the new algorithms using the hit position information.
This is partly caused by a lower hit position resolution in the pTC tracking compared to
the CDCH tracking. However, it is also due to the diﬀerence in the evaluation method.

Table 10.1: The eﬀects of the new algorithms on the pTC resolution using the pER2017
data.
Algorithm
pTC resolution
Simple mean
∼ 36.0 ps
Energy deposit inter-pixel weight∼ 34.6 ps
Hit position intra-pixel weight∼ 35.6 ps
Hit position intra- and inter-pixel weight∼ 35.4 ps

Resolution improvement∼ 4.6 %
∼ 1.1 %
∼ 1.8 %

128

Chapter 10. Evaluation of pTC Performance

Table 10.2: The eﬀects of the new algorithms on the pTC resolution using MC data withintrinsic time oﬀsets between SiPMs.
Algorithm
pTC resolution
Simple mean
∼ 38.7 ps
Energy deposit inter-pixel weight∼ 37.4 ps
Hit position intra-pixel weight∼ 37.0 ps
Hit position intra- and inter-pixel weight∼ 36.9 ps

Resolution improvement∼ 3.2 %
∼ 4.4 %
∼ 4.6 %As described in 10.2.2, the evaluation method of the pTC resolution is diﬀerent for
MC simulation and the real data. Taking into consideration the newly-found hit position
dependence of the time center, the two methods can potentially yield diﬀerent resolutions.
Although the time ﬂuctuation depending on the hit position is correctly taken into accountin the MC evaluation, it is partly canceled out in the even-odd analysis between even hits
and odd hits. That is why the new algorithms using the hit position information seem tobe less eﬀective when applied to the real data.
This interpretation can be veriﬁed by performing the even-odd analysis to MC data.
Tab. 10.3 shows a comparison of the pTC resolutions obtained using the two methods
for diﬀerent datasets. The two methods clearly yield diﬀerent results, meaning that theeven-odd analysis cannot compute the true pTC resolution. It is also obvious from thelarge discrepancy in the dataset with the enhanced time oﬀsets that the even-odd analysis
is partly insensitive to the position-dependent time oﬀsets.
Table 10.3: A comparison of the pTC resolution in the two evaluation methods using MC
data.
Time oﬀset
No time oﬀset
Intrinsic time oﬀset
Enhanced time oﬀset

10.4.2MC evaluation Even-odd analysis∼ 38.1 ps∼ 34.8 ps∼ 38.7 ps∼ 35.9 ps∼ 44.4 ps∼ 39.2 ps

Evaluation of pTC resolution

As the pTC resolution obtained using the even-odd analysis is not true, the resolution
value obtained using the even-odd analysis must somehow be converted to what canbe assumed to be the correct one. This can be performed using the diﬀerence of theinconsistent resolution values obtained using the two methods in MC data. In a similarway, an estimation of the pTC resolution with the availability of the CDCH track can bemade by comparing the resolutions using the two tracking methods in MC data.
A comparison of the two evaluation methods and the two tracking methods are shownin Tab. 10.4 using the MC dataset with the intrinsic time oﬀsets. The already-obtainedpTC resolution of 36.0 ps corresponds to the bottom right value in Tab. 10.4. Therefore,
the true pTC resolution with the availability of the CDCH tracking can be estimated to10.4. pTC resolution evaluationbe(36.0 ps )≃ 38.4 ps
36.0 ps ⊕ (39.0 ps ⊖ 36.6 ps) ×36.6 ps129(10.5)

assuming that the MC CDCH precisely embodies the real detector. The factor 36.0 ps/36.6 ps
is used to scale the MC resolution to ﬁt the data. The required pTC performance of≤ 46 ps resolution is achieved.
Table 10.4: A comparison of the pTC resolution in the two evaluation methods and thetwo trackings using MC data with intrinsic time oﬀsets.
MC evaluation Even-odd analysis
CDCH tracking
38.7 ps
35.9 ps
pTC tracking
39.6 ps36.6 ps

10.4.3

Estimation of pTC resolution degradation

From the viewpoint of the long-term operation of the detector, the eﬀects of radiation
damage to SiPMs must be taken into account in the pTC resolution evaluation in thelong term. One eﬀect is the resolution degradation caused by the worsening of the S/N
due to the dark noise increase, which is already known to be suppressed to ∼ 5 % with
10 ◦ C operation. Another is the resolution degradation caused by the enhanced position
dependence of the time center. The eﬀect of the latter can also be estimated by comparing
the MC datasets with the intrinsic and the enhanced time oﬀsets.
Tab. 10.5 shows a comparison of the two evaluation methods and the two tracking
methods using the MC dataset with the enhanced time oﬀsets. The eﬀect of the enhanced
position dependence of the time center can be estimated by comparing Tab. 10.4 andTab. 10.5. Thus, the pTC resolution at the end of the three-year physics data-taking canbe estimated to be{(
36.0 ps )}36.0 ps ⊕ (44.4 ps ⊖ 36.6 ps) ×× 1.05 ≃ 45.9 ps(10.6)
36.6 pswhich is at the limit of the required performance level.
Table 10.5: A comparison of the pTC resolution in the two evaluation methods and thetwo trackings using MC data with enhanced time oﬀsets.
MC evaluation Even-odd analysis
CDCH tracking∼ 44.4 ps∼ 39.2 ps
pTC tracking∼ 45.1 ps∼ 40.0 ps

However, the pTC resolution can be recovered to some extent by applying the optimization schemes and the new algorithms introduced in this thesis. The eﬀect of the bias
voltage optimization will be neglected here since its eﬀect has not yet been veriﬁed using
the detector. The eﬀect of the CF optimization will be assumed to be ∼ 3 % as veriﬁedin 7.4.3. The eﬀect of the new algorithms combined are evaluated below.

130

Chapter 10. Evaluation of pTC Performance

Applying all the weighted mean algorithms to the pER2017, the pTC resolution improves from 36.0 ps to 34.3 ps in the even-odd analysis. To estimate the true expected
pTC resolution using the CDCH tracking and with the enhanced time oﬀset, this value
must be converted taking into account the diﬀerence of the tracking, the evaluation andthe time oﬀsets using MC data.
Summarized in Tab. 10.6 are the pTC resolutions obtained in diﬀerent analysis andevaluation conditions using MC data. In the last row, the resolution using the pER2017
data is also shown. From this table, the additional conversion factor is found to be(40.8 ps ⊖ 34.7 ps) × 34.3 ps/34.7 ps taking into account the new algorithm.
Table 10.6: A summary of the pTC resolution and the eﬀect of the new algorithms using
both MC data and the real data. The new algorithm here refers to the combination of all
the weighted mean algorithms.
Data Time oﬀset

Evaluation Tracking

MC
MC
MC
MC
MC
MC
MC
MC
Real

MC
MC
Even-odd
Even-odd
MCMC
Even-odd
Even-odd
Even-odd

Intrinsic
Intrinsic
Intrinsic
Intrinsic
Enhanced
Enhanced
Enhanced
Enhanced
Intrinsic

CDCH
pTC
CDCH
pTC
CDCH
pTC
CDCH
pTC
pTC

pTC resolution
Original algorithm New algorithm
38.7 ps
35.5 ps
39.6 ps
37.4 ps
35.9 ps
33.7 ps36.6 ps
34.7 ps44.4 ps40.8 ps45.1 ps
42.6 ps
39.2 ps36.5 ps40.0 ps
37.7 ps36.0 ps34.3 ps

In conclusion, the expected pTC resolution using the CDCH tracking can be estimatedas follows:{(
34.3 ps )}34.3 ps ⊕ (40.8 ps ⊖ 34.7 ps) ××1.05 × 0.97 ≃ 41.1 ps(10.7)
34.7 pswhere 1.05 is the factor from the dark noise increase, 0.97 is the factor from the CF
optimization, and (40.8 ps ⊖ 34.7 ps) × 34.3 ps/34.7 ps is the factor from the enhanced
position dependence of the time center, also taking into consideration the bias in theeven-odd analysis. The required pTC resolution of ≤ 46 ps is expected to be easily
achieved also in the long run.
One optimistic view is that the position dependence of the time center vanishes by
increasing the CF threshold in the analysis (see Fig. 6.17). This is not eﬀective in thecase of the pER2017 data, as a lower CF value is preferred at the waveform analysis level.
However, with the accumulation of the radiation damage to SiPMs, a higher CF value
is preferred both from the waveform analysis and the position dependence point of view.
Therefore, pulling up the CF threshold in the long term, may potentially slow down the
degradation of the pTC resolution. This is discussed in more detail in Appendix B. The
CF parameter for the above MC studies was ﬁxed to 0.2 in order to compare with the
pER2017 analysis.

10.4. pTC resolution evaluation131

It should also be noted that the evaluations and estimations made in this chapter
are fairly rough incorporating many uncertainties. The pTC resolution obtained above
uses the MC simulation to extrapolate the eﬀect of the radiation damage to SiPMs, butsome eﬀects that are inherent in the real detector are not taken into account in the MC
simulation. For instance, the radiation damage level in all pTC channels are assumed
to be exactly the same in the MC setup, which is clearly not the case. For another, theeﬀect of the gain variation among series-connected SiPMs stated in 6.4.2 is neglected in
the MC simulation.

Part IV
Summary and Prospect133

Chapter 11
Summary and Prospect
11.1

Summary of this thesis

This study was performed for the purpose of• Developing a stable long-term operation system and• Improving the analysis methodof the MEG II pTC in order to bring out its maximum performance.

11.1.1Long-term operation of the pTC

18 new pixels were constructed from the long-term operation point of view, and theirbasic performance was evaluated. The SiPMs used for the new pixels are slightly diﬀerent
from the old ones, which resulted in relatively high resolutions of the new pixels. For their
better performance, some of the old pixels were replaced with the new ones, and they wereoperated successfully in the pER2019. The replaced old pixels are kept as spares.
The eﬀect of radiation damage to SiPMs, especially a gradient damage to seriesconnected SiPMs, were studied in detail. In this study, an intrinsic time oﬀset between
SiPMs arsing from a ﬁnite signal propagation speed was found, which causes hit-position
dependent time ﬂuctuations. It was also found that gradient radiation damage to SiPMs
can cause an overvoltage variation among series-connected SiPMs, which can potentiallyenhance the position dependence of the time center. Its eﬀect on the pTC performancewas evaluated using MC simulation, and an estimate of ∼ 13 % degradation of the pTC
resolution was made.
In order to make up for the drop in pTC resolution, a scheme was developed to
optimize both the bias voltage applied to SiPMs, and the constant fraction parameterused in the waveform analysis. The optimal values of these parameters shift with theincrease of the dark noise, and therefore optimizations at each time point is necessary
to exploit the maximal pTC performance. The newly-developed scheme optimizes thesevalues solely from the observed S/N, and dedicated DAQs are not required. The eﬀect of
the CF optimization was veriﬁed to improve the pTC resolution by ∼ 3 %.
135

136

11.1.2

Chapter 11. Summary and Prospect

Analysis method of the pTC

As another attempt to improve the pTC resolution, a study was conducted to correct
the position-dependent time oﬀsets in the oﬄine analysis. By correcting the time oﬀsets
using the CDCH track information, the pTC resolution could be recovered to some extent.
This approach was found to show higher eﬀects when the time oﬀsets between SiPMs wereenhanced by the gradient radiation damage.
Some completely new algorithms to enhance the pTC resolution were also developed.
Compared to the original algorithm which treats diﬀerent channel times or hit times
equivalently, the new algorithms inﬂict appropriate weights on each time information by
utilizing the energy deposit and the hit position information of the positron in a pixel.
The new algorithms were tested using MC simulation, and was found to recover the pTC
resolution by ∼ 8 %.
The new algorithms were applied to the real data, and a moderate improvement in
the pTC resolution was found. However, it was newly found that the standard evaluation
method of the pTC resolution (the even-odd analysis) does not yield the true resolution,
especially when considering the position-dependent time oﬀsets. Therefore, a data-based
evaluation method, but also making use of the MC results, was developed, and the pTC
resolution was evaluated to be 38.4 ps. Considering the eﬀects from radiation damage
to SiPMs, this value was estimated to degrade to 45.9 ps in the three-year physics datataking. However, applying all the attempts to recover the resolution introduced in thisthesis, the degradation is expected to be suppressed to 41.1 ps, and the required pTC
performance is expected to be achieved also in the long term.

11.2

Future prospects and plans

11.2.1

Positron time resolution

The originally-expected te+ γ resolution at the vertex point is expected to be achieved
even with the assumption of a conservative tγ resolution. However, if the tγ resolution
is better than this value and comparable to the te+ resolution, then enhancing the pTC
resolution still further allows a deeper search of the µ → eγ, as the number of accidental
background events increase linearly with σte+ γ (c.f. Eq. (3.8)).
As stated in 8.4.3, the resolution is strictly limited by the hit position resolution in
the CDCH tracking, resulting in an ineﬃcient position-dependent time oﬀset correction.
A better position resolution should enhance the eﬀect of the time oﬀset correction, as wellas the weighted mean algorithms using the hit position information.
We already know that some hit position bias exists in the CDCH positron tracking.
Fig. 11.1 and Fig. 11.2 show the overall xy hit position distributions in 4 cm pixels, using
MC-true and reconstructed position values respectively. The CDCH tracking clearly hassome position bias in y direction, which is likely to suppress the eﬀect of the time oﬀset
correction. This position bias has not been investigated in detail yet, but it is assumed toderive from a bias in the y estimation in the pTC tracking, used as initial values for the
CDCH track ﬁt. Removing this bias somehow is expected to improve the pTC resolution.

11.2. Future prospects and plans

137

[cm]
MC

y

600
1.5

y rec [cm]Hit position distribution
Hit position distribution
2

500

1
0.5

400

2

500

1
0.5

400

0

300

−0.5

0
−0.5

300

−1

200

−1.5

100

−2
−6

−1.5
−2
−6

600

1.5

−4

−2

0

2

4

200

−1

100
−4

−2

0

2

4

6

x rec [cm]6x MC [cm]Figure 11.1: Hit position distribution in
4 cm pixels in MC data obtained using MCtrue hit positions.

Figure 11.2: Hit position distribution in
4 cm pixels in MC data obtained using reconstructed hit positions with the CDCH
tracking.

One idea to improve the position resolution of hit points, is to somehow combine the
CDCH and the pTC tracking algorithms. Although the CDCH tracking shows a better performance in general, they have comparable hit position resolutions (see Fig. 8.5
and Fig. 8.6). If these tracking methods have independent sources of bias, then a better
position resolution should be obtained by some weighted combination of the two methods. Therefore, understanding the exact characteristics of each tracking method, anddeveloping a way to combine them may be a worthwhile study for the future.

11.2.2

Positron eﬃciency

This thesis focused on the time resolution of the pTC. However, another importantparameter on the positron side which directly aﬀects the MEG II sensitivity is the positroneﬃciency. The target positron eﬃciency is 70 %, but the best achieved in MC simulation
so far is ∼ 63 %. Now that the basic operation and calibration systems for the pTC has
been developed and their performance veriﬁed, eﬀorts must be put into developing thesoftware tools to achieve the target positron eﬃciency.
One way to achieve this is to develop an eﬃcient positron matching algorithm between
the pTC and the CDCH using MC data. All the pTC analysis algorithms up to tracking(see Fig. 4.8) has already been reﬁned, and their performance has been conﬁrmed using
the real data. The next step is to study an eﬀective way to combine the CDCH and thepTC tracks at MC level. By utilizing the pTC track information, a better rejection of the
fake hits in the CDCH should be possible.
Another possible way is to improve the CDCH analysis based on the real data. The
ﬁrst beam-data taking using the CDCH was performed in the pER2018, but the CDCH
data analysis has not been progressed much yet. Therefore, it is of the upmost importanceto check whether the expected performances for the CDCH are achieved in the real data. If
not, further investigations to understand the detector performance is essential to progresswith the positron analysis.

11.2.3

Evaluation of pTC resolution

One problem confronted in this thesis was that we had no viable data-based evaluation
method of the pTC resolution. The even-odd analysis failed to correctly reﬂect the eﬀectof the position-dependent time ﬂuctuations, and even without the time oﬀsets between
SiPMs, the even-odd analysis did not yield the true pTC resolution (c.f. Tab. 10.3).

138

Chapter 11. Summary and Prospect

Therefore, the MC results had to be used in this thesis to convert the obtained resolution
to the what seems to be the true resolution. However, this strategy should only workwhen the MC embodies the real physical processes precisely enough, and is not expected
to work in the long run considering the eﬀect from radiation damage to SiPMs.
It is possible to evaluate the ﬁnal te+ γ resolution using RMD events whose photon andpositron are detected by the LXe calorimeter and the positron spectrometer respectively.
However, it is, of course, better to have individual evaluation method for each detector
to conﬁrm that we understand each detector performance well enough. One possible way
to evaluate the pTC resolution is the “double-cluster method”. A signal positron cancreate more the one pTC clusters, and the idea is to use the positron time obtained in
one cluster as a reference on the positron time obtained in another cluster. This methodshould, in principle, also be insensitive to the position-dependent time ﬂuctuations, but
having multiple evaluation methods could be useful, for instance, to understand any
systematics in each method.
Assuming that a completely data-based evaluation is not possible, the MC resultsmust be used for the evaluation, but to do so, one must conﬁrm that the resolutions
obtained using the MC data are truly correct. For instance, as already mentioned, thegain variation among series-connected SiPMs was neglected in this study. These neglectedeﬀects must be conﬁrmed to have no signiﬁcant impact on the pTC resolution and further
study is necessary.

Appendix
A

Radiation dose calculation

The radiation damage to SiPMs in the case of MEG II pTC is dominated by thebulk damage caused by the collision of ∼ 50 MeV positrons. This bulk damage increases
the bulk leakage current in SiPMs, which is observed as an increase of the dark current.
Therefore, it is common to quantify the damage level using the dark current increase.
The bulk damage caused by the irradiation of hadrons is known to be proportional tothe displacement damage cross section and is equivalent to the classical calculation of the
NIEL [61]. Thus, the NIEL scaling is widely used to standardize damage levels causedby diﬀerent particles with diﬀerent energies, and it is common to normalize the damagelevel with respect to 1 MeV neutrons.
However, we know that the NIEL scaling is violated in the case of electron irradiation[61]. In attempts to standardize the damage level from electron irradiation, modiﬁed
calculations of the NIEL have been proposed, and an “eﬀective NIEL calculation” using
molecular dynamics simulation [62] is known to demonstrate good linearity between thecalculated damage and the current-based damage for high-energy electrons [63]. In thisthesis, we adopt the classical NIEL calculation for the damage from neutron irradiation,
and an eﬀective NIEL calculation for the damage from electron (or positron) irradiation.
For instance, current increase in SiPM arrays was observed in past pERs, which bya simple extrapolation indicates an average current level increase of ∼ 100 µA in thethree-year physics run. The SiPMs in the highest hit-rate region are expected to be
exposed to 1 × 1011 /cm2 ∼ 50 MeV positrons with the absorbed dose of ∼ 25 Gy in three
years. Using the eﬀective NIEL calculation, the total ﬂux is estimated to be equivalentto ∼ 5 × 109 /cm2 1 MeV neutrons. A similar calculation is performed for the electronirradiated samples for the lab test. For the neutron-irradiated samples, the classical NIEL
calculation is used.

BEﬀect of CF parameter on position dependence oftime center

As mentioned in 6.5.3, the position dependence of the time center changes with the CF
parameter, and it generally vanishes by pulling up the CF threshold. Fig. B.1 shows the
position dependence of the time center in channel 1 for edge hits (xhit < −5 cm) in MCdata with the intrinsic time oﬀsets, analyzed with diﬀerent CF parameters in the analysis.
The position dependence is slightly lessened in the case of a higher CF threshold. Thiseﬀects appears more prominently in the case of the enhanced time oﬀsets.
139

140

Chapter 11. Summary and Prospect

−0.25
−0.3

Time center v.s. y−9t}ch1-tave-TOF [s]t}ch1-tave-TOF [s]−9−0.2 ×10

4cm pixel−0.2 ×10−0.25

5cm pixel

−0.35

−0.3

5cm pixel

−0.35

−0.4

−0.45

−0.4

−0.45

−0.5

−0.5

−0.55

−0.55

−0.6

−0.6

−0.65

−0.65

−0.7

Time center v.s. y

4cm pixel

−2

−1

0

1

−0.7

2

Reconstructed y [cm]

−2

−1

0

1

2

Reconstructed y [cm](a) 20 % threshold(b) 50 % threshold

Figure B.1: y hit position dependence of the time center for edge hits (xhit < −5 cm) inchannel 1 using MC data with the intrinsic time oﬀsets using diﬀerent CF parameters in
the analysis. The pTC tracking is used to obtain the hit position.
This means that a higher CF threshold should yield a better pTC resolution from theviewpoint of the position dependence of the time center. However, as already mentioned
in 7.4.1, another optimal CF value exists from the waveform analysis point viewpoint,
which depends on the noise level. When the noise level is small, the former optimalvalue should be larger than the latter, and an overall optimal value should lie somewhere
between the two.
Tab. B.1 shows the pTC resolution obtained using diﬀerent CF parameters in the
waveform analysis using MC data with the intrinsic time oﬀsets implemented. As we
assumed, the optimal value lies somewhere around ∼ 30–40 %, which is relatively higher
than the default 20 % preferred in the waveform analysis level.
Table B.1: The pTC resolutions obtained using diﬀerent CF parameters in the waveform
analysis for the MC dataset with the intrinsic time oﬀsets.
Time oﬀset
Intrinsic

CF threshold
20 %
30 %
40 %
50 %

pTC resolution
38.7 ps
37.1 ps
37.4 ps
41.3 ps

In principle, the best pTC resolution should be obtained by optimizing the CF parameter considering both eﬀects, but such an optimization is highly complicated in thelong run. Therefore, we decided to optimize the CF parameter in the former stage of theanalysis, namely after the hit reconstruction, as was performed in chapter 7, and correct
the remaining position dependence of the time center at the end of the oﬄine analysis.

Acknowledgements
First, I would like to mention that many of the studies introduced in this thesis wereachieved with the help of the members of the MEG II pTC group. The irradiation of
SiPMs in chapter 7 was performed by Masashi Usami and Paolo Cattaneo, and the labdata of the irradiated samples was partly taken by Masashi Usami. The pTC laser data
was obtained with the help of Mitsutaka Nakao who developed the laser system in theﬁrst place. The greatest contribution comes from Dr. Yusuke Uchiyama, who taught me
everything to do the with the pTC, including the pixel assembly procedure in chapter 5,
and always gave me insightful advice when I was badly stuck with my work.
Second, I would like to thank my academic supervisor Prof. Wataru Otani and Prof.
Toshinori Mori for giving me the opportunity to work with such brilliant colleagues in
the MEG II collaboration. It is thanks to them that I could dedicate my two years to theresearch in physics.
Thirdly and lastly, I would like to thank all the members of the MEG II collaboration
for their generous help and work to progress the experiment. In particular, my Japanesecolleagues were not only helpful for the fruitful discussions on my study, but also a great
comfort for me during the days in Switzerland, namely Dr. Toshiyuki Iwamoto, Dr.
Yusuke Uchiyama, Dr. Kei Ieki, Shinji Ogawa, Mitsutaka Nakao, Masashi Usami, Satoru
Kobayashi, Rina Onda, Kazuki Toyoda, Atsushi Oya, Kohei Shimada, Taku Yonemoto
and Kensuke Yamamoto. I am heartfully grateful to all of them.

141Bibliography[1] M. Tanabashi et al. Review of Particle Physics. Phys. Rev., D98(3):030001, 2018.
doi:10.1103/PhysRevD.98.030001.
[2] Stephen P. Martin.
A Supersymmetry Primer.
Advanced Series on Directions in High Energy Physics, page 1–98, Jul 1998.
ISSN 1793-1339.
doi:10.1142/9789812839657 0001.
[3] E. P. Hincks and B. Pontecorvo.
Search for Gamma-Radiation in the
2.2-Microsecond Meson Decay Process.
Phys. Rev., 73:257–258, Feb 1948.
doi:10.1103/PhysRev.73.257.
[4] Francesco Renga. Experimental searches for muon decays beyond the Standard Model.
Reviews in Physics, 4:100029, 2019.
ISSN 2405-4283.
doi:https://doi.org/10.1016/j.revip.2019.100029.
[5] A. M. Baldini et al. Search for the lepton ﬂavour violating decay µ+ → e+ γwith the full dataset of the MEG experiment. Eur. Phys. J., C76(8):434, 2016.
doi:10.1140/epjc/s10052-016-4271-x.
[6] U. Bellgardt et al. Search for the Decay µ+ → e+ e+ e− . Nucl. Phys., B299:1–6, 1988.
doi:10.1016/0550-3213(88)90462-2.
[7] Wilhelm H. Bertl et al. A Search for muon to electron conversion in muonic gold.
Eur. Phys. J., C47:337–346, 2006. doi:10.1140/epjc/s2006-02582-x.
[8] William J. Marciano, Toshinori Mori, and J. Michael Roney. Charged Lepton Flavor
Violation Experiments. Annual Review of Nuclear and Particle Science, 58(1):315–
341, 2008. doi:10.1146/annurev.nucl.58.110707.171126.
[9] Ivan Esteban, M. C. Gonzalez-Garcia, Michele Maltoni, Ivan Martinez-Soler, andThomas Schwetz. Updated ﬁt to three neutrino mixing: exploring the acceleratorreactor complementarity. Journal of High Energy Physics, 2017(1), Jan 2017. ISSN
1029-8479. doi:10.1007/jhep01(2017)087.
[10] Yoshitaka Kuno and Yasuhiro Okada. Muon decay and physics beyond the standard model. Reviews of Modern Physics, 73(1):151–202, Jan 2001. ISSN 1539-0756.
doi:10.1103/revmodphys.73.151.
[11] Stefan Antusch, Ernesto Arganda, Maria Herrero, and Ana Teixeira. Impact ofθ 13 on lepton ﬂavour violating processes within SUSY seesaw. Journal of High
143

144

Bibliography
Energy Physics - J HIGH ENERGY PHYS, 2006:090–090, 11 2006. doi:10.1088/11266708/2006/11/090.

[12] Riccardo Barbieri, Lawrence Hall, and Alessandro Strumia. Violations of lepton
ﬂavour and CP in supersymmetric uniﬁed theories. Nuclear Physics B, 445(2-3):
219–251, Jul 1995. ISSN 0550-3213. doi:10.1016/0550-3213(95)00208-a.
[13] Lorenzo Calibbi, Michele Frigerio, Stephane Lavignac, and Andrea Romanino.
Flavour violation in supersymmetric SO(10) uniﬁcation with a type II seesaw mechanism. JHEP, 12:057, 2009. doi:10.1088/1126-6708/2009/12/057.
[14] Andrzej Buras, Björn Duling, Thorsten Feldmann, Tillmann Heidsieck, andChristoph Promberger. Lepton Flavour Violation in the Presence of a Fourth Generation of Quarks and Leptons. Journal of High Energy Physics, 2010, 06 2010.
doi:10.1007/JHEP09(2010)104.
[15] Kaustubh Agashe, Andrew E. Blechman, and Frank Petriello. Probing the RandallSundrum geometric origin of ﬂavor with lepton ﬂavor violation. Physical Review D,
74(5), Sep 2006. ISSN 1550-2368. doi:10.1103/physrevd.74.053011.
[16] Lorenzo Calibbi and Giovanni Signorelli. Charged Lepton Flavour Violation: An
Experimental and Theoretical Introduction. Riv. Nuovo Cim., 41(2):71–174, 2018.
doi:10.1393/ncr/i2018-10144-0.
[17] J. Adam, X. Bai, A. M. Baldini, E. Baracchini, C. Bemporad, G. Boca, P. W. Cattaneo, G. Cavoto, F. Cei, C. Cerri, M. Corbo, N. Curalli, A. De Bari, M. De Gerone,
L. Del Frate, S. Doke, S. Dussoni, J. Egger, K. Fratini, Y. Fujii, L. Galli, S. Galeotti, G. Gallucci, F. Gatti, B. Golden, M. Grassi, A. Graziosi, D. N. Grigoriev,
T. Haruyama, M. Hildebrandt, Y. Hisamatsu, F. Ignatov, T. Iwamoto, D. Kaneko,
K. Kasami, P.-R. Kettle, B. I. Khazin, O. Kiselev, A. Korenchenko, N. Kravchuk,
G. Lim, A. Maki, S. Mihara, W. Molzon, T. Mori, F. Morsani, D. Mzavia, R. Nard￥‘o, H. Natori, D. Nicol￥‘o, H. Nishiguchi, Y. Nishimura, W. Ootani, K. Ozone,
M. Panareo, A. Papa, R. Pazzi, G. Piredda, A. Popov, F. Raﬀaelli, F. Renga,
E. Ripiccini, S. Ritt, M. Rossella, R. Sawada, M. Schneebeli, F. Sergiampietri, G. Signorelli, S. Suzuki, F. Tenchini, C. Topchyan, Y. Uchiyama, R. Valle, C. Voena,
F. Xiao, S. Yamada, S. Yamamoto, S. Yamashita, Yu. V. Yudin, and D. Zanello.
The MEG detector for µ+ → e+ γ decay search. The European Physical Journal C,
73(4):2365, Apr 2013. ISSN 1434-6052. doi:10.1140/epjc/s10052-013-2365-2.
[18] W Ootani, W Odashima, S Kimura, T Kobayashi, Y Makida, T Mitsuhashi, S Mizumaki, Roger J M Y Ruber, and A Yamamoto. Development of a thin-wall superconducting magnet for the positron spectrometer in the MEG experiment. IEEE Trans.
Appl. Supercond., 14(2):568–571. 4 p, 2004. doi:10.1109/TASC.2004.829721.
[19] Malte Hildebrandt.
The low-mass drift chamber system of the MEG experiment.
IEEE Nuclear Science Symposium Conference Record, 10 2011.
doi:10.1109/NSSMIC.2011.6154677.
[20] MEG Drift Chamber. URL https://meg.web.psi.ch/subprojects/dc/dc.html.

Bibliography145[21] M. De Gerone, S. Dussoni, K. Fratini, F. Gatti, R. Valle, G. Boca, P. W. Cattaneo,
R. Nardo, M. Rossella, L. Galli, and et al. Development and Commissioning of theTiming Counter for the MEG Experiment. IEEE Transactions on Nuclear Science,59(2):379–388, Apr 2012. ISSN 1558-1578. doi:10.1109/tns.2012.2187311.
[22] Saint-Gobain Ceramics and Plastics Inc.
BC-400, BC-404, BC-408,
BC-412, BC-416 Premium Plastic Scintillators, .
URL https://www.
crystals.saint-gobain.com/sites/imdf.crystals.com/files/documents/
bc400-404-408-412-416-data-sheet.pdf.
[23] Photomultiplier Tubes and Related Products.
[24] Hamamatsu Photonics. Si APD S8664 series, . URL https://www.hamamatsu.com/
jp/ja/product/type/S8664-55/index.html.
[25] Satoshi Mihara. MEG liquid xenon detector. Journal of Physics: Conference Series,
308:012009, jul 2011. doi:10.1088/1742-6596/308/1/012009.
[26] Stefan Ritt, Roberto Dinapoli, and Ueli Hartmann. Application of the DRS chipfor fast waveform digitizing. Nuclear Instruments and Methods in Physics Research
Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 623(1):486 – 488, 2010. ISSN 0168-9002. doi:https://doi.org/10.1016/j.nima.2010.03.045.
1st International Conference on Technology and Instrumentation in Particle Physics.
[27] A. M. Baldini, E. Baracchini, C. Bemporad, F. Berg, M. Biasotti, G. Boca, P. W. Cattaneo, G. Cavoto, F. Cei, M. Chiappini, G. Chiarello, C. Chiri, G. Cocciolo, A. Corvaglia, A. de Bari, M. De Gerone, A. D’Onofrio, M. Francesconi, Y. Fujii, L. Galli,
F. Gatti, F. Grancagnolo, M. Grassi, D. N. Grigoriev, M. Hildebrandt, Z. Hodge,
K. Ieki, F. Ignatov, R. Iwai, T. Iwamoto, D. Kaneko, K. Kasami, P.-R. Kettle, B. I.
Khazin, N. Khomutov, A. Korenchenko, N. Kravchuk, T. Libeiro, M. Maki, N. Matsuzawa, S. Mihara, M. Milgie, W. Molzon, Toshinori Mori, F. Morsani, A. Mtchedilishvili, M. Nakao, S. Nakaura, D. Nicol￥‘o, H. Nishiguchi, M. Nishimura, S. Ogawa,W. Ootani, M. Panareo, A. Papa, A. Pepino, G. Piredda, A. Popov, F. Raﬀaelli,
F. Renga, E. Ripiccini, S. Ritt, M. Rossella, G. Rutar, R. Sawada, G. Signorelli,
M. Simonetta, G. F. Tassielli, Y. Uchiyama, M. Usami, M. Venturini, C. Voena,
K. Yoshida, Yu. V. Yudin, and Y. Zhang. The design of the MEG II experiment. The European Physical Journal C, 78(5):380, May 2018. ISSN 1434-6052.
doi:10.1140/epjc/s10052-018-5845-6.
[28] Davide Reggiani, Mike Seidel, and Christopher Allen. Transverse Phase-space Beam
Tomography at PSI and SNS Proton Accelerators. Conf. Proc., C100523:MOPE065,
2010.
[29] Anna Kolano, Andreas Adelmann, Roger Barlow, and Christian Baumgarten. Intensity limits of the PSI Injector II cyclotron. Nuclear Instruments and Methods inPhysics Research Section A: Accelerators, Spectrometers, Detectors and AssociatedEquipment, 885, 07 2017. doi:10.1016/j.nima.2017.12.045.
[30] The PSI proton accelerator.
the-psi-proton-accelerator.

URL

https://www.psi.ch/en/media/

146

Bibliography[31] A.E. Pifer, T. Bowen, and K.R. Kendall. A high stopping density µ+ beam.
Nuclear Instruments and Methods, 135(1):39 – 46, 1976.
ISSN 0029-554X.
doi:https://doi.org/10.1016/0029-554X(76)90823-5.
[32] G. Chiarello. The full stereo drift chamber for the MEG II experiment. Journal of Instrumentation, 12(03):C03062–C03062, mar 2017.
doi:10.1088/17480221/12/03/c03062.
[33] M. De Gerone, F. Gatti, W. Ootani, Y. Uchiyama, M. Nishimura, S. Shirabe, P. W.
Cattaneo, and M. Rossella. Design and test of an extremely high resolution Timing
Counterfor the MEG II experiment: preliminary results. JINST, 9:C02035, 2014.
doi:10.1088/1748-0221/9/02/C02035.
[34] Shinji Ogawa. Liquid xenon calorimeter for MEG II experiment with VUV-sensitive
MPPCs. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 845:528 – 532, 2017.
ISSN 0168-9002. doi:https://doi.org/10.1016/j.nima.2016.06.085. Proceedings of theVienna Conference on Instrumentation 2016.
[35] K. Ieki, T. Iwamoto, D. Kaneko, S. Kobayashi, N. Matsuzawa, T. Mori, S. Ogawa,R. Onda, W. Ootani, R. Sawada, and et al. Large-area MPPC with enhanced VUV sensitivity for liquid xenon scintillation detector. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers,
Detectors and Associated Equipment, 925:148–155, May 2019. ISSN 0168-9002.
doi:10.1016/j.nima.2019.02.010.
[36] Saint-Gobain Ceramics and Plastics Inc. BC-418, BC-420, BC-422 Premium Plastic Scintillators, . URL https://www.crystals.saint-gobain.com/sites/imdf.
crystals.com/files/documents/bc418-420-422-data-sheet.pdf.
[37] Hamamatsu Photonics. MPPC S13360-3050PE, . URL http://www.hamamatsu.
com/jp/en/S13360-3050PE.html.
[38] Hamamatsu Photonics. MPPC S12572-025, . URL https://www.hamamatsu.com/
resources/pdf/ssd/s12572-025_etc_kapd1043e.pdf.
[39] Atsushi Oya. Development of ultra-low material RPC for further sensitivity improvement of MEG II experiment. Master thesis. 2020.
[40] Keisuke Ogawa. 炭素スパッタを用いた積層型 Fast Timing RPC の開発. Masterthesis. 2018.
[41] Marco Francesconi et al. The WaveDAQ integrated Trigger and Data Acquisition
System for the MEG II experiment. 2018.
[42] Marco Francesconi. The MEG II Trigger and Data Acquisition System. Masterthesis. 2017.
[43] Radiall USA Inc. RF and Microwave cable assemblies, . URL https://www.radiall.
com/media/files/RFCableAssemblies%20D1C004XEe.pdf.

Bibliography147

R[44] Inc. DuPont de Nemours. DUPONTTM TEDLAR⃝
Polyvinyl Fluoride (PVF) Films.
URL https://www.dupont.com/content/dam/dupont/products-and-services/
membranes-and-films/pvf-films/documents/DEC_Tedlar_GeneralProperties.
pdf.

[45] Satoru Uozumi Masashi Yokoyama. Multi Pixel Photon Counter の研究開発. 高エ
ネルギーニュース 26-3, 216, 2007.
[46] AdvanSiD. NUV SiPMs. URL http://advansid.com/attachment/get/up_53_
1432731710.pdf.
[47] Miki Nishimura et al.
Pixelated Positron Timing Counter with SiPMreadout Scintillator for MEG II experiment. PoS, PhotoDet2015:011, 2016.
doi:10.22323/1.252.0011.
[48] Usami Masashi. Development and application of track reconstruction method withMEG II positron timing counter. The Physical Society of Japan (JPS) 2019 Autumn Meeting. URL https://kds.kek.jp/indico/event/32275/contributions/
122019/attachments/95016/113174/17pT12-02.pdf.
[49] Mitsutaka Nakao. Commissioning of positron timing counter for MEG II Experimentin 2017: Calibration. The Physical Society of Japan (JPS) 2018 Annual Meeting, . URL https://kds.kek.jp/indico/event/27235/contributions/91614/
attachments/73204/86751/25aL401-03.pdf.
[50] Hamamatsu Photonics. Picosecond light pulser PLP-10, . URL http://www.
hamamatsu.com.cn/UserFiles/DownFile/Product/SOCS0003E13_PLP-10.pdf.
[51] Mitsutaka Nakao. MEG II positron timing counter -construction, calibration andperformance evaluation by using high itensity muon beam, . Master thesis. 2017.
[52] Mitsutaka Nakao. MEG II Timing Counter pre-engineering run 2017: Calibration. Developments of Researches in Lepton Flavor Physics with Muons, 2018.
URL https://indico.psi.ch/event/6267/contributions/13227/attachments/
11381/14635/nakao0405.pdf.
[53] Chen Xu, Robert Klanner, Erika Garutti, and Wolf-Lukas Hellweg. Inﬂuence of X-ray
irradiation on the properties of the Hamamatsu silicon photomultiplier S10362-11050C. Nuclear Instruments and Methods in Physics Research Section A: Accelerators,
Spectrometers, Detectors and Associated Equipment, 762:149 – 161, 2014. ISSN 01689002. doi:https://doi.org/10.1016/j.nima.2014.05.112.
[54] Masashi Usami. Research on radiation tolerance and long-term stable operation of
MEG II positron timing counter. Master thesis. 2018.
[55] LabTech. Water Chillers Cooling Solutions. URL https://www.labtechsrl.com/
images/labtech/download/waterchillers/Water%20Chiller.pdf.
[56] Maxim Integrated. 1-Wire Digital Thermometer with Sequence Detect and PIO.
URL https://datasheets.maximintegrated.com/en/ds/DS28EA00.pdf.

148

Bibliography[57] Honeywell
International
Inc.
HIH-4000
SeriesHumidity
Sensors,.
URL
https://sensing.honeywell.com/
honeywell-sensing-hih4000-series-product-sheet-009017-5-en.pdf.
[58] Keithley Instruments Inc. Model 6487 Picoammeter/Voltage Source, . URL
https://jp.tek.com/low-level-sensitive-and-specialty-instruments/
series-6400-picoammeters-manual/model-6487-picoammeter.
[59] Hamamatsu Photonics. MPPC (multi-pixel photon Chamber), . URL http://www.
hamamatsu.com.cn/UserFiles/DownFile/Product/20130812160713344.pdf.
[60] Miki Nishimura. Positron Timing Measurement to Search for Lepton Flavor Violating Decay in MEG II. PhD thesis, The University of Tokyo, School of Science,
Department of Physics. PhD thesis. 2018.
[61] Jihad Srour, Cheryl Marshall, and Paul Marshall. Review of displacement damage
eﬀects in silicon devices. Nuclear Science, IEEE Transactions on, 50:653 – 670, 07
2003. doi:10.1109/TNS.2003.813197.
[62] C. Inguimbert, P. Arnolda, T. Nuns, and G. Rolland.
Eﬀective NIEL
in Silicon: Calculation Using Molecular Dynamics Simulation Results. IEEE
Transactions on Nuclear Science, 57(4):1915–1923, Aug 2010. ISSN 1558-1578.
doi:10.1109/TNS.2010.2049581.
[63] Roxana Radu, Ioana Pintilie, Leona Nistor, E. Fretwurst, Gunnar Lindstroem, andLeonid Makarenko. Investigation of point and extended defects in electron irradiatedsilicon―Dependence on the particle energy. Journal of Applied Physics, 117:164503,
04 2015. doi:10.1063/1.4918924.