Doctorate Dissertation
博士論文

Positron Timing Measurement to Search for
Lepton Flavor Violating Decay in MEG II（荷電レプトン非保存現象探索のための
MEG II 実験における陽電子時間測定）

A Dissertation Submitted for Degree of Doctor of Philosophy
May 2018
平成 30 年 5 月博士（理学）申請

Department of Physics, Graduate School of Science,
The University of Tokyo東京大学大学院理学系研究科物理学専攻

Miki Nishimura
西村 美紀

Abstract
A new positron timing counter has been developed for the MEG II experiment which aims
to explore new physics beyond the standard model of the particle physics by searching forthe µ+ → e+ γ decay with the world’s highest sensitivity. The most stringent upper limit
for the branching fraction for the decay was set by the MEG experiment in 2016 to be
4.2 × 10−13 (90 % confidence level) by reducing background eﬀectively [1]. The dominantbackground was the accidental coincidence between uncorrelated positrons and photons.
Therefore the precise timing measurements of the positrons and the photons were strongly
required to separate the signals from the background.
To realize a further deep search for the µ+ → e+ γ decay in the MEG II experiment,
further development of detectors is essential to reduce the background which increases withthe planned higher beam intensity. Moreover the detectors should keep their performanceat the higher background rate.
To satisfy the requirements, we established the innovative concept of the timing counter:the pixelated timing counter. It is composed of 512 small counters, each of which consistsof a fast plastic scintillator plate with 6 silicon-photomultipliers (SiPM) at both ends. This
innovative pixelated design helps to reduce pile-up events and allows simultaneous multiple timing measurements to obtain a better overall resolution. Furthermore the timing
counter takes a role as a trigger of timing. The online time resolution reduces the trigger
rate and data size eﬀectively.
Positron timing measurement can be improved by the single counter resolution below
100 ps and the multiple measurement scheme. The design of the single counter is optimized
to achieve the best time resolution. We assembled and tested ∼550 counters and obtained
the time resolution (σ) of 65–90 ps.
Via several beam tests we also demonstrated the improvement of the time resolution
with the multiple counters. Furthermore to extract the maximum performance of themultiple timing measurement, we established a reconstruction algorithm treating multiple
hits eﬀectively, and calibration systems among the counters.
After finalizing the design of the timing counter and the several beam tests, the final
detector was constructed and installed in 2017. We successfully carried out a pilot runof the timing counter including the calibration system, slow control system, and trigger
system. An time resolution below 40 ps with more than 8 counters is demonstrated.
Taking into account the number of hits from the signal positron obtained by a MonteCarlo simulation, the result corresponds to an average resolution of 38.5 ps for the signal
positrons.
The overall positron time resolution including the eﬀect from uncertainty from tracking by drift chamber is 40 ps, which is more than twice better than that in the MEG
experiment. The resolution of the relative time between the positrons and the photons isi

ABSTRACT

ii

estimated to be 64–80 ps by assuming the time resolution of photon to be 50–70 ps. The
result indicates 35–50 % background reduction from the MEG experiment from the timing
measurement point of view and it satisfies to realize a sensitivity of 6 × 10−14 . In conclusion, the timing counter enables the MEG II experiment to realize the unprecedentedly
deep search for the µ+ → e+ γ decay .

Contents
Abstracti

1 Introduction

12 Physics Motivation
2.1 Physics beyond the Standard Model . . . . . . . . . . . . . . . . . . . . . .
2.1.1 Supersymmetry [2] . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 µ → eγ Decay as Touchstone for New Physics . . . . . . . . . . . . . . . . .
2.2.1 µ → eγ decay in the SM . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.2 µ → eγ decay in BSMs . . . . . . . . . . . . . . . . . . . . . . . . . .

3
3
4
4
5
5

3 MEG II Experiment
3.1 Principle of µ → eγ Search . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1 Signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.2 Backgrounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.3 Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.4 MEG to MEG II . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Muon Beam in MEG II . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Proton Accelerators at PSI . . . . . . . . . . . . . . . . . . . . . . .
3.2.2 Muon Production and πE5 Beamline . . . . . . . . . . . . . . . . . .
3.2.3 Beam Transport System after πE5 Beamline . . . . . . . . . . . . .
3.2.4 Beam Intensity in MEG II . . . . . . . . . . . . . . . . . . . . . . . .
3.2.5 Muon Stopping Target in MEG II . . . . . . . . . . . . . . . . . . .
3.3 Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 Positron Spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.2 Photon Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.3 Radiative Decay Counter . . . . . . . . . . . . . . . . . . . . . . . .
3.4 Trigger and Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.1 WaveDREAM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.2 Synchronization . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.3 Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5 Current Status of MEG II . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6 Timing Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7
7
7
8
12
13
16
16
16
18
18
19
23
24
32
38
41
43
44
44
44
44

4 Timing Counter
4.1 Requirement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.1 Multiple Hit Principle . . . . . . . . . . . . . . . . . . . . . . . . . .

46
46
46
47
48

iii

CONTENTS
4.4

iv

Single Counter Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4.1 Scintillator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4.2 Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4.3 SiPM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Property of Single Counters . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5.1 Measurement of Single Counter Resolution . . . . . . . . . . . . . .
4.5.2 Scintillator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5.3 Silicon Photo Multiplier . . . . . . . . . . . . . . . . . . . . . . . . .
4.5.4 Single Counter Assembly . . . . . . . . . . . . . . . . . . . . . . . .
4.5.5 Single Counter Performance . . . . . . . . . . . . . . . . . . . . . . .
4.5.6 Radiation Hardness . . . . . . . . . . . . . . . . . . . . . . . . . . .
Readout Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Laser System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.7.1 Time Oﬀset of Laser System . . . . . . . . . . . . . . . . . . . . . .
Assembly and Installation . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.8.1 Support Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.8.2 Counter Assignment and Assembly . . . . . . . . . . . . . . . . . . .
4.8.3 Installation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.8.4 Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Slow Control System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.9.1 High Voltage Control . . . . . . . . . . . . . . . . . . . . . . . . . .
4.9.2 Temperature and Humidity Control . . . . . . . . . . . . . . . . . .

49
49
50
52
55
55
55
57
63
64
67
70
70
71
72
72
74
75
75
75
75
76

5 Timing Counter Analysis
5.1 Time Reconstruction for µ → eγ Search . . . . . . . . . . . . . . . . . . . .
5.2 Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.1 Waveform Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.2 Hit Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.3 Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.1 Timing Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.2 Position Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.3 Energy Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.1 Event Generation and Interaction . . . . . . . . . . . . . . . . . . . .
5.4.2 Event Mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.3 Waveform Simulation . . . . . . . . . . . . . . . . . . . . . . . . . .

80
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81
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82
83
83
85
85
86
86
86
86

6 Performance of Multiple Hit Scheme
6.1 Multiple Hit Scheme in Clean Environment . . . . . . . . . . . . . . . . . .
6.1.1 Set up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1.2 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1.3 Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1.4 Resolution Improvement with Multiple Hits . . . . . . . . . . . . . .
6.2 Rate Dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.1 Set up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.2 DAQ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.3 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.4 Electronics Jitter . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.5 Time Resolutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

89
89
89
90
91
92
93
93
94
95
97
98

4.5

4.6
4.7
4.8

4.9

CONTENTS

v

6.2.6

Multi-Counter Resolutions . . . . . . . . . . . . . . . . . . . . . . . . 102

7 Timing Counter Performance103
7.1 Pilot Runs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
7.1.1 Pilot Run 2015 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
7.1.2 Pilot Run 2016 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
7.1.3 Laser test with the final DAQ . . . . . . . . . . . . . . . . . . . . . . 104
7.1.4 Pilot Run 2017 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
7.1.5 MC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
7.2 Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
7.2.1 Discriminator Threshold . . . . . . . . . . . . . . . . . . . . . . . . . 107
7.2.2 Online Time Resolution . . . . . . . . . . . . . . . . . . . . . . . . . 107
7.3 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
7.3.1 Optimization of Waveform Analysis . . . . . . . . . . . . . . . . . . 108
7.4 Hit Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
7.5 Time Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
7.6 Basic Properties of Counters . . . . . . . . . . . . . . . . . . . . . . . . . . 118
7.6.1 Time Resolutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
7.6.2 Energy Dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
7.7 Overall Time Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
7.8 Radiation Hardness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
8 Sensitivity Estimation
128
8.1 Performance of Positron Spectrometer . . . . . . . . . . . . . . . . . . . . . 128
8.1.1 Combined Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . 128
8.1.2 MC Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
8.1.3 Positron Time Resolution . . . . . . . . . . . . . . . . . . . . . . . . 128
8.2 Eﬃciency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
8.3 Expected Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
9 Summary and Conclusion

137

A Global Bias of Time Calibration

140

B Optimization of Waveform Analysis

145

Chapter 1

Introduction
The theory of everything has been dreamed by particle physicists for more than a hundred
year. Everything means all interactions and fundamental particles. The trial is still underway and what is known is the standard model (SM) in the particle physics. The SM havesucceeded in explaining a lot of phenomena, but still it does not explain everything suchas the origin of the dark matter and the neutrino oscillation observed by experimentalists.
Moreover from the theoretical point of view, it is not exactly unified, nor does it explain
the generations of the particles. Consequently, new physics beyond the SM (BSM) should
be exist.
The conservation of the lepton flavor is one of the huge questions which the SM cannot
explain because the origin of three generations of leptons is not described. Therefore there
is a room for BSM to drop their hints. Actually the neutrino flavor oscillation was alreadydiscovered, which cannot be explained by the SM because of the assumption of the massless neutrinos. On the other hand, in the charged lepton sector, no flavor violation isobserved. However, many models of new physics predict charged lepton flavor violation(cLFV) large enough to be detected by near future experiments.
The most stringent upper limit on the branching fraction of µ+ → e+ γ decay, which isone of cLFV decays, was set by the MEG experiment [1], which yielded the upper limit of
4.2×10−13 (90 % confidence level). In general this result from MEG is most stringent limit
on BSMs in every cLFV decays. For a deeper search physicists of the MEG experiment
aim at a sensitivity enhancement and planned an upgrade experiment, called the MEG II
experiment. To realize the ultimate sensitivity of the µ+ → e+ γ search, the upgrade of thedetectors is essential against the increasing background with the beam intensity increase.
Since the dominant background is accidental background made by detecting the uncorrelated positron and photon at the same time, the accurate time measurement is strongly
required. Therefore we innovated a new positron timing counter for the MEG II experiment. Use of silicon photo multipliers (SiPMs) allows finer segmentation of the detector.
One counter is composed of 120×(40–50)×5 mm3 fast plastic scintillator and 6-SiPMs at
the both end. To extract the maximum performance from the SiPMs, we employed seriesconnection. In total 512 counters are used. This novel design reduces pile up events andimproves the overall positron timing resolution significantly.
In this thesis, we will discuss the positron timing measurement focusing on the timing
counter performance and ability for the µ+ → e+ γ search in the MEG II experiment.
First the physics motivation of the search will be discussed in detail in Chapter 2 andthen Chapter 3 will describe the overall of the MEG II experiment. The detailed design
and the quality of each component of the timing counter will be introduced in Chapter 41

CHAPTER 1. INTRODUCTION

2

and the analysis concept will be described in Chapter 5. After proving the performanceby the multiple time measurement with the counters by several beam tests in Chapter 6,
we will show the final performance of the timing counter obtained with the final set up of
the beam, the magnetic field, the electronics, and the calibration system in the MEG II
experiment in Chapter 7. Finally the expected final performance of the time measurementof µ+ → e+ γ and the expected final sensitivity of MEG II will be discussed in Chapter 8
and the thesis will be concluded in Chapter 9.

Chapter 2

Physics Motivation
In this chapter, we will discuss the physics motivation of the µ → eγ decay search. Thismuon decay is forbidden in the standard model (SM) of the particle physics, but many of
new physics beyond the SM (BSM) predict this decay at a branching fraction of O(10−13 )–O(10−14 ).

2.1

Physics beyond the Standard Model

The ultimate goal of particle physics is to understand all the interactions and all theparticles in the Universe by the simplest formula. The standard model in particle physic
is a very successful theory to explain many phenomena. It is based on the gauge symmetryof SU(3)c × SU(2)L × U(1)Y . Though the SM is a successful model, several questions arestill remained. First of all it is not exactly unified. The gauge symmetry which the SM
has is represented as the direct product of three gauge groups, which have independent
coupling constants. Moreover the SM does not include the gravitational interaction at all.
Secondly, the SM does not explain the generations of the particles though we know
three generations of quarks and leptons which are distinguished with their masses andflavors. The fundamental reason is the existence of Higgs boson. It is not required by agauge symmetry but is added artificially to generate spontaneous breaking of the gauge
symmetry. Therefore the Yukawa coupling between Higgs boson and each particle, andthe mixing pattern between the generations are free parameters independent of the gauge
symmetry in the SM. The discovery of the Higgs boson in 2012 [3, 4] realized the problemof the lack of the underlying principle for the Higgs existence as well as confirmed themechanism of generating mass. These two problems of non-single gauge groups and thegenerations ordered by nobody are the origins of all the free parameters in the SM.
Due to the problems discussed above, it is natural that the SM is not regarded as acomplete theory but an eﬀective theory at a low-energy scale. In general, the high energy
scale (Λcut-oﬀ ) of the new physics should be much higher than the weak interaction scale(MW ≪ Λcut-oﬀ ). However in the process of explaining this huge diﬀerence among theenergy scales, the absence of the requirement for Higgs boson from any gauge symmetryraises the quadratic divergence in the radiative corrections, which requires a fine tunning
between the bare mass and the radiative corrections in Higgs mass. This unnaturalness iscalled the hierarchy problem.
Moreover some experimental results also indicate the existence of BSM. The neutrino
oscillation, which is not described by the SM, was discovered. It demands the modificationof the SM. The observation of the cold dark matter also suggests the existence of a newparticle in the Universe.
3CHAPTER 2. PHYSICS MOTIVATION

2.1.1

4

Supersymmetry [2]The Supersymmetric (SUSY) model is one of the candidates for BSM to solve these problems. By introducing a SUSY partner for each SM particle and the symmetry under
the super-transformation between boson and fermion, the divergence in the radiative corrections in the Higgs mass is canceled by the diﬀerence of statistics between boson andfermion. Furthermore, supersymmetry induces the gravitational interaction naturally.
Since the gravitational interaction is not a linear interaction, in general it cannot berenormalized because of the divergence. However, the divergence is suppressed by combining the Poincaré symmetry and the supersymmetry. Another point to notice is thatthe lightest SUSY particle can be the dark matter.
In the real world any SUSY particles are observed which means that the supersymmetryis broken. Therefore SUSY breaking mechanism is essential and depends on the models.

2.2µ → eγ Decay as Touchstone for New Physics

U.L. on BR (90% CL)

Muon is the particle in the second generation of charged leptons with heavier mass thanelectron mass. It was discovered in 1937 in cosmic rays [5]. Historically studies on muon
decays including the search for µ → eγ decay have contributed to the deep understandingof the SM such as the lepton flavor conservation. Since the first search of µ → eγ in 1947,
beams and detectors developments have pushed down the upper limit on the branching
fraction of the decay as shown in Fig. 2.1. Nowadays the search changes its role to provide
deep insight for new physics.
1
10−2
10−4
10−6
10−8
10−10
10−12
10−14
10−16
10−181940

1960

1980

2000

2020
Year

Figure 2.1: Development of the upper limits on µ → eγ (blue), µN → eN (green), andµ → 3e (red).

CHAPTER 2. PHYSICS MOTIVATION

2.2.1

5

µ → eγ decay in the SM

In the SM µ → eγ decay is forbidden. However the discovery of the neutrino oscillation
tells us non-zero mass of the neutrino and thus lepton flavor is not conserved. This result
can be implemented to the SM in the simplest way and in that case a non-zero branching
fraction of the µ → eγ decay is calculated as [6, 7],
B(µ → eγ) =Γ(µ → eγ)Γ(µ → eν ν̄)

(2.1)
2

=

m2
3α
Uµi Uei 2i
32π
MW

=

3α
δm2
∗
Σi=2,3 Uµi
Uei 2i1
32π
MW

(2.2)
2

(2.3)

By substituting measured values [8] for U and δm2i1 , the branching fraction is obtained as.
B(µ → eγ) ≤ 10−54 .

(2.4)

It is too small to be detected by experiments in near future.

2.2.2µ → eγ decay in BSMs

While the SM does not allow the µ → eγ decay, many BSMs predict the decay with thelarge branching fraction around the current limit obtained by experiments. Especiallyin most cases of SUSY models, in general, the new source of the flavor mixing in mass
matrices of the SUSY particles induces the cLFV including the µ → eγ decay. The
following demonstrates some of the attractive models induce the µ → eγ decay.
SU(5) SUSY GUTThe SU(5) SUSY grand unified theory (GUT) is the model which unifies the gauge groups
of SU(3)c , SU(2)L , and U(1)Y into a single SU(5) group at the order of 1016 GeV energy
scale. In this model the cLFV is induced by the oﬀ-diagonal elements of the mass matrixof the SUSY lepton partners (sleptons) when the matrix of the SM leptons is diagonalized.
That is when
VR ye VL† = diagonal,(2.5)

the oﬀ-diagonal elements for the right handed sleptons are given as [9](m2ēR )ij ≃ −3MP,(VR )i3 (VR )∗j3 |yu33 |2 m20 (3 + |A0 |2 )ln
2
8π
MG

(2.6)

where MP is the reduced Planck mass; MG represents the GUT scale; and m0 and A0
are the universal scalar mass and trilinear coupling. Fig. 2.2 shows the possible Feynman
diagrams induced by this oﬀ-diagonal elements.
SUSY Seesaw
Tiny neutrino mass is also a question for which we do not have any explanation. The
seesaw mechanism [10–13] provides a natural explanation by introducing the Majorana
mass term of right-handed neutrinos. When the Majorana neutrinos are included, twoCHAPTER 2. PHYSICS MOTIVATION

6

Figure 2.2: Feynman diagrams inducing µ → eγ in SU(5) SUSY GUT. [9]Yukawa coupling matrices appear in the lepton sector to couple the right-handed neutrino
supermultiplets. Since the two matrices are independent, in SUSY seesaw model, theleft-handed slepton mass matrix has oﬀ-diagonal element, which enhances cLFV.
In particular the high-scale SUSY, where the mass of the SUSY particles are inO(10) TeV, predicts a large branching ratio of µ → eγ of 10−13 –10−14 [14]. The recent results of no observation of the SUSY particles in the energy frontier experiment at
the LHC and light Higgs mass of 126 GeV favor the high-scale SUSY.

Chapter 3

MEG II Experiment
In this chapter an overview of the MEG II experiment will be described. At the beginningthe principle and requirements of the experiment will be introduced. Then the beamline
used by MEG II will be described in the second section, and finally the detectors in MEG
II in the third section.

3.1

Principle of µ → eγ Search

The signal can be identified simply because the decay is a two-body decay, whereas the
backgrounds arise from an accidental coincidence of uncorrelated positrons and photons,
called accidental background, and a four-body decay of muons, called physics background.
The schematic of the signal and the two backgrounds are shown in Fig. 3.1.

Figure 3.1: Drawing of µ → eγ decay (a) and backgrounds (b, c).

3.1.1

SignalThe µ → eγ decay is a simple two-body decay. A muon emits a back-to-back, monoenergetic, time coincident pair of a photon and a positron in the rest frame of the muon,that is• teγ = 0
• Eγ = Ee = mµ /2 = 52.8 MeV• Θeγ = 180◦
7

CHAPTER 3. MEG II EXPERIMENT

8

where teγ is the time diﬀerence between the photon and the positron; Eγ and Ee are theenergies of the photon and the positron, respectively; mµ is the muon mass; and Θeγ isthe opening angle between the photon and the positron.
The expected number of signals can be written with the branching fraction B,
Nsig = Rµ × T × Ω × B × ϵe × ϵγ × ϵcut

(3.1)

where Rµ is the instantaneous muon intensity and T is the total acquisition time; Ω isthe solid angle of the detector; ϵe and ϵγ are the detection eﬃciencies of positrons andphotons respectively; and ϵcut is the eﬃciency of the event selection. All of these values
except for the branching fraction given by the nature should be increased to observe theµ → eγ decay.

3.1.2

Backgrounds

We utilize a positive muon beam; otherwise a nucleus in target material can form a muonic
atom by capturing a negative muon. The decay from the muonic atom is no longer a twobody decay, which means we can not distinguish the signals kinematically.
Even though we use a positive muon beam, there are two backgrounds from muon
decays of SM for µ+ → e+ γ search. One is the accidental background from the accidental
coincidence of a positron from Michel decay (µ+ → e+ νe νµ ) and a high-energy photon
from any sources. The other background is a physics background from a radiative muon
decay (RMD), µ+ → e+ νe ν¯µ γ.
Concerning muon decays in SM, the fraction of Michel decay mode is almost 100 % asshown in Tab. 3.1.
Table 3.1: The fraction of muon decay [8]Decay Mode
Fraction−−µ → e ν¯e νµ≈ 100%−−µ → e ν¯e νµ γ
(6.0 ± 0.5) × 10−8−−+−
µ → e ν¯e νµ e e(3.4 ± 0.4) × 10−5

Since the signal is characterized by the energies, the timing, and the opening angle ofthe emitted positron and photon as discussed above, the dependence of the backgrounds
fraction per muon decay on these observables should be considered. In the following
discussion, the positron and photon energies normalized to a half of the muon mass,
x = 2Ee /mµ and y = 2Eγ /mµ , and the opening angle, z = π − Θeγ , are used. The
eﬀective partial branching fractions of the backgrounds are defined for the signal region ofthe µ+ → e+ γ search. Taking δteγ , δx, δy, and δz 1 to be the ranges of the signal region
for the corresponding observables, the interesting region can be written as,
1 − δx ≤ x ≤ 1 + δx
(3.2a)
 1 − δy ≤ y ≤ 1 + δy
(3.2b)
0 ≤ z ≤ δz
(3.2c)
−δteγ ≤ teγ ≤ δteγ
(3.2d)√√
Considering the positron mass, the maximum range of y is 1 − r and that of x is 1 + r wherer = (me /mµ )2 . However the eﬀect is small enough to be ignored compared with the resolutions inprinciple.
1

CHAPTER 3. MEG II EXPERIMENT

9

As a reference the performance of the MEG experiment which set the most stringent
upper limit on the branching ratio of µ → eγ decay is shown in Tab. 3.2. Taking 90%
of signal region is covered, which can be obtained by multiplying σs by 1.64, the signal
region can be obtained as,δx ≈ 0.015δy ≈ 0.019
(3.3)

δz
≈
20
mrad



δt ≈ 200 ps.
eγ

Table 3.2: Resolutions (in σ) in the MEG experiment [1]. The fractions are shown inparentheses when resolutions changed event by event.
Observables
Resolutions (σ)
Photon Energy (σEγ )2.3% (fraction: 42%), 1.6% (58%)
Positron Energy (σEe )330 keV (82%), 1.1 MeV (18%)
Opening Angle θ (σθe γ )15.0-16.2 mrad
Opening Angle ϕ (σϕe γ )8.9-9.0 mrad
Time (σte γ )122 psPhysics Background
The positron and photon from RMD mimic a µ+ → e+ γ signal. They are emitted simultaneously and, moreover, when little momentum is carried oﬀ by the neutrinos, the positronand photon are emitted like back-to-back with the momentum close to that of the signal.
RMD branching the fraction can be written in the V−A interaction as [9],dB(µ+ → e+ ν¯µ νe γ) =αdyβdx dΩe dΩγ [F (x, y, d)364πy−β P⃗µ · p̂e G(x, y, d)(3.4)−P⃗µ · p̂γ H(x, y, d)],where dΩe and dΩγ are solid angles of the emitted positron and photon with energy
intervals of dx and dy respectively; P⃗µ is the vector of muon polarization; p̂e and p̂γ are theunit vectors of a positron and a photon momenta defined by p̂e ≡ p⃗e /|⃗pe | and p̂e ≡ p⃗e /|⃗pe |as p⃗e and p⃗γ are momenta of a positron and a photon; β is defined as β ≡ |⃗pe |/Ee ; and d
is given by d ≡ 1 − β p̂e · p̂γ . F (x, y, d), G(x, y, d), and H(x, y, d) are given in Appendix Aof [9].
As discussed above, an RMD decay mimics a µ+ → e+ γ signal when x ≈ 1, y ≈ 1, andz ≈ 0. The background branching fraction in an experiment depends on its resolutionsof x, y, and z, and can be calculated by integrating Eq. 3.4 over Eq. 3.2a, Eq. 3.2b, andEq. 3.2c,∫ 1+δx ∫ 1+δy ∫ δzdB(µ+ → e+ ν¯µ νe γ)(3.5)
dBRM D (µ+ → e+ ν¯µ νe γ) =
dx
dy
dz
.
dxdydz1−δx1−δy0
The MEG experiment [1], which is the most recent experiment of µ → eγ search,calculated the eﬀective branching fraction as shown in Fig. 3.2 (b). Since the observed

CHAPTER 3. MEG II EXPERIMENT

10

shape of dB(µ+ → e+ ν¯µ νe γ) is smeared by the detector resolutions in the experiment,
Eq. 3.4 is folded with the detector responses in their calculation. They set the upper edges
for Ee , and Eγ to 53.5 MeV corresponding to 1.0127 in x and y, and cosΘeγ to −0.9996 as∼0.0283 in z instead of their detector resolutions and show the eﬀective branching fraction
as the function of the lower edges for Ee and Eγ of the signal region. In MEG the energy
resolutions of positron (σEe ) and photon (σEγ ) are 330 keV1 and 2.3%, respectively. The
partial branching ratio in 52.5 < Ee < 53.5 MeV and 52.0 < Eγ < 53.5 MeV is,dBRM D (µ+ → e+ ν¯µ νe γ) ∼ 1 × 10−14(3.6)

E γ ,min (MeV)This level of background is not such a large number but not negligible for a µ → eγ searchgoing down its sensitivity to O(10−14 ) while it is negligible in MEG in which the single
event sensitivity is (5.84 ± 0.2) × 10−13 . This background can be reduced by improving
detector resolutions for the opening angle and momenta.
53

53

(a)

(b)
-13

52

52

10
10-12

51

48
50

50
10-11

51

10-14
10-13

51

50
49

10-15

10-12

49

52

53

48
50

51

52
53
E e+,min (MeV)

Figure 3.2: Eﬀective branching ratios of the backgrounds in the MEG experiment [1]. The
kinematic windows are defined by Ee+ ,min < Ee < 53.5 MeV, Eγ,min < Eγ < 53.5MeV,|teγ | < 0.24 ns and cosΘeγ < −0.9996. (a) Accidental background (b) RMD backgroundcalculated by theoretical branching ratio (Eq. 3.5) smeared by MEG detector responses.

Accidental Background
The accidental background is the dominant background in a high intensity environment.
Uncorrelated positron and photon can mimic the µ+ → e+ γ signal by an accidental
coincidence when their momenta are around the signal momentum of 52.8 MeV.
The source of the background positron is a Michel positron. Its momentum is aroundthe signal momentum when the opening angle of the two neutrinos are small. On the other
hand, the photon background sources come from an annihilation in flight of a positron(AIF) and an RMD. Fig. 3.3 shows the photon background rate in the MEG experiment[15] and indicates that AIF and RMD are the dominant background of photon. In addition
accidental pileup of photons is also another source of background.
The eﬀective branching fraction of the accidental background (Bacc ) to one muon canbe written with an instant intensity of muon beam (Rµ ) as,
Bacc = Rµ · fe0 · fγ0 ·1(δz)2· (2δteγ ),4This is the core value. Tail component of ≈ 18% is observed with σEe ≈ 1.1 MeV(3.7)

Rate (Hz /0.50 MeV)

CHAPTER 3. MEG II EXPERIMENT

11102
MC AllAIF
RD
Pileup
Data

10

1
2.4
2.2
2
1.8
1.6

10-1 1.4
1.2
1
0.8

400.6
0.4

45
40

45

50

55

60

50

55

60

65
65

70
Eγ (MeV)Figure 3.3: Trigger rate of photon background in MEG experiment [15].

where fe0 and fγ0 are the integrated energy spectra of a positron and a photon within thesignal region respectively. fe0 can be calculated by integrating the Michel positron energy
spectrum given by Fig. 3.4 [16]. At the signal region x ≈ 1 the spectrum is almost flat,
therefore,fe0 ≈ 2(δx).
(3.8)
By contrast, fγ0 can be obtained by combining AIF and RMD gamma spectra. While
the spectrum of AIF depends on material distribution in an experiment, that of RMD
can be calculated by integrating Eq. 3.4 over all positron energy and opening angle, andEq. 3.2b for photon energy. It is described in [17]. At first the result of the integration of
the positron energy and the opening angle is,
dB(µ+ → e+ ν¯µ νe γ) = [J+ (y)(1 + Pµ cosθγ ) + J− (y)(1 − Pµ cosθγ )] + O(√dy(r))] d(cosθ)y(3.9)

where J+ (y) and J− (y) are given byα
1 − y 171−y(1 − y)[(3ln− ) + (−3ln+ 7)(1 − y)
6πr2r
1 − y 13+(2ln
− )(1 − y)2 ],r
3(3.10)α1 − y 93
1 − y 29
(1 − y)2 [(3ln− ) + (−4ln+ )(1 − y)
6π
r
12
r
3
1 − y 55+(2ln
− )(1 − y)2 ].
r12(3.11)

J+ (y) =J− (y) =In the interesting region y ≈ 1 the eﬀect of J+ (y) is much larger than that of J− (y) because
J− (y) has the larger power of (1 − y). The partial branching ratio integrated over 3.2b
can be obtained as,∫ 1+δydB(µ+ → e+ ν¯µ νe γ)
dy
dbγ =
dy
1−δy
α
≈
(δy)2 [ln(δy) + 7.33](1 + Pµ cosθγ )d(cosθγ ).
(3.12)
4π

CHAPTER 3. MEG II EXPERIMENT

12

Assuming the unpolarized muon, Pµ = 0, it can be written as,bγ ≈α(δy)2 [ln(δy) + 7.33].
2π(3.13)

In conclusion, assuming the photon from RMD as the dominant source of the photon
background, the number of the accidental background can be written as
Nacc = Rµ × T × Ω × Bacc × ϵ˜e × ϵ˜γ∝Rµ2 × T × δy 2 × δx × δz 2 × δteγ ,(3.14)(3.15)

where ϵ˜e and ϵ˜γ are the detection eﬃciencies of background positrons and photons respectively, which have small diﬀerence from those of signals because of diﬀerence of the
distribution of momenta, opening angle, and so on. Consequently, the background can be
reduced by tightening the signal region of x, y, z, and teγ , while it is increased with thesquare of Rµ .
The eﬀective branching ratio of the accidental background is estimated in the MEG
experiment by using time side-band events. Fig. 3.2a describes it as a function of theminimum integral range of Ee and Eγ . In the MEG environment the partial branching
fraction is obtained as,
Bacc ∼ O(10−13 )(3.16)

2

Differential Branching Ratio

Differential Branching Ratio

The partial branching ratio of the accidental background is one or two order of magnitudelarger than that of RMD in 3.6 and is the dominant background with recent detector
performance. This background level is not acceptable to achieve the sensitivity down toO(10−14 ). The reduction of the accidental background is essential for MEG II experiment.

1.5
1
0.5
0
0

0.2 0.4 0.6 0.8
1
Normalized Positron Energy (x)Figure 3.4: Positron energy spectrum
from Michel decay [16]

3.1.3

1
10−1
10−2
10−3
10−4
10−5
10−6
0

0.2 0.4 0.6 0.8
1
Normalized Photon Energy (y)Figure 3.5: Photon energy spectrum

Requirements

The necessity of background reduction is described in the previous subsection. In particular, reducing accidental background, which is the dominant background, is essential.

CHAPTER 3. MEG II EXPERIMENT

13

There are several requirements for the µ → eγ search. Firstly a high intensity direct
current (DC) muon beam is required. Comparing Eq. 3.1 and Eq. 3.14, the number of
the accidental backgrounds depends quadratically on the instant muon intensity while thesignal events increases only in proportion to the instant intensity of muon beam. Hencea DC beam matches the experiment to acquire large statistics eﬀectively with minimizing
the accidental background.
Secondly, the detector improvement is equally important to reduce the background.
Eq. 3.7 and Eq. 3.14 indicate that the improvement in resolutions of the momenta, and theopening angle and the time between a positron and a photon suppresses the background.
Furthermore we can make an eﬀort to reduce the photon background source unlike
the positron background which depends on only muon beam intensity. As explained
above, photons of accidental background mainly come from RMD and AIF. To avoid
the AIF, material should be minimized throughout the positron path. In addition, any
kind of detector or analysis to identify the RMD and AIF also help to suppress the photon
background. In summary, the requirements for the µ+ → e+ γ search are,• High intensity DC muon beam
• Minimized material detectors having high performance for measurement of momenta,
opening angle and time of positron and photon

3.1.4

MEG to MEG II

The requirements above are satisfied in the MEG experiment, which is why they achieved
the highest sensitivity for the search in the world. A schematic of the MEG experimentis described in Fig. 3.6. The beam line employed by MEG is in Paul Scherrer Institut(PSI) and provides the most intense DC muon beam in the world. Muons are stopped
in a target, and then emitted photons are detected in a liquid xenon calorimeter withwhich the positions, times, and energies are measured, and emitted positrons are bent
by a superconducting magnet and their momenta, vertex and times are measured by adrift chamber and a timing counter. These detectors made it possible to yield the moststringent upper limit on branching ratio of µ+ → e+ γ of 4.2 × 10−13 (90 % confidence
level) [1].
However further enhancement of the sensitivity is diﬃcult in MEG because of theincrease of the number of backgrounds as shown in Fig. 3.7. The figure indicates thatthe degree of the sensitivity enhancement becomes less with accumulation of the data andfurther data acquisition in MEG makes little sense. The upgrade of detectors is, therefore,
mandatory to reach the sensitivity of O(10−14 ).
The key of the upgrade to MEG II is the maximum usage of the muon beam in PSI.
Since the drift chamber could not operate in a highly radiation environment which induces
discharge and unacceptable background level for the MEG detectors, the intensity of muon
beam was limited and was reduced by a factor of 2-3 from the maximum intensity. We
can exploit full intensity of the muon beam by• Development of high rate tolerable positron spectrometer.
• Resolution improvement for all the detectors
Furthermore the MEG experiment had a poor detection eﬃciency (∼40 %) of positron.
The material between the drift chamber and timing counter, such as the drift chamberelectronics and support, induced scattering of positrons before timing counter resulting in
the poor eﬃciency and poor timing resolution at the positron side. Consequently,

CHAPTER 3. MEG II EXPERIMENT

Figure 3.6: Schematic of the MEG experiment• Low mass positron spectrometeris also required.

14

Branching ratio

CHAPTER 3. MEG II EXPERIMENT15

MEG 2009

10−11

Obtained 90% UL

MEGA

90% UL sensitivity
±1 σ
±2 σ

MEG 2011

10−12

MEG 2013
MEG Final

10−13
0

100

200
300
Accumulated DAQ days

Figure 3.7: Sensitivity improvement in MEG.

CHAPTER 3. MEG II EXPERIMENT

3.2

16

Muon Beam in MEG II

To achieve an unprecedented sensitivity of the µ+ → e+ γ search, the requirements for themuon beam are:• High intensity,• DC,• Low momentum muon
The key to a high intensity muon beam is using surface muon. This section will introduce
a beamline from generation of the proton beam providing muon beam to the area for MEG
II experiment. Overview of the beamline is shown in Fig. 3.8.

3.2.1

Proton Accelerators at PSI

Muon beams in PSI originate from the protons. The proton acceleration in PSI is suitablefor production of high intense low momentum muon beams. Several reactions are relevant
to generation of pions, which is the source of muons, such as p + p → p + n + π + , andp + n → n + n + π + . At least protons should have ∼280 MeV in the lab frame where
one of the protons is at rest for these pion generation processes. Beyond the energy
threshold of the pion generation, the cross section increases continuously with the energyof the protons. Furthermore, when the proton energy is beyonds ∼580 MeV, double pion
creation, such as p + n → p + n + π + + π − and p + p → n + n + π + + π + , can occur.
On the other hand, the pion generated from higher energy proton beam tends to havelarger kinetic energy. Concerning low momentum muon production, the production peakis obtained around 500 MeV of proton energy [18].
PSI proton accelerator pushes up the proton energy to 590 MeV. There are three stagesof the proton accelerators before the muon production. At the beginning Cockcroft-Walton
pre-accelerator generates protons from a hydrogen source and accelerate them up to 870
keV. The pre-accelerated protons are injected into a separate-sector isochronous cyclotron
called Injector II , which consists of four magnets and two main RF cavities (∼ 400 kV)
and two third-harmonic cavities (∼30 kV) [19]. The picture is shown in Fig. 3.10. This
first cyclotron delivers 2.4 mA beam to the main ring cyclotron by accelerating energy
up to 72 MeV. The second cyclotron is composed by five cavities including four main RF
cavities and eight magnets (schematic is shown in Fig. 3.12), and accelerates the beam up
to 590 MeV and provides 2.2 mA beam, that is 1.3 MW beam. Frequency is 50 MHz andbunch width is 0.3 ns.

3.2.2

Muon Production and πE5 Beamline

The accelerated protons reach to two graphite target, Target M and Target E, sequentiallyand the rest protons (∼70%) arrive the Spallation Neutron Source target or a beam dump.
Thickness of target M is 5 mm and that of target E is 40 mm along beam axis and theyrotate to avoid being heated too much by high energy proton beam. They are attachedseven beamlines having variety momentum and intensity and providing pion, proton, andmuon beams. In the targets, pions are produced as discussed above and generate muonsby π + → µ+ νµ decay. The lifetime of a pion is ∼ 26 ns at the rest and that of muon is
2.2 µs, while the pulse of the proton beam is 20 ns. Therefore produced muon beam is
DC beam eﬀectively. Since πE5 beamline providing the highest intensity muon beam in
the seven beamlines, it is employed for MEG II experiment.

CHAPTER 3. MEG II EXPERIMENT

17

Figure 3.8: Overview of Beamlines in PSI. (1) Cockcroft-Wolton injector. (2) Injector. (3)590 MeV Ring Cyclotron. (4) Target E. πE5 area is encircled in red.

CHAPTER 3. MEG II EXPERIMENT

Figure 3.9: Cockcroft-Wolton linear accelerator [20]. It is the first stage of the
proton acceleration. Condensers linked
by orange bars produce the charge accumulation only upwards.

18

Figure 3.10: Injector2 [21]. Magnets areturquoise-colored and silver-colored staﬀs inter magnets are resonators.

πE5 beamline is the most backward beamline with respect to the primary proton beamfrom Target E. The angle is 165◦ , which is tuned for surface muon [23] originating frompion stopping ”skin” of a production target and decaying at rest. Muons generated frompions at the rest have monochromatic momentum of 29.8 MeV/c and are ∼100 % polarized.
The muons with small momentum can be stopped easily on a thin target. Componentof πE5 beam line is shown in Fig. 3.15. It consists of bending magnets, quadrupoles,
hexapoles, and slits. They determine momentum and/or acceptance. Behind the second
bending magnet AST momentum flux of Fig. 3.13 is obtained. Enhancement of µ+ flux
around 29.8 MeV/c is shown in the figure. 1 In MEG II sub-surface muon is also used.

3.2.3

Beam Transport System after πE5 Beamline

After πE5 beamline, there is the transport system to a stopping target in the MEG
II detector. It is composed by first quadrupole triplet magnet (Triplet1), a cross-field
separator (Wien-filter), second quadrupole triplet magnet (Triplet2), and Beam Transport
Solenoid (BTS) as shown in Fig. 3.15. The two set of magnets and the separator separate
between surface muons and positron contamination from Michel decay or pair creation ofa photon from π 0 decay in the production target. In front of MEG II detectors the final
adjustment of muon momentum is performed by BTS.

3.2.4

Beam Intensity in MEG II

In MEG II beam intensity increases to ∼7×107 µ+ /s, which is two times higher that in
MEG, 3×107 µ+ /s. The intensity in MEG is much lower than the maximum ability ofπE5 beam line, ∼ 108 . Positron spectrometer in MEG could not tolerate high rate hits, so
it limited the beam intensity. A beam blocker decreased the intensity. Development of thedetectors in MEG II enables us to utilize almost full beam ability. Though backgrounds
1
Negative pions are captured by nuclei before their decaying. Therefore no peak can be observed innegative muon flux.

CHAPTER 3. MEG II EXPERIMENT

19

Figure 3.11: Picture of Ring Cyclotron
Figure 3.12: Schematic of main ring cyclotron in PSI [22]also increases as Eq. 3.7 with higher beam intensity, they are also reduced by detector
development.

3.2.5

Muon Stopping Target in MEG II

Muon stopping targets is placed at the center of COBRA magnet. It is required to perform
high muon stopping eﬃciency with low material to avoid multiple scattering of emitted
positrons, photon conversion from RMD, and background photon yield from positron
bremsstrahlung, or annihilation in flight (AIF). Moreover for target alignment reconstruction of the positron vertex is required. In the MEG experiment polyethylene/polyester
target is placed with slant angle of 20.5◦ and the target has six holes as shown in Fig. 3.16
to reconstruct vertex and check the target alignment. However they found the deformationof the target and it could not be monitored or corrected. Since reconstructed positron
trajectory is projected on the target plane, the deformation makes a large error of positron
direction. As a result in MEG largest systematics error of 13 % came from the deformationin their final result while the total contribution from the other items is less than 1 % [1].
Therefore the target in the upgraded experiment MEG II should be mechanically stable
and monitoring system is also needed.
For the new target several materials are tested as shown in Tab. 3.3 [24]. In thesematerials a scintillator plate is a strong candidate, because it is large advantage that thebeam intensity and profile can be measured by catching scintillation light by CCD camera.
It was already tested and sub-millimeter level of beam image was obtained.
To monitor the target deformation photogrammetric monitoring is planned and tested.
Dots are printed on target and monitored by CCD camera. The picture is shown in
Fig. 3.17. Furthermore laser survey by putting low-mass cubic ball on target frame, andcoordinate measurement machine are also planned.

CHAPTER 3. MEG II EXPERIMENT

20

10 11
10 10

-1 -1

N (mA s )

10 9
10 8
π+
πmeasured pointsµ+µmeasured points

10 7
10 6
10 5
10 4
0

20

40

60

80

100

120

140

160

P (MeV/c)

Figure 3.13: Muon and pion flux in πE5Table 3.3: The parameters of candidate target [24]. Inclination angle are set 15.0◦ anddegrader thickness is 350 µm.
Material
Thickness Thickness Density Stop Eﬃciency
Multiple Scattering
(µm)
(X0 )
(g cm−3 )(%)(mrad)+µ [18MeV] e+ [52MeV]
−4
CH2
140
2.8×10
0.893
83
52.0
3.0
−4
Be
90
2.6×10
1.848
83
49.3
2.9
Mylar
100
3.5×10−4
1.390
84
58.5
3.4
−4
Scint. PVT
130
3.1×10
1.032
84
54.5
3.2
Diamond40
3.3×10−4
3.515
81
56.8
3.3

CHAPTER 3. MEG II EXPERIMENT

Figure 3.14: PiE5 Beam line

Figure 3.15: Beam transport system

21

CHAPTER 3. MEG II EXPERIMENT

Figure 3.16: Target in MEG. There Figure 3.17: Scintillator target with marking
are six holes for vertex study and for monitoring.
target alignment.

22

CHAPTER 3. MEG II EXPERIMENT

3.3

23

Detectors

COBRA
superconducting magnet

Liquid xenon photon detector(LXe)

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

Cylindrical drift chamber(CDCH)

Figure 3.18: MEG II overview

Overview of the MEG II detectors is shown in Fig. 3.18. The global coordinates in MEG II
are defined with the target center as the origin; z is along the beam direction, y is assigned
an axis from bottom to top direction, and x is the rest axis in the right-handed rectangularcoordinate. A muon is stopped on target placed at center of the COBRA coordinate. We
also define the θ as the polar angler from z-axis, and the ϕ as an azimuthal angle.
A muon is stopped on the target and emits a gamma-ray and a positron in the signal
decay. The gamma-ray is detected by a liquid xenon (LXe) photon detector. Position andtime on first interaction point with LXe, and energy of gamma-ray are measured. It is
C-shape detector which acceptance to whole solid angle is ∼11 %. On the other hand, apositron is bent by a special magnet called COBRA and measured by two detectors, wire
drift chamber (DCH) and timing counter (TC), which acceptances cover the positrons
emitted to opposite side from the gamma acceptance region. The DCH reconstructs
positron trajectories, which is propagated to target plane and reconstruct the vertex andthe direction on the target, while time of positrons is reconstructed by TC which consistsof plastic scintillator with photo sensor readout. Flight time of photon to the interaction
point in the LXe photon detector is reconstructed by the positron momentum and vertex
reconstructed by DCH.
The overall concept of MEG II as described above is similar to that of MEG, so we reuseCHAPTER 3. MEG II EXPERIMENT

24

the COBRA magnet and liquid xenon, and its cryostat. By contrast, the performance ofevery detectors of LXe, DCH, and TC are upgraded, especially DCH and TC are replacedwith quite new ones. Furthermore a new detector, radiative decay counter (RDC), which
idea is based on the background study in MEG is installed in the MEG II experiment.
To reduce the background photon originated from RMD, a low momentum positron from
RMD is tagged by RDC. In following sub sections, we will get into detail of each detector.

3.3.1

Positron Spectrometer

The positron spectrometer is one of most important detectors in MEG and MEG II. What
we should consider is high background rate from Michel decay following the momentum
distribution as shown in Fig. 3.4. The positron spectrometer should survive in the highrate environment. In MEG the unique magnet called COBRA was developed. The nameis abbreviation of COnstant Bending RAdius. The magnet forces for the same momentum
positron to have the same radius independent on its incident angle and sweep the positronaway out of detector region quickly. Fig. 3.19 describes the principle of the COBRA
magnet and the power of the background reduction is shown in Fig. 3.20. Owing to
COBRA the hit rate in drift chamber region is decreased. Only the positrons having
signal momentum reach to detectors and remain hits in only twice or three times turn.
The trajectory of the bent positron is measured by drift chamber typically in the first or
second turn and then the positron time is measured a positron timing counter composedof plastic scintillator readout by photo sensors typically in the second turn. The measured
timing on the timing counter is translated to the time on a vertex by subtracting the flighttime between the timing counter and the vertex, which reconstructed by DCH.
In the MEG II experiment, we reuse the COBRA magnet. On the other hand, totallynew detectors are installed as a drift chamber and a timing counter. Upgrade conceptof the positron spectrometer is shown in Fig. 3.21. In MEG positron scattering between
DCH and TC made the eﬃciency and timing resolution of positron worse than expectation.
The positron detection eﬃciency was 30 % while it was expected to be 65 %. The timing
resolution was 107 ps which is composed of TC resolution of 76 ps and the flight time
resolution of 75 ps. In MEG II, we will reduce the material between DCH and TC to
avoid scattering by employing a single volume DCH unlikely the MEG DCH, which wasmoduled. As a results the contribution of the flight time reconstruction is expected to be
reduced down to 15 ps.

CHAPTER 3. MEG II EXPERIMENT

25

Figure 3.19: Principle of COBRA magnet. The region colored by yellow is detector
region. Normal solenoid magnet a positron hits a detector many times (a), while the
COBRA magnet sweep it away quickly (c). Positrons with diﬀerent emitting angles havediﬀerent bend radius in the field of a solenoid magnet (b). COBRA magnet bends thesame momentum positrons in the same radius (d).

Figure 3.21: Schematic of MEG and MEG II positron spectromenter.

Here, detailed description of the COBRA magnet and the drift chamber will be givenrate(Hz/cm2 )CHAPTER 3. MEG II EXPERIMENT

26

5

10

104

3

10

Uniform B-field

102
COBRA B-field

10

1
0

DC region

5

10

15

20

25

30
radius(cm)Figure 3.20: Michel positron rate (/cm2 ) as a function of radius in the COBRA magnetic
field with comparison to that in uniform magnetic field. The muon stopping rate is
assumed 3×107 /s which corresponds to the rate in MEG.

and the brief concept of the upgrade of the timing counter will be shown and the next
chapter will take over in detail.
COBRA Magnet
The COBRA magnet is a super conducting magnet which consists of two central coil, two
gradient coils, and two end coils. Each coil has diﬀerent radius and length as shown in Fig.
3.22. Since photon should penetrate the magnet wall to the LXe detector, the wall should
be as thin as possible, which is 0.197 X0 equal the penetration of 85 % signal photons.

CHAPTER 3. MEG II EXPERIMENT

27
�����������������

������������
�������������
��������������
��������������

���������������
��

Figure 3.22: Schematic of COBRA magnet.

Bz (T)

Its magnetic field is 1.27 T at the center and decreasing down to 0.49 T with |z| increase
as shown in Fig. 3.23. However PMT for LXe photon detector loose their gain with strong
magnetic field of more than ∼50 Gauss. Therefore compensation coils is also placed asshown in Fig. 3.22. Fig. 3.24 shows the magnetic field in the experiment site, which is
successfully reduced by the compensation coils.

1.2
1.1

Compensation coil1
0.9
End coil

0.8[Tesla]

0.7
0.6
0.5
0

Gradient coil
Central coil

0.2

0.4

0.6

0.8
1
1.2
Distance along axis (m)Center of magnet

LXe Gamma-ray detector

Figure 3.23: Profile of the COBRA mag- Figure 3.24: Contour of the magnetic
field around photon detector.
netic field.

Drift Chamber
Structure
A tracker in MEG II is single volume wire drift chamber. Sketch of the DCH structure isshown in Fig. 3.25. Inner radius is 17 cm, and outer 29 cm. Length is optimized to avoid
multiple scattering between DCH and TC which was the reason of poor positron detection

CHAPTER 3. MEG II EXPERIMENT

28

eﬃciency in the MEG experiment. In case of the MEG II DCH, as indicated in Fig. 3.26,
DCH endcap has largest eﬀect on eﬃciency of TC and longer DCH, more than 180 cm, isbetter for the eﬃciency as shown in Fig. 3.27. In conclusion, we decided 191 cm length.

Figure 3.25: DCH structure.

Figure 3.26: Dependence of TC hit counton z coordinate with several DCH material in MC. DCH length is fixed at 90 cm.

Figure 3.27: TC hit count dependence on z
coordinate with several DCH length. Lengthis written as active length of DCH.

The volume of the DCH is enclosed by a carbon fiber support structure for outerradius, aluminum Mylar foil for inner radius to separate from target region filled withR
spacer (see Fig. 3.29)
pure helium, and end-plate attached PCB for wires and PEEK⃝
for outer along z-coordinate. The end-plate are helm shape gold-plated aluminum ones
with 30 mm thickness as shown in Fig. 3.28.

CHAPTER 3. MEG II EXPERIMENT

Figure 3.28: Picture of end-plate.

29

Figure 3.29: Picture of end-plate with
PCB and spacer during wiring each layer
by using fixing tool shown in top of thepicture.

Wire Configuration
The DCH consists of 13056 wires and low mass mixed gas of helium and isobutane (C4 H10 )in the ratio of 90:10. These materials correspond to ∼ 1.58 × 10−3 X0 of radiation lengthfor single turn. As shown in Fig. 3.31, the wires compose 10 drift cell layers each ofwhich divided into 12 sectors per 30◦ . We employ alternating stereo angles for wiring. In
Fig. 3.30 configuration of stereo angle is drown. The stereo angle can be written as,εi = arctan(2ri
sinαi ),
L

(3.17)

where stereo angle is εi in ith layer; L is DCH length; αi is angle projected to end-plate; andri is radial position of a wire. We choose α = 30◦ , therefore the angles are approximatelyfrom 6.0◦ to 8.5◦ at several radii. The sign of the stereo angles are chosen both of positive
and negative to make two criss-crossing planes, which allow to reconstruct position alongz-axis precisely. The size of single cell is almost square from 6.6 mm to 9.0 mm dependingon the radius. The center of the cell is sense wire made of gold plated tungsten whichdiameter is 20 µm and silver plated aluminum field wires with 40 µm diameter surroundthe sense wires.
Status
DCH is now being prepared towards 2018 run. However during DCH construction we foundbroken wires several times (totally 14 wires are broken) from July to September in 2017
due to chemical contaminants in wires. The contamination induced the wire corrosion,
which was accelerated by tension. After finding the problem we decided to loose the wire
stretching from +4 mm to +3.5 mm. In addition, since humidity also influences chemical
reaction strongly, that of small volume around DCH is controlled down to 20 % against
wire broken, while before that humidity in only whole clean room was controlled down to
60 %. In parallel we are planning construction of second DCH with alternative wires. Its
financial support is already secured and study on wire is on going. However first DCH will
be installed to check all the procedures for its operation. Wiring of first DCH was stopped
after finishing 9th layer in February 2018 by accepting eﬃciency reduction of ∼10 % whichis expected by MC study. First one will be installed by end of July.

CHAPTER 3. MEG II EXPERIMENT

30

Figure 3.30: Schematic of stereo angle (εi ) of wire in ith layer. L is DCH length; li wire
length; αi angle projected to end-plate; and ri radial position of a wire

Timing Counter
The timing counter (TC) measures the positron time after DCH tracks the positrons.
It placed outer DCH and inner COBRA both of the upstream (US) and the downstream(DS). The TC is segmented by 512 counters in total. Fast plastic scintillator in TC detects
the positron and its scintillation light is read out by the 12 SiPMs attached at the both end.
The size of the single scintillator counter is 120×40×5 mm3 or 120×50×5 mm3 dependingon the position. It is totally new detector from MEG which used the 30 scintillator bars
(40×40×800 mm3 ) attached two PMTs at the both ends. As a result, we can overcome
the higher positron hit rate on the TC. The next chapter will explain the TC in detail.
StatusTC construction and installation were completed in November 2017. Its engineering run
with full counters and laser calibration system was also curried out. In following threechapter the detailed result will be discussed. Maintenance of dead fibers and counters is
on going towards run in 2018.

CHAPTER 3. MEG II EXPERIMENT

Figure 3.31: Configuration of cells in the drift chamber at z = 0.

31CHAPTER 3. MEG II EXPERIMENT

3.3.2

32

Photon Detector

Photon are measured by LXe as scintillator in the MEG and the MEG II experiment,
not by a magnetic spectrometer reconstructing converted electron-positron pair. In the
LXe detector, 900 l of liquid xenon is surrounded by photo sensors as shown in Fig. 3.32.
As photo sensors metal diode photomultiplier tubes (PMT) are used for all the surfaces
in MEG, while in MEG II PMTs on inner face are replaced with silicon photomultiplier(SiPM). Fig. 3.33 is the design of the LXe detector and shows the definition of the six
faces of inner, outer, upstream, downstream, top and bottom. The development view withthe definition of the local coordinate system is described in Fig. 3.34. The inner face is on
the r = 67.85 cm and depth of the active volume is 38.5 cm.

Figure 3.32: Overview of LXe detector. Configuration of photo sensors is one in MEG.

Since photons convert close to the inner face, photo sensors on it are basically illuminated by direct scintillation light. The position and time of the conversion point arereconstructed by distribution of illuminated photo sensors nearby the point, while totalenergy are reconstructed by summing up all the surrounding photo sensors.
Liquid Xenon
Using liquid as scintillator has an advantage to be uniform and free from radiation hardness, and to be purified whenever it need. We can keep its performance. The advantagesof LXe scintillator are a lot more than that. Thanks to large atomic number of 54 andCHAPTER 3. MEG II EXPERIMENT

33

Liquid xenon
Top face
Upstream face
Level meter

Outer face

PMT
γ

γ

Stopping target

Stopping target

67.85cm1m

125.5 deg.
Inner face
Inner face

Outer face
Downstream

1m

Bottom face

Figure 3.33: Schematic of LXe detector with MEG configuration of the photon sensor.

high density (2.978 g/cm3 at 161.4 K), LXe performs large stopping power. Normally thephotons convert within ∼10 cm in the detector so we do not have to construct a huge
detector. Its light yield of ∼75 % of that of NaI is also great advantage, and its decay time
is fast, 45 ns. Since scintillation light produced via a excited dimer (Xe∗2 ) not via a excitedxenon atom (Xe∗ ) itself in LXe, the yielded light is not absorbed by LXe in principle.
On the other hand, there are two disadvantages to adopt LXe. The first is the diﬃculty
to keep it in liquid state. Fig. 3.35 shows the xenon phase diagram and indicates thatkeeping liquid state is allowed in a small temperature region around the atmosphericpressure. Therefore control of temperature to be around 165 K is essential. A cryogenic
system composed of vacuum-tight vessels is already promised in the MEG experiment. For
photon entering the LXe as much as possible, the entrance window is as thin as possible
to stand ∼3 atm and it is 0.075 X0 . A 200 W pulse-tube refrigerator developed for the
LXe in MEG was used [25]. Basically the cryogenic system in MEG is taken over to MEG
II. However due to increasing number of the cables from the detector for replacement with
SiPMs to be described in next sub section in detail, another refrigerator is added.

CHAPTER 3. MEG II EXPERIMENT

34
outer

top

100

downstream

upstream

80
60
40
20

v-axis148.6cm0

w-axis
inner

.5
38

58cm

cm

z

u-axisbottom96cm

Figure 3.34: Development view of LXe with local coordinate system.

Pressure [atm. absolute]

102liquid

10

solid

gas

1

10

−1

120

140

160

180

200

220

240

260

Temperature [K]Figure 3.35: Phase diagram of xenon.

LXe scintillation light of vacuum ultra-violet (VUV) is the second disadvantage to be
overcome. The VUV light, which wavelength is short (10-200 nm), is namely absorbedby the oxygen and nitrogen in the atmospheric air. The wavelength of scintillation lightfrom the excited xenon dinar is ∼175 nm, which is easily absorbed by contamination in
LXe detector, mainly oxygen and water. Therefore purification system is required. In
MEG purification system in liquid phase using molecular sieves and copper beads, andthat in gas phase with metal-heated getter were prepared. These systems succeeded toCHAPTER 3. MEG II EXPERIMENT

35

remove contaminations down to acceptable level of ppb order. They are re-used in MEG
II. As LXe handling system, a storage system which enable purification and transfer to beeﬀective and flexible was also developed in the MEG experiment and is re-used in MEG
II.
Photo Sensors
The requirement for the photon sensors are (1) to be sensitive to VUV, and (2) lessmaterial to prevent photon from interacting a PMT on inner face, (3) to work properin the low temperature. To satisfy them, new PMT (R9869) was developed by Hamamatsu photonics and MEG. The properties are summarized in Tab. 3.37 and the pictureis shown in Fig. 3.3.2. They chose the quartz window which is transparent for VUV light,
and Bialkali (K-Cs-Sb) for photo-cathode which is sensitive for VUV. Moreover to keep
the performance against low temperature, the photo-cathode has aluminum strips which
avoid the sheet resistance increasing. In MEG the 846-PMTs are installed on every LXesurrounding faces.
Figure 3.37:(R9869).

Properties of LXe PMT

Size
Active are size
PMT Length
Photo-cathode material
Dynode type
Number of dynode
Typical HV
Figure 3.36:
Picture of PMT
Typical gain
(R9869) for LXe detector
Typical quantum eﬃciency
Rise time
Transit time
TTS

57 mm ϕ45 mm ϕ32 mm
K-Cs-Sb
Metal channel
12
900 V
1×106
15 %
2 ns
12.5 ns Typ.
0.75 ns Typ.

In the upgrade to MEG II, we replace all PMTs on the inner face to SiPMs. As shownin Fig. 3.34, because of round shape of PMTs there were large interval of 63 mm among
PMTs on inner face while diameter of photo-cathode is 46 mm. This non-uniformity of the
PMT coverage made event-by-event fluctuation of the eﬃciency of the scintillation lightcollection as shown in Fig. 3.38. In shallow events the eﬃciencies were quite diﬀerence
between events where a photon interacts close to a certain PMT (event A in the figure),and does on a intermediate point among PMTs (event B). This non-uniform response
deteriorated the energy and position resolutions of shallow events as described in Fig. 3.40
and as red markers in Fig. 3.39, even though oﬀ-line correction partially recovered thedeterioration. Therefore in upgrade the SiPMs are employed to improve uniformity for
detection of scintillation light and achieve higher granularity as shown in Fig. 3.41. Moreover SiPM is not sensitive magnetic field while gain of the PMT decreased with magnetic
field as described in Fig. 3.42. Though magnetic field around LXe is reduced down to∼50 Gauss, it deteriorated PMT performance. Less material property of SiPMs than thatof PMT is also an advantage, which improves the detection eﬃciency of the photons 9 %.

CHAPTER 3. MEG II EXPERIMENT

36

Figure 3.38: Eﬃciency of scintillation light collection.

Figure 3.39: Position resolution along v-axis (left) and u-axis (right) in MEG (red marker),and MEG II (blue marker).

Figure 3.40: Energy PDFs for signal gamma energy. The distribution of shallow (w <2 cm) events (left) is larger than that of deep (w ≥ 2 cm) events (right) in MEG.

CHAPTER 3. MEG II EXPERIMENT

37
1200

100
80

100

60

80

40

60

20

40

0

20

494

203

84

0

34

-20
14

-40
-60

5

-80
2

-100
-100

0

100

200

300

z

1
1200

100
80

100

60

80

40

60

20

40

0

20

494

203

84

0

34

-20
14

-40
-60

5

-80
2

-100
-100
z

0

100

200

300
1

Figure 3.41: Example of an photon event with a pile up in MEG (top) and in MEG II(bottom) in MC. Because of higher granularity by SiPMs, the image of the photon becomes
clear and the pile up is clearly separated from signal photon.
The development of the photo sensors is most challenging thing in the LXe detector
upgrade, while the control system of LXe is already confirmed in the MEG experiment.
What to be overcome are poor VUV sensitivity and small size of commercial SiPM. First,
as discussed above, SiPMs should be sensitive to VUV light. We chose the p-silicon on
n-substrate (p-on-n) type of SiPM which has higher performance for blue light region thann-on-p type. However the materials in front of sensitive area of the SiPM is not optimized
to the VUV and loose photon detection eﬃciency (PDE). By optimizing a protection layer
and anti-reflection coating layer which decreased the PDE, we achieve the PDE higher than
15 % from measurement with photons from α source. The performance which is similar
with MEG PMT (∼16 % quantum eﬃciency), is enough to upgrade LXe detector because
the 50 % larger sensor coverage of SiPM increases the total statistics.
Second problem is small size of SiPM. Largest size of commercial one is 6×6 mm2 , but
limited number of the readout channels does not allow such a small SiPM to cover whole
inner face. However a larger SiPM is faced with such problems as higher dark current
rate, larger non-uniform gain, and larger sensor capacitance which causes longer tail andlarger noise. To solve these problems, a 12×12 mm2 SiPM composed of four 6×6 mm2
SiPMs is developed as shown in Fig. 3.43
The other properties of new SiPMs for LXe have been studied to make sure keeping
their performance in high rate and low temperature environment.

Relative output [%]CHAPTER 3. MEG II EXPERIMENT

140

38

x-axisYZy-axis120

z-axis

X

100

80

60

40

20

0
-300

-200

-100

0

100
200
300
Magnetic flux density [ Gauss]

Figure 3.42: PMTs gain dependence on magnetic flux density.

Figure 3.43: Drawing of SiPM for LXe.

Status
The construction and installation of the LXe detector is completed in 2017. Though thenumber of the read out channels is limited due to the delay of the mass production of theelectronics, the pilot run is successfully performed at the MEG II beam line.

3.3.3

Radiative Decay Counter

The radiative decay counter (RDC) is newly installed in the MEG II detector to reduce thephoton background. As described in Sec. 3.1.2 the dominant background is the accidental
coincidence between a positron from Michel decay, and a photon from AIF and RMD. The
expected ratio of the photon background is shown in Fig. 3.44. Due to the reduction of
the DCH material in MEG II, the photon originated from AIF is expected to be reducedin the simulation study. Therefore RMD should be the dominant source of the photon
background. When the photon from RMD has a high energy of more than 48 MeV, whichbecomes the background, a low momentum positron of 1-5 MeV is also emitted. RDC
detects this low momentum positrons. According to simulation study, the sensitivity ofCHAPTER 3. MEG II EXPERIMENT

39

the MEG II experiment will be improved by 15 % by RDC.

Figure 3.44: Fraction of photon background source.

DesignThe schematic of RDC is shown in Fig. 3.45. RDC is placed downstream on the beam axis
because in the COBRA magnetic field the bending radii of the low momentum positrons
are smaller than 6 cm. By taking the coincidence with the LXe detector, we can identify
the background photon as shown in Fig. 3.46. Moreover to distinguish the RMD positrons
from the Michel positrons, which does not emit any photon, the energy is also measured
by RDC. The energy distribution of RMD positron and Michel positron at RDC is shownin Fig. 3.47. The Michel positrons tend to have higher energies than the RMD positrons.

Figure 3.45: Conceptual drawing of RDC.

CHAPTER 3. MEG II EXPERIMENT

40

fraction (%)

1

10−1
10−2

10−1

10−3
10−2

10

10−4
10−5

−3
−9

×10
0

10

20

30

40

10

20

T RDC - T γ (s)

30

40
50
Energy (MeV)

Figure 3.46: Distribution of relative time Figure 3.47: Expected energy distribubetween the RDC and the LXe detectors tion in RDC from RMD positrons which
in MC. Time resolution of 100 ps is as- photon energy is more than 46 MeV(red) and Michel positron (blue).
sumed.

Fig. 3.48 shows the design of RDC. The RDC detector composed of two parts, 12
plastic scintillator bars for the timing measurement in front and 76 LYSO (Cerium-doped
Lutetium Yttrium Oxyorthosilicate) crystals for the energy measurement behind.
The detailed schematic view of the scintillator bars is shown in Fig. 3.49. SiPMs(S13360-3050PE Hamamatsu Photonics) readout the scintillation light from the several
size (7-19 cm length, 1 or 2 cm width, 5 mm thickness) of the plastic scintillator bars
wrapped a 65 µm thick reflective sheet (ESR from 3M). Using the beta-ray from 90 Srsource, the time resolution of ∼90 ps is obtained in each bar.
Because of the high light yield, LYSO crystal is suitable for the energy measurement.
Tab. 3.4 shows the properties of the LYSO crystal. Fig. 3.50 shows the picture of LYSO
crystal wrapped with ESR film. Each LYSO crystal is a 2 cm cube and attached one
SiPM (S12572-025 from Hamamatsu Photonics) on the downstream side of the crystal bya spring. This calorimeter part of RDC is also measured with 60 Co source and the energy
resolution is ∼6 % for the 1 MeV photon for all the crystals.
Table 3.4: Properties of LYSO crystal [26]Density
7.4 g/cm3
Radiation length 1.14 cm
Decay constant
42 ns
Emission peak
420 nmLight yield
3 × 104 photons/MeV

Performance
The construction of the full RDC detector was completed. It was installed and tested atthe πE5 beam line. By using 16 BGO crystals attached PMT as the substitute of the LXedetector, we obtained the RMD peak in the relative time distribution between the photons
and the positrons as shown in Fig. 3.51. Moreover the energy is also successfully measured

CHAPTER 3. MEG II EXPERIMENT

41

Figure 3.48: Overview of RDC design. Height and width are ∼22 cm.

by the LYSO part as shown in Fig. 3.52. The red colored histogram in Fig. 3.51 shows thetime distribution after rejecting the event in which the energy measured by LYSO is morethan 4 MeV. By this cut the background is reduced to ∼1/10 while the RMD event is to∼1/3. The optimization of the trigger threshold and more sophisticated analysis such as
likelihood analysis will develop the identification of RMD.
StatusAs described above, RDC is ready for the physics run and the ability of the RMD tagging
is demonstrated. Furthermore, upstream RDC is under consideration. It is more challenging because RDC in upstream is exposed to the high intensity muon beam. One of thecandidates is a synthetic diamond detector. It has fast signal, and high radiation resistance. Assuming the 100 % detection eﬃciency of the upstream RDC, the enhancementof the sensitivity is expected to be 10 %.

3.4

Trigger and Data Acquisition

In the MEG experiment the raw waveforms from the detectors are obtained for eﬃcientoﬀ-line analysis. The digitizer was developed in PSI, which is Domino Ring Sampler(DRS) [27]. While the performance of the electronics should be kept in MEG II, the totalchannels increase with the usage of SiPMs and the finer cells of the DCH. Moreover thesignal of the SiPMs is smaller than that of PMTs which were mainly used in the MEG
experiment. Therefore the amplifiers are also required in the new electronics with flexible
amplification to satisfy the necessity of the several detectors.
To deal with increase of the channels and SiPMs, the electronics is redesigned. Fig. 3.53
shows the comparison of the design of the electronics in MEG and MEG II. The trigger
and DAQ system becomes compact in MEG II by rejecting the active splitter between theCHAPTER 3. MEG II EXPERIMENT

42

Figure 3.49: Schematic view of scintillator bar attached SiPMs for time measurement.

Figure 3.50: Picture of LYSO crystal
wrapped by reflector.

350

300

250

10

h_Elyso
Entries 15447
Mean
7.664
RMS
8.182

3

200

102

150
100

10

50

0
− 20

−9

−15

− 10

−5

0

5

×10
10
15
20
T RDC - T BGO - offset (s)

0

5

10

15

20

25

30

35
40
E (MeV)

Figure 3.51: Distribution of relative time
Figure 3.52: Energy distribution meabetween the RDC and the BGO detecsured by LYSO crystal
tors.

trigger line and DAQ line in MEG and by integrating the basic trigger, DAQ functionalities, high voltage chip, and amplification onto the same board called WaveDREAM board(WDB) developed in PSI.
In MEG II the WaveDAQ crate is also developed. It is a 3 HE 19” crate with 18 slots tosatisfy the requirement of Gbit links, common high voltage source, and the concentrators
for the trigger, the clock to correct the jitter, and the data. The Crate Management Board(CMB) is placed in each crate, and generates the crate power of 24 V with 359 W andstand-by power for a shelf manager. Furthermore CMB controls and monitors the slow
control in MEG II based on MIDAS (Maximum Integration Data Acquisition System) [28]which was used in MEG successfully.
Each crate also has 16 slots for WDBs each of which has 16 channels, and two of
so-called concentrator boards of the Trigger Concentrator Board (TCB) and the Data
Concentrator Board (DCB) to operate the trigger and DAQ at the same time. TCB isalso used the higher hierarchy of the trigger as a Master board (see Fig. 3.53 again). The
MEG II experiment use the 39 crates in total including the global trigger boards.

CHAPTER 3. MEG II EXPERIMENT

43

The MIDAS controls the whole of the system. The raw data from the detectors are
stored in the MIDAS file.
PMT
DC

PMT
SiPM
DC

Crate
Chip

Board

PC
HV
DRS

Type 1
Trigger
Board

Type 2
Trigger
Boards

ADC

DRS

FP
GA

ADC

WaveDREAM
Board

LV

ADC

FP
GA

DRS
Board

TRG
Conc

FP
GA

T2

LV

DAQ
Conc

Inter
face

T2

HV

TRG
Conc

Inter
face

TRG
Conc

PC

PC

PC

PC

Figure 3.53: Schematic view of TDAQ electronics overview.

3.4.1

WaveDREAM

Fig 3.54 shows the schematic view of the WaveDREAM. It contains an amplifier and a
waveform shaper. We can select the flexible gain from 0.5 to 100, and shape the waveform through a programmable pole-zero cancellation. One WaveDREAM has two DRS4
chips connected to two 8 channel ADCs. They digitize the waveform with the maximum
sampling speed of 5 GSPS with 1024 cells. The out put of the ADCs are transmitted to
Field-Programmable Gate Array (FPGA), which treats trigger algorithms.
MCX
TRG IN
Temperature sensors 1-Wire®

MCX
TRG OUT

previous channel

Attn.
:2

Input

Attn.
:1,2,4

x10

DAC
DAC

Comp
C

PHY

Trigger

offsetDAC

Shaper

x10

x2

DRS4

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

ADC

XTAL
calibration

SiPM

next channel

PLL
(LMK)

RAM

FPGA

Input

... 2 x 8 channels ...

RJ45

PoE optional

x2

DRS4

DC

DC in
24 V

DC
power on

DAC

24 V

RGB

BUS

SPI

ADC
SPI

DAC

HV Piggy-back
58-63V58-63V

5 V DAC

58 V

Comp
C

Trigger

Temp

PROM

CockroftWalton
TR BUS CLK

DC
+24V

DC

Osc.

En

HV
ON

LVDS

MCX
CLK INMCXCLK OUT

Figure 3.54: Schematic view of WaveDREAM board.

CHAPTER 3. MEG II EXPERIMENT

44

The bias voltages for SiPMs are also generated in the WaveDREAM board by a
Cockcroft-Walton (CW) voltage multiplier. Moreover a simple 5 V DAC is mounted
after the CW to allow the channel-by-channel biases from +0 V to +5 V. The accuracyof the high voltages is below 1 mV. The currents are measured with a resolution of 1 nA.

3.4.2

Synchronization

The synchronization system with ultra-low jitter has been developed for MEG II. The timereference clock is generated by an ancillary board which provides the DCB in WaveDAQ
crate. In the WaveDAQ crate the DCB distributes the master clock to the WDBs via
the dedicated clock signal distributer having a jitter cleaner (LMK03000 from Texas Instruments). We performed the jitter less than 10 ps at the input of WDB. Moreover foroﬀ-line synchronization the clock pulse itself is readout in WaveDREAM.

3.4.3

TriggerWith increase of the beam intensity, the trigger in MEG II is required suppressing backgrounds to make the trigger rate of 10 Hz or less for the eﬀective DAQ and the reductionof the overall data size. Since DCH signal is too slow to be used for the trigger, the LXedetector and TC are used. The observables reconstructed on-line are the photon energy,
the relative time of the photon and the positron, and the opening angle. These algorithms
are implemented in FPGA.
In the LXe detector, the summing waveform over 4×4 SiPM patch is transmitted tothe trigger system as a single detector. The photon energy is obtained by summing up
the signal amplitude taking into account each photo-sensor gain.
The relative time is reconstructed from the on-line time of TC and LXe. The photon
time is reconstructed from the patch of SiPMs with the correction of time walk. In MC
study, the on-line photon time resolution is expected to be 284 ps with requirement of morethan 45 MeV for the photon energy. On the other hand, the positron time is extracted
from the single counter of TC which is placed at most inner z in all the hit counters. The
time is obtained by averaging the raising times of two channels in the single counter withthe correction of the track length from the target to the counter. Since we do not use theDCH information for the trigger, the online time resolution includes the diﬀerence of the
track length for each positron turn, which is 2-3 ns for each.
Thanks to the pixelated design of TC and higher granularity of LXe in MEG II, we
can select the events more tightly from the opening angle view point by preparing thelook-up table for the correlation of the position distribution between TC and LXe.

3.5

Current Status of MEG II

We completed the construction and installation of almost all the detectors in the MEG II
experiment except for DCH. In summer 2018 DCH will be installed and full engineering
run will be started in 2019 toward the physics run.

3.6

Timing Measurement

The theme of this thesis is the timing measurement. The distribution of the relative
time between the photon and the positron measured in MEG is shown in Fig. 3.55 [1].
The time of the accidental background distributes uniformly in the time window, while

CHAPTER 3. MEG II EXPERIMENT

45

that of the signal makes a peak. Therefore, as written in Eq. 3.7, the resolution of therelative time between the photon and the positron reduces background lineally. The timing

Figure 3.55: PDFs of the relative time between positrons and photons with the data
spectra for the full dataset in MEG [1]measurement in MEG was limited by the positron spectrometer. LXe photon detector had
the time resolution of 67 ps, while the time resolution of the positron spectrometer was
107 ps. As described above, in the MEG II experiment, the measurement of the flight time
between TC and the vertex will improve to 15 ps by reducing the material between DCH
and TC. Therefore, the time resolution of the timing counter will be dominant contribution
to the timing measurement of the positron. Its development is essential.

Chapter 4

Timing Counter
The time of the positron is measured by the timing counter (TC) as described in Chap. 3.
The positron time on the vertex is reconstructed by subtracting the path length reconstructed by the drift chamber (DCH), which is placed in front of the TC, from the timeon the TC. Since the DCH signal is too slow to be used as a trigger, the TC signal also
takes a role as the trigger signal of the positron side. The TC is pixelated by scintillator
counters readout by SiPMs. This fine segment design improves for the timing measurement significantly. This chapter will explain the concept and design of the timing counterfor the MEG II experiment in detail. Furthermore the detailed quality of the counters andthe operation system including the calibration system, and the slow control system will
be described.

4.1

Requirement

In MEG II the time resolution of the positron side should be improved to be comparable
or better than that of the photon side. In MEG II the time resolution of the photon side
is expected to be 50–70 ps. Therefore the time resolution of ∼40 ps is required for thetiming counter.
In the MEG experiment a timing counter was composed of 30 scintillator bars (80 × 4 ×
4 cm3 ) with PMT readout. It achieved ∼70 ps time resolution and led the MEG experimentto success. However, the resolution was worse than the expectation (40 ps) obtained fromresults in beam tests due to a large variation of the reconstructed hit positions on thebars, a degradation of the PMT gain in magnetic field, poor time calibration among thebars, the electronics jitter, and the eﬀect of pile up hits.
Furthermore, the hit rate on the timing counter is increased with planned increasingof the beam intensity in MEG II. In MEG a PMT had signal event at 1 MHz. In the MEG
II environment it will be 2 MHz, which corresponds to one pile up in every event in the
DAQ time window. A new positron timing counter should operate at this hit rate.

4.2

Concept

The concept of a new timing counter in the MEG II experiment is a finer segmented
counter to overcome these issues. We realize the timing counter by using a new photon
sensor, silicon-photomultiplier (SiPM), which is a compact (1–6 mm square) and highgain (105 –106 ) photon sensor. Furthermore, SiPM is not aﬀected by magnetic fields. By
employing the SiPMs, the timing counter can be pixelated with smaller plastic scintillator.

46

CHAPTER 4. TIMING COUNTER

47

Thus, a signal positron is measured by several counters, which results in better resolutions
than that in MEG.

4.3

DesignW = 50 mm

W = 40 mm

Figure 4.1: Timing Counter Overview
The positron timing counter consists of two sectors: one on the downstream (DS) andthe other on the upstream (US) of the target, which are mirrored each other. They aremounted between the drift chamber and COBRA magnet , and in 23.0 < |z| < 116.7.
Its coverage along ϕ direction is −165.8◦ < ϕ < 5.2◦ to match the photon acceptance of
the Xe detector, . One sector of positron timing counter consists of 256 counters, each ofwhich is composed of a fast plastic scintillator plate (120×40/50×5 mm3 ) and 6 siliconphotomultipliers (SiPMs) at each end. The six SiPMs at each end are connected in series
to obtain sharper signal. Signals from the counters pass through long PCB (∼80 cm)
called back plane on which counters directly connected. At the end of the PCB the signals
are transmitted by non-magnetic coaxial-cable (RG178) to WaveDREAM, in which thesignals are amplified and shaped by pole zero cancellation.
The overall counters configuration and size are optimized for better experimental sensitivity in MC. Fig. 4.2 shows the counter configuration in which the 16-counters are placedwith the interval of 5.5 cm along z in each 16 ϕ line at 10.3◦ interval. Each two ϕ line isstaggered to maximize positron detection eﬃciency. All counters are tilted at 45◦ so that
positrons from the target penetrate the counters perpendicularly. Fig. 4.3 shows a typicalsignal positron event. The distribution of the incident angles of the signal positrons to thecounters is shown in Fig. 4.4.

CHAPTER 4. TIMING COUNTER

48

3030*
Φ

10
0

- 10
- 20

- 30
- 40

- 50
- 60
- 70
- 80

- 90

- 100

- 50

0

50

100
z (cm)

Figure 4.2: Counter configuration. Two counters with 40 mm (red) and 50 mm (blue)
height are used.

Figure 4.3: An example of typical signal
positron event in MC. Signal positrons
enter counters perpendicular.

4.3.1

Figure 4.4: Districution of incident angles tocounters

Multiple Hit Principle

Thanks to the pixelated design, a signal positron hits several counters as shown in fig.
4.5, which is a typical signal event. Fig. 4.6 shows the number of TC hits from a signal
positron in MC simulation, and the average is 8.8 hits.
The overall time resolution is described as a function of the number of hits (Nhit ),2
σtotal(Nhit ) =2
22
σsingle+ σinter-counter+ σelec

Nhit

2
+ σMS
(Nhit ),

(4.1)

where σsingle is a single counter resolution; σinter−counter is miss time alignment among thecounters; σelec is electronics jitter; σMS is the eﬀect of multiple scattering,∑Nhit2
n=1 (n − 1)σMSsingle
2
σMS (Nhit ) ∼
,
(4.2)
Nhit
where σMSsingle is time spread after a positron passes through one counter, and is several
pico seconds with a 5 mm thickness counter. The eﬀect of jitter and miss time alignment
become small by measurement with several counters, thus the overall time resolution is

CHAPTER 4. TIMING COUNTER

49

5
0

0

−5

−5

y
x

−10 −10−15 −15−20 −20−25 −25−30 −30−−30
30 − 25 −−20
20 − 15 −
−10
10

0
0
− 10
− 20 −10− 30− 40 −20− 50− 60 −30− 70− 80 −40
− 90

−5

00

10

20

30

80

90 100 110 120

φ

−50

z

−60
−70
−80
−100

−50

0

0

10

20

30

40

50
50

60

70

100

Figure 4.5: A typical signal event in MC. The magenta circles show hits on counters andthe cyan line is a trajectory of a signal positron. The top figure is x-y view, and thebottom is z-ϕ view. The trajectory in 28 ≤ r ≤ 38 cm is described in z-ϕ view.

improved. The estimation of the overall resolution from these formula is showed in fig.4.7.
It indicates resolution improvement with a large number of hits.

4.4

Single Counter Design

Concept of single counter design is explained in this sub section. The picture of the single
counter with definition of counter local coordinate is shown in Fig. 4.8. We defined thecoordinate along length, width, and thickness as (v, u, w), and on both ends along length
6-SiPM-arrays are attached.
The optimized components for single counter are summarized in Tab. 4.1. The resolution depends on photon statistics. Fig. 4.9 shows energy deposit dependence of theresolution. A fast rise time is also required to obtain the ultimate timing resolution below
hundred pico-second because scintillator rise time is typically several hundred pico-seconds.

4.4.1

Scintillator

Ultra-fast plastic scintillator is used. The time resolution is aﬀected by photon statistics
and rise time, which require large light yield, long attenuation length and fast rise time to
scintillator. Since there is trade-oﬀ between these properties as summarized in Tab. 4.2,

Mean

50

8.807

0.1

Resolutions (psec)

Probability

CHAPTER 4. TIMING COUNTER

80
60
40

0.05
20
0
0

2

4

6

8

10 12 14 16 18 20
Number of Hit Counters

Figure 4.6: Number of hits from signal
positron in the same turn.

0
0

2

4

6

8

10 12 14 16 18 20
Number of Hit Counters

Figure 4.7: Overall resolution as a functionof number of hit counters

Figure 4.8: Conceptual drawing of single counter

we tested several types of scintillators. The results are also written in Tab. 4.2 and countermade from BC-422 performed best with respect to time resolution. Compared with MEG
the size of single detector is small, and that allows for faster rise time scintillator to havegood performance against its short attenuation length.

4.4.2

Size

The size is optimized to acquire the best time resolution concerning trade-oﬀ between
single counter resolution and the number of hits of a positron with the limited number ofreadout channels. With regard to single counter, a smaller counter has better resolution.
Along length, a longer counter has a worse resolution because of attenuation of scintillation
light. Along height, a shorter counter increases SiPMs coverage to scintillator surface,which results in better resolution than a taller counter. Several size of counters were
tested and the result is shown in Fig. 4.10 [32].
However the overall TC resolution also depends on the number of hits from a signal
positron, not only single counter resolution (to be explained in detail in next subsection).
A larger counter can cover the TC acceptance region with smaller space among counters
and increase the number of hits, and, furthermore, eﬃciency. These eﬀects are studied bysimulation. In particular, height of the counter is well-optimized. Though signal positrons
are concentrated around r ∼ 30 by COBRA magnet, spread of the distribution depends

CHAPTER 4. TIMING COUNTER
Components
Plastic Scintillator
Size of Scintillator
Reflector
SiPM
Number of SiPMs
Connection of SiPMs

51

OptimalBC-422120×40/50×5 mm3enhanced specular reflector (ESR)
ASD-NUV3S-P-High-Gain
12 (6 on each end)
seriesManufacture
Saint-Gobain–
3M
AdvanSiD––

Time resolution (ps)Table 4.1: Summary of single counter components optimized by comparison test.

102
90
80

ASD
HPK

70
60
50
40
6×10−1

2

1
E TC (MeV)

Figure 4.9: Resolution dependence on the energy deposit. Scintillator is BC418 (SaintGobain) with 90×40×5 mm3 . Two type of SiPMs, S10943-2547(X) from HAMAMATSU(Red), and NUV Type from AdvanSiD (Blue), are used. [29]Table 4.2: Properties of ultra-fast plastic scintillators from Saint-Gobain. The properties of
BC-404, which was used in the previous timing counter bar, is also shown for comparison.
Properties
BC-418 BC-420 BC-422 BC-422Q BC-404
Light Outputa) (% Anthracene)
Rise Timea) b) (ns)Decay Timea) (ns)Peak Wavelengtha) (nm)
Attenuation Lengtha) (cm)Time Resolutionc) (ps)

67
0.5
1.4
391
100
48 ± 2

64
0.5
1.5
391
110
51 ± 2

55
0.35
1.6
370
8
43 ± 2

19
0.11
0.7
370
8
66 ± 3

68
0.7
1.8
408
140
–

a)

From Saint-Gobain catalogue [30].
Those values are dominated by the measurement setup. The intrinsic values are much faster. For
example, a BC-422 rise time of <20 ps was reported in [31].
c)Measured value in [32] with 60×30×5 mm3 sized counter read-out with 3 HPK SiPMs (S10362-33050C) at each end.
b)

on z as shown in Fig. 4.11. Hence we found that optimal height is 50 mm for |z| <∼ 70 cm

Resolution (ps)

CHAPTER 4. TIMING COUNTER

52

80
50 mm wide
70

40 mm wide
30 mm wide

60

50

40

30

60

80

100

120
Length (mm)Figure 4.10: Resolution dependence on scintillation sizeand 40 mm for |z| >∼ 70 cm. In spite of the optimized value, we chose 40 mm-heightcounters for |z| <∼ 40 cm because of the space limitation from the COBRA magnet.
Counter configuration is shown in Fig 4.2.

4.4.3

SiPM

Silicon photomultipliers (SiPMs) are photon-sensors for reading out scintillation light. In
principle a counter with more SiPM readouts has larger coverage bringing better time
resolution because of increase of photon statistics. However because of a constraint of
the number of readout channels (∼1000), all SiPMs on each side of the counter has tobe combined to one channel. Both connection schemes of parallel and series are tested
and the resolutions are shown in the right figure in Fig. 4.12. As shown in the left figure
in Fig. 4.12, waveform from SiPMs connected in series becomes sharper than the others,
because total capacitance with series connection becomes smaller than that of individual
SiPM while that with parallel becomes larger. The waveform analysis is optimized at eachpoint. (AppendixB)
The scintillation light is in the near-ultraviolet (NUV) range. Therefore the SiPMs for
TC should be sensitive to NUV light. The SiPMs based on p-on-n diode are sensitive to
the NUV light. We tested the p-on-n SiPMs developed by several manufactures. Fig. 4.13
shows the results. The SiPMs of HAMAMATSU Photonics have the best performancefor the time resolution because their photo detection eﬃciencies are highest in the tested
SiPMs. It also indicates that the time resolution depends on photon statistics.
On the other hand, we also confirmed that increasing the number of SiPMs improves
timing resolution as shown in Fig. 4.14. The number of SiPMs per counter is limited bycost. Therefore the final design of the single counter is decided on the basis of the balance
between cost and quality of the SiPMs. Finally we adopted the 6-series AdvanSiD SiPMs
per one side of the counters.

CHAPTER 4. TIMING COUNTER

53-R (cm)e+ trajectory
0
200

-5

180
-10
160
-15

140

-20

120

-25

100
80

-30

60
-35
40
-40

20

-45

-100

-50

0

50

0

100
z (cm)

e+ trajectory-R (cm)

900

-5

800
-10

y (cm)

e+ trajectory
0

400
30
350
20

300

700
-15
600

10

250

0

200

-10

150

-20
500
-25

400

-30

300

-35

200

-40

100

-45

-150

-100

-50

0

50

0
φ (deg)

100

-20

50
-30
-30

-20

-10

0

10

20

30
x (cm)

0

1

3-SiPM Parallel
Single SiPM

0.8

3-SiPM Series

0.6

Resolution (ps)Normalized signal amplitude (arb. unit)

Figure 4.11: Accumulated positron trajectory.

100

Parallel

90

Series
80
70

0.4

60

0.2
50

0
0

20

40

60

80
100
Time (ns)123Over Voltage (V)Figure 4.12: Connection comparison with test counter made from 60×30×5 mm3 BC422
scintillator attached 3 Hamamatsu Photonics SiPMs (S10362-33-050C). Averaging waveforms with several thousand events are shown in left figure [32]. They are normalized bytheir amplitudes. The resolution comparison between parallel and series connections is inright figure in which over voltage is written as that for one SiPM.

Resolution (ps)

CHAPTER 4. TIMING COUNTER

100

54

S10362-33-050C
S12572-025C(X)PM3350 prototype-A
MicroFB-30050-SMT

90S12572-050C(X)
3X3MM50UMLCT-B
ASD-NUV3S-P-50

80
70
60
50
40
30

2

4

6
8
Over voltage/SiPM (V)Resolution (ps)Figure 4.13: Time resolution dependence on manufactures. Scintillator is 60×30×5 mm3of BC422. Three SiPMs are attached at both ends of scintillator.

100
90
80
70
60
50

3-Series

40

5-Series
6-Series

30
3

3.5

4

4.5
5
5.5
6
Over voltage/SiPM (V)Figure 4.14: Time resolution dependence on number of SiPMs. BC422 scintillator of sizeof 90×40×5 mm3 attached 3, 5, and 6 AdvanSiD SiPMs (NUV3S-P-50) in series.

CHAPTER 4. TIMING COUNTER

4.5

55

Property of Single Counters

In this section, properties of the single counter will be described. Before single counter
assembly, each component of the counters such as SiPM, SiPM array, and scintillator istested. Selecting better stuﬀ by the tests, mass production of the counters is performed.
Finally we confirmed the counter property such as time resolution and position dependenceby mass test for all the counters.

4.5.1

Measurement of Single Counter Resolution

We started mass production of the counters in 2014. Before that scintillators and SiPMs
are tested separately. Here the basic test set up for scintillator, SiPM, and assembled
counter is shown before showing each result in detail.
Test counters are irradiated by β-ray from 90 Sr sources whose energy is < 2.28 MeV andintensity is 250 kBq or 3.7 MBq. Intensity is tuned to be the same by changing the distanceof the source. Set up is shown in Fig. 4.15. By triggering with hits (Edeposit > 0.5MeV)
on a small reference counter (5×5×5 mm3 ) placed behind of a test counter, only electrons
penetrating test counter is selected. In MC mean of energy deposit in the test counter
is estimated to be 0.95 MeV. The scintillator of the reference counter is BC422 wrappedin Teflon tape, and one SiPM (HAMAMATSU, S10362-33-050C) is attached. The signal
is propagated by 7.4 m coaxial cable to an amplifier developed in PSI and then reaches
DRS4 digitizer. The circuit of amplifier is described in Fig. 4.16. It is voltage amplifier,and also takes a role of a pulse shaper in which pole-zero cancellation is applied for signal
to be sharper. Via the amplifier bias voltage is applied to SiPM arrays by picoammeters(KEITHLEY 6487 PICOAMMETER/VOLTAGE SOURCE).

Figure 4.15: Single counter test set up.
In analysis to select the high energy electron from the source, a charge cut in reference
counter is applied. The resolution is estimated from the distribution of the time diﬀerence
between the test counter and reference counter. The resolution of the reference counter
is estimated to be 30 ps. Subtracting the reference counter resolution, the resolution of atest counter is obtained.

4.5.2

Scintillator

We obtained 400 scintillator plates of 120×50×5 mm3 and 600 plates of 120×40×5 mm3 by
cutting 7 original plates. We observed that each scintillator plate has diﬀerent light yield

CHAPTER 4. TIMING COUNTER

56

Figure 4.16: Circuit of amplifier developed in PSI.

and the resolution of the counter made of the lower light yield plate was worse as shown in
Fig. 4.17. The test set up obtaining the figure is the same as described in Sec. 4.5.1, andtest scintillators were attached to the same SiPM array by optical grease. Since it takes
too much time to check the resolution of all scintillator plates, one side measurements as
described in Fig. 4.18, in which only current readout by SiPMs is checked, are performedat room temperature. The measured currents clearly correlate to the time resolutions asshow in Fig. 4.19. The resolutions of the other original plates are also distributed from60 to 100 ps for 4 cm-height-counters, and from 70 to 110 ps for 5 cm-height-counters.
Therefore selection of scintillator plate bases on the one-side measurement by choosing inorder from the high current plates.

Figure 4.17: Correlation between signal amplitude and resolution with several scintillator
plates (120×40×5 mm3 ) from two original plates. In all measurement of these plot thesame SiPM array is used.

CHAPTER 4. TIMING COUNTER

57

Figure 4.18: Set up for testing the scintillator light yield by SiPM current.

Figure 4.19: Correlation between the resolution measured in counter test set up, and thecurrent from one-side measurement. The size of scintillator is 120×40×5 mm3 (right) and120×50×5 mm3 (left) scintillators from two original plates).

4.5.3

Silicon Photo MultiplierSingle SiPMs
We used two types of SiPM (ASD-NUV3S-P High-Gain(MEG), and ASD-NUV-SiPM3SP) from AdvanSiD, because the production line of the first type (Type 1) was closed. For
almost all counters the first type is used, but SiPMs for 40 counters are second one (Type2). IV curves are measured for all of single SiPMs. The results of type 1 is shown in
Fig. 4.21. We found two diﬀerent IV behavior in the first version of SiPM though theirbreak down voltages are stable as shown in Fig. 4.20. 45.5 % of Type1 SiPMs show fasterbrow up of the current than the others because the former has the larger dark current.
Fig. 4.22 shows the current at over voltage of 3.05 V. Some group (Type1-1) have lower
dark current, but that in the other group (Type1-2) spread in wide range. Therefore
optimal operation range of HV for Type1-2 is narrower than that for Type1-1. On theother hand, the current of Type 2 (ASD-NUV-SiPM3S-P) with voltage increases slowly
which allows wider operation voltage range as discussed in the next section.
Array of SiPMs
Six SiPMs for an array are chosen to have close current at over voltage of 3 V. The
selected SiPMs are soldered to the PCB designed for TC shown in Fig. 4.23. A non-

CHAPTER 4. TIMING COUNTER

58

800

600

Mean

24.39

RMS

0.03427

400

200

0
24

24.2

24.4
24.6
24.8
25
Break Down Voltage (V)Figure 4.20: Breakdown voltage of all Figure 4.21: IV curves of all the single
SiPMs of Type 1.
the single SiPMs of Type 1.

magnetic connector is also soldered to a PCB. Three types of the PCB are prepared forstraight for 4 cm-height-counter and 5 cm-height-counter, and L-shape for the countersinstalled inner step of COBRA due to limited space.
IV measurements of the SiPM arrays are also performed for the all arrays. To extract
the maximum performance of SiPM arrays, the optimal bias voltage is decided based on
results of counter bias scanning with several SiPM arrays. Basically the optimal bias
voltage is decided by a trade-oﬀ between signal-to-noise ratio and dark current of SiPM.
On one hand, low bias voltage makes signal amplitude low and then noise aﬀects theresolution to be worse. On the other hand, high bias voltage increase the dark current
which also makes the resolution worse. Therefore the optimal voltage depends on theenvironment. Though we should tune the optimal voltage in the real experiment site,
we performed bias scanning in a diﬀerent room, which is more quiet than the MEG II
experimental site, to decide the nominal operation bias. Fig. 4.24 shows the result withType 2 SiPM whose resolutions are stable over bias voltage from 3 to 5 V. It meansthat even if the noise becomes large the best resolution can be kept. On the other hand,Type 1 has steeper IV curve, which result in a narrow optimal range of the bias voltage
especially Type 1-2 as shown in Fig. 4.25. Therefore optimal voltages should be decided
one by one. After the counters were assembled, bias dependence of the resolution with 16
counters with Type 1 SiPMs were measured as shown in Fig. 4.26. As a result from fitting
the dependence with the quadratic function of a × (v − p)2 + q, where v is over voltage,
optimal range is obtained by defining it as a region where the time resolution is within 2
ps from the best value as shown in Fig. 4.27. Since the common region lays in a current
range from 3 µA to 5 µA, finally operation voltages are adjusted to the same current pointof 4 µA in IV curve.
The variation of SiPM performance is not small as shown in Fig. 4.28. It can bechecked by the one-side measurement in Fig. 4.29 same set up of scintillator quality checkbut by checking its signal amplitude not its current because it depends on each SiPM
IV behavior. The result is shown in Fig. 4.30 and we observed the fluctuation of thelight yeild. The resolution variation of 5 cm-height-counter is expected about 74-92 ps forexample. Though we observed such a large variation of the performance, due to limited
number of SiPMs almost all SiPMs are used for the counters. Combinations of two SiPM
arrays for each counter are chosen to have similar properties such as IV curve and signal

Current @3.05 OV (µA)

CHAPTER 4. TIMING COUNTER

59

25
20
15
10
5
0
0

1000

2000

3000
Production Number

Figure 4.22: Current at OV 3̄.05 V. Saturated point of the IV measurement is 25 µA.

Figure 4.23: PCBs for SiPM arrays. Three types are prepared for 5 cm height (top), 4 cm
height (middle), and L-shape (bottom)

amplitude in one-side measurement.

Resolution (psec)

CHAPTER 4. TIMING COUNTER

60

90
80
70
60
50
40
2

3

4

5
6
Over Voltage (V)Figure 4.24: The resolution dependence Figure 4.25: The resolution dependenceon bias voltage of Type 1-1 and Type 1-2
on bias voltage of Type 2 SiPM.
SiPM.

Figure 4.26: The resolution dependence on bias voltage of Type 1 SiPMs. They are fit
with a × (v − p)2 + q where v is over voltage.

CHAPTER 4. TIMING COUNTER

61

Figure 4.27: The optimal point and range as a function of current in IV curves. Coloredband describes common optimal range over all 16 counters.

Figure 4.28: Resolution and amplitudeof the counters with several SiPM array Figure 4.29: Correlation between signal
attached to the same scintillator plate amplitude from the one-side measure(120×50×5 mm3 ).
ment and the resolution.

CHAPTER 4. TIMING COUNTER

62

Figure 4.30: Signal amplitude in one-side measurement. SiPMs. Half of all SiPM arrays
are measured. Red line shows the result of SiPMs for 4 cm-height counters; blue line for
5cm; and green line for L-shape.

CHAPTER 4. TIMING COUNTER

4.5.4

63

Single Counter AssemblySingle counters are assembled one-by-one by hand. Optical cement (BC600) is used toattach the SiPM arrays to the scintillator. To remove void in the cement, it is evacuatedand heated. The schematic of the assembly tool is shown in Fig. 4.31. Taking into accountvariation of thickness of scintillators, SiPM position is adjusted to be on the center of thescintillator. After SiPM attachment, scintillator is wrapped by the reflector and then thebar for the fiber insertion and the thermal links made of aluminum are attached. At theend, the fibers are installed and light shielding is completed. For the shielding polyvinylR
fluoride film (Tedlar⃝) and black tape are used. These process is summarized in Fig. 4.32.

Figure 4.31: Schematic of assembly tool (Left) and its picture (right).

Figure 4.32: Picture of assembled counters.

Detachment Problem
We found detachment between scintillator plate and SiPM array as shown in Fig. 4.35
after the pilot runs in 2015 and 2016. In particular, a lot of 5 cm height counters had thedetachment as shown in Fig. 4.33 and a lot of detached SiPMs are located the bottom or
the top as shown in Fig. 4.34. The possible reason is the distortion of the SiPM arrayas described in Fig. 4.36. The mismatch between the counter interval and the connectors
on support structure causes the force to peel oﬀ the SiPMs. We also find that once small
air-gap appears it is easy for SiPM to be detached.

CHAPTER 4. TIMING COUNTER64

In the last pilot run in 2017 the precision of the support structure was improved (seeSec. 4.8 in detail). Moreover to strengthen SiPM array mechanically against the distortion,
additional optical cement is put between some SiPMs and the top and bottom of the arrayas described in Fig. 4.37. The scintillator surface where the additional optical cement is
put is scratched with a thin jig-saw to reinforce the adhesiveness.

Figure 4.33: Number of detached coun- Figure 4.34:
Location of detachedters which have more than one detached SiPMs. Numbering is in the order from
SiPM.
the bottom.

Figure 4.36: Schematic drawing of distortion which induces detachment of
Figure 4.35: Picture of SiPM detach- SiPMs.
ment.

Fiber Insertion
Fibers for laser calibration are inserted to 432 counters which are all counters except forthe counters at the inner COBRA step. Since the calibration is sensitive to the amountof inserted light, the fibers need to be inserted stably. A hole is drilled on bottom of thescintillator for the fiber tip. The fibers are fixed by special screws fixed in the bar whichis placed at the bottom of the counters as shown in Fig. 4.39. The schematic of the screwis shown in Fig. 4.38.

4.5.5

Single Counter Performance

The final performance of the counters are measured with β-ray from 90 Sr source as explained in Sec. 4.5.1. The time resolutions from this measurement is summarized in

CHAPTER 4. TIMING COUNTER

65

Figure 4.37: Schematic of additional treatment against detachment.

Scintillator

1.0 mm
1.9 mmFibre

fibre end
(Ceramic, 1.8 mm)

0.9mm
2.5 mm
7 mm

Screw

1.5 mmFigure 4.39: Picture of counter inserted
fiber.

Figure 4.38: Schematic of fiber insertion
method.

Fig. 4.40. The mean values of the resolutions are 72.35 ps and 80.70 ps for 4 cm and 5 cm
height counters, respectively.
Dead Counters
Out of ∼550 assembled counters, there are ∼20 dead counters except for mechanicallybroken ones by human error. One of the channels in the dead counters suddenly haveno current, no signal or small signal. Some of them are caused by the mechanical force
because when we pushed the SiPM array these channels worked properly from the output
current point of view. We rejected these counters and the other side channels are recycled
to the diﬀerent counters.

Counts

CHAPTER 4. TIMING COUNTER

66

50
4 cm height
40

Entries

325

Mean

72.35

5 cm height

30

Entries
Mean

20

204
80.7

10
0
40

50

60

70

80

90

100 110 120
Resolution (ps)Figure 4.40: Resolution distribution of single counters. Magenta line show that of 4 cm
height counter; Blue line, 5 cm.

CHAPTER 4. TIMING COUNTER

4.5.6

67

Radiation Hardness

Generally the radiation damage concerns the high energy physicist. It is known that SiPM
are damaged by heavy particles, gamma-ray, and charged particle such as electrons andpositrons. TC has the radiation damage from Michel positron at <100 kHz as discussed
in Chap. 7. Assuming the total DAQ time in the MEG II physics run to be 75 weeks, thetotal flux is estimated as 9.5 × 1011 e+ /cm2 . The radiation test is performed with a test
beam for Type 2 SiPMs and with 90 Sr source for Type 1 SiPMs. The time resolutions ofboth of the irradiated SiPMs are measured with the same set up as described in Fig. 4.5.1
at 30 degree. The resolution is estimated by the time diﬀerence between the reference
counter and the irradiated channel.
The irradiation by 90 Sr source is separated into 4 times. Since the flux cannot be
estimated directly, the increase of the SiPM current becomes the reference of the irradiatedflux. In the MEG II environment, the current increase is expected to be ∼100 µA. Fig. 4.41
shows the IV curves at the each irradiated point. The radiation damage increases the darknoise of SiPM as shown in Fig. 4.42 and Fig. 4.43, therefore the current increases with theradiation damage. The resolution degradation can be seen in Fig. 4.44 and Fig. 4.45.

Figure 4.41: IV curves of a SiPM array with irradiation.

On the other hand, the SiPMs of Type 2 are irradiated by the positron beam in
Beam Test Facility (BTF) in Italy. The resolutions after irradiation with the total flux of
1.1 × 1012 e+ /cm2 is shown in Fig. 4.46. Though the total flux is one order of magnitude
higher than the MEG II expectation, this resolution level of ∼140 ps is similar to the 1st
irradiation of Type 1 SiPMs as shown in Fig. 4.45. Therefore the radiation damage ofType 2 SiPM is not larger than that of Type 1 SiPM.
In conclusion, the radiation damage makes the resolutions of SiPM worse in the MEG
II experiment. However cooling reduces the dark current so eﬀectively the resolution
degradation by the radiation damage is reduced by cooling. Fig. 4.46 also shows the time
resolutions measured at 10 degree. It indicates that the resolutions improved by cooling
down to 10 degree. Therefore the cooling system for TC is installed as described in thefollowing section.

CHAPTER 4. TIMING COUNTER

68

Noise RMS (V)Figure 4.42: Waveforms in Sr radiation test. The top is waveform before irradiation, andthe total flux is increased to the bottom.

0.01

0.008

0.006

0.004

0.002
0

1

2

3

4
ith Measurement

Figure 4.43: Noise level with irradiation.

CHAPTER 4. TIMING COUNTER

Figure 4.44: Resolution vs current in
90 Sr radiation test. Each color indicates Figure 4.45: Resolutions with over voltthe diﬀerent applied voltage. Analysis is age with each irradiated point.
optimized at the each point.

Figure 4.46: Resolutions with over voltage of SiPMs irradiated by positron beam.

69

CHAPTER 4. TIMING COUNTER

4.6

70

Readout Electronics

Resolution (ps)The signals from the counters are propagated by BP and the 7 m coaxial cables and thenamplified, shaped, and digitized in WD as described in the previous chapter. From the
TC point of view, the time resolution is most important and set up of WD is optimized
to realize the best time resolution. In the WD pole-zero cancellation is applied, because
sharper waveform has better time resolution and the smaller tail can suppress pile up
eﬀect. Moreover the time resolution depends on the sampling speed of WD as shown in
Fig. 4.47. The sampling speed is limited by trigger and it is planned to be 1.8 GSPS.

60
58
56
54
52
50
48
46
2

3

4
5
Sampling Speed (GSPS)

Figure 4.47: Resolutions dependence on sampling speed.

4.7

Laser System

There are two methods for time calibration among counters to be discussed in detailin the next chapter. One method is the laser calibration in which split laser light isinjected to bottom of the counters. The overview of the laser system is shown in Fig. 4.48.
Limited space at the inner step of COBRA magnet does not allow all the counter to beequipped with fibers, so 432 counters out of 512 counters can be calibrated by the laser
calibration. Since the laser power is not high enough to be distributed to all the laser
counters simultaneously, an optical switch is used to separate the laser counters into 8
sectors. One sector has 50-60 laser counters. The laser light is supplied to the countersby the optical fibers via the two passive splitters which divide up the light among 64
fibers. After the optical switch placed outside of the experimental area, the laser pulse
is transmitted to the first splitter in the experimental area by the 10 m optical fibers
and then 2.5 m fibers distribute the pulse to the second splitters and the counters. The
laser synchronized pulse is also supplied to the DAQ electronics as the reference time tocalibrate the time oﬀset of each counter. To monitor the stability of the laser light, aphoto diode is prepared and its signal is also readout. The frequency of the laser pulse
and the optical switch are controlled via MIDAS system. To install the laser system inCHAPTER 4. TIMING COUNTER

71

the limited space, the splitter boxes and winding tool are prepared as shown in Fig. 4.49.
For the safety, the fibers are covered by tubes.

Optical fibre

Laser
head

1×2
Mode scrambler

PhotodiodeOptical switch

Photodiode signal

SYNC signal

Laser
controller

DAQ electronics

1×9

1×8

1×8
Optical splitter
Counter module

Counter signal

Figure 4.48: Schematic of laser calibration.

Figure 4.49: Picture of splitter box.

4.7.1

Time Oﬀset of Laser System

To subtract the intrinsic time oﬀset from the laser system which comes from the variationof the fiber length and amount of light of the splitter output, the oﬀsets from just after the
optical switch to the counters are measured in advance. The result is shown in Fig. 4.50.
The splitter output depends on the manufacturing batch, so in US the large fluctuation isobserved.

CHAPTER 4. TIMING COUNTER

72

[ns]

Toffset in laser mass test

60
58
56
54
52
0

100

200

300

400

500
PositionID

Figure 4.50: Time oﬀset in laser system. The diﬀerence of the splitter batch makes thefluctuation of the time oﬀset in US.

4.8

Assembly and Installation

4.8.1

Support Structures

The TC support frame with long PCB (948×25 mm2 ) called backplane (BP) are shown in
Fig. 4.51. The BP is fixed on the frame by screws. Counters are mounted to non-magnetic
connectors on the BPs and also fixed on the support frame by screws via the thermal links.

Figure 4.51: The picture of support structures. The backplanes are placed on support
frame.

Support Frame
The support frame is made from an aluminum cylinder to achieve high machining precisionbecause the prototype frame which made from a plate had unacceptable distortion. The
frame is composed of the 4 parts as shown in Fig. 4.52. Three parts are main part ofCHAPTER 4. TIMING COUNTER

73

TC, while the other is the frame for the counters at the inner COBRA step. The mainparts of the frame have the grooves to put the BPs. Fig. 4.53 shows xy view of the frame.
Backside of the frame also has grooves for cooling piles as described in detail later. The
frame also has screw holes to fix the counters via the thermal links and through holes toinsert the fibers for the laser system. Fig. 4.54 shows the backside of TC after finishingassembly. The cooling pipes and fibers are installed.

Figure 4.52: Picture of support frame. (1) Middle part (< ϕ <) in main part of the frame.
(2) Smaller (right) and larger (left) ϕ part (ϕ and ϕ). Small ϕ part is turned over. The
backside has groove for cooling pipe. (3) Frame for COBRA inner counters.

Figure 4.53: xy view of the main support frame.

Backplane
Fig. 4.55 is the picture of BPs and the drawing of the signal line in the BP is also shown in
Fig. 4.56. One BP is put along z and transmits the signals from the channels of one sideof 16 counters and two additional channels for thermometers and hygrometers (Sec. 4.9
in detail). We put 64 BPs on DS and US support frame. To reduce noise in the signallines, they are sandwiched with two guard layers as shown in Fig. 4.57. The BP has 18
layers and each of the three layers composed two guard layers and signal layer for threechannels. The schematic of the ends of the BP is shown in Fig. 4.58. The signals fromcounters at the inner COBRA step are transmitted by cables (RG178) to inner end of theCHAPTER 4. TIMING COUNTER

74

Figure 4.54: Backside of the support. Cooling piles and fibers fixed by tape are installed

BP. The every signal from SiPM arrays are output to cables (RG178) at the outer end of
the BP. Every connectors on BP are non-magnetic ones. The cables are 7.4 m long andtransmit the signal to the WaveDREAM in which the signals are shaped and amplified.

Figure 4.55: The picture of the backplane.

Figure 4.56: Signal lines of three channels in the backplane.

4.8.2

Counter Assignment and Assembly

The counter assignment is decided based on the property of the IV curves and the time
resolutions. As discussed above the radiation damage of the SiPMs increases the darknoise, which induces the resolution deterioration at the higher over voltage. As a result,the optimal range of the bias voltage defined in the previous section becomes narrower.
Therefore at the position having relatively higher rate of Michel positrons, the counterswith the smaller dark current SiPMs are assigned. All of Type 2 SiPMs, which have large
optimal range, are used for 5 cm height counter. Considering that the voltage can beapplied in the range of 4 V in one WD and the diﬀerence of the optimal voltage between
Type 1 and Type 2 is more than that, Type 2 counters are assigned to the positions withthe high Michel positron rate as shown in Fig. 4.59. In the Type 1 SiPMs, as discussed
above, Type 1-2 has larger dark current than Type 1-1 has. Therefore, the Type 1-1
counters are assigned to the higher rate positions as shown in Fig. 4.59. In the assignment

CHAPTER 4. TIMING COUNTER

75

Figure 4.57: Three layers of top (red), inner (blue), and bottom (green) layers.

by the type each counter is assigned based on its resolution. With the hit probability ofthe signal positrons expected from MC, the better resolution counters are assigned to thehigher probability position as shown in Fig. 4.60
Following the assignment of the counters, the counters are mounted one by one. The
counters with the straight shape of the SiPM arrays are fixed by the two thermal links
and the connectors as shown in Fig. 4.61 while the connectors are not used for the Lshape SiPM arrays as shown in Fig. 4.62. The overview of the assembled TC is shown in
Fig. 4.63.

4.8.3

Installation

TC is installed by the rail system as shown in Fig. 4.64. The support frame has thetwo groove for the rail system. By the system the maintenance work of TC is also done
independent of DCH easily.

4.8.4

Alignment

For the global alignment of TC to the MEG II coordinate, reference points are attachedon the TC support frame as shown in Fig. 4.65. The cube put on the reference points isviewed by laser tracker. On the other hand, for the internal alignment of the each counter,the top of the counters is scanned by 3D scanner.

4.9

Slow Control System

All of slow control system for TC is based on MIDAS system.

4.9.1

High Voltage Control

The high voltage control and the current monitor for TC SiPMs are implemented in the
MEG II MIDAS system. IV curves for all SiPM arrays are also obtained simultaneously
by the system.

CHAPTER 4. TIMING COUNTER

76

Figure 4.58: Drawing of the BP both ends of outer z side (left) and inner z side (right).

4.9.2

Temperature and Humidity Control

As discussed above, the dark current of SiPMs can be suppressed by cooling. Water coolingsystem is installed. The chiller (CustomChill, CRAL300-230PE) with 400 W cooling power
provides cooled water to the pipes which are placed backside of the support frame. The
water cools whole of the support structure and the SiPM arrays is cooled via the thermal
link, which touch the support structure. The cooling is possible to increase the humidityof TC. To avoid dewing, dry air is supplied.
The temperature and the humidity in TC are monitored via MIDAS system. Threethermometer are readout via one BP. Two of them are placed around the outer edge andmiddle point of the BP, and the other is on COBRA inner step. The sensor is 1-wire digital
thermometer (DS28EA00) which is a serial protocol used by single line. One hygrometer(HIH4000) is also attached on the middle of the BP.

CHAPTER 4. TIMING COUNTER

77

Figure 4.59: Counter assignment in US with Michel hit probability map. Each colored cellcorresponds to a position of a counter. The color shows the rate of Michel positron rate
scaled by the number of hits on the maximum hit counter. Numbers in the cell means thetype of Type 1 SiPMs; 1 means Type 1-1; 2 for Type1-2; and 1.5 for Type 1-1 and Type1-2 mixed counters.

Figure 4.60: Hit probability of signal positron which gamma is accepted in LXe region.
They are scaled by the number of hits of maximum hit counter. Written numbers are thetime resolutions measured in the mass test with 90 Sr.

CHAPTER 4. TIMING COUNTER

Figure 4.61: Picture of the assembled
Figure 4.62: Picture of the assembled
counter.
COBRA inner step counter.

Figure 4.63: Picture of overall view of TC.

78

CHAPTER 4. TIMING COUNTER

Figure 4.64: Installation of TC into COBRA magnet by rail system.

Figure 4.65: Reference point for global alignment.

79

Chapter 5

Timing Counter Analysis
5.1Time Reconstruction for µ → eγ Search

One of the physical quantities reconstructed in the µ → eγ search is Teγ ; which is thediﬀerence between reconstructed time of photon and positron (Tγ − Te ) on the vertex. As
discussed in Sec. 3.1, the precision of the time measurement is directly reflected in thesensitivity of the µ → eγ search. While the photon time is reconstructed by the LXephoton detector alone, the positron time is reconstructed by combining the informationof two detectors as,
Σn (tT C − li /c)
Te = i i− LDCH /c,(5.1)
nwhere i is a hit counter in TC when a positron hits n counters; li is the path length fromthe first hit counter in TC to the ith hit counter; LDCH is path length from vertex to thefirst hit counter in TC reconstructed by DCH; and tTi C is the time measured by the ith
counter in TC. Therefore the requirements for the TC analysis are• Precise time extraction from the individual counters,• Careful treatment of multiple hits,
Moreover though basically DCH reconstructs positron trajectory including li , there isroom for a further improvement by utilizing the TC hit positions which are able to recoverscattering eﬀects on the reconstruction of the path length. From these points of view, reconstruction and calibration algorithms have been developed. The detail will be discussed
in the following sections.

5.2

Reconstruction

Fig 5.1 shows overview of the positron reconstruction chain. At the beginning TC and DCH
reconstruct positrons independently. When DCH finds tracks after the hit reconstruction,
an initial time is needed and it is supplied by TC. On the other hand, the path length
among the hit counters in TC cannot be reconstructed by TC itself. Therefore the tracks
reconstructed by DCH is used in precise time reconstruction in TC. In this section, thetime reconstruction in TC will be focused on. The overall positron time reconstruction
will be discussed Chap. 8.

80

CHAPTER 5. TIMING COUNTER ANALYSIS

81

Figure 5.1: Overview of positron reconstruction chain.

5.2.1

Waveform Analysis(mV)

In the MEG II experiment, the raw waveform (Fig. 5.2) data of the detector signals aretaken so that we can directly analyze them to extract the signal time, charge, amplitude
and so on. At the beginning, peaks are searched for by setting a threshold. To avoid
double counting a pulse, only one maximum peak is found in a fixed local region of 10 ns.
To obtain the baseline of the waveform, at first, the amplitude at every sampling point
is put in a histogram and then the average around its mode is calculated as the baseline.
It is a stable way to get baseline against pile up and spike noise. The bin size of thehistogram and the region for the average from the mode is optimized to give the best time
resolution. The signal amplitude is defined as the diﬀerence between the found peak andthe calculated baseline. The signal charge is obtained by integrating the pulse for a fixedregion, 20 ns. To obtain the time, a digital constant fraction method is used. We define
the signal time as the time at a fixed ratio to the signal amplitude. The optimal ratio
depends on the signal shape and noise situation. Therefore, we optimized that in eachtest. Typically it is 20-30%. Depending on the noise situation, a moving average low passfilter is applied.

50
0
−50
−100
−150
−200
−400

−200

0
(ns)

Figure 5.2: Typical waveform from single counter.

5.2.2

Hit Reconstruction

A hit time and position in each counter are reconstructed based on the results fromthe waveform analysis in the two channels. Matching of signals in the first and second

CHAPTER 5. TIMING COUNTER ANALYSIS

82

channels is based on the signal time. If signal times in the two channels are in 4 ns, they
are regarded as a signal from the same hit. The hit time is defined as the average time of
the two channel times, that is,(tch1 + tch2 )
T =
(5.2)
2
where tch1 and tch2 are the reconstructed times in the first channel and the second channel
respectively. The hit position is also reconstructed from the times of the two channels. The
eﬀective velocity of light, vef f , in our counter is obtained formerly by position scanningwith a 90 Sr source as explained in the next chapter in detail. Using it the hit position canbe obtained asvef f (tch1 − tch2 )
x=
(5.3)
2
We also tried to use the pulse charges to reconstruct the hit position, but the position
resolution is worse than that of the former way because of a short attenuation length(8 cm) of the scintillator.

5.2.3

Clustering

Since a signal positron leaves several hits on TC and in parallel pile up positrons may
often hit TC, we should distinguish which hits belong to which positron. Moreover evenone positron is able to make a tail event when its second turn is small and hits on thesame counter hit in the first turn or its close counter, which is called double turn hits.
Two methods have been developed to make clusters of the same positron hits. One isso-called local clustering: this algorithm simply checks a hit in geometrically next counterfrom a counter having a fastest hit time, and make a chain to the next counters if a hit
in the next counter is found. Fig. 5.3 describes typical hit patterns. If one finds a hit,
these three patterns are all to be checked. In this process, a timing cut which rejects thehits far from the first hit more than 1 ns is also applied. In contrast, the other method
constructs clusters globally. As the fastest hit is a seed, this algorithm uses the correlation
between counter positions and time in the counters. We defined geometrical order whichis the order for a positron to hit as shown in the left figure in Fig. 5.4. The right ofFig. 5.4 shows the correlation between the geometrical order and the time. By fitting itwith a liner function, we obtained the slope. With the slope every hit time is projected asshown in Fig. 5.5 for an example. Peaks are searched for from the projected histogram,and become cluster seeds. A cluster consists of the hits in 1 ns from the seed time.

Figure 5.3: Schematic of three possible hit patterns.

We adopted the global clustering for the final analysis for the TC because it succeededin removing tail events as shown in Fig. 5.6 and 5.7 which is obtained with the dataobtained in a pilot run of TC described in Chap 7 in detail. The global clustering improves

CHAPTER 5. TIMING COUNTER ANALYSIS

83

Figure 5.4: Drawing of the counter geometry and hit order (left) and the correlation
between the order and time (right).

the time resolution as shown in Fig. 5.6 by reducing the tail events as described in Fig. 5.7
for an example.

5.3

Calibration

5.3.1

Timing Calibration

In the µ → eγ search, Teγ is reconstructed and time coincident events are searched for.
Therefore the coincident window should be known in advance. This global time oﬀset
between the positron spectrometer and the LXe photon detector can be calibrated by using
the radiative decay of muon, µ+ → e+ νe ν¯µ γ (see Tab. 3.1). The decay emits a photon anda positron simultaneously, and thus the peak from the decay in the Teγ window enables
us to calibrate the global time easily.
On the other hand, it is also important to calibrate relative time oﬀsets inter counters in TC. We use the following two methods. One is track-based calibration. In the
MEG II experiment we have abundant calibration source of positrons from Michel decay.
Subtracting known path length by simulation or reconstructed track by DCH, the relative
time oﬀset can be extracted. In addition, there is an advantage that even during the datataking we can check the time oﬀsets. The other method is laser calibration in which laser
light is injected into the counters simultaneously. The relative time oﬀsets can be obtainedby using the counter signal generated from the laser light. Short DAQ time for the laser
system (∼30 minutes) without a need for beam is an advantage of the laser calibration.
Since the track-based calibration need ∼ 2 days for obtaining enough data, the laser calibration is useful to monitor time dependence. These two methods are independent of eachother.

CHAPTER 5. TIMING COUNTER ANALYSIS

84

Figure 5.5: Explanation of the clustering with an example event. Correlation between geometrical order and measured time (top) and projected time distribution in the event. (1)The measured times are projected, (2) peaks are found in the projected time distribution
as seeds, and then (3) clusters are made within 1 ns width from the seeds.

Track-based Calibration
The relative time oﬀsets are obtained to minimize χ2 as,
event Nhit
χ2 = Σ N
Σj=1 (i

Tijmeas. − Tijexpec. 2
)
σ

meas.
Tijexpec. = Ti1+ T OFij + ∆Tj

(5.4)

(5.5)

where Tijmeas. is the measured time on the jth hit counter in the ith event, T OFij is time offlight from the first hit counter to jth counter, and ∆Tj is the intrinsic counter time oﬀset
which are the target to be known in the calibration. To calculate this, Millepede II [33] isused. It calculates the linear least squared with the local parameters that is event-by-event
parameters such as trajectories and the global parameters such as the counter time oﬀsets
simultaneously. The key of the track-based calibration is to estimate time of flight (TOF)
between counters which is basically given by DCH.

CHAPTER 5. TIMING COUNTER ANALYSIS

Figure 5.6: Resolutions dependence on
number of hits with and without global
clustering

85

Figure 5.7: Time distribution with 4 hitswith and without global clustering

Laser Calibration
The detailed set up is already showed in Sec. 4.7. The time oﬀsets are obtained relative
time to the time from laser synchronized pulser.

5.3.2

Position Calibration

The hit position is reconstructed by the time diﬀerence between the two channels as discussed above. The calibration of the two channels time oﬀsets is performed by comparing
the simulation and data. Simulated distribution of the hit position is shown in Fig. 5.8.

Figure 5.8: The distribution of the hit position on a counter. The green line show the original distribution and the black is after taking moving average. By convolving a trapezoid(blue and red lines) with Gaussian, the distribution of the hit position is fit.

5.3.3

Energy Calibration

The energy deposited into the counter by a positron hit is reconstructed by the pulse
charge. In principle, the time resolution of a single counter depends on the energy deposit
and including this dependence in the likelihood analysis for the µ+ → e+ γ search improves
the sensitivity of the experiment. Conversion factors from reconstructed charge to energy

CHAPTER 5. TIMING COUNTER ANALYSIS

86

deposit are calibrated so that the distribution of the reconstructed energy deposit fits tothat of the MC simulation described in the next section.

5.4

Simulation

The software for MEG II is composed of three parts, named gem4, MEGBartender, andMEGAnalyzer. The first one is for generating events and simulating any interaction in
our detectors. The second one takes the two roles of event mixer and waveform simulator.
The last one is analysis software for the output data from both of the real experiment andthe simulation.

5.4.1

Event Generation and Interaction

Events in the simulation are generated in gem4 based on Monte Carlo simulation software,
GEANT4 [34], written in C++. Muon decays of Michel, radiative, and µ+ → e+ γ are
prepared in gem4. We can choose the kinematic of these decays if needed. The event
generation also can start from the muon beam not from the decay on the target to simulate
the background from the beam. The starting point is -564.70 cm at the z-coordinate whichcorresponds to just after the last magnet of Triplet II (see Fig. 3.15). This is such thatthe collimator system is included.
Any interaction in our detectors is also simulated in gem4. The geometry and materials
in the experiment including degrader in BTS are implemented.
Simulation of Positron Track
The positron track and the secondary particles are simulated based on the tracking in
GEANT4. Interaction between the injected particle and material in the electromagnetic
such as bremsstrahlung, multiple scattering, and photo-electric eﬀect are included. Track
momenta and positions at each step are recorded and when a particle goes into a detector
sensitive volume step size becomes small to simulate detector response precisely. Once aparticle interacts with the volume, the hit information is also recorded.
Simulation of Interaction in TC
When a positron or a secondary particle reaches scintillator part of TC, scintillation photons are generated and they are tracked in the simulation. These processes take into
account the known scintillator properties which are amount of light yield, rise time, reflectivity, and attenuation length. If a scintillation photon reaches SiPM region, its timeis recorded. This information is used in the waveform simulation explained following
sub-section.

5.4.2

Event Mixing

To know the pile up eﬀects, MEGBartender is developed for MEG and MEG II. It
makes events mixture of diﬀerent type of events. For example we can simulate signal
events with Michel background events at a certain rate using output files of gem4.

5.4.3

Waveform Simulation

In MEGBartender, a waveform simulation including pile up is performed using theinformation from the optical photon tracking in gem4.

CHAPTER 5. TIMING COUNTER ANALYSIS

87

TC Waveform Simulation
Scintillation photons that reach a SiPMs are converted to a waveform signal based on the
response of the 6-SiPM-array which can be obtained from single photon data. However
the signal from a single photon is too small to measure because of the series connectionR
as explained in Sec. 4.4. Therefore an electronics simulation software SPICE (LTspice⃝
IV [35]) is used. The equivalent circuit to a SiPM pixel is described in Fig. 5.9. First wemeasured the response of a single SiPM from the single photon data to decide parameters
for the electronics simulation. Tab. 5.1 shows the used values in the simulation which
reproduce the measured waveform. Using these parameters the single photon output
from 6-SiPM-array is simulated by the SPICE. The distribution of the arrival time ofthe scintillation photons is convoluted with the single photon response. In this way, thewaveform from a counter is simulated. At the end white noise and noise originated from
SiPMs are added. The noise from SiPMs are also measured and the parameter values are
summarized in Tab. 5.2.

Figure 5.9: Equivalent circuits of pixels in a SiPM which are not fired (left) and fired(right). Rq is quench resistance, and its capacitance, diode capacitance and global stray
capacitance are written as Cq , CD , and Cg , respectively.

Table 5.1: Parameters for waveform simulation in SPICE.
Parameters
Rq1150 kΩCq
14.0 fF
CD
97.0 fFCg
141 pFCHAPTER 5. TIMING COUNTER ANALYSIS

Table 5.2: Measured parameters for SiPM noise.
Parameters
Dark Current Rate
1.4 MHz
Recovery Time185 ns
Cross Talk Probability
8.6 %After Pulse Probability
31.6 %
After Pulse Time Constant
115 nsDelayed Cross Talk Probability
22.6 %
Delayed Cross Talk Time Constant
86 ns

88

Chapter 6

Performance of Multiple Hit
SchemeWe performed several beam tests to confirm that multiple hits improve the overall resolution of TC. First, two beam tests in ideal environment were performed by using a beam
delivering positrons at a fixed momentum. Secondly, another beam test was performed
in high-rate environment to study the pile up eﬀect on the time resolution. In this chapter, we describe these beam tests and the results, which demonstrated the multiple hits
scheme. Based on the success of these beam tests, the design of TC such as counter design
and readout scheme, was finalized.

6.1

Multiple Hit Scheme in Clean Environment

We had the two beam tests to confirm the multiple hit scheme. In this section we focus
on the first test beam in 2013, since the obtained results is similar to that in the second
test beam from the multiple hit scheme point of view though the counter design and theelectronics are diﬀerent from those in the final configuration.

6.1.1

Set upThe beam test is carried out at the Beam Test Fasility (BTF) of the INFN Laboratori
Nazionali di Frascati in Italy [36]. The beam is monochromatic positron beam at 48 MeV,
which is similar to the signal positron energy of 52.8 MeV. There are 1–3 positrons per
bunch at 50 Hz. The beam spot is σx ∼15 mm and σy ∼5 mm as y is direction frombottom to top, z is the same as the beam axis, and the rest axis is x.
The schematic of the set up is shown in Fig.6.1. Prototype counters are placed on
the beam line and in front of the counters one or two time reference counters are also
prepared. The scintillator of the prototype counters is 90×40×5 mm2 BC418 from SaintGabain Crystals wrapped in a reflector of 3 M radiant mirror film. We prepared counterswith two types of SiPMs: eight counters with S10943-2547(X) from Hamamatsu Photonics
K.K. and six counters with ASD-NUV-SiPM3S-P from AdvanSiD.
One reference counters is composed of 5×5×5 mm3 scintillator of BC422 coupled toa Hamamatsu Photonics K.K. SiPM (S10362-33-050C), and the other is 25×12×5 mm3
scintillator of EJ232 (BC422 equivalent) with two Hamamatsu photonics SiPM (S1036233-050C) connected in series on each side. This second reference counter is used only toestimate the time resolution of the other reference counter. On the other hands, the first89CHAPTER 6. PERFORMANCE OF MULTIPLE HIT SCHEME

90

reference counter is not used only as a time reference but also as a collimator by triggeringby itself.

Figure 6.1: Set up in the beam test in Frascati.

The signals are transmitted on a 7-m long coaxial cable (without using the Back Plane)
to amplifiers developed by PSI which is the same ones used in mass test as described in
Chap. 4.
The transmitted signals are digitized by the DRS4 evaluation board V4 [37, 38] whichhas 4 channels. The sampling speed is set at 2.5 GSPS. For the prototype counters andthe reference counter, we used the six boards. To synchronize among the boards, the sine
waves divided by passive splitters are inserted into one channel in each board.

6.1.2

Analysis

Synchronization(V)

Synchronization between DRS boards is important to obtain good time resolution. Originally the time diﬀerence among the boards is several hundred ps. In this beam test, we
inserted sine wave, fit it and obtained time oﬀset of each board event by event. A higher
signal-to-noise ratio allows better quality of the fit. However, since the dynamic rangeof DRS is tuned to the counter signal, which is from −0.05 to 0.95 V, only positive sideof sine amplitude is used for synchronization analysis, while negative side is saturated asshown in Fig. 6.2. Each DRS board is synchronized by the maximum point obtained byfitting.

0.1
0.05
0
−0.05

−6

−0.6

−0.5

−0.4

−0.3

−0.2

−0.1

0
Time (s)×10

Figure 6.2: Inserted sine wave for the synchronization. Since the dynamic range is limited,
we fit only positive part of the sine amplitude. Red line is the fit sine.

CHAPTER 6. PERFORMANCE OF MULTIPLE HIT SCHEME

91

Event Reconstruction
The reconstruction of single counter hit is the same as the final way as described in Chap. 5.
A hit time is reconstructed by taking average on two channels in a counter. To eliminate
the pile up hits, clusters are made, so that each hit time in a cluster is into 1 ns. Fig. 6.3
shows an event which has two pile up positrons as an example and they are successfully
separated by the clustering.

Figure 6.3: An example of a pile up event. Cyan markers show the hits from triggered
positron which hits to the reference counters. On the other hand, blue and magenta
markers describe hits from pile up positrons. Using reconstructed time, we can separate
these pile up events.

Tracking by using reconstructed hits is also applied after clustering. The tracking isbased on Kalman Filter [39] assuming straight positron trajectory as an initial state. Far
hits from reconstructed trajectory are removed.

6.1.3

Event Selection

Multi-positron events are removed by energy deposit cut for former two counters as shownin Fig. 6.4. .

E TC2 (MeV)

4
3
2
Cut
1
0
0

1

2
3
E TC1 (MeV)

4

Figure 6.4: Distribution of energy deposit on first counter and second counter.

CHAPTER 6. PERFORMANCE OF MULTIPLE HIT SCHEME

92

Estimation of Time Resolution
Simply the overall time with n hits can be obtained as,
∑n
i Ti
,
n

(6.1)

where Ti is time of ith counter.
Estimating the overall resolution of prototype counters, we performed two analysis
methods. One is reference counter analysis in which resolution is estimated by σ of∑ni Ti
− TRC1 ,(6.2)
nwhere TRC1 is the reference counter time. At the end, the resolution of reference counters,
which is estimated to be 30.3 ps, should be subtracted .
The other analysis is even-odd analysis which takes the diﬀerence between averagetime of even counters and odd counters, that is,
∑n/2
j

T2j

n/2

∑n/2
−

j

T2j+1

n/2

,

(6.3)

The σ of this time distribution is the same as that of Eq. 6.1 if there is no correlation
between each Ti . This analysis is independent with reference counter analysis.

6.1.4

Resolution Improvement with Multiple Hits

The overall timing resolutions of the counter arrays as a√function of number of hits are
σ2

ASD

80
60

σ(N ) =

75.0 / N + 0.0

σ(N ) =

74.52/ N

22HPKσ(N ) =

64.6 / N + 8.0

σ(N ) =

63.52/ N

2

2

40
20
0

1

2

3

4

5
N

6

7

8

Time resolution (ps)Time resolution (ps)singleall2
shown in Fig. 6.1.4. The result is fit by a function of+ σconst. In principleNof multiple hit scheme, the σconst is zero. With the reference independent analysis it iszero, which means multiple scheme works well. On the other hand, the result by analysis
with reference counter, the best fitted function has constant term of 8.0 ps in Hamamatsu
counters. However it is negligibly small and we demonstrated the resolution improvementwith increasing number of hit counters.

ASD OE-analysis
FB-analysis
σ(N ) = 74.52/ N

80

HPK OE-analysis
FB-analysis
σ(N ) = 63.52/ N

60
40
20
0

1

2

3

4

5

6

7

8

N

Figure 6.5: Overall resolution vs. number of hits (N ) obtained by analysis with reference
counter (left), and even-odd analysis (right).

CHAPTER 6. PERFORMANCE OF MULTIPLE HIT SCHEME

6.2

93

Rate Dependence

In MEG II environment TC will have positron backgrounds at 50–170 kHz. To estimate
the eﬀect, we performed a beam test at piE5 beam line in 2014.

6.2.1

Set upOverview of the beam test are described in Fig. 6.6 and Fig. 6.7.
2 small counters

Michel Positrons

Muon Beam

Collimator

Back plane

8 Prototype Counters

Figure 6.6: Set up of the high rate test in PSI

Figure 6.7: Picture of set up in beam test for checking rate dependence in PSI

The test beam is performed in front of the MEG II experimental area where is outof the COBRA magnet. The muon beam line is the same as described in Sec. 3.2. The
muon rate is ∼ 108 Hz. After a collimator the Michel positrons are generated on atarget. Therefore, we obtained a time uniform Michel positron background. We placed two

CHAPTER 6. PERFORMANCE OF MULTIPLE HIT SCHEME

94

reference counters each of which consists of 5×5×5 mm3 plastic scintillator (Saint-Gobain
BC422) attached by 1 SiPM (HAMAMATSU S10362-33-050C, 3 × 3 mm2 , 50 µm-pitch)with Teflon wrapping in front of the prototype counters. Using them for coincidence
trigger we selected straight positron events. The distance between the two counters is
3 cm. They also give us the reference time in time analysis explained later on.
Eight prototype counters are placed 8.5 cm behind the latter reference counter. Theseare put at an interval of 5.5 cm. Scintillator is EJ232 from ELJEN which is not the final
one (BC422) but have the same characteristics: the attenuation length is 8 cm and therise time is 0.35 ns. The size of the first six counters is 120 × 40 × 5 mm3 and that of thelast two counters is 120 × 50 × 5 mm3 . The six SiPMs (AdvanSiD NUV type) connected
in series on the final version of PCB are attached to the scintillator at the both ends. The
configuration of the prototype counters are almost the same as the final version. However
the scintillator and SiPMs have a bad performance due to quality control issues of vendors
and the single counter resolution of these prototype counters are ∼90 ps in pre-test with
90 Sr source evaluated in the same way as described in Sec. 4.5.1.
Counters connected to Back Plane which is also prototype for the final detector. The
signals from counters are read by 7 DRS evaluation boards with 1.6 GSPS. A DRS evaluation board has 4 channels and sine wave is inserted to one channel in each board for
oﬄine synchronization among boards. We also recorded the RF signal from the cyclotron
to eliminate positron contamination originated in the beam.

6.2.2

DAQ

We took data at three diﬀerent hit rates, 18–64 kHz, 53–166 kHz, and 89–290 kHz bychanging a slit in the beam line. The rates in latter counters become lower due to thesmaller solid angle. Furthermore low momentum positrons can be scattered largely on theformer counters and then they does not hit on latter counters. The detailed hit rates ineach counter are shown in Fig. 6.8. These values are estimated by random trigger data.
No-signal events are counted and converted to hit rate by Poisson distribution. (Theexpected hit rate in MEG II from an MC study is 20–100 kHz depending on z.) The
trigger rate was 55 Hz.
The waveforms of a reference counter and a prototype counter are shown in 6.9 as an
example. We found that the prototype Back Plane picked up noise and made resolutionbad.

Rate (kHz)CHAPTER 6. PERFORMANCE OF MULTIPLE HIT SCHEME

95

350
300

Low Rate
Middle Rate
High Rate

250
200
150
100
50
0

1

2

3

4

5

6

7

8

Counters(mV)

Figure 6.8: Hit rate in each counter in each configuration. Since the height of counter 7
and 8 is larger than the others, their rates are relatively high.

150
100
50
0

(mV)

−600

−500

−400

−300

−200

−100
0
Time (ns)

−300

−200

−100
0
Time (ns)

150
100
50
0
−600

−500

−400

Figure 6.9: Waveform of a reference counter (top) and a prototype counter (bottom)

6.2.3

Analysis

Event reconstruction and synchronization is the same as the Frascati test beam as deRC2
scribed in Sec. 6.1.2, but reference time is calculated by the two counters as TRC1 +T.
2
The resolution of the reference time is estimated to be 32 ps as shown in Fig. 6.10. Since
reference counters are small enough and far enough from each other, the resolutions do
not change in the diﬀerent hit rate environments. Thus, the single counter resolution isestimated with the two reference counters in the same way as Sec. 6.1.2.

CHAPTER 6. PERFORMANCE OF MULTIPLE HIT SCHEME

1751 ± 18.5

Constant

Sigma

−0.2

Constant

1982 ± 19.3

Mean −9.051e −12 ± 2.564e− 13

Mean −9.497e −12 ± 2.546e− 13

3.168e− 11 ± 1.986e− 13

Sigma 3.193e−11 ± 1.802e− 13

0.2

(T

1939 ± 19.4

Sigma 3.156e−11 ± 1.858e− 13

×10−9
0

Constant−1.05e− 11 ± 2.69e− 13

Mean

−0.4

High Rate

Middle Rate

Low Rate

96

0.4

−0.4

-TRC1)/2 (s)

−0.2

×10−9
0

0.2

(T

RC2

RC2

−0.4

0.4

−0.2

-TRC1)/2 (s)

×10−9
0

0.2

(T

0.4

-TRC1)/2 (s)RC2Figure 6.10: Time diﬀerence between two reference counters.

Event Selection
We took average on times of the two reference counters as reference time. The muon beam
had positron contamination, and we could recognize it by looking the time distribution
between the reference time and RF time as shown in Fig. 6.11. The positron from beamitself makes a peak, while the positron generated in the target from muon beam distributes
uniform. The red colored region in the figure is used.

−15

−10

−5

0

5

10

×10−9
15

TRC - TRF (s)Figure 6.11: Time diﬀerence between the reference counter and the RF signal. A peakcomes from the positron contamination in the beam and red colored region is selected foranalysis.

To select straight positron events a strict cut for charge of the reference counters is
also applied. Fig. 6.12 is the distribution of the charge and the region filled with red is
selected. The peak values are diﬀerent between the two reference counters by a factor.of
0.62, and these red region in the two distributions are the same range after correction.
In addition, the events which have enough energy deposit in all the counters are used
for following analysis to select good straight events. The amplitude distributions in eachchannel are shown in Fig. 6.13. The hits having more than 0.04 V signal are used in theCHAPTER 6. PERFORMANCE OF MULTIPLE HIT SCHEME

0

0.1

0.2

0.3

0.4

0.5

97

0.6

chargeFigure 6.12: Charge of reference counters. Red region is selected for analysis.

figure.

Counter 1
Counter 2
Counter 3
Counter 4Counter 5
Counter 6
Counter 7
Counter 8

−0.05

0

0.05

0.1

0.15

0.2

Amplitude (V)Figure 6.13: Amplitude of each channel of all the counters. We set the threshold at 0.04 V.

6.2.4

Electronics Jitter

The electronics jitter is estimated by inserting pulses from a pulser into diﬀerent channels
by dividing passively. The pulser is NIM Pocket Pulster MODEL 417 from PHILLIPS SCIENTIFIC whose pulse width is 6 ns and repetition rate is at 10 kHz. The synchronizationeﬀect is also included in the result. The jitter between reference counters and prototype
counters should be subtracted to evaluate the overall TC performance. On the other
hand, the jitter intra prototype counters should be taken into account. Tab. 6.1 shows

CHAPTER 6. PERFORMANCE OF MULTIPLE HIT SCHEME

98

the measured jitter for estimating single counter resolutions. They are obtained from thetime distribution of (Tch1 + Tch2 )/2 − (TRC1 + TRC2 )/2 for jitter from the reference, andTch1 − Tch2 for the jitter intra prototype counter.
Table 6.1: Electronics jitter (ps)Counter
12
3
45
b/w RC and prototype counter 21.9 19.3 22.1 22.3 18.8
intra prototype counters
7.3 13.1 6.2
7.8 13.2

6.2.5

6
21.8
6.8

7
19.7
7.1

8
26.3
6.7

Time Resolutions

Single Counter
The single counter resolutions are estimated by the reference counter analysis. The time
distribution of each counter is shown in Fig. 6.14. Fig. 6.15 shows the result from thebeam test and precedence tests with 90 Sr source. Since energy deposit in the beam test
and 90 Sr source test is diﬀerent, the resolutions from the 90 Sr test are corrected by scaling
the resolutions with the square root of the ratio of the energy deposit diﬀerence expectedby MC. In the figure the resolutions of the latter three counters are consistent with thosein the 90 Sr test but the other resolutions are worse than those in the 90 Sr test. Since theformer counters have higher hit rates as discussed above, their resolution become worse.
Counter 1

Counter 3

Counter 2

103

102

103

103

102

102

Counter 4

103

102

1
−9

7.5

8

8.5

9

9.5

×10
10

1
7

−9

7.5

8

8.5

Tc1 - Trc

9

×10
9.5

1
6.5

−9

7

7.5

8

Tc2 - Trc

Counter 5

8.5

×10
9

1
6.5

103

103

102

102

102

102

−9

7.5

8

8.5

×10
9

Tc5 - Trc

1
6.5

−9

7

7.5

8

8.5

×10
9

Tc6 - Trc

1
6.5

−9

7

7.5

8

8.5

×10
9

Counter 8

103

7

8

Tc4 - Trc

Counter 7

Counter 61

7.5

Tc3 - Trc

103

6.5

−9

7

8.5

×10
9

1
6.5

Tc7 - Trc

−9

7

7.5

8

8.5

×10
9

Tc8 - Trc

Figure 6.14: The time distribution of each counter.

Fig. 6.16 shows the resolution dependence on the hit rate in each counter. Though theresolution degradation at higher rate is observed, it is negligible and the diﬀerent between

Resolutions (ps)

CHAPTER 6. PERFORMANCE OF MULTIPLE HIT SCHEME

99

140
120
100
80
60

Low Rate
Middle Rate

40

High Rate

20
0

Sr scaled by edep

1

2

3

4

5

6

7

8

Counters

Figure 6.15: The single counter resolutions with 90 Sr test results which are scaled byenergy deposit.

Single Counter Resolution (ps)the counters are much larger than that.

Counter 1

140Counter 2
Counter 3
Counter 4Counter 5
Counter 6

120Counter 7
Counter 8

100

80
0

50

100

150

200
250
300
Hit Rate (kHz)

Figure 6.16: The single counter resolution as a function of hit rate in each counter.

Noise
The distribution of noise RMS in each counter is shown in Fig. 6.17 and it indicates someof channels have larger noise than that in the others. By fitting with Landau function
convoluted with Gaussian the peaks of noise RMS are obtained as described in Fig. 6.18.
Noise of Counter 3 and Counter 4 is slightly larger than that of the other counters, and weCHAPTER 6. PERFORMANCE OF MULTIPLE HIT SCHEME

100

identified that the noise is picked up by back plane by swapping several channels. Afterthe beam test, we decided to add layers of electronic shielding to each signal line in theback plane and thus we did not observe channel-dependent-noise from the back plane.
Counter 1

Counter 2

Counter 3

1200

Counter 4

1200

1000

1000
1000

1000

Ch1

800

800
800

800
600

600

Ch2

600

600
400

400

400

400

200

200

0
0

0
0

0.002 0.004 0.006 0.008 0.01
Noise RMS (V)Counter 5

200

0
0

0.002 0.004 0.006 0.008 0.01
Noise RMS (V)Counter 6200

0.002 0.004 0.006 0.008 0.01
Noise RMS (V)00Counter 7

0.002 0.004 0.006 0.008 0.01
Noise RMS (V)Counter 8

1400
1500

1000

500

0
0

0.002 0.004 0.006 0.008 0.01
Noise RMS (V)

1000

1000

800

800

600

600

400

400

200

200

0
0

1500

1200

1200

0
0

0.002 0.004 0.006 0.008 0.01
Noise RMS (V)

1000

500

0.002 0.004 0.006 0.008 0.01
Noise RMS (V)000.002 0.004 0.006 0.008 0.01
Noise RMS (V)Noise RMS (V)Figure 6.17: Distribution of Noise RMS in each counter. Their peaks are obtained byfitting with Landau convoluted with Gaussian which is drown in black line. Even in thesame counter, the noise situation of the two channels is not the same.

0.005
0.004
0.003
0.002

Ch1
Ch2
Average

0.001
0

1

2

3

4

5

6

7

8
Counters

Figure 6.18: Noise RMS obtained from Fig. 6.17.

Fig. 6.15 also indicates hit rate dependence of the single counter resolution. In theCHAPTER 6. PERFORMANCE OF MULTIPLE HIT SCHEME

101

Noise Increment (V)high rate environment, a small degradation of the resolutions can be seen because tailsof signal from pile up positrons make noise situation worse as shown in Fig. 6.19. Higher
noise is observed in the high rate environment, while they are almost same in middle andlow rate environment. It is consistent with tendency of the rate dependence of single
counter resolutions.
0.00150.001
0.00050−0.0005−0.001

1

2

3

4

5

6

7

8

Counters

Figure 6.19: Noise increase in each counter in middle rate (Red) and high rate (Blue) fromlow rate environment (Green).

Resolution Degradation from Sr Data (ps)Clear correlation between noise and resolution degradation is observed in Fig. 6.20. The
variation of single counter characteristics is largest eﬀect on its resolution as indicated inFig. 6.15. However the resolution degradation in high rate environment can be seen after
subtracting the variation obtained by 90 Sr test.

100
80

Low rate
Middle rate
High rate

60
40Counter 1
Counter 2

20Counter 3
Counter 40Counter 5
Counter 6−20Counter 7
Counter 8−400.0015 0.002 0.0025 0.003 0.0035 0.004 0.0045 0.005

Average Noise RMS (V)Figure 6.20: The correlation between noise and degradation of single counter resolution
from 90 Sr source test.

CHAPTER 6. PERFORMANCE OF MULTIPLE HIT SCHEME

6.2.6

102

Multi-Counter Resolutions

0.1

Even-Odd
RC

0.08

Middle Rate

×10−9
0.1

Even-Odd
RC

0.08

Expectation

0.06

Resolution (s)Low Rate

×10−9

Resolution (s)Resolution (s)The overall resolution as a function of the number of hits are estimated as described in theanalysis section. Overall resolutions obtained by two analysis and expectation from single
counter resolution is shown in Fig. 6.21. The resolutions are consistent with expectations.
The total eﬀects of the high rate environment can be seen in Fig. 6.22. At the high rate
the small deteriorate of time resolution is observed. We consider two reasons: pile up
positron make noise situation worse as discussed above; and pile up makes tail of time
distribution measured by several counters. For the TC this deterioration is not crucial.
Moreover in the MEG II experiment the expected positron rate is less than 100 kHz and in
middle environment is similar situation to MEG II. In conclusion, we demonstrated thatexcellent timing resolution with multiple hits can be obtained in the MEG II experiment.

0.1

0.06

RC

0.04

0.02

0.02

0.02

2

3

4

5

6

7

0

8

Expectation

0.06

0.04

1

Even-Odd

0.08

Expectation

0.04

0

High Rate

×10−9

1

2

3

4

Number of Hits

5

6

7

0

8

1

2

3

4

Number of Hits

5

6

7

8

Number of Hits

RF Analysis

×10−9
0.1

Resolution (s)Resolution (s)Figure 6.21: Overall resolution comparison among two analysis results and expectation.

Low Rate
Middle Rate
High Rate

0.08
0.06

0.1

0.06
0.04

0.02

0.02

1

2

3

4

5

6

7

8

Number of Hits

Low Rate
Middle Rate
High Rate

0.08

0.04

0

Even-Odd Analysis

×10−9

0

1

2

3

4

5

6

7

8

Number of Hits

Figure 6.22: Overall resolution in each rate with RF analysis (left) and Even-Odd analysis(right).

Chapter 7

Timing Counter Performance
The final detector was constructed and installed as described in Chap. 4. We performed
three pilot runs from 2015 to 2017 at the MEG II beam line. Moreover in 2017 laser test
runs with the final DAQ system was also performed. This chapter will discuss the overall
TC performance obtained by these runs.

7.1

Pilot Runs

We had three pilot runs in 2015, 2016, and 2017, and the run for the test of laser systemand final DAQ in summer 2017 before the final pilot run in November and December
2017. The main diﬀerences includes the number of the counters and the fibers, the DAQ
electronics, and the beam set up as summarized in Tab. 7.1. Only half of the downstream(DS) counters (128) was installed and tested in 2015 and 2016. The counter configurationsin 2015 and 2016 are the same, but the number of the laser system was increased in 2016.
From 2016 to 2017 all counters were dismounted and assembled again. During this reassembly period, we installed the full laser system, and added the thermal links on all thecounters and the additional optical cement for the counters to be mechanically strong.
The counter assignment in 2017 was totally changed in the re-assembly. In particular, allcounters used in 2015 and 2016, which were installed to DS, were assigned to US . The
detailed set up will be described following each subsection.
Table 7.1: Summary of diﬀerence among runs for TC.
Year2015 2016 2017 Laser
2017
Number of Counters
128
128
256
512
Number of Fibers
840216432 (Full)
Number of DAQ channels 256256512
512 (Half of all)Counter assignment and the definition of position identification is described in Fig. 7.1.
In 2015 and 2016, we installed and tested counters from the row of 5 to 12.

7.1.1

Pilot Run 2015

The first pilot run with the 1/4 counters was performed in December 2015. Beam set up
was the same as MEG II one whose muon rate is 7×107 on the target. Because of a delayof the DAQ system meaningful data taking was only for 10 hours. This is not enough to103

CHAPTER 7. TIMING COUNTER PERFORMANCE

104

Figure 7.1: Counter assignment and position IDs. Counters colored cyan are 5cm-heightcounters, and the others are 4cm-height-counters. In them, outer (|z| > 70 cm) counterscolored magenta are attached straight SiPM arrays, and inner is L-shape ones, and yellow
colored ones are mix counter in which one SiPM array is L-shape and the other is thestraight. Positions are counted along ϕ decreasing starting most inner DS counters.

estimate overall timing resolution with several counter hits. Moreover data quality is notgood such like large noise, poor dynamic range, and lack of online synchronization.
However it is the first installation of TC, and test of several triggers for TC is performedin this pilot run. We prepared four types for TC. Three of them is for positron data taking
as single counter trigger, multi-counter trigger, and track-like trigger. Single counter
trigger is the coincident trigger of two channels for a counter with certain threshold forthe signal amplitude. We can trigger OR for all the single counters or for only specificcounters. Multi-counter trigger is based on the single counter trigger, and namely thresholdfor number of hits in certain time window can be applied for triggering. Moreover, totake into account geometrical order of hit counter, track-like trigger is implemented. In
addition, pedestal trigger was also implemented. Every triggers can be mixed each otherwith scaling as needed.

7.1.2

Pilot Run 2016

Since the beam time was not enough in 2015 due to the DAQ debugging, the second pilot
run was performed. We modified several problems of the DAQ system written above, andmoreover the increased number of fibers for laser calibration as shown in Fig 7.2.

7.1.3

Laser test with the final DAQ

Before the pilot run 2017, the laser system in DS got ready to test except for the switching
device. Therefore we operated it without any beam to check its stability.

7.1.4

Pilot Run 2017

We mainly use the data in 2017 to estimate TC performance. Here detailed set up of thepilot run will described.

CHAPTER 7. TIMING COUNTER PERFORMANCE

105

Figure 7.2: Configuration of the counters with laser fiber in 2016

Beam and Target
The overview of the beam line was already described in Sec. 3.2. Since the spallation target,
SINQ, was removed, the proton current was set to ∼1500 µA or ∼1380 µA which is lower
than planned value of 2200 µA in the MEG II experiment. To recover the lower muon yield
due to the lower proton current, the muon beam rate at the center of COBRA magnet was
tuned to be 30 % higher than the nominal MEG II value (∼8.1×107 µ+ /s at 2200 µA).
The absolute stopping rates were ∼6.1×107 µ+ /s at 1500 µA and ∼5.6×107 µ+ /s at1380 µA respectively with the assumption of 85 % stopping eﬃciency on the target whichis estimated by MC study. They were still 13 % and 20 % lower rate than the expected
stopping rate in MEG II, ∼7×107 µ+ /s.
The beam center is -2.1 mm along X direction, and -12.2 mm along Y direction spreading 11.3 mm and 11.2 mm (σ) respectively. These beam parameters are measured by a
5 mm Raster scan of ∼270 point measurements. Fig. 7.3 shows the result of the Rasterscan. We use a scintillator target in the run. Thickness of the targets is not uniform.

Figure 7.3: The result of Ratter scan of beam.

CHAPTER 7. TIMING COUNTER PERFORMANCE106

DCH Mock up
A mechanical mock up DCH is installed. Its outer frame made from 2-mm thick carbon
fiber and inner frame made of 20 µm thick Mylar film is installed. One sector of theanode wires and related electronics are mounted. To operate and test gas system of DCH,
aluminum spacers fill the remaining empty sectors. Therefore end-cap material is not thesame as the final DCH, while the chamber gas is the same.
DAQ Electronics
We use the final electronics, WaveDREAM. Since mass production of all channels is still
under way, data taking of upstream and downstream are separately performed by recabling. Some connectors of WaveDREAM are fragile and their ground line are unstable.
It made noisy channels or dead channels not applied bias voltage correctly. It is soldering
problem and will be fixed. The sampling speed is 2 GSPS. The gain of the amplifier in
WaveDREAM is set 100 for the normal SiPM counter and 50 for the high gain SiPM
counters.
One crate has 16 slots each of which has 16 channels placed on 2 chips. Two channels
in a counter are connected to the same chip. Defining Z inner channel as a first channel,
every channels connected to WaveDREAM in order of position ID. In summary, every twoslots correspond to outputs from counters in the same column.
Synchronization
For synchronization between chips, a main clock signal is supplied to each WaveDREAMboard. Then a PLL chip control the synchronization of the two chips. Though the PLL
synchronization accuracy is abour 10 ps, the online synchronization is limited by intrinsic
jitter from DRS4 to around 60 ps. Therefore a sine wave generated from the PLL output
is inputed to DRS4 to synchronize between every chips in oﬄine analysis.
Trigger
The single counter trigger is used. It requires one or more counter hits as explained above.
Counter Operation
Though we lost a few signal or observed the deterioration of the time resolution in somecounters due the fragile connector of some of WaveDREAM channels, from the counterview points all counter except for one counter worked properly, which is confirmed byswapping the noisy or dead channels for a normal channel. One channel of the broken
counter was a short circuit and the current was saturated when the bias voltage wasapplied. Therefore we turned oﬀ the channel during the run.
Temperature Control and Monitor
Temperature control was a new system in 2017 run. We use a water cooling system.
Data
We take Michel positron data, ∼932 kilo-events for downstream; ∼1,333 upstream.

CHAPTER 7. TIMING COUNTER PERFORMANCE

7.1.5

107

MC

An MC simulation for the pilot run 2017 is prepared. The muon beam is generated
from z = −564.7 mm, just after the last magnet of Triplet II (see Fig. 3.14), so thatBTS contribution and the oﬀ-target muon decay are taken into account. Fig. 7.4 shows
the decay points of muons in MC. As defining target region |z| < 15 cm, the stopping
eﬃciency, which is defined as the ratio of the number of muons decaying on the target
to the total muons decaying on the target and in DS, is estimated as 85.7 %. The muonpolarization is set 0.9. The triggered event is defined as the event whose Michel positronfrom the muon beam remains a hit on TC. Background events, which is not required TC
hit, are mixed with the triggered event at 7.16 × 107 Hz. In addition, all the frames of the
final DCH are also implemented. Notice that the implemented materials are not exactly
the same as mock up DCH. In MC final DCH is implemented; there is all wires, and theend-cap material corresponding to the electronics for the wires.
5

hDeacayPointX

4

10

3

10

Entries

1644870

Mean

0.03412

Std Dev

1.594

hDeacayPointY

4

10

3

10

Entries

1644870Mean

0.3082

Std Dev

1.52

10hDeacayPointZ

104

Entries

1644870

Mean

1.255

Std Dev

70.7

3

10
102

102
102

10

10

1

1

10

− 20

− 10

0

10

20
x (cm)

− 20

− 10

0

10

20
y (cm)

1

−400

−200

0
z (cm)

Figure 7.4: Muon decay point in MC. Region colored blue is the vertex of the muon
decaying on the target.

7.2

Trigger

7.2.1

Discriminator Threshold

The trigger rates strongly depend on the discriminator threshold as shown in Fig. 7.5.
The pedestal trigger is flat at several thresholds. To check the laser trigger we flashed thelaser at 10 Hz. It is clear that the rate becomes stable once the threshold crosses the laser
signal. On the other hand, with the triggers for the positron signals, the rates gradually
go down because of signal amplitude depends on energy deposit. From a result of the laser
trigger, we choose the value of 1000 for threshold.

7.2.2

Online Time Resolution

Fig. 7.6 shows the distribution of the online time diﬀerence between two adjacent counter.
The√resolution is ∼590 ps, therefore the online time resolution of the single counter divided
by 2 is estimated to be ∼415 ps. The clock speed is 800 MHz, that is the time√width of
1.25 ns from which the intrinsic resolution of ∼360 ps is expected by dividing by 12. The
diﬀerence between the intrinsic and observed time resolution comes from the electronics
jitter on FPGA processing.

CHAPTER 7. TIMING COUNTER PERFORMANCE

108

Figure 7.5: Scanning of discriminator threshold. Laser is flushed at 10 Hz. The thresholdsetting parameter has an oﬀset. Higher value means lower threshold.

This online time resolution reduces the trigger rate in MEG II eﬀectively. Fig. 7.7
shows the online positron time distribution in the MC simulation. Since the positrons hit
TC in several times of turns, there are several peaks in the distribution. The sigma of eachpeak is ∼460 ps and the intervals are 2–3 ns. Taking into account the photon online time
resolution (284 ps) estimated by MC, the sigma of each peak is 560–600 ps. Finally thetrigger eﬃciency is obtained as Fig. 7.8 The figure also shows the eﬃciency in MEG. Since
the single channel resolution was ∼2.5 ns in the MEG experiment, the eﬀect of multi-turnis smeared. Therefore the online time resolution itself limited the teγ trigger window forµ → eγ decay.
In MEG the trigger eﬃciency was 99 % with 20 ns trigger time window. To achieve thesame trigger eﬃciency in MEG II, the trigger window is 14 ns in MEG II from Fig. 7.8.
This reduction of the trigger time window from MEG to MEG II corresponds to the
reduction of the trigger rate of a factor 1.5–2.

7.3

Analysis

7.3.1

Optimization of Waveform Analysis

The fraction to the signal amplitude for the constant fraction analysis in the waveform
analysis should be optimized in each environment, because optimized value strongly depends on the noise situation. The time resolutions with several fraction are studied bychecking the time distribution of adjacent two counters ((Ti+1 − Ti )/2). Fig. 7.9 shows
dependence of the average resolution of the two hits on the fraction in the pilot run 2017.
The dependence is also checked for specific counters in 2015, 2016, and pre-test with 90 Srsource before the installation as shown in Fig. 7.10. Since the noise situation in the experimental site is worse than that in a room for the pre-test, higher fraction should be
set. Finally we use the fraction of 20 % for 2017 data, and 35 % for 2015 and 2016 as the
optimal fraction.

CHAPTER 7. TIMING COUNTER PERFORMANCE

109

Figure 7.6: Online time resolution distribution.

Figure 7.7: Online positron time distribution in MC.

Moreover Fig.7.11 indicates that the optimal fractions depends on counters, especiallycounters with Type 2 SiPMs (position ID is ∼100), which have larger signal amplitude,
requires smaller fraction because of signal and noise ratio is better than the others. On
the other hand, if there is a noisy channel, the optimal fraction becomes higher.

7.4

Hit Rate

The hit rate on each counter is calculated by counting pulses measured in an oﬀ-trigger
window in the single-hit trigger data. The distribution of the reconstructed hit times
on DS counters is shown in Fig. 7.12. The peak is from the triggered signal and before
them no signal is observed because of trigger bias, that is, triggered signal should be firstsignal in a certain time window, otherwise the forward signal should be triggered. Thus,
only the region after triggered signal can be used for counting random backgrounds. The
region from −280 ns to −100 ns is defined as pedestal region. Because of the limitation

Efficiency

CHAPTER 7. TIMING COUNTER PERFORMANCE

110

1
MEG
MEG II expected

0.8

0.6

0.4

0.2

0
−20

−15

−10

−5

0

5

10

15

20
t e+γ (ns)Figure 7.8: teγ trigger selection eﬃciency.

of signal separation, ratio of no signal events are calculated and translated to the hit rateby assuming Poisson distribution.
The hit rates on every counter are shown in Fig. 7.13 with MC results. Moreover
the average hit rate over the same Z position counters is shown in Fig. 7.14. The hit
rates are less than 100 kHz. In |Z| >∼ 100 cm, hit rates in data is larger than simulated
ones because of the mock-up DCH end-cap is not simulated and is expected less material
than the final (and MC) DCH. However basically the behavior of the background rate isconsistent with MC result, and we did not find any strange background in our experimental
environment.
This background rate also indicates that DS has more background than US does. The
reason is studied by MC in detail and muon decays in flight remain more backgroundto DS counters. Fig. 7.15 shows the Z position of the muon decays and indicates moremuons decay in DS than in US. As a result almost all backgrounds in US come frommuons decaying on the target, while backgrounds of 20-60 %, depending on z, in DS are
originated from muons decaying oﬀ target as shown in Fig. 7.16, and 7.17. Remaining
asymmetry between DS and US as shown as blue marker in Fig. 7.17 comes from thepolarization of muon.

CHAPTER 7. TIMING COUNTER PERFORMANCE

111

Resolution (psec)

Average Resolution (s)Fraction Dependence of Resolution

×10−12
76
74

100
Lab
Engineering 2015
80

Engineering 2016

72
60

70
68
66

40

10 15 20 25 30 35 40 45 50

10

20

30

Fraction (%)

40
50
Fraction (%)

Figure 7.10: Resolutions with several
Figure 7.9: Resolutions with several fraction for the waveform analysis in pifraction for the waveform analysis in pi- lot run 2015, 2016 and pre-test with 90 Sr
lot run 2017. The result of all DS coun- source. Expected resolution decreasingters are averaged.
from energy deposit point of view is 510 %.

50
40
30
20
10
0

50

100

150

200

250

Figure 7.11: Optimized fraction (Y-axis) of each counter combination in fractions of 1050 %. Numbers of X-axis correspond to position ID of a first counter of the two counter
combinations.

CHAPTER 7. TIMING COUNTER PERFORMANCE

112

60000

40000

20000

−6

0

−0.5

−0.4

−0.3

−0.2
−0.1
Reconstructed Hit Time (s)×10

Figure 7.12: Reconstructed hit time in DS counters.

150

50

50

50

00

0

0

10

12

14 16
Position16

18 20 22 24

26 28 30 32
Position

150

150

100

50

50

0

0

0

150

82 84 86 88

90 92 94 96
Position

150

100

38 40

42 44

48

50 52 54 56

58

60 62 64
Position

150

100

50

0

96 98 100 102 104 106 108 110 112
Position

150

100

0

46 48
Position

Rate (kHz)80

Rate (kHz)Rate (kHz)78 80
Position

32 34 36100

50

70 72 74 76

50

150

100

64 66 68100

Rate (kHz)8

Rate (kHz)6

Rate (kHz)

4

150

100

Rate (kHz)100

2Rate (kHz)

150

100

112 114 116 118 120 122 124 126 128
Position

Rate (kHz)

150

113

Rate (kHz)Rate (kHz)Rate (kHz)CHAPTER 7. TIMING COUNTER PERFORMANCE

150

100

100

0 176 178 180 182 184 186 188 190 192
Position

150

100

150

100

100

50

50

50

0

0

0

150

150

100

100

50

150

100

0

224 226 228 230 232 234 236 238 240
Position

Rate (kHz)208 210 212 214 216 218 220 222 224
Position

Rate (kHz)Rate (kHz)192 194 196 198 200 202 204 206 208
Position150

240 242 244 246 248 250 252 254 256
Position

Rate (kHz)150

Rate (kHz)50

0 160 162 164 166 168 170 172 174 176
Position

Rate (kHz)50

0 144 146 148 150 152 154 156 158 160
Position

Rate (kHz)50

0 128 130 132 134 136 138 140 142 144
Position

Rate (kHz)

50

150

100

100

0 256 258 260 262 264 266 268 270 272
Position

0 272 274 276 278 280 282 284 286 288
Position

0 288 290 292 294 296 298 300 302 304
Position

0 304 306 308 310 312 314 316 318 320
Position

150

100

100

100

50

0

150

0

336 338 340 342 344 346 348 350 352
Position

150

100

100

50

Rate (kHz)Rate (kHz)320 322 324 326 328 330 332 334 336
Position

150

50

150

100

0

352 354 356 358 360 362 364 366 368
Position

Rate (kHz)

50

0

150

368 370 372 374 376 378 380 382 384
Position

Rate (kHz)150

Rate (kHz)50

Rate (kHz)50

Rate (kHz)50

Rate (kHz)

50

150

100

100

0 384 386 388 390 392 394 396 398 400
Position

0 400 402 404 406 408 410 412 414 416
Position

0 416 418 420 422 424 426 428 430 432
Position

0 432 434 436 438 440 442 444 446 448
Position

150

150

100

150

100

150

100

50

50

50

0

0

0

448 450 452 454 456 458 460 462 464
Position

Rate (kHz)50

Rate (kHz)50

Rate (kHz)50

Rate (kHz)50

464 466 468 470 472 474 476 478 480
Position

100

50

480 482 484 486 488 490 492 494 496
Position

0496 498 500 502 504 506 508 510 512
Position

Figure 7.13: Hit rate on every counters calculated with data (Magenta), and MC (Black).

Rate (kHz)CHAPTER 7. TIMING COUNTER PERFORMANCE

114

150

100

DS (data)
US (data)
DS (MC)US (MC)

50

0
0

50

100

Z (cm)

Figure 7.14: Z dependence of hit rate. Large rates on Z ∼ 70 cm come from counterswhich DAQ channels are noisy.

Figure 7.15: Muon decay point (Z) in MC)

CHAPTER 7. TIMING COUNTER PERFORMANCE

Figure 7.16: Hit rate in MC.

115

CHAPTER 7. TIMING COUNTER PERFORMANCE

116

Figure 7.17: Top figure shows Z dependence of hit rate from all background (red), andfrom on-target muon decay (blue). Bottom figure shows the ratio of them.

CHAPTER 7. TIMING COUNTER PERFORMANCE

7.5

117

Time Calibration

As explained in the previous chapters, there are two ways for the inter-counter time
calibration. In pilot run 2017, we operated the laser system. The measured laser signal
times on counters relative to the the laser emission time are stable for about one monthas shown in Fig. 7.18, and the average fluctuation in sigma is 2.5 ps. By subtracting theoptical length variation for the laser system components such as splitters and fibers fromthe measured laser signal times, time oﬀsets in signal lines are obtained. The result of thecalibration is shown in Fig. 7.19.

Figure 7.18: History of time oﬀset with one splitter for an example for a month.

Figure 7.19: Time oﬀset obtained by laser system.
On the other hand, track-based calibration is also tested. Because of absence of track
information from DCH, expected time of flight (TOF) for each counter combination inCHAPTER 7. TIMING COUNTER PERFORMANCE118

MC is used. The obtained time oﬀsets are shown in Fig. 7.20.

Figure 7.20: Time oﬀset obtained by track-based time calibration.

The diﬀerence between these two methods is shown in Fig. 7.21. We observed global
bias of ∼60 ps in the calibrated time along z. The diﬀerence between the true TOF andthe estimated TOF is expected to make the global bias in the track-based calibration. The
time oﬀsets among far counters are never calibrated in one event, that is, the far counters
are never fit simultaneously. Therefore, a mis-calibration in a front counters seems tobe accumulated to the rear counters. The detailed MC study for the bias is shown inAppendix A. Even if there is the global bias, in MEG II this bias can be corrected byusing radiative muon decay (RMD) events. Since RMD emits a photon and a positron
simultaneously, it makes peak in the relative time between a photon and a positron asshown in 3.55. Therefore, the time oﬀset bias for the counter position can be observed
directly and corrected. The calibration accuracy summed up both of laser and track-based
calibration accuracy is estimated to be 61 ps for DS, and 52 ps for US.

7.6

Basic Properties of Counters

At the beginning, the time resolutions of two counters (σ(Ti −Tj )/2 ) is discussed for checking
the basic property.

7.6.1

Time Resolutions

To obtain time resolutions with two hits, adjacent counters, which position IDs are i and
i + 1 (i is even) or j and j − 15 (j is odd), are selected. These combinations of two
counters are the geometrically same but their channel assignments are diﬀerent.Fig. 7.22
shows the resolutions of all these combinations. Mean value of the time resolutions are
67.2 ps for the combination in the same chip, and 67.5 ps for that in diﬀerent chips.
Considering fluctuation of the resolution of each counter, the diﬀerence from expected
resolution from pre-test is also checked as also shown in Fig. 7.22. The diﬀerences fromthe expectation are 36.7 ps in same chip and 38.6 ps in diﬀerent chips. These diﬀerence may
come from larger noise situation than that in pre-test. Furthermore comparing between
these combinations, an eﬀect of synchronization between diﬀerent slots can be seen. The
diﬀerence between same chip combination and diﬀerent chip configuration is small thatmeans the synchronization system works well.

CHAPTER 7. TIMING COUNTER PERFORMANCE

119

Figure 7.21: Time oﬀset diﬀerence between laser system and track-based calibration. Lines
are fit results with linear function

In addition, since two type of 4 cm and 5 cm height counters are installed, the resolutions map shown in Fig. 7.23 have position dependence as expected.

7.6.2

Energy Dependence

Fig. 7.24 shows the distribution of the energy deposit. The calibration factor from signal
charge to energy deposit is decided by comparing with a peak value of energy depositin MC. The measured time and resolution depends on energy deposit on counters. In
Fig. 7.25 and 7.26, the dependences are indicated with each heights of counters and eachchannel assignment. The time walk with energy dependence is observed in the figure. In
main energy region of 0.5–1.5 MeV it is about several tens of pico-seconds. It is not large
but correction of this eﬀect will improve the time resolution. Concerning time resolution
with energy deposit is also changed. In principle, the time resolution with larger energy
deposit becomes better because of larger photon-electron statistics. However, in Fig. 7.26
it is not in the case from ∼13 MeV. It may come from pile up events in which two hits
in the same counter are merged and the reconstructed energy looks large. Utilizing thisresolution dependence on energy deposit to make probability density function event-byevent for likelihood analysis, final physics analysis in MEG II will be improved.

7.7

Overall Time Resolution

To estimate TC overall time resolution, even-odd analysis is applied as described inSec. 6.1.2. Distribution of number of all hits is shown in Fig. 7.27. To eliminate pile
up positrons, clustering is applied. The number of obtained clusters and the number ofhits in a cluster is shown in Fig. 7.28.
Since we do not have any track information from DCH, we can not precisely reconstruct
event-by-event trajectory in TC. Instead, we evaluate the multiple-hit time resolution

CHAPTER 7. TIMING COUNTER PERFORMANCE
Difference from Expected Resolution

Two Hit Resolutions

15

15

10

10

5

5

0
55

60

65

70

×10−12808590Resolutions (s)

75

120

0
0

20

40

60
80
Difference (s)×10−12

0 496

480
497

498

482
499

−5

500

502

490
507

508

474
491

492
509

510

476
493

494
511

− 30

458
475
460
477

478
495

442
459
444
461

462
479

426
443
428
445

446
463

− 25

410
427
412
429

430
447

394
411
396
413

414
431

− 20

378
395
380
397

398
415

362
379
364
381

382
399

346
363

− 15

330
347

348
365

366
383

349

314

333

− 10

317

282

301

263

50

0

285

16
1
2

−5 5

10
11
12
13

10

−5
0
Z Number

0

26
27− 15 15
0

42
43

28
29

14

44
45

30
31

58
59

61

77

92
93

78
79

106
107
108
109

94
95

10

122
123
124
125

110
111

138
139
140
141

126
127

154
155
156
157

142
143

15

170
171
172
173

158
159

186
187
188
189

174
175

20

202
203

205

221
206

207

25

234

237

30

252

254
255

30
Z NumberFigure 7.23: Resolutions map with two counter hits. Left is US result, and right is DS
result. Numbers are position IDs of counters.

using fixed combinations of counters and the even-odd analysis. Each counter combinationconsists of counters with position IDs (i, i + 1, i + 16, i + 17, i + 33, i + 18, i + 49, i + 34, i +50, i + 51) when i is even, and (i, i − 15, i + 16, i + 1, i + 17, i + 18, i + 33, i + 34, i + 50, i + 35)
when i is odd, as shown in Fig. 7.29. We evaluate the Nhit resolution using events with hitson the first Nhit counters in each counter combination, and then, average them for all the
combinations to get the overall time resolution for Nhit . The result as a function of Nhit isshown in a blue line in Fig. 7.30. In addition, we evaluate the overall time resolutions ina diﬀerent way: we accumulate the fit Gaussian functions over all the combinations andfit the accumulated distribution with a Gaussian to get the overall resolution, as shownin Fig. 7.31. In this way, the local contribution of time calibration error can be taken into
account because the center values of time diﬀerence distribution for diﬀerent combinations
vary due to the errors on the counter time oﬀsets. It is to be noticed that the global bias
eﬀect is not seen in even-odd analysis in which the global bias is canceled out in thesubtraction. As discussed in Sec. 7.5, the global bias can be corrected by the√ RMD events.
The red line in Fig. 7.30 shows the result. These two curves are fitted by

20

253
238

239

40

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251

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223

50

248
249

235
220

60
246

232

218

70

247

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219
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191

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217

80
244

245

231

×90
10−12

242
243

228

214

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201

226

229

215

240
241

227
212

198

184
185

210

213

199

224
225

211
196

182

168
169

194

197

183

208
209

195
180

166

152
153

178

181

167

192
193

179
164

150

136
137

162

165

151

176
177

163
148

134

120
121

146

149

135

160
161

147
132

118

104

90

130

133

119

144
145

131
116

117

105

91
76

62
63

5

74

114

102

88

128
129

115

103

89

75
60

46
47

86

72
73

98

100
101

87

112
113

99
84

70

56
57

82

85

71

96
97

83
68

54

40
41

66

69

55

80
81

67
52

38

24
25

50

53

39

64
65

51
36

22

8

− 10

34

37

23

48
49

35
20

6

269

271

18

21

9

32
33

19
4

7

20

270

17

3

267
268

287

40
30

266

286
303

60

265

283
284

302
319

261

264
281

299
300

318
335

280

298

70

262
279

297

315
316

334
351

278

296
313

331
332

350
367

312

80

259
260

277

295

257
258

275
276

294
311

329

274

293

×90
10−12

256
273

291
292

310

328
345

290

309

327

272
289

307
308

326

344
361

306

325

343

288
305

323
324

342

360
377

322

341

359

304
321

339
340

358

376
393

338

357

375

320
337

355
356

374

392
409

354

373

391

336
353

371
372

390

408
425

370

389

407

352
369

387
388

406

424
441

386

405

423

368
385

403
404

422

440
457

402

421

439

384
401

419
420

438

456
473

418

437

455

400
417

435
436

454

472
489

434

453

471

416
433

451
452

470

488
505

450

469

487

432
449

467
468

486

504

− 15

466

485

503

448
465

483
484

501

− 10 506

464
481

Phi Number

Phi Number

Figure 7.22: Resolutions of two counter hits (left) and resolution diﬀerence from theexpectation of pre-test with 90 Sr source. The expectation values are corrected with energy
deposit diﬀerence.

2
σsingle-all
2
+ σMS
Nhit

2
2
2
2
where σsingle-all= σsingle+ σinter-counter+ σelec
in Eq. 4.2. When just average of sigmas

100CHAPTER 7. TIMING COUNTER PERFORMANCE

121

5 cm (Position 90)
4 cm (Position 149)

0

0.002

0.004

0.006
0.008
Energy (GeV)

Figure 7.24: Distribution of energy resolution in 4 cm (red), and 5 cm (blue) height
counter.
−9

−9

0.1

0.15 ×10

Resolution (s)Mean (s)0.15 ×10

4 cm in same chip
4 cm in diffrent chip
5 cm in same chip
5 cm in diffrent chip

0.05

0

0.1

0.05

0.001

0.002

0.003
Energy (GeV)

0

4 cm in same chip
4 cm in diffrent chip
5 cm in same chip
5 cm in diffrent chip

0.001

0.002

0.003
Energy (GeV)

Figure 7.25: Measured time as function Figure 7.26: Time resolution as functionof the energy deposit.
of the energy deposit.

2= 96.4 ps for average overall
is taken, σinter-counter is zero. The fit results are σsingle-all2resolution, and σsingle-all = 98.1 ps for the overall resolutions by Gaussian accumulation
way with negligibly small σMS . Consequently, σinter-counter is estimated to be 18 ps fromthe diﬀerence between the two fit results.
The overall resolutions in 2017 pilot run are still worse than expectation from the mass
test with 90 Sr source as shown in Fig. 7.30. The expected σsingle is 80.1 ps. Therefore
additional contribution (calculated as the diﬀerence in quadrature) is 53.6 ps including
electronics jitter. The electronics is measured before the pilot run in 2017, and it is∼20 ps. After subtracting the jitter, the diﬀerence between the pilot run and the Sr testis ∼50 ps. This deterioration of the time resolution comes from the diﬀerence of the noise
situations. Fig. 7.32 shows an example of the noise in two counters in the pilot run and
the Sr test. The noise in the pilot run is ∼5 mV which is doubled from that in Sr test. In
Sec. 6.2.5, we observed that the noise aﬀects the time resolution deeply. Fig. 6.20 indicatesthat doubled increased noise is possible to worsen the time resolution by several tens ofps.

CHAPTER 7. TIMING COUNTER PERFORMANCE

122

0.06
0.05

US

0.04

DS

0.03
0.02
0.01
0
0

10

20

30

40

50
60
Number of Hits

Figure 7.27: Number of hits distribution.

However even though the single resolutions are worse√ than the expectation, thanks tomultiple hit scheme the degradation is suppressed by Nhit as shown in Fig. 7.33 andFig. 7.34.
Finally the overall resolution for signal positrons is estimated to be 38.5 ps by weighting with the number of hits distribution of the signal positrons obtained by MC. The
distribution is shown in Fig. 7.35. It is obtained after applying the whole reconstruction
analysis. The time resolution of TC is improved by a factor of 2 from the MEG experiment(76 ps) and satisfy the requirement of ∼40 ps time resolution for a new TC in the MEG
II environment.

7.8

Radiation Hardness

We monitored the current of the each channel. The current increasing indicates how
much radiation damage counters had. Fig. 7.36 shows the distribution of the observed
current increase for 32 hours for US and for 36 hours for DS. We observed 0.4 µA and1 µA increasing in US and DS, respectively, which correspond to 158 µA and 394 µA
current increasing for three years of MEG II running time. In the radiation tests as shownin Sec. 4.5.6, the resolution deterioration of 30 % is expected for the current increase of
100 µA. However by keeping the temperature at 10 degree the dark current can be reduced
and the resolution deterioration are suppressed.

CHAPTER 7. TIMING COUNTER PERFORMANCE

0.35

0.35

0.3

data

0.25

0.3

0.15

0.1

0.1

0.05

0.05
10

15
20
Number of Clusters

0.35

0
0

5

10
15
20
Number of Hits in a Clusters

0.35

0.3

data

0.25

0.3

data

0.25

MC

0.2

MC

0.2

0.15

0.15

0.1

0.1

0.05

0.05

0
0

MC

0.2

0.15

5

data

0.25

MC

0.2

0
0

123

5

10

15
20
Number of Clusters

0
0

5

10
15
20
Number of Hits in a Clusters

Figure 7.28: Number of clusters (left) and number of hits in a cluster (right) for DS (top)and US (bottom).

Figure 7.29: Schematic of the selection way for the resolution estimation with several
number of hits.

Resolutions (s)CHAPTER 7. TIMING COUNTER PERFORMANCE

124

Overall Resolutions−12
80 ×10

60

40

20

0

Pilot Run (Gaussian Accumulation)
Pilot Run (Average)
Expectation from Pretest with 90Sr
2

4

6

8

10
Number of Hits

Figure 7.30: Overall time resolution as a function of number of hits.

Figure 7.31: Gaussian obtained by accumulating fit Gaussian over every counter combinations.

CHAPTER 7. TIMING COUNTER PERFORMANCECounter 150 (Ch 1)

400

Mean

0.005483

Counter 150 (Ch 2)

400

300

300

200

200

100

100

0
0

0.005

0.01
0.015
Noise RMS (V)00Counter 151 (Ch 1)

400

Mean

125

Mean

0.005

0.005407

0.01
0.015
Noise RMS (V)Counter 151 (Ch 2)

0.005526

Mean

0.005757

300
300
200
200
100

100

0
0

0.005

0.01
0.015
Noise RMS (V)00Counter 150 (Ch 1)

600

Mean

0.002564

Mean

0.002481

600

400

200

200

0.005

0.01
0.015
Noise RMS (V)00Counter 151 (Ch 1)

500

0.01
0.015
Noise RMS (V)Counter 150 (Ch 2)

400

0
0

0.005

Mean

0.002487

0.005

0.01
0.015
Noise RMS (V)Counter 151 (Ch 2)

600

Mean

0.002445

400
400
300
200

200

100
0
0

0.005

0.01
0.015
Noise RMS (V)

0
0

0.005

0.01
0.015
Noise RMS (V)Figure 7.32: Typical noise RMS. The top figure is that in the pilot run, and the bottom
is that in the Sr test.

CHAPTER 7. TIMING COUNTER PERFORMANCE
2 Hit

4 Hit

6 Hit

126
8 Hit

10 Hit

50

6
50

50

40

30
40

40
4

30

20

30

30

20

20

20

10

10

10

×10−120−20−10 0 10 20 30 40 50 60 70

×10−120−20−10 0 10 20 30 40 50 60 70

×10−120−20−10 0 10 20 30 40 50 60 702
10

Difference of Time Resolution (ps)Difference of Time Resolution (ps)Difference of Time Resolution (ps)×10−120−20−10 0 10 20 30 40 50 60 70
Difference of Time Resolution (ps)×10−120−20−10 0 10 20 30 40 50 60 70
Difference of Time Resolution (ps)Figure 7.33: Resolution diﬀerence from the expectation from mass test.

Frequency (a.u.)

Figure 7.34: Resolution diﬀerence from the expectation from mass test with number of
hits.

Mean

0

5

8.042

10
15
20
Number of Hits (in Cluster)Figure 7.35: The number of hit distribution from the signal positrons after the full chainof the TC reconstruction in MC.

CHAPTER 7. TIMING COUNTER PERFORMANCE

Figure 7.36: Current increase in pilot run 2017.

127

Chapter 8

Sensitivity Estimation
In this chapter, the sensitivity of the MEG II experiment will be discussed focusing on theperformance of the positron spectrometer.

8.1

Performance of Positron SpectrometerAs shown in the previous sections, the multiple hit scheme is confirmed. The constructed
TC indeed achieves the time resolution of ∼ 38.5 ps. The final goal of the positron
spectrometer for the µ+ → e+ γ search is precisely to reconstruct the positron momentum,
angle, vertex and time on the target. Moreover concerning the poor detection eﬃciency in
the MEG experiment (30 %), achieving a high detection eﬃciency is another goal of the
new spectrometer. In this section, the overall performance of the positron spectrometer
will be discussed.

8.1.1

Combined Reconstruction

The DCH reconstructs the positron trajectory using TC hits information as the time seedand extrapolates the trajectory back to the target to reconstruct the momentum vector at
the emission. At the other end, matching between DCH tracks and TC hits is examined.
A reconstructed track in DCH is propagated to the first hit in each cluster in TC by
calculating the equation of motion in COBRA magnetic field. If propagated position andTC hit position are in 5 σ of their combined resolution, they are matched.

8.1.2

MC Setup

Since DCH installation is not completed yet, the performance is estimated by the simulation. The signal positrons are generated uniformly in 0 < |cos(θ)| < 0.45, and−7/18π < ϕ < 7/18π to cover the acceptance of the spectrometer. In addition, to estimate
pile up eﬀect of Michel positron background, Michel positrons are mixed at 7×107 /s tothe signal events.

8.1.3

Positron Time Resolution

There are two components which contribute to the positron timing resolution, while theother resolutions such as momenta and vertexes come from only DCH directly. One is the
TC measurement whose independent performance is already demonstrated with the realdetector as demonstrated in the previous sections, and the other is the flight time from128

CHAPTER 8. SENSITIVITY ESTIMATION

129

the target to the first hit point on TC calculated from the trajectory reconstructed by
DCH.
As for the first point, all the information of hits in a cluster has to be combined into
a time at the matched point (at the first hit counter). The hit time of each counter isconverted into the time at the matched point by subtracting the propagation time fromthe matched point to the counter impact point, and then all the converted times areaveraged to get the best estimate of the time at the matched point. To estimate thepropagation times, we use the reconstructed trajectory extrapolated from the last DCH
hits. This process was not tested in the pilot run analysis, in which we evaluate the TC
overall performance to be 38.5 ps by the even-odd analysis, due to the lack of DCH. In thesimulation, the time resolution at the matched point is obtained to be 31.0 ps as shownin Fig. 8.2.
The second contribution is shown in Fig. 8.1 and is 14.8 ps. It is large improvementfrom MEG. In the MEG experiment this contribution was 75 ps [40] which is almost
the same as TC performance itself due to scattering by the material between DCH and
TC. The single volume DCH having ability to track positrons just before TC realizes the
reduction of scattering eﬀect, which is one of the keys of positron spectrometer upgrade.

Figure 8.1: Reconstructed flight time between the target and TC obtained by
DCH.

Figure 8.2: TC timing resolution in MC.

The tails in the distribution does not come from pile up. The comparison of theresults between with and without background mixing is shown in Fig. 8.3. There is nolarge diﬀerence in the tail in the comparison. Poor track reconstruction in DCH, multiturn, or delta ray originated signal are possible to make the tail.
In conclusion the overall time resolution of the positron spectrometer is estimated tobeσTe = 41.2 ps(8.1)
as the sum of squared of the measured time resolution of TC and the track contribution
from MC. The time resolution of the spectrometer is more than twice better than that of
MEG (107 ps).

CHAPTER 8. SENSITIVITY ESTIMATION

130

Figure 8.3: Time distribution comparison with pile up (red) without pile up (shaded).
Left shows the flight time between the target and TC, and right shows time distribution
measured by TC.

8.2

Eﬃciency

Since the LXe photon detector limits the geometrical signal acceptance, the positron detection eﬃciency is defined as the ratio to the number of accepted photon events. The
photon acceptance is |u| < 23.9cm, |v| < 67.9cm on the inner face at r = 64.84cm,
and in the simulation the judgment of photon accepted event or not is performed by the
propagation from the inverted momentum of the true positron momentum. The positrondetection eﬃciencies are summarized in Tab. 8.1. The detailed definition and discussion
are as follows.
The distributions of the diﬀerence between the reconstructed observables of the signal
positron and the true ones in MC are shown in Fig. 8.4 for the MC events of signal only
and in Fig. 8.5 for those of signal and background mixed. When seeing the distributionsin Fig. 8.4 and Fig. 8.5, one notices the long tails. When these tail events have correlation
among the observable, it is likely to increase ineﬃciency. To simplify the event which atleast one of reconstructed observable is out of 5 σ is not counted as an event detecting signal
positron and becomes ineﬃciency. Fig. 8.6 shows that which combination of observables
are out of window in the ineﬃciency event by the tail cut. Indeed in ∼70 % of cut events
all the variables are reconstructed out of 5 σ.
Table 8.1: Eﬃciencies (%) in each step in the positron spectrometer.
w/o pile up w/ pile up
Photon accepted events
100
DCH Reconstruction
81.9
63.0
Matching between DCH and TC
78.8
60.6
TC Reconstruction
76.4
56.1

In the DCH reconstruction, since almost all signal positron remain hits in DCH, main
ineﬃciency comes from track reconstruction from reconstructed hits. There are three
ineﬃciency in DCH reconstruction algorithm; (1) tail cut for vertex along Y, vertex alongZ, θ, ϕ, and momentum as mentioned above; (2) propagation miss to TC region definedfrom r = 27 cm; and (3) further quality cut for reconstructed signal track having fake hits

CHAPTER 8. SENSITIVITY ESTIMATION

131

more than 50 %.
Firstly, to recover the ineﬃciency from the tail cut track merge should be improvedin the DCH track reconstruction. Fig. 8.7 shows the number of the reconstructed tracks
without any pile up from Michel positron in MC. Even in the no background environment,
the track merge is sometimes failed. The failure in the track merge worsens the qualityof the reconstruction, which increases the ineﬃciency. The algorithm of the track merge
should be optimized against multiple scattering.
Secondly, 20-30 % of the propagation miss to TC from DCH can be recovered by themodification of the algorithm, while the other is the intrinsic ineﬃciency coming fromthe multiple scattering as shown in Fig. 8.8. The former events have TC hits in thereconstructed track in DCH in which the starting point of the propagation is after TC
hits and lose these hits. Using track segments before merging, the propagation should be
succeeded.

8.3

Expected Sensitivity

The resolutions and the eﬃciencies summarized in Tab. 8.2 are assumed to estimate the
MEG II sensitivity. Notice that the muon decay vertex reconstructed by the positron
spectrometer is used to determine the photon emission angle as the direction from thevertex to the reconstructed photon conversion point in the LXe photon detector; therefore
the resolutions of the vertex aﬀects the measurement of the opening angle.
The time resolution of the LXe photon detector is expected to be 50–70 depending on
the noise situation. Therefore as the positron time resolution is ∼40 ps, the resolutionof teγ is estimated to be 64–80 ps. On the other hand, in the MEG experiment thetime resolutions of the photons and the positrons were 67 ps and 107 ps, respectively,
and the resolution of teγ was 126 ps. Since the timing measurement in the positron side
is significantly improved by the innovative TC, we overcome the limitation of the timemeasurement from the positron side.
Table 8.2: Resolutions (σ) and eﬃciencies of MEG II parameters. Those in MEG are also
shown for comparison.
Parameters
Performanceunit
MEG II
MEG
Resolution (σ)
θe+
5.3
9.4
mrad
ϕe +
3.7
8.7
mrad
Ee+
130
380
keV
+
e vertex (Y)
0.7
1.2
mm
e+ vertex (Z)
1.6
2.4
mm
uγ /vγ /wγ
2.6/2.2/5 5/5/6mm
Eγ (w < 2 cm)/(w > 2 cm)
1.1/1.0
2.4/1.7
%
te+ γ
64-80
126
ps
Eﬃciency (%)
Trigger
≈99
≈99
γ
69
63
e+
56
30

CHAPTER 8. SENSITIVITY ESTIMATION132

In the MEG experiment, the number of the signals, and backgrounds were estimatedto extract the upper limit of µ+ → e+ γ decay at 90 % confidential level by the maximum
likelihood analysis technique with the probability density functions (PDFs) of the observables prepared event by event [1]. The PDFs were also used to generate an ensemble ofthe simulated experiments (toy MC) with the assumption of zero signal to estimate thesensitivity. The sensitivity of MEG was thus defined as the medium of the upper limits
distribution.
Following the MEG analysis, the sensitivity of the MEG II experiment is estimated withthe two assumptions for σte γ to be 64 ps and 80 ps as Fig. 8.9. Even in the conservative
estimation of 70 ps photon timing resolution (which corresponds to σte γ = 80 ps), thesensitivity goes down to 6.3 × 10−14 in three years with the assumption the 140 DAQ daysin each year. Moreover when the time resolution of the LXe photon detector is 50 ps, thesensitivity reaches 5.6 × 10−14 .

CHAPTER 8. SENSITIVITY ESTIMATION

133

Figure 8.4: Distribution of the reconstructed observables without eﬀect of pile up.

Figure 8.5: Distribution of the reconstructed observables with pile up.

CHAPTER 8. SENSITIVITY ESTIMATION

134

Figure 8.6: Correlation between each variable. Combinations are described as binary of(vertexY, vertexZ, θ, ϕ, P, T). When the reconstructed variable is out of 5 σ, 0 is assigned,
while when in the window 1 is assigned.

Figure 8.7: Number of reconstructed tracks with (left) and without (right) quality cut toreconstructed observables

CHAPTER 8. SENSITIVITY ESTIMATION

135

Figure 8.8: Event display of propagation miss to TC from reconstructed track in DCH in
MC. Left: intrinsic ineﬃciency by multiple scattering, Right: event having TC hit amongreconstructed trackBR(µ→ eγ )CHAPTER 8. SENSITIVITY ESTIMATION136

σ Teγ = 64 ps
σ Teγ = 80 ps

−12

10

MEG Final Result

10−13

MEG II in 3 years

10−14
0

20

40

60

80

100
weeks

Figure 8.9: Expected sensitivity in MEG II to exclude the branching fraction with 90%
C.L.

Chapter 9

Summary and Conclusion
To realize the search for the charged flavor violating decay, µ+ → e+ γ, with an unprecedented sensitivity in the MEG II experiment, we have developed a positron timing counter.
It is essential to increase the intensity of the muon beam two times higher than that in
MEG. However it also makes more backgrounds, so the suppression of them is the key ofthe MEG II experiment. In the µ+ → e+ γ decay, a muon emits a positron and a photon
simultaneously toward back-to-back direction having the energy of the half of the muon
mass at the rest coordinate. The µ+ → e+ γ search is exposed to the positrons backgrounds
from Michel decays and the photons backgrounds from the interaction of the positron withany material or the radiative muon decays. At the MEG II beam intensity, the accidental
coincidence of the background positrons and the background photons becomes the dominant background. Since the distribution of the accidental background in the relative time
window is the flat while the signals make a peak, the time measurement of both of positronand photon should be improved to enhance the sensitivity of the µ+ → e+ γ search.
The pixelated design is employed by using a new generation photo sensor, the silicon
photo-multipliers (SiPM), and an ultra-fast plastic scintillator to measure the positron
time with multiple hits which drastically improves the overall time resolution. The finesegmentation of TC also reduces the hit rate of the single counters, which enables TC to
keep its time resolution even in higher positron background environment in the MEG II
experiment.
The construction and installation of TC were completed in 2017. We conducted apilot run successfully in late 2017. The calibration system and slow control system wereoperated in the pilot run. In the pilot run all the counters except for one counter worked
properly. The single counter resolution including electronics jitter is obtained as 98.1 ps.
Though the single counter resolution is worse than the expectation from the intrinsic
counter resolution of ∼80 ps without electronics jitter, the ultimate time resolution below
40 ps is achieved with 8 counters. The obtained performance of the timing counter in thepilot run corresponds to 38.5 ps of the overall time resolution of the timing counter forthe signal positron by scaling the expected number of hits from the signal.
The new trigger system is also successfully tested in the pilot run and we demonstrated
the online time resolution of 415 ps, which reduces the trigger rate more than 50 % from
the MEG experiment.
In the MC study the drift chamber is expected to reconstruct the flight time from thevertex to the timing counter with 14.8 ps resolution. Combining the drift chamber contri137

CHAPTER 9. SUMMARY AND CONCLUSION

138

bution and the timing counter resolution, the time resolution of the positron spectrometeris expected to be 41.2 ps with the positron detection eﬃciency of 56.1 %. The time resolution for the signal positrons is improved to 38% of that in the MEG experiment. Though
the detection eﬃciency still has room for improvement, it is already a large improvementfrom MEG by a factor of 1.87. As a result we can reduce the increasing background withthe higher beam intensity in MEG II. It is concluded that the unprecedented sensitivity in
the MEG II experiment 6 × 10−14 , which improves the sensitivity of the MEG experiment
by one order of magnitude, is achievable with the MEG II detector including the new
innovative timing counter discussed in this thesis.

CHAPTER 9. SUMMARY AND CONCLUSION

139

Appendix A

Global Bias of Time Calibration
The global bias of the time calibration is observed as shown in Fig. 7.20. MC study
indicates that the bias of estimation of the time of flight (TOF) among the counters
makes the global bias in the track-based calibration though the detailed pattern of thebias is diﬃcult to be predicted by MC.
In the MC study, at the beginning, true time oﬀsets are prepared at random with
Gaussian assumption. The true time oﬀset is artificially added to true hit time in MC,
and then the summed time are smeared with the counter resolutions as the reconstructedtime.
In the pilot run, we use the TOFs estimated by MC instead of the tracks reconstructedby DCH. Almost all hits can be classified in three patterns as shown in Fig. 5.3. The true
TOFs of the three pattern in MC are shown in Fig. A.1. By using the mean value of each
TOF distribution, we calibrated the time oﬀsets. Fig. A.2 shows the diﬀerent between thetrue time oﬀsets and the calibrated time oﬀsets. The result has the global bias of ∼50 ps

Figure A.1: TOF distributions for each hit pattern.

Fig. A.3 shows the closer view of Fig. A.1. The true TOF distributions have tailcomponent. When the tail events are not used for the calibration, the bias becomes small
as Fig. A.4. In this case the bias becomes smaller down to ∼20 ps.
140

APPENDIX A. GLOBAL BIAS OF TIME CALIBRATION

141

Figure A.2: Diﬀerent between true time oﬀsets and calibrated time oﬀsets with threepattern TOF estimation

The mean of the TOF distributions are slightly diﬀerent with the counter positions
as shown in Fig. A.5 and these values are used in the pilot run tracked-based calibration.
The result in the MC study is shown in Fig. A.6.
Fig. A.7 shows the result of another MC study in which the estimation of TOF haveno bias, +20 ps bias, and −20 ps bias artificially. We smeared true TOFs with 10 ps
Gaussian event by event as the TOFs used in the fit in track-based calibration. In the
result no global bias is observed. On the other hand, when the estimations have bias, theglobal bias appears in the calibration result. The 20 ps bias generates ∼1 ns global bias.
Therefore even a few ps bias is expected to make observed global bias.
These MC study indicates that the track-based calibration is sensitive to the TOF
estimation and the global bias observed in the pilot run is likely to be caused by the biasof the estimation of TOFs. The global bias is aﬀected by TOF estimation bias of a few pslevel. It is diﬃcult to understand all components which change the TOF distribution, such
as TC position, beam centering, background hits, and so on, in the level of ps. Though wecannot directly expect the global bias behavior for data, this global bias can be detected
and corrected by using RMD events.

APPENDIX A. GLOBAL BIAS OF TIME CALIBRATION

142

Figure A.3: Closer view of TOF distributions for each hit pattern.

Figure A.4: Diﬀerent between true time oﬀsets and calibrated time oﬀsets with tail cut of
three pattern TOF estimation.

APPENDIX A. GLOBAL BIAS OF TIME CALIBRATION

143

Figure A.5: TOF in each position.

Figure A.6: Diﬀerent between true time oﬀsets and calibrated time oﬀset with same TOF
estimation in the pilot run.

APPENDIX A. GLOBAL BIAS OF TIME CALIBRATION

144

Figure A.7: Diﬀerent between true time oﬀsets and calibrated time oﬀsets with TOF
estimation with Gaussian (10 ps) error (black), +20 ps bias (blue), and −20 ps bias (red).

Appendix B

Optimization of Waveform
Analysis
The waveform analysis for the single counter is optimized to perform the best resolution.
The optimization of the single counter design we optimized the analysis for each set up.
In Fig. 4.12 the connection of the SiPMs are compared. Since the waveforms are diﬀerent
each other, we also applied another constant fraction method based on amplitude andrisetime compensation timing, while the final analysis for the TC extracts the time at a
fixed ratio to the signal amplitude as described in Chap. 5. The data and optimal analysis
in Fig. 4.12 is summarized in Tab. B.1.
Table B.1: Resolutions and optimized analysis.
Connection Over Voltage (V) Resolution (ps) Optimal Analysis
Parallel
1.2
85.8
20%
1.4
77.1
15%
1.6
66.1
10%
1.8
62.9
8%
2
59.0
10%
2.2
57.4
8%
2.4
57.2
8%
2.6
57.0
10%
2.8
55.1
8%
Series
0.83
88.4
15%
1.03
74.6
15% 1.5 ns delay
1.23
68.5
15% 2 ns delay
1.43
62.7
10%
1.63
56.4
10% 2 ns delay
1.83
55.3
20% 2 ns delay
2.03
51.4
3%
2.23
50.4
3%
2.33
48.9
3%
2.43
48.9
3%
2.53
51.2
5%

145

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Acknowledgments
Through this study my dreams came true. They were to study science deeply, and to go
abroad and work with colleagues all over the world. I was really lucky to have enrichingtime in Switzerland.
First of all I am deeply grateful to Prof. Toshinori Mori for giving me an opportunity towork on such a wonderful experiment. He supported me and gave me a lot of advice with agenerous heart throughout my PhD. I would like to thank Prof. Wataru Ootani. He always
gave me insightful comments and suggestions. I am thankful to Dr. Toshiyuki Iwamoto.
He is greatly tolerant and supportive for me and all the members of our laboratory all thetime.
My heartfelt appreciation goes to all the members of Timing Counter Group. Dr. Yusuke
Uchiyama led TC group with incisive comments. I learned a lot of things from his advice
and discussion with him. Without his help, this thesis would not have materialized. Dr.
Matteo De Gerone also led TC group from the first stage of TC R&D. He always supported
and encouraged me kindly. Many thanks goes to Mitsutaka Nakao and Masashi Usami forhuge help for this study and sharing wonderful time in Switzerland. I would like to thanksProf. Flavio Gatti, Prof. Gianluigi Boca, Dr. Paolo Cattaneo, Dr. Massimo Rossella,
Fabio Siccardi, Adriano Bevilacqua. They are always very kind for me and gave me helpfuladvice. I feel all the members of TC Group like family in Europe.
I am thankful to all the MEG II collaborators. Advice and comments given by them has
been a great help in this study. I would like to thank to all I met in PSI and Switzerland.
In particular, I really really appreciate Dr. Giada Rutar for being a nice friend andcheering me up. I appreciate all the members of our laboratory, Dr. Ryu Sawada, Dr.
Kei Ieki, Dr. Daisuke Kaneko, Dr. Yuki Fujii, Shinji Ogawa, Kohei Yoshida, Shota
Nakaura, Naoya Shibata, Ryoto Iwai, Linghui Liu, Nobuo Matsuzawa ,Satoru Kobayashi,
Rina Onda, Naoki Tsuji, Tatsuro Torimaru.
My appreciation can not be described enough here. I would like to appreciate all theexperience in Switzerland. Finally my deepest appreciation goes to my family for constantencouragement and moral support.

149