Liquid Xenon Scintillation Detector
for the New µ → eγ Search Experiment
Ph. D. Thesis

Kenji Ozone
March 2005

Department of Physics,
Faculty of Science, University of Tokyo

Abstract

A liquid xenon scintillation detector was constructed as a prototype γ-ray detector
for the MEG experiment, which will start in 2006 at PSI, Switzerland. The prototype
has an active volume of 68.8 liter viewed by 228 PMTs immersed in liquid xenon to
detect γ-rays with precision. The detector performance strongly depends on the purityof liquid xenon. The purification system to remove contaminations in liquid xenon wasestablished to enable the large-sized liquid xenon detector with a long absorption length
over 1 m (90% C.L.). In 2003 a beam test with laser Compton scattering γ rays up
to 40 MeV was performed at AIST. In this test we evaluated the performance of the
prototype detector and verified the performance expected for the 1000-liter liquid xenon
scintillation detector in the MEG experiment. The energy resolution of 5.2% (FWHM)
and the position resolution of 9.9 mm−11 mm (FWHM) are expected for 52.8 MeV γ-rays.
It allows a sensitivity to reach two order below the current upper limit of Br(µ → eγ ).

Acknowledgments
First, I would like to express my great appreciation to my adviser Prof. Toshinori
Mori, the spokesperson of the MEG experiment, for providing me with this work. I am
glad to have learned many things from his insights and deep knowledge of physics andhis enthusiasm for physics experiment. Without his generous help and support this thesis
could not completed.
I would like to express my gratitude to Dr. Satoshi Mihara for his continuous encouragement. I have learned a lot of things from his prominent talent and insight since I
joined the MEG experiment.
I would like to thank Dr. Wataru Ootani for his suitable advice and generous support.
I am glad to feel his great store of knowledge on physics, it stimulated me greatly.
I would like to especially thank Prof. Tadayoshi Doke and Prof. Satoshi Suzuki for
their useful suggestions and information on liquid xenon.
I gratefully acknowledge Prof. Akihiro Maki, Prof. Tomiyoshi Haruyama, and Katsuyu Kasami for supporting us, especially, when we stayed at KEK to perform the purification test.
I would like to acknowledge Prof. Satoru Yamashita for his continuous encouragement
and useful advice.
I would like to thank MEG collaborator, especially Dr. Giovanni Signorelli and Dr.
Donato Nicolò for great help all over the prototype R&D, Stefan Ritt for quickly establishing the data acquisition system and support us in every respect, and Yu. Yuri, A. A.
Grebenuk and D. N. Grigoriev for helping the installation of the prototype detector at
the early stage of the R&D.
I greatly appreciate Dr. Toshiyuki Iwamoto, Dr. Shuei Yamada, Dr. Toshio Nanba,
Hajime Nishiguchi, Ryu Sawada, Yasuko Hisamatsu, Atsuhi Yamaguchi, Toshiya Mitsuhashi, and Takefumi Yoshimura for many discussions and joyful research life. I sincerely
admire their attitude and enthusiasm for MEG experiment. I am glad to have studied
with them in my graduate school life.
I would like to express sincere gratitude to Hiroyuki Toyokawa, Dr. Hideaki Oogaki
for supporting us all over the beam test at TERAS. Without their generous help andsupport, we could not successfully complete the beam test of the LXe detector.
I wish to express my sincere thanks to Prof. Sachio Komamiya for his encouragement
and Prof. Tetsuro Mashimo for useful advice on MC simulation.
I would like to thank the member of ICEPP, University of Tokyo, especially Hajime
Nanjo for discussing many things at midnight.
Thanks to the people who is now working in another place, Dr. Yasuchika Yamamoto
and Dr. Daisuke Toya for joyful research life.
Special thanks go to the people who performed small prototype tests at Waseda university together, Dr. Kazuhiro Terasawa, Toshiyuki Miyazawa, Sunao Takenaka, Dr. Jun
Yashima, Dr. Masaki Yamashita, Go Tejima. I never forget those days at Ookubo.
Finally, I would like to thank my parents, Masataka and Chieko Ozone for theirunderstanding, help, and encouragement on my research.

Contents
Introduction

1

1 Physics in µ → eγ Decay Search Experiment
1.1 Lepton Flavor Violation . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Supersymmetric Grand Unified Theory . . . . . . . . . . . . . . . . . . . .
1.3 Connection with Neutrino Oscillations . . . . . . . . . . . . . . . . . . . .
1.4 µ → eγ Decay Search Experiments . . . . . . . . . . . . . . . . . . . . . .

3
3
3
5
7

2 MEG Detector
2.1 Liquid Xenon Scintillation Detector . . . . . . . . . . . . . . . . . . . . . .
2.2 Beam and Target . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.2 Target . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 The COBRA Positron Spectrometer . . . . . . . . . . . . . . . . . . . . . .
2.3.1 Concept of the Spectrometer . . . . . . . . . . . . . . . . . . . . . .
2.3.2 Thin-wall Superconducting Magnet . . . . . . . . . . . . . . . . . .
2.3.3 Chamber System . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.4 Timing Counter . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10
10
14
15
16
18
18
20
24
25

3 Liquid Xenon Scintillation Detector
3.1 Liquid Xenon Scintillator . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1 Why Liquid Xenon? . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.2 Properties of Xenon . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.3 Scintillation of LXe . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Strategy of Development of LXe Detector . . . . . . . . . . . . . . . . . . .
3.3 100-liter Prototype of LXe Scintillation Detector . . . . . . . . . . . . . . .
3.4 Photomultiplier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5 Cryogenics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5.1 Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6 Monte Carlo Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . .

28
28
28
29
31
33
35
38
40
42
44

4 Purification and Absorption Length
4.1 Optical Properties of LXe . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Xenon Purification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 Absorption Length Estimate . . . . . . . . . . . . . . . . . . . . . . . . . .

45
45
47
47

i

CONTENTS

ii

5 Performance of the 100-liter Prototype
5.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Laser Compton Scattering beam test at AIST . . . . . . . . . . . . . . . .
5.3 Trigger and Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . . .
5.4 PMT Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.1 Gain Adjustment . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.2 QE Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.3 Long-term Stability . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.4 Noise Estimate . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5 Incident Beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.6 Position Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.6.1 Position Reconstruction in Simulation . . . . . . . . . . . . . . . . .
5.6.2 Depth Reconstruction in Simulation . . . . . . . . . . . . . . . . . .
5.6.3 Position Reconstruction . . . . . . . . . . . . . . . . . . . . . . . .
5.6.4 Depth Dependence . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.6.5 Energy Dependence . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.6.6 Difference between the Data and the Simulation . . . . . . . . . . .
5.6.7 Intrinsic Position Resolution . . . . . . . . . . . . . . . . . . . . . .
5.6.8 Systematic Error . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.6.9 Position Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.7 Energy Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.7.1 Compton Edge . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.7.2 Fitting Function . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.7.3 Fitting Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.7.4 Depth Dependence . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.7.5 Energy Dependence . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.7.6 Intrinsic Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.7.7 Systematic Error . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.7.8 Energy Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.7.9 Energy linearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

53
53
54
58
61
61
64
67
67
68
70
70
73
74
74
79
81
81
82
83
83
83
84
85
86
90
90
91
93
95

6 Expected Performance96
6.1 Expected Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
6.1.1 Effect of Absorption Length . . . . . . . . . . . . . . . . . . . . . . 96
6.1.2 Energy Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
6.1.3 Position Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
6.1.4 Timing Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
6.1.5 Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
6.2 Backgrounds and Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . 102
6.2.1 Prompt Background . . . . . . . . . . . . . . . . . . . . . . . . . . 103
6.2.2 Accidental Background . . . . . . . . . . . . . . . . . . . . . . . . . 103
6.2.3 90% C.L. Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . 107
6.3 Decay Angular Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . 107
6.4 Prospects for Further Improvements of Performance . . . . . . . . . . . . . 109
6.4.1 New PMT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
6.4.2 Waveform Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
6.5 Calibration Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

CONTENTS

iii

7 Conclusion

114

A 10-liter prototype of Liquid Xenon Scintillation Detector

115

List of Figures
1.1
1.2
1.3
1.4

Diagrams of µ+ → e+ γ in SU(5) SUSY models. . . . . . . . . . . . . . . .
Predictions of µ+ → e+ γ branching ratio in SU(5) SUSY models. . . . . . .
Possible solutions for solar neutrino oscillations in the tan2 θ vs ∆m2 parameter space after the recent SNO measurements. . . . . . . . . . . . . .
µ → eγ branching ratios as a function of the mass of the right-handed
gauge singlet νR2 for the different (LMA and LOW) solutions allowed by
the solar neutrino experiments. . . . . . . . . . . . . . . . . . . . . . . . .

4
4
6

6

2.1
2.2
2.3

Schematic view of the MEG detector. . . . . . . . . . . . . . . . . . . . . . 11
Principles of the MEG detector. . . . . . . . . . . . . . . . . . . . . . . . . 12
A schematic view of the liquid xenon scintillation detector for the MEG
experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.4 PSI accelerator facility and ring cyclotron. . . . . . . . . . . . . . . . . . . 14
2.5 Schematic of the MEG beam line layout up to the injection into the COBRA spectrometer magnet. . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.6 Schematic view of the COBRA positron spectrometer. . . . . . . . . . . . . 18
2.7 Problems with an uniform solenoidal magnetic field and advantages of agraded magnetic field. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.8 Rate of Michel positrons per cm2 per second. . . . . . . . . . . . . . . . . . 20
2.9 Design view of the coil and cryostat of the COBRA magnet. . . . . . . . . 21
2.10 Contour plot of the magnetic field produced by the COBRA magnet andmagnetic field along the magnet axis measured with a coil current of 200 A. 22
2.11 Stray magnetic field measured in the photon detector region in the excitation test. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.12 Cross-sectional view of a part of a chamber sector. It consists of two layersof drift cells staggered by half-cell. . . . . . . . . . . . . . . . . . . . . . . 24
2.13 Structure of the cathode vernier strips. . . . . . . . . . . . . . . . . . . . . 25
2.14 A sector of the drift chamber and an assembly of 16 sectors. . . . . . . . . 26
2.15 Configuration of the timing counter. . . . . . . . . . . . . . . . . . . . . . . 27
2.16 Geometry of the timing counter hodoscope with PMTs. . . . . . . . . . . . 27
3.1
3.2
3.3
3.4
3.5

Xe phase diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Photon cross section of Xe atoms and mean free path in LXe. . . . . . . .
Xe and NaI(Tl) pulse form. . . . . . . . . . . . . . . . . . . . . . . . . . .
Decay curves of scintillation signals from LXe measured for electrons, αparticles, and fission fragments. . . . . . . . . . . . . . . . . . . . . . . . .
Schematic view of the 100-liter prototype of the LXe scintillation detector.

iv

30
32
33
34
36

LIST OF FIGURES
Schematic view of the PMT holder and picture of the PMT holder in the
100-liter prototype detector. . . . . . . . . . . . . . . . . . . . . . . . . . .
3.7 Charge multiplication process in the metal channel dynode PMT. . . . . .
3.8 Voltage divider circuit of R6041Q. . . . . . . . . . . . . . . . . . . . . . . .
3.9 Tolerance of R6041Q against magnetic field. . . . . . . . . . . . . . . . . .
3.10 Pulse tube refrigerator for LXe detector. . . . . . . . . . . . . . . . . . . .
3.11 Control software of the cryogenic system of the 100-liter prototype developed with LabVIEW. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.12 An example of MC simulation for 40-MeV γ ray. . . . . . . . . . . . . . . .

v

3.6

4.1
4.2
4.3
4.4

4.5
4.6
5.1
5.2
5.3
5.4
5.5
5.6
5.7

Absorption coefficient and light absorption. . . . . . . . . . . . . . . . . . .
Mass spectrum obtained in the residual gas analysis. . . . . . . . . . . . .
Setup for circulation and purification of xenon. . . . . . . . . . . . . . . . .
A number of photoelectrons when the purification had just begun and when
the purification was finishing and light yield transition for cosmic-ray muon
events. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Light yield transition for α particle events. . . . . . . . . . . . . . . . . . .
Comparison of α data in the LXe to simulation data. . . . . . . . . . . . .

37
39
39
40
41
43
44
48
49
49

50
51
51

Schematic view of TERAS. . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
Setup for LCS beam. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
Experimental setup in TERAS beam test. . . . . . . . . . . . . . . . . . . 56
Energy spectra depending on the diameter size of the 2nd collimator. . . . 57
The clusters for generating trigger. . . . . . . . . . . . . . . . . . . . . . . 59
Data flow diagram in LCS beam test. . . . . . . . . . . . . . . . . . . . . . 60
ADC spectra and the relation between σ 2 s and the mean channels in gain
adjustment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.8 Gain distribution of 228 PMTs. . . . . . . . . . . . . . . . . . . . . . . . . 63
5.9 The relation between ADC mean and variance for 4 pairs of LEDs. . . . . 63
5.10 Short-term and long-term stability. . . . . . . . . . . . . . . . . . . . . . . 64
5.11 The spectra for α particle in the experiment and in the simulation. . . . . 65
5.12 QE estimated from gas and liquid data. . . . . . . . . . . . . . . . . . . . . 66
5.13 Long-term stability in α runs over the beam test. . . . . . . . . . . . . . . 67
5.14 Typical pedestal distribution of 1 channel and the sum of all channels. . . . 68
5.15 Impinging points of γ rays in this test. . . . . . . . . . . . . . . . . . . . . 69
5.16 Schematic histograms of charge distribution on the front face. . . . . . . . 71
5.17 Difference between true and reconstructed positions in simulation. . . . . . 72
5.18 Difference between the local weighted mean and simple weighted mean. . . 72
5.19 The relation between Nf (0.5) and local weighted mean in MC simulation. . 73
5.20 The relation between Nf (0.5) and the first conversion depth. . . . . . . . . 73
5.21 Scatter plot of reconstructed and the true first conversion depths and residual distribution after reconstruction. . . . . . . . . . . . . . . . . . . . . . 74
5.22 The relation between the depth parameter Nf and the local weighted mean. 75
5.23 Examples of the fitting result with a 2-dimensional double Gaussian. . . . 75
5.24 Position resolution as a function of Nf (0.5) for EC = 10 MeV, impinged at
P0 and P9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

LIST OF FIGURES

vi

5.25 Position resolution as a function of Nf (0.5) for EC = 20 MeV, impinged at
P0 and P9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.26 Position resolution as a function of Nf (0.5) for EC = 40 MeV, impinged at
P0 and P9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
5.27 The resolution of the local weighted mean in σ as a function of γ-ray energy. 80
5.28 LCS beam spectra in this test. . . . . . . . . . . . . . . . . . . . . . . . . . 84
5.29 Pile-up events in high beam current (EC =10 MeV). . . . . . . . . . . . . . 84
5.30 Measured energy spectrum for LCS beam. . . . . . . . . . . . . . . . . . . 85
5.31 The relation between χ2 /ndf as a function of the lower limit of the fitting
range, and an example of the fitting. . . . . . . . . . . . . . . . . . . . . . 86
5.32 Energy resolution as a function of Nf (0.5) for EC = 10 MeV, impinged at
P0 and P9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.33 Energy resolution as a function of Nf (0.5) for EC = 20 MeV, impinged at
P0 and P9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.34 Energy resolution as a function of Nf (0.5) for EC = 40 MeV, impinged at
P0 and P9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.35 LCS beam spectra with various horizontal electron bunch size in TERAS. . 91
5.36 LCS beam spectra for collimator displacement of 0 mm to 4 mm. . . . . . 92
5.37 The energy resolution σu as a function of γ-ray energy. . . . . . . . . . . . 94
5.38 Incident LCS beam energy vs measured energy in Npe and energy linearity
for data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
6.1
6.2

A reconstructed energy spectrum for 52.8-MeV γ rays by the linear fit. . . 97
The expected energy resolutions for 52.8 MeV γ rays as a function of theabsorption length. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
6.3 The energy resolution vs. absorption length in the final detector by MC
simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
6.4 Energy resolution by mask analysis. . . . . . . . . . . . . . . . . . . . . . . 100
6.5 Selection efficiency as a function of Nf (0.5). . . . . . . . . . . . . . . . . . 102
6.6 Integrated photon yield per muon decay fγ (y). . . . . . . . . . . . . . . . . 106
6.7 Integrated pile-up photon yield per muon decay fγγ (y). . . . . . . . . . . . 106
6.8 The relation between the muon stop rate and the 90% C.L. sensitivity. . . 107
6.9 The sensitive region for the decay angular measurement with an assumptionof SU(5) SUSY-GUT and Br(µ+ → e+ γ )> 10−12 . . . . . . . . . . . . . . . 109
6.10 Two types of PMTs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
6.11 The principle of the operation of the DRS chip. . . . . . . . . . . . . . . . 111
6.12 Typical waveform of PMT signal from about 50-MeV γ rays taken with theprototype of the DRS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
6.13 Schematic view of calibration with CEX beam. . . . . . . . . . . . . . . . . 113
A.1 Cross-sectional view of 10-liter prototype of LXe scintillation detector andits vessel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
A.2 The position resolution with the 10-liter prototype detector. . . . . . . . . 116
A.3 The energy resolution with 10-liter prototype detector. . . . . . . . . . . . 117
A.4 The timing resolution with the 10-liter prototype detector. The resolution
is expected to be about 50 psec for over 20, 000 photoelectrons. . . . . . . . 117

List of Tables
1.1
1.2

Upper limits of Br(µ → eγ ) in the last 30 years. . . . . . . . . . . . . . . .
LFV search experiments in the near future. . . . . . . . . . . . . . . . . . .

7
9

2.1
2.2
2.3
2.4

Characteristics of the Ring Cyclotron. . . . . . . . . . . . . . . . . . . . . .
Main properties of πE5. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Comparison of material for the target. . . . . . . . . . . . . . . . . . . . .
Parameters of the COBRA magnet. . . . . . . . . . . . . . . . . . . . . . .

15
15
17
22

3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8

Properties of various scintillators. . . . . . . . . . . . . . . . . . . . . . . .
Main properties of liquid Xe. . . . . . . . . . . . . . . . . . . . . . . . . . .
Scintillation photon of LXe. . . . . . . . . . . . . . . . . . . . . . . . . . .
Three versions of LXe scintillation detectors. . . . . . . . . . . . . . . . . .
The properties of the PMT (R6041Q). . . . . . . . . . . . . . . . . . . . .
Refrigerator performance. . . . . . . . . . . . . . . . . . . . . . . . . . . .
Heat load in the cryostat of the 100-liter prototype. . . . . . . . . . . . . .
Parameters and values in the MC simulation for the 100-liter prototype
detector. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

29
29
31
33
38
42
42

4.1

44

Optical properties of LXe. . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8

Ring parameter and laser properties for LCS beam. . . . . . . . . . . . . . 55
Typical overall noise results. . . . . . . . . . . . . . . . . . . . . . . . . . . 68
Energy and position of impinging beam in this test. . . . . . . . . . . . . . 69
Position resolution from measured data. . . . . . . . . . . . . . . . . . . . 79
Position resolution from MC simulation. . . . . . . . . . . . . . . . . . . . 79
Deterioration of position resolution by electronics noise. . . . . . . . . . . . 81
The effect by fluctuation of LCS beam energy. . . . . . . . . . . . . . . . . 82
Difference of the position resolution by changing parameters in the MC
simulation for QE estimate. . . . . . . . . . . . . . . . . . . . . . . . . . . 83
5.9 Energy resolution measured in LCS beam test. . . . . . . . . . . . . . . . . 90
5.10 Energy resolution in MC simulation. . . . . . . . . . . . . . . . . . . . . . 90
5.11 Deterioration of energy resolution by electronics noise. . . . . . . . . . . . 90
5.12 Difference in position resolution between collimator displacement of 0 mm
and one of 3 mm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
5.13 Deterioration of the energy resolution by changing parameters in QE estimate. 93
5.14 Combined systematic errors for energy resolution. . . . . . . . . . . . . . . 93
6.1

Energy resolution by mask analysis. . . . . . . . . . . . . . . . . . . . . . . 101
vii

LIST OF TABLES
6.2

viii

Expected detector performances. Every values are in FWHM. . . . . . . . 103

Introduction
Now that the neutrino oscillation phenomena have been established, any new physics
scenario beyond the Standard Model (SM) necessarily involves lepton flavor violation(LFV) also in the charged lepton sector. There is no way to prevent it in principle.
Particularly, TeV supersymmetry, the most expected among various new physics scenarios, predicts large branching ratios for some of the LFV processes that are alreadyconstrained by the current experimental limits. These large LFVs may be induced byultra heavy right-handed neutrinos that cause seesaw mechanism and/or by grand unification of quarks and leptons at the GUT energy scale. Thus an experiment capable
to detect these LFV processes should be able to explore new physics at extremely highenergies beyond the SM and even beyond the supersymmetric (SUSY) SM.
The most promising LFV process is the rare muon decay µ+ → e+ γ . The pastexperimental searches for this process were limited by accidental background events, where
positrons from the standard Michel decays of muons coincide with gamma rays comingfrom either radiative muon decays or annihilations of positrons. In order to go beyond
the limitations of these past experiments, it is essential to devise innovative detectors ofhigher performance.
A µ → eγ event is characterized by the clear 2-body final state where the decay
positron and the gamma ray are emitted in opposite directions with energies equal to half
the muon mass (E = Mµ /2 = 52.8 MeV). While positrons with the signal energies areabundant from the Michel decays, gamma rays with such high energies are very rare: thegamma ray spectrum falls off rapidly near the signal energy region. If we improve theenergy resolution for gamma rays δEγ , the accidental background rate decreases, at least,as (δEγ )2 . Thus a gamma ray detector with a very good energy resolution is a key to any
new µ → eγ experiments.
A novel liquid xenon scintillation detector, which we are presenting in this thesis, wasproposed and has been developed to fulfill the requirements of a new µ → eγ experiment
MEG [1–3] that is planned to start physics runs at Paul Scherrer Institute in 2006 withan initial sensitivity of 10−13 . In this thesis, ideas, preparations, various examinations,and performance of this newly devised detector are described in detail.
The structure of this thesis is as follows. The physics motivation of the MEG experiment is described in Chapter 1. In Chapter 2 the detectors of the MEG experiment aresummarized. Logistics and technical details of the liquid xenon scintillation detector are
given in Chapter 3. The most important issue of this detector, absorption of scintillation
light inside the detector, is fully discussed in Chapter 4. Chapter 5 deals with the main
subject of this thesis, i.e. evaluation of the performance of the liquid xenon scintillation
detector, where a beam test using gamma rays from laser Compton scattering and its re-1

LIST OF TABLES

2sults are presented in detail. After we discuss the evaluated detector performance and theprospects for the MEG experiment in Chapter 6, a brief conclusion is given in Chapter 7.

Chapter 1
Physics in µ → eγ Decay SearchExperiment
1.1

Lepton Flavor Violation

In the Standard Model, lepton flavor conservation is built in by hand with assumed
vanishing neutrino masses. The introduction of neutrino masses and mixing into theStandard Model also predicts immeasurably small lepton flavor violation (LFV). On theother hand, fundamental theories such as Supersymmetry (SUSY) generically predict LFVat a measurable level. Lepton-flavor-violating processes such as µ+ → e+ γ are therefore
very clean (i.e. not contaminated by the background of the Standard Model) and at thesame time present a promising area to hunt for signals of profound new physics.
Taking the case of the recent (gµ − 2) results. Despite the improvement of a factorof two in the experimental uncertainty [4] the measured value lies between 1.6 σ − 2.6 σStandard Model prediction, depending on the way the theoretical value is computed. We
just note here that a real discrepancy between the measured and the Standard Model
predicted (gµ − 2)/2 ∼ 10−9 could imply µ+ → e+ γ rates close to 10−11 in the frameworkof supersymmetric theories [5].
In the following two sections we briefly discuss the predicted rates for the µ+ →e+ γ decay in grand unified supersymmetric theories caused by slepton mixing due toradiative corrections and by the inclusion of a see–saw mechanism for the neutrino masses.
We observe that these two sources of LFV are independent and always present in all
supersymmetric grand unified models.
LFV has recently been examined also in the framework of theories with extra spatial
dimensions (see for instance [6]). Rates above 10−14 are again expected and the experiment
proposed here would therefore be crucial even in testing these new ideas.

1.2

Supersymmetric Grand Unified Theory

LFV processes are especially sensitive to the supersymmetric extensions of the Standard
Model, in particular supersymmetric grand unified theories (SUSY-GUT). In SUSY-GUT,
finite slepton mixing appears through radiative corrections in the renormalization groupevolution from the GUT to the weak energy scale, even if the slepton mass matrix isassumed to be diagonal at the Plank scale [7]. It has been pointed out that the slepton
3CHAPTER 1. PHYSICS IN µ → Eγ DECAY SEARCH EXPERIMENT

4mixing thus generated can be very large owing to the heavy top-quark mass [8], thereby
enhancing µ+ → e+ γ decay through the loop diagrams shown in Fig. 1.1.
~0
B

(a)

2

M1

(b)

~0
B

µ

( m l~R ) e

mµ
~
µR

µ

~e
R

~
µR

~
µL

µ

e

µ

2

( m l~R ) e<h1,2>

~e
R

e

γ

γ
<h2>

(c)

µ

~0
H1
µ

fµ

~0
B

2

µ

( m l~R ) e
~
µR

~e
R

~0
B

0
1

M1
~0
B

0

H2

<h1>

(d) H~

2µ( m l~R ) e
µ

e

fµ

~
µR

~e
R

e

γ

γ

Figure 1.1: Diagrams of µ+ → e+ γ in SU(5) SUSY models.
The predicted branching ratio of µ+ → e+ γ in SUSY SU(5) models [9] is shown in
Fig. 1.2. It ranges from 10−15 to 10−13 for the singlet smuon mass mµ̃R of 100 to 300 GeV.
ft (M)=2.4

-10

µ >0

M 1 =50GeV

ft (M)=2.4

-10

10

µ <0

M 1 =50GeV

10
Experimental boundeγ )Experimental bound

Br( µ

-12

-12

10

10

tan β =30

tan β =30
tan β =10tan β =10

-14

10

-14

10

tan β =3tan β =3

-16

-16

10

10

-18

-18

10

10

-20

10

-20

100

120

140

160

180

200

220

240

260

280

300

10

100

120

140

160

180

200

(GeV)

m ~e

m ~e

(a)

(b)

R

220

240

260

280

300

(GeV)

R

Figure 1.2: Predictions of µ+ → e+ γ branching ratio in SU(5) SUSY models [7].

CHAPTER 1. PHYSICS IN µ → Eγ DECAY SEARCH EXPERIMENT

5

Recent combined analyses of the four LEP experiments have excluded most of the
SUSY parameter space with tan β < 10 [10]. The predicted µ → eγ rates for higher tan βvalues should be measurable by the experiment proposed here.
The SO(10) SUSY-GUT models predict an even larger rate than for SU(5) (10−13 to10−11 ) due to an enhancement factor of (m2τ /m2µ ) ∼ 100 [8], induced by the loop diagrams
whose magnitude is proportional to the tau-lepton mass.

1.3

Connection with Neutrino Oscillations

The phenomenon of neutrino oscillations which has been established by experimental
observation of atmospheric [11–13] and solar [14–20] neutrinos implies both non-zero neutrino masses and LFV.
In SUSY models, neutrino mixing is expected to enhance the rate of LFV processes
such as µ+ → e+ γ [21–23]. A possible contribution to the slepton mixing between µ̃ andẽ is from V21 (between ν1 and ν2 ), corresponding to the mixing needed to explain the solar
neutrino deficit.
The recent SNO solar neutrino observations [15], when combined with all the previous
measurements, confine the mixing parameters to two allowed regions, namely the MSW
large mixing angle solution (LMA) and the MSW large angle–low ∆m2 (LOW) solution,
as shown in Fig. 1.3. The plot in Fig. 1.4 shows the predictions for µ+ → e+ γ decay
corresponding to the two solutions as a function of the mass of the right-handed gauge
singlet νR2 . The vacuum solutions is also shown for completeness though it is excludedby the SNO analysis. The width of the predicted bands is associated with the possible
tan β parameter values. We observe again (see the previous section) that the lowest tan βvalues, corresponding to lower µ → eγ rates, are highly disfavored by the recent analysesof the LEP data [10].
In conclusion, the µ+ → e+ γ branching ratio, when combined with ∆m2 and mixing
angle measurements by solar neutrino experiments, will determine or severely constrain
the mass scale of the right-handed gauge singlet, postulated to exist at ultra high energies(1012 − 1015 GeV).

log(∆m 2/eV 2 )CHAPTER 1. PHYSICS IN µ → Eγ DECAY SEARCH EXPERIMENT

6

(b)
-4

LMA

-5
-6

LOW

-7
-8
90% CL-995% CL
99% CL-10

99.73% CL

-11
-12

-4

-3

-2

-1

0

1

log(tan2 θ)Figure 1.3: Possible solutions for solar neutrino oscillations in the tan2 θ vs ∆m2 parameter
space after the recent SNO [15] measurements.
-3

-8

10

10

-4

10

-9

10

MSW large angle
MSW small angle

-5

10

-10

10

Experimental
bound

-6

A
LM

-7

10

-11

10

-12

10

SW

MSW large angle
small massM

Br( µ e γ )∆ m2 (eV 2 )

10

-8

uu

-14

Just so

10

-11

Va
c

-10

10

m

-13

10

-9

10

M
SW

LO

W

10

-15

10

10
-3

10

-2

-1

10

10

sin2 2 θ

1

1012

1013

1014

MνR2 (GeV)

Figure 1.4: µ → eγ branching ratios as a function of the mass of the right-handed gauge
singlet νR2 for the different (LMA and LOW) solutions allowed by the solar neutrino
experiments. The vacuum solution case is shown for completeness though excluded by
the SNO experiment (from ref. [23]).

CHAPTER 1. PHYSICS IN µ → Eγ DECAY SEARCH EXPERIMENT

1.47µ → eγ Decay Search Experiments

A history of µ → eγ search experiments and their obtained upper limits of the µ →eγ branching ratio are listed in Table 1.1
Year Experiment
1977
–
1977
TRIUMF1979–
1986 Crystal Box
1999
MEGA

Site
SIN (presently PSI)
–
LANL
LANL
LANL

Upper Limit
1.0 × 10−9
3.6 × 10−9
1.7 × 10−10
4.9 × 10−11
1.2 × 10−11

Reference[24, 25][26][27, 28][29][30]

Table 1.1: Upper limits of Br(µ → eγ ) in the last 30 years.
A µ → eγ event is characterized by the clear 2-body final state. The decay electron
and the gamma ray are emitted in opposite directions with the same energy equal to half
the muon mass. To utilize this simple kinematics in the search, muons are stopped ina material (a stopping target). Positive muons are used to avoid capture by the target
nuclei.
So-called “surface muons” are abundantly produced by bombarding primary protons
into a thick production target. The surface muons come from the decays of pions thatstop near the surface of the production target and have a sharp momentum spectrum
around 29 MeV/c. Because of this narrow momentum spread, they are easily stopped bya thin target (≈ 100 µm). This is important for achieving good resolutions in measuring
positrons and reducing background of annihilation gamma rays. With the naturally 100%spin polarized surface muons, angular distribution of µ → eγ can be measured after the
discovery. This measurement could eventually pin down the right GUT model.
The major background in a µ → eγ search is accidental coincidence of a positron,coming from standard Michel decays, and a gamma ray, coming from radiative muon decays or annihilation of positrons. Since the accidental background increases quadraticallyas the muon rate, a continuous, DC muon beam, that has the lowest instantaneous rate,
is best suited for a µ → eγ search, rather than a pulsed beam. To achieve a sensitivityof 10−14 with a detection efficiency ² ≈ 10% within one year’s time T ≈ 107 sec, a muon
rate of 1014 /²/T = 1014 /0.1/107 ≈ 108 /sec is necessary.
Requirements on detectors, particularly gamma ray detectors, are very severe. They
must have very good resolutions in energy, position and time, both for positrons andgamma rays, to distinguish µ → eγ from the accidental background. In short, very good
detectors are most demanding in a µ → eγ search.
Another LFV process, a so-called µ− → e− conversion (µN → eN), has a similar
physics sensitivity as µ → eγ in terms of possible experimental reach for generic SUSYLFV vertices.
In a µ− → e− conversion a muon converts into an electron by exchanging a virtual photon (or something more exotic) with the capture nucleus. The electron has amonochromatic energy of Eµ→e = Mµ − δ, where Mµ is the muon mass and δ is a sumof the binding energy of the muonic atom and the nuclear recoil energy. So the experimental signature is simple: a single monochromatic electron with Eµ→e (105.1 MeV for
Al target). Negative muons must be used to form muonic atoms with the target nuclei.

CHAPTER 1. PHYSICS IN µ → Eγ DECAY SEARCH EXPERIMENT

8

For generic photonic LFV vertices, physics sensitivity of µ → e conversion is two ordersof magnitude lower than µ → eγ : (µ → e conversion)/(µ → eγ) = 1/390 for Al target,
1/249 for Ti, and 1/340 for Pb in terms of branching ratios. Thus, a µ → eγ branchingratio of 1×10−14 corresponds to 3×10−17 for µ → e conversion. To achieve this sensitivity,
a negative muon beam of an intensity of 1010 - 1011 /sec is necessary.
Getting such a high muon rate is a big issue. Because there is no “surface muon beam”
for negative muons, such a high intensity beam tends to have a much broader spectrum
and is usually contaminated by various other particles, particularly pions.
Major backgrounds in a µ → e conversion search are (a) electrons from muon decays
in orbit and (b) beam-related background.
The energy Ee of the “decay in orbit” electron has a spectrum falling off rapidly as(Eµ→e −Ee )5 . By improving the electron energy resolution σEe , this background decreases
as σE5 e . Since the energy resolution is dominated by energy loss in the stopping target, athinner target is required. However, stopping efficiently a broad spectrum of muons in athin target is quite difficult.
There are various beam-related background caused by beam contaminants such aspions. For example, pions may be radiatively captured by the target nuclei, emitting
gamma rays which subsequently convert into electrons. Thus, in short, a very good muon
beam is most demanding in a µ → e conversion search.
The MECO (Muon Electron COnversion) experiment [31], the first of the plannedµ− → e− experiments, was proposed to search for µ → e conversion at a sensitivity below
10−16 . For µ → e conversion events occurring at 1×10−16 , 5 signal events may be detectedwith 0.5 background events in one year running according to their proposal. It was scientifically approved in 1997 by Brookhaven National Laboratory and its construction wasrecently approved for the fiscal year of 2005. It will take at least 5 years for construction.
The use of a graded-field solenoid to collect pions leads to a 1000 fold increase in muon
intensity (to 1011 /sec) over the previous experiment. This idea was originally proposed
for a Russian experiment [32].
A 30 nsec pulsed proton beam is extracted every 1.35 µsec during a 0.5 sec beam spillfrom the Alternating Gradient Synchrotron (AGS). To avoid beam-related background,the MECO experiment only operates 0.6 µsec after the beam pulse, when all the backgrounds have fallen off.
To stop a broad spectrum of muons, 17 layers of 0.2 mm thick Al targets are used.
Aluminum is chosen as target material, because its muon capture lifetime (0.9 µsec)
matches the measurement cycle while heavier elements have much shorter lifetimes.
PRISM (Phase-Rotated Intense Slow Muons) [33] is an ambitious project to produce
high intensity muon beam with narrow energy spread and less contamination, proposed
to be built at the J-Parc 50 GeV proton ring, currently under construction at Tokai,
Japan. A Fixed-Field Alternating Gradient synchrotron (FFAG) is used to carry out“phase rotation,” i.e. a conversion of an original short pulse beam with wide momentum
spread (±30%) into a long pulse beam with narrow momentum spread (±3%) by strong
RF field. After 5 turns in the FFAG ring for the phase rotation, pions in the beam all
decay out. Given 1014 protons /sec from the J-Parc ring, the PRISM facility should be
able to provide 1011 − 1012 muons/sec.
There are still several R&D items to study: for example, low energy pion production
and capture system, and injection/extraction of muons into/from the FFAG ring. A
real-size FFAG ring, which may be used for PRISM later, is being constructed at Osaka

CHAPTER 1. PHYSICS IN µ → Eγ DECAY SEARCH EXPERIMENT

9

University for R&D studies.
PRIME (PRISM Mu E) [33] is a proposed experiment to search for µ → e conversion
at the future PRISM facility. Because of a very low duty factor of the PRISM beam,
the experiment has to handle an extremely high instantaneous rate of 1010 - 1011 muons
per beam bunch. In the PRIME experiment a curved solenoid spectrometer is used totransport only electrons with desired momenta from the stopping target to the detector.
Thanks to PRISM’s good quality muon beam, with a higher efficiency and a better momentum resolution, a sensitivity of the level of 10−18 may be expected according to theirLetter of Intent, although a detailed design of the experiment still does not exist.
Table 1.2 summarizes these coming LFV experiments.
Experiment
Site (Country)
Search for
Sensitivity in BR
Beam Intensity (µ/s)
Start in/at

MEG
MECO
PSI (Switzerland) BNL (U.S.A.)µ → eγµN → eN
−13
−14
10
− 10
3 × 10−17
8
up to 1 × 10
1011
2006
>2010

PRISM/PRIME
J-Parc (Japan)µN → eN10−181011 ∼ 1012
unknown (LoI only)

Table 1.2: LFV search experiments in the near future. Note that physics sensitivity of a
µN → eN experiment with the same sensitivity in branching ratio is 1/300 - 1/400 worse
than a µ → eγ experiment.

Chapter 2
MEG Detector
A schematic view of the MEG detector is shown in Fig. 2.1. The MEG detector consistsof two characteristic detector components: a liquid xenon (LXe) scintillation detector anda COBRA positron spectrometer.
Principles of the MEG detector are illustrated in Fig. 2.2. A positive muon beam witha intensity of 108 /sec extracted from the πE5 beam channel at the PSI is brought to stopin a thin target placed at the center of the superconducting magnet. The γ-rays fromthe target traverse the thin superconducting magnet of the COBRA spectrometer andare detected by the LXe scintillation detector. The momentum and the emission angle ofthe positrons from the target are precisely measured by the drift chamber system placed
inside the superconducting magnet and the timing of the positrons are also measured by
the timing counters.
In this chapter we will give a brief description of each detector component.

2.1

Liquid Xenon Scintillation Detector

Xenon has been widely used as a detector material in different fields. It can be usedas either scintillation detector or ionization detector. Xenon scintillator has high lightyield (75% of NaI(Tl)) and fast signals as shown in Table 3.3 and Fig. 3.3. These properties
enable very precise energy and time measurements of γ-rays. Scintillation signal fromliquid xenon has a short tail which serves to minimize pile-up of accidental γ-rays underhigh-rate background. The properties of xenon are described in detail in Sec. 3.1.
The design of the γ-ray detector in MEG experiment is shown in Fig. 2.3. We use
only scintillation photons from the LXe and do not attempt to collect ionizations. This
makes the design of the detector quite simple. Scintillation photons from the LXe arecollected by ∼800 photomultiplier tubes (PMTs) from all sides which are immersed in
800-liter LXe.
All the PMTs will be read with high-precision waveform digitizers with a sampling
speed of 2.5 GHz or higher. The precise measurements of the total charge and the arrival
time of each pulse result in accurate determination of the energy and the timing of the
γ-ray. Furthermore, the waveform analysis allows us to avoid pile-up of accidental γrays which is quite important in searching for rare event under high-rate background.
The output distribution over the 800 PMTs also provide us detailed information on theinteraction positions of the γ-rays and the pile-up of accidental γ-rays.

10

CHAPTER 2. MEG DETECTOR

11

Compensation coil
COBRA magnet

µ

m
a
e
b

LXe scintillation
detector
Drift chamber
Timing counter
Figure 2.1: Schematic view of the MEG detector.

The design goal of the LXe detector to enable search for µ → eγ with a sensitivity ofBr ∼ 10−13 is the following:• Time resolution: ∆t = 100 psec (FWHM).
• Position resolution: ∆x = ∆y = 2 mm, ∆r = 7 mm (FWHM).
• Energy resolution: ∆E = 1.4% (FWHM).
• No deterioration even under high rate background.
This design is quite challenging because LXe scintillation detector with this scale has
never been built before as far as we know. We therefore built two smaller prototypes
before starting the construction of the full-scale detector to gain experiences in detector
operation and to prove the excellent performance of this novel detector.
The first prototype was a 10-liter LXe detector. After some feasibility study withthe 10-liter prototype we built the second prototype with 100-liter LXe in order to verify
the performance of the final detector with more realistic conditions. In this thesis, wewill mainly discuss the expected performance of the final detector on the basis of theresults from the various tests carried out with the 100-liter prototype. The details will be
described in later chapters.

CHAPTER 2. MEG DETECTORCOBRA Magnet

12

Liquid Xenon
Scintillation Detectorγ

Thin Superconducting Coil

Stopping Target+

Muon Beam

Timing Countere

Drift Chamber

1m

γ

+

e

Drift Chamber

Figure 2.2: Principles of the MEG detector.

CHAPTER 2. MEG DETECTOR

13

H.V.
Signals

Refrigerator
Cooling pipe

Vacuumfor thermal insulation

Al Honeycomb
window

MEG

Liquid Xe

TargetPMT

Epoxy−Resin filler

050

100 cmFigure 2.3: A schematic view of the liquid xenon scintillation detector for the MEG
experiment.

CHAPTER 2. MEG DETECTOR

2.2

14

Beam and Target

Figure 2.4: PSI accelerator facility (right) and ring cyclotron (left).
The PSI accelerator facility is one of the most prominent in the world. The facility
and the ring cyclotron are shown in Fig. 2.4. This accelerator can create a proton beamof the highest power of the world.
The protons are accelerated to a fixed energy of 590 MeV in the ring cyclotron. Its
principal components are eight sector magnets and four accelerator cavities (50.63 MHz
frequency) with a peak voltage each of 730 kV.
The 72 MeV beam from either one of two injector cyclotron (Injector 1 or Injector2) enters from the back of the cyclotron, is injected into an orbit in the center of thering, accelerated over about 220 revolutions and extracted at the full energy as shown in
2.4. The design is based on criteria that allow operation at very high beam intensities:
an open structure of four large and powerful RF-cavities providing a high acceleration
voltage, and a flat-top cavity operating at the third harmonic of the accelerating RFvoltage. The resulting strong, phase-independent energy gain per revolution gives goodturn separation and hence beam extraction with low beam losses. This is a mandatory
condition for high current operation in a cyclotron. The properties of the ring cyclotron
is summarized in Table 2.2.

CHAPTER 2. MEG DETECTOR
Injection Energy
Extraction Energy
Extraction Momentum
Energy spread (FWHM)
Beam EmittanceBeam Current
Accelerator Frequency
Time Between Pulses
Bunch Width
Extraction Losses

15
72 MeV590 MeV
1.2 GeV/c∼ 0.2 %∼ 2π mm·mrad
1.6 mA DC
50.63 MHz19.75 ns
∼ 0.3 ns
∼ 0.03

Table 2.1: Characteristics of the Ring Cyclotron.

2.2.1

Beam

The πE5 channel in the PSI facility extracts low-energy pion and muon beams from thethick production target at an angle of 175◦ with respect to the primary proton beam. The
main characteristics of the beam are listed in Table 2.2. For the MEG experiment thebeam channel will be tuned to ≈ 28 MeV/c to collect surface muons (muons coming fromthe decay at rest of pions on the production target surface). Measurements, performed
before starting the MEG experiment, indicate that we can expect a beam intensity up to(8 − 10) × 108 µ+ /s for the primary proton current of 1.5 mA [34].
solid angle acceptance
momentum range
lengthmomentum band (FWHM)
momentum resolution (FWHM)
horizontal emittancevertical emittancespot size

150 msr
20 − 120 MeV/c
10.4 m10%2%
15.3 cm·rad
3.6 cm·rad
4 × 4 cm2

Table 2.2: Main properties of πE5.
In order to be able to reach the best sensitivity to the µ → eγ decay it is necessary
to have a well understood beam transport system delivering a high intensity surface
muon beam (up to 1 − 2 × 108 µ+ /s) with a minimum spot-size and a small momentum
spread, that must be stopped in a thin target, with a minimum of contaminant particles(positrons) entering the detectors.
For examining these issues extensive studies have been performed at the πE5 channel[35] and the final design of the transport system from the exit of the beam line up to theinjection into the COBRA spectrometer magnet has been made recently. This will becomprised of a ’two-stage’ arrangement, as shown schematically Fig. 2.5.
There are four main components in the system: (i)The extraction element, Triplet I,a quadrupole triplet which couples to the present ’Z’-branch 1 of the πE5 channel. (ii)1

There are two branches in the PSI πE5 channel, called ’U’ and ’Z’. The MEG experiment will beCHAPTER 2. MEG DETECTOR

16

Figure 2.5: Schematic of the MEG beam line layout up to the injection into the COBRA
spectrometer magnet.

The WIEN-filter, an (E∧B) crossed-field, vertically deflecting separator, necessary forgood beam positron suppression. (iii) Triplet II, necessary for good optical focusing at
the collimator system placed behind this triplet. (iv) BTS or beam transport solenoid,
which is used as a coupling element to the final COBRA spectrometer, as well as housing
the momentum degrader/ collimator system.
It has been proved, in these consecutive studies, that a good separation quality between
the muons and background positrons can be achieved with a vertical spot-separation of
approximately 12 cm, corresponding to a 7.2σ separation and that a stop rate on thetarget can reach close to 1×108 µ/s at a beam current of 1.8mA and a 6cm production
target for secondary beam [35].
Setup of the beam line is in progress and will be finished in the year 2005 together
with construction of the beam line elements such as the WIEN-filter, BTS, and collimatorsystem.

2.2.2

Target

The target will be placed at a slant angle of 22◦ (corresponding to a slant ratio of 1 : 2.5) atthe center of the COBRA spectrometer magnet. Three kinds of material, Mylar, Polyethylene, and Kapton, have been investigated for the target material from view points of multiple scattering and radiation length. The result is summarized in Table 2.3. Assuming
a central beam momentum of 28MeV/c, with a momentum bite of 6.4%, the mean range
is calculated to be ∼1100µm for Polyethylene and ∼870µm for both the other material.
Supposing that we use a 100µm Mylar or equivalent thickness Polyethylene/Kapton, necessary thickness for the degrader will be as summarized in Table 2.3. Note that the target
will be places with a slant angle, resulting in total thickness of the target and degradersmaller than the mean range.
performed at the ’Z’-branch.

CHAPTER 2. MEG DETECTOR

17

Material

Density

Radiation Length

Mean Range
Target Degrader(28 MeV/c muon)∼870µm
100µm
600µm

Mylar

1.39 g/cm3

28.7cm

0.95 g/cm3

47.9cm∼1100µm

150µm

700µm

1.42 g/cm3

28.6cm∼1100µm

150µm

700µm

(C5 H4 O2 )nPolyethylene(CH2 )nKapton(C22 H10 N2 O5 )nTable 2.3: Comparison of material for the target.

Thus, overall, it seems that Polyethylene is the best material from both a background suppression (radiation length) and a beam quality (multiple scattering, or material amount) point of view. Design work of the mechanical structure to fix the target,with a ”zero-material” target suspension system, is underway. It is quite important totake into account the experience and knowledge obtained by the previous experiments,
mainly MEGA and the Crystal Box Collaborations. In addition the use of special calibration targets, like a liquid-hydrogen target for producing π 0 s through the charge exchange
process, has been duly noted and will also be taken into account carefully.

CHAPTER 2. MEG DETECTOR

2.3

18

The COBRA Positron Spectrometer

The COBRA (COnstant Bending RAdius) positron spectrometer consists of a magnet
specially designed to form a graded magnetic field, a drift chamber system to measure
the positron momentum, and scintillation counters to measure the positron timing. Its
schematic view with a typical trajectory of a 52.8-MeV positron is shown in Fig. 2.6.

Stopping Target
Muon Beame+e+Superconducting
Solenoid

Timing Counter
Drift Chamber

Drift Chamber

1m

Figure 2.6: Schematic view of the COBRA positron spectrometer.

2.3.1

Concept of the Spectrometer

Most of spectrometers makes use of solenoidal magnetic field to select charged particles’
momentum. In case of muon decay it can confine low momentum tracks within a certain
radius so that a large fraction of Michel positrons do not reach the track-detectors locatedat large radii. However, as shown in Fig. 2.7(a), in a simple uniform solenoidal field suchas the one adopted in the MEGA experiment, positrons emitted close to 90◦ make manyturns in the tracking chamber, therefore causing problems in pattern recognition or evendisturbing a stable operation of the chambers. Also, the bending radius of positrons of agiven absolute momentum depends on the production angle, which makes it difficult toselect high momentum tracks, as shown in Fig. 2.7(b).
In order to avoid these problems, we have adopted a solenoid with a graded magnetic
field, which provides the central field of 1.27 Tesla at z = 0 and slowly decreasing field as|z| increases. As shown in Fig. 2.7(c), the positrons emitted close to 90◦ are swept awayby this graded magnetic field much more quickly than in the case of the uniform magnetic
field.
The graded magnetic field is arranged such that monochromatic positrons from thetarget follow trajectories with a constant projected bending radius independent of theemission angle, as shown in Fig. 2.7(d): the bending radius is determined by the absolute
momentum and not by its transverse component. This allows us to define the absolute
momentum window of positrons to be detected by the drift chamber cells.

CHAPTER 2. MEG DETECTOR

19

(a)

(b)

(c)

(d)

Figure 2.7: Problems with an uniform solenoidal magnetic field and advantages of a gradedmagnetic field: (a) r − z view of the solenoid shown with the trajectory of a particle
emitted at 88◦ making many turns inside the detector. (b) Trajectories of monochromaticparticles emitted at various angles. The bending radius depends on the emission angle.
(c) r −z view of the COBRA spectrometer shown with the trajectory of a particle emitted
at 88◦ . The particle is swept away much more quickly than one in (a). (d) Trajectories
of monochromatic particles emitted at various angles. The bending radius is independentof the emission angle.

CHAPTER 2. MEG DETECTOR

20

Figure 2.8: Rate of Michel positrons per cm2 per second as a function of radius assuming
a muon decay rate of 1 × 108 /s.

Fig. 2.8 shows the rate of Michel positrons estimated by Monte Carlo simulation. It
is shown in a unit of the rate per cm2 per second as a function of radius for a muon decayrate of 1 × 108 /s. By placing the chamber at a radius larger than 20 cm the counting rate
can be contained to a level below the limit of stable chamber operation. It is important toremark that the rates at the outermost radii are especially low, which facilitates reductionof the background in the signal region.

2.3.2

Thin-wall Superconducting Magnet

The COBRA magnet consists of a main superconducting magnet and a pair of compensation coils which is adopted to reduce the stray magnetic field around the photon detector.
The superconducting magnet consists of five coils with three different radii; one central
coil, two gradient coils, and two end coils. A resistive (i.e. non superconducting) cable
will be used for the compensation coil. Fig. 2.9 shows the layout of the magnet coils.
The magnet is designed to form a graded magnetic field so as to achieve the good
features of the positron spectrometer as explained in the previous section.
The parameters of the COBRA magnet are listed in Table 2.4, whereas Fig. 2.10(a)shows the contour plot of the calculated magnetic field distribution produced by the
COBRA magnet. The field intensity along the magnet axis is shown in Fig. 2.10 (b)superimposed with measured values. The performance of the spectrometer and the strayfield around the photon detector were optimized by adjusting the diameter, length, andcurrent density of the coils. The five superconducting coils are connected in series andthe current density of the coil is controlled by changing the density of the cable winding
and operating current, as summarized in Table 2.4. A detailed description of the COBRA
magnet can be found in [35–37].
Within the acceptance of the photon detector (|θ| ≥ 70◦ ), the thickness of the magnet
is reduced to 0.197X0 so that the photons from the target, placed at the center of the mag-

CHAPTER 2. MEG DETECTOR

21

Figure 2.9: Design view of the coil and cryostat of the COBRA magnet.

net, can traverse. In order to achieve this thickness a high-strength aluminum-stabilized
conductor was specially developed [38, 39].
The stray field produced by the superconducting coils, has to be reduced to a levelof 50 Gauss in the vicinity of the photon detector as will be described in later sections.
This is necessary since the photomultiplier tubes used in the photon detector would sufferCHAPTER 2. MEG DETECTOR

22

Table 2.4: Parameters of the COBRA magnet.
Coil
Conductivity
Inner dia. (mm)Outer dia. (mm)Length (mm)z of coil center(mm)
LayersCentral
Super
699.1
711.6
240.3

Gradient
Super
809.1
820.6
110.4

Inner end
Super
919.1
929.5
189.9

Outer end
Super
919.1
929.5
749.2

Compensation
Resistive
2210
2590
265

0

±235

±405.4±874.95

±1190

4

3

267

Turns (total)
Winding density(Turns/m)

1068

240

3
624 (1st-2nd)
92(3rd)1548

14Turns per layer

4
123 (1st)
92(2nd-4th)
399

280

4444.43614.11263.82066.21056.6f-w

f-w

double pancake

0.35
360
23
7
3.3

2.29
360
148
28
5.3

0.54
360
35
1620
0.02

e-w

Inductance(H)Current (A)Energy E (kJ)
Weight M (kg)E/M (kJ/kg)

1.64
360
106
9
11.8

e-w(1st)f-w(2nd-4th)
0.62
360
40
4
10.0

B [T]

Winding

80

20

0.7

0.65
0.6

Compensation coilz>0z<0Calculation

0.55
0.5
0.45
[Tesla]

0.4
0.35
0.3
0.25

Center of magnet

End coil
Gradient coil
Central coil

Liquid xenon

(a)

0.2
0

0.2

0.4

0.6

0.8

1

1.2

1.4
|Z| [m](b)

Figure 2.10: (a) Contour plot of the magnetic field produced by the COBRA magnet; (b)Magnetic field along the magnet axis measured with a coil current of 200 A.

from gain variations as the applied magnetic field strength was changed. This would
lead to a performance degradation of the calorimeter and will be avoided by the use of

CHAPTER 2. MEG DETECTOR

23

200
B[Gauss]

180
160
140
120
100
80

m
R[

200
180
160
140
120
100
80
60
40
20
0
1200
1100
1000
900
800
700
600

B[Gauss]the compensation coils. Fig. 2.11 shows a distribution of stray magnetic field aroundthe photon detector measured during excitation tests. The measurement was done at
50% operating current and the field strength shown in the figure is normalized to the fulloperating current. It can be seen that the field strength in the photon detector region iscompensated as designed and well below requirement.
Excitation tests were carried out several times on site. Quench propagation was measured by inducing a quench via several methods as described in [35], enabling us to confirm
safe operation of the magnet.

m

60

]

40

-400 -200-800 -600

0

200

400

600

20
800
Z[mm]

Figure 2.11: Stray magnetic field measured in the photon detector region in the excitation
test. The measurement was done at 50 % operating current. The field strength shown inthis figure is normalized to the full operating current.

CHAPTER 2. MEG DETECTOR

2.3.3

24

Chamber System

Positron tracks are measured with 16 drift chamber sectors aligned radially at 10◦ intervals
in azimuthal angle. Each sector consists of two staggered arrays of drift cells, as shownin Fig. 2.12.

t1
sense
wire

t2

Vernier Pads

Particle trajectory

10mm←− radial direction
Figure 2.12: Cross-sectional view of a part of a chamber sector. It consists of two layersof drift cells staggered by half-cell.
This staggered-cell configuration allows us to measure the r-coordinate and the absolute time of the track simultaneously. It is expected that the difference between the drift
times (t1 − t2 ) in the adjacent cells gives the r-coordinate of the track with 100 − 200 µm
accuracy, while the mean time (t1 + t2 )/2 gives the absolute time of the track with ∼ 5 ns
accuracy. This excellent timing resolution is important for the pattern recognition.
By the ratio of charges observed at both ends of a sense wire the z-coordinate along
the wire can be initially located with an accuracy of ∼ 1 cm. The chamber walls are madeof thin plastic foils. A thin layer of aluminum deposit on the four cathode foils is shaped
to make a Vernier pattern as shown in Fig. 2.13. By a comparison of the charges inducedon the two sets of Vernier pads of each cell it is possible to determine the z position withan accuracy of about 300 µm as reported in [35]The chamber sectors and the volumes between them are filled with 50% He − 50%
C2 H6 gas mixture at 1 atm. Such a mixture is chosen to have sufficient ionization loss
in the gas (∼ 65 e− /cm for minimum ionizing particles) as well as to minimize multiple
Coulomb scattering of tracks (X0 ∼ 650 m). This mixture has proved to work well inseveral existing experiments like BELLE [40] and BaBar [41]. The drift velocity saturates
at roughly 4 cm/µs for a relatively low electric field (∼ 1.5 kV/cm) [42].
Fig. 2.14 shows the structure of a chamber sector and an assembly of 16 sectors to
be inserted into the COBRA magnet. A foil of Kapton, 12.5 µm thick, is stretched on aframe made of carbon fiber. An array of sense and potential wires are also strung between
the end-arms of the frame. Each frame with wires and foils is fixed to a support structure
made of G10, which is then fixed to the inner wall of the magnet cryostat.

CHAPTER 2. MEG DETECTOR

25

Figure 2.13: Structure of the cathode vernier strips.

2.3.4

Timing Counter

This detector is designed to measure the positron timing with a resolution better than
100 ps in FWHM and to be used in the trigger for selecting events containing a positron
coincident in time and collinear in direction with a photon identified in the photon detector. Hodoscope arrays of plastic scintillators are placed on both ends of the positron
spectrometer to provide the positron timing and trigger signal.
Fig. 2.15 shows the configuration of the timing counter, which consists of scintillator
hodoscope and fiber bundle layers, orthogonally placed along φ and z directions, respectively. Each scintillator hodoscope is viewed from both ends by two photomultipliers,
which measure the pulse heights as well as the arrival times of the scintillation light (tLand tR ) at both ends. The time difference tL − tR provide another measurement of the
impact point along the scintillator, while the mean time (tL + tR )/2 measure the absolute
impact time. For obtaining redundancy in z measurement a scintillating-fiber bundle layer
is equipped on each hodoscope layer. Each scintillating-fiber bundle (5mm × 10mm) isviewed by avalanche photo-diodes from both ends.
Because the detector is located under the magnetic field of the COBRA magnet,
all the relevant devices must be operational under magnetic field. Due to this a finemesh dynode type photomultiplier (PMT) with a 2-inch diameter is chosen for hodoscope
readout and the relative angle of the PMT to the magnetic field is carefully designed asshown in Fig 2.16. Performance tests of a full-size prototype have been conducted in thereal COBRA magnetic field using a pulsed blue laser (60 psec pulse width) in order toinvestigate the gain and transition time spread of the PMT, and light transmission in thehodoscope.
As already mentioned above, an avalanche photo-diode (APD) will be employed for the
scintillating-fiber bundle readout. This is because the APD keeps a good response evenunder the magnetic field due to its compact structure, and has better sensitivity to lightthan the PMT although attention has to be paid to handle small amplitude signal due
to its lower gain. Vigorous studies on the APD is in progress to finalize the design in thecollaboration. It is also an important issue to develop readout electronics with minimum
amount of material in the magnet to avoid unexpected background to the photon detector
while keeping the signal quality.

CHAPTER 2. MEG DETECTOR

26

Figure 2.14: A sector of the drift chamber and an assembly of 16 sectors. Only 6 sectors
are shown in the assembly.

CHAPTER 2. MEG DETECTORe+27(t ϕ) R
int
t Po
pac

Im

(t z ) R(t ϕ) Le+(t z )L
e+

z
ϕ

1m

Figure 2.15: Configuration of the timing counter.

Figure 2.16: Geometry of the timing counter hodoscope with PMTs.

Chapter 3
Liquid Xenon Scintillation Detector
We adopt liquid xenon scintillator as a detector material as described in Sec. 2.1. The
general properties of liquid xenon as a scintillation material and the technical details of
the design of the 100-liter prototype detector are described in this chapter.

3.1

Liquid Xenon Scintillator

As described in Sec. 2.1, the requirement for γ-ray detector in MEG experiment is quite
high. After some investigation, we chose liquid xenon (LXe) scintillator instead of crystal
scintillators such as NaI, CsI, BGO, and so on in order to detect 52.8 MeV γ rays withaccuracy. In this section, we describe the properties of the LXe scintillator as a detectormaterial to show the advantages of the use of LXe in the γ-ray detector in the MEG
experiment.

3.1.1

Why Liquid Xenon?

The requirements for the scintillator medium for the gamma-ray detector in the MEG
experiment are the following,• Large light yield• Short radiation length• Short decay time
• Short rise timeIs there such a scintillator medium? In general scintillators can be classified into two
categories: organic and inorganic. Organic scintillators have fast response but have low
light yield. Inorganic ones have high light yield but have slow response. Table 3.1 showsmain features of various scintillators. For example PbWO4 has a short decay time but
a low light yield. NaI(Tl), BGO, and CsI(Tl) have high light yield but long decay time.
On the other hand LXe has good points of both organics and inorganics. LXe can beconsidered the best scintillator for the γ-ray detector in the MEG experiment.
LXe has some other advantages. Because LXe is not a crystal, the shape can bechanged as we like and it is free from a problem of non-uniformity, cracks, and aging.
28

CHAPTER 3. LIQUID XENON SCINTILLATION DETECTOR

29

Table 3.1: Properties of various scintillators.
Density (g/cm3 )Radiation length (cm)Mollier radius (cm)Decay Time (nsec)
slow component
Emission peak (nm)slow component
Light yield relative to NaI

LXe
2.98
2.77
4.2
45

NaI(Tl)
3.67
2.59
4.5
250

178

LAr
1.40
14
7.2
6.7
1620
127

0.75

0.9

1

410

CsI(Tl) CsI
4.53
4.53
1.85
1.85
3.8
3.8
1000
10
36
565
305
480
0.4
0.1

BGO PbWO4
7.13
8.28
1.12
0.89
2.4
2.2
300
5
410

440

0.15

0.01

It is difficult for crystal scintillators to be purified again after starting experiments. In
case of LXe, it is possible to remove impurities at any moment. In fact, we developed acirculation purification system for xenon, which will be detailed in Sec. 4.2.

3.1.2

Properties of Xenon

Chemical and physical properties of xenon are summarized in Table 3.2.
Disadvantage of LXe is that we have to keep it at low temperature. We overcome thisproblem by using a vacuum-insulated cryostat and proper cooling system.
Table 3.2: Main properties of liquid Xe.
Material Properties
Atomic Number
Atomic Mass
Density at 161.35 K
Boiling point
Melting point
Temperature at triple point
Pressure at triple point
Density at triple point
Gas/Liquid volume ratio
Radiation length
Critical Energy
Moliere radius

Value & Unit54
131.29 amu
2.98 g/cm3
165.05 K
161.25 K
161.30 K
0.805 atm
2.96 g/cm3
518.9
2.77 cm
14.5 MeV
4.2 cm

Ref.
[43]
[44]

[45]
[46]
[47]
[47]

Fig 3.1 shows the phase diagram of xenon. LXe is normally kept at 165 K and 1.3 atm
in our detector. In this figure it can been seen that the temperature range of the liquid
at 1.3 atm is narrow. A stable and powerful cryogenic system to keep the liquid stably isa key technology in the LXe detector. The cryogenic system in the 100-liter prototype isbased on a cooling with a mechanical refrigerator and liquid nitrogen and is described indetail in Sec. 3.5

CHAPTER 3. LIQUID XENON SCINTILLATION DETECTOR

Pressure [atm. absolute]

10

30

2

liquid

10

solid

gas

1

10

−1

120

140

160

180

200

220

Temperature [K]Figure 3.1: Xe phase diagram.

240

260

CHAPTER 3. LIQUID XENON SCINTILLATION DETECTOR

3.1.3

31

Scintillation of LXe

LXe has been known as a good medium for scintillators. Since the late 1970s, many new
devices with liquid rare gas have been proposed and developed in the fields of elementary particle physics, nuclear physics, and astrophysics experiments. Properties of xenon
scintillation are listed in Table 3.3. Some properties of xenon scintillation are not yet
understood well.
Table 3.3: Scintillation photon of LXe.
Properties
Emission peakSpectral width
Refractive index
Wph for 1 MeV electrons
Wph for α particles
Decay time (recombination)
Decay time (Fast Components)
Decay time (Slow Components)
fast : slow
Absorption length
Scattering length

Value & Unit
Ref.
178 nm[48, 49]
14 nm[48, 49]
1.57 to 1.72
[50–53]21.6 eV[54]
17.9 eV
[54]
45 ns
[55]
4.2 ns
[55]
22 ns
[55]
1 : 0.43[55]> 100 cm
Chap. 429 cm to 50 cm [56–59]

The spectrum of LXe scintillation light has a single peak at 178 nm. The wavelengthis slightly shorter than that of gaseous xenon (GXe).
Decay of LXe scintillation signal has two components: fast component and slow component. The fast and slow component is related to the light emission process:Xe∗ + Xe + Xe → Xe∗2 + Xe,
Xe∗2 → 2Xe + hν,

(3.1)
(3.2)

where Xe∗ is the first excited level of xenon, and hν is VUV scintillation photon. The
recombination process is presented by
Xe+ + Xe
Xe+
2 +e
Xe∗∗
Xe∗ + Xe + Xe
Xe∗2

→
→
→
→
→

Xe+
2,
∗∗
Xe + Xe,
Xe∗ + heat,Xe∗2 + Xe,
2Xe + hν,

(3.3)
(3.4)
(3.5)
(3.6)
(3.7)

where Xe+ is a singly-ionized xenon, and Xe∗∗ is the second excited level. In both processes, the excited dimer (excimer) Xe∗2 is de-excited to the dissociative ground state byemitting a single VUV photon since the energy gap between the lowest excited level andthe ground state is so large that there is no decay channel such as non-radiative transition.
It is impossible for Xe scintillation photons to be re-absorbed by Xe molecules. since
they are not emitted by the excited state Xe∗ but by the excimer Xe∗2 [55]. This meansthat the scintillation photons are not absorbed by xenon itself.

CHAPTER 3. LIQUID XENON SCINTILLATION DETECTOR

32

104

2

Attenuation Coefficient [cm /g]

Fig. 3.2 shows a cross section and mean free path of photon in xenon. The mean freepath is 4.8 cm for 52.8 MeV and the maximum of mean free path is about 10 cm. In
order to let 52.8-MeV gamma rays deposit their whole energy, the detector depth has tobe 50 cm at least, being estimated from a simulation.

103

10

L-shell2

Photoelectric Absorption
K-shell

10Rayleigh Scattering

Total Attenuation1
10-1
Compton Scattering

Pair Production

10

-2

10-3
10-3

10-2

10-1

1

10

102

103

Mean Free Path [cm]Photon Energy [MeV]
102

10

1
10-1

10

-2

10-3

10

-4

10-5
10-3

10-2

10-1

1

10

102

103

Photon Energy [MeV]
Figure 3.2: Photon cross section of Xe atoms (upper) and mean free path in LXe whenits density is 2.98 g/cm3 (lower).

CHAPTER 3. LIQUID XENON SCINTILLATION DETECTOR

33

Fig. 3.3 shows a typical LXe scintillation signal from γ-ray of 320 keV. In this figurea typical NaI(Tl) signal is also shown for comparison. It is clearly seen that the rise anddecay time of LXe signal are much shorter than NaI(Tl) signal. LXe signal has the risetime of less than 10 nsec and the pulse settles down to ground level typically in 200 nsec.
The short rise time and decay time of the signal are quite important features of the
LXe scintillator for precise timing measurements and minimizing pile-up under high rate
background, respectively.
Fig. 3.4 shows signals of the LXe scintillator from various kinds of particles. It can beseen that the decay time strongly depends on the particle type. This indicates that it ispossible to discriminate particle type using pulse shape.

PMT output

0
−0.4
−0.8

LXe

−1.2

NaI(Tl)
0

200

400

600

Time [nsec]
Figure 3.3: Typical LXe scintillation signal from 320 keV γ. A NaI(Tl) scintillation signal
is also shown. The unit of PMT output is arbitrary. The pulses are normalized in thepulse height for comparison.

3.2

Strategy of Development of LXe Detector

We constructed two prototypes for demonstrating the performance of the planned LXe
γ-ray detector in the MEG experiment. For comparison the specifications of the two
prototypes and the planned final detector are summarized in Table 3.4.
Table 3.4: Three versions of LXe scintillation detectors.
Type
Fiducial volume
Shape
PMT
Cooling method
γ-ray energy for testing

Prototype10-liter
100-liter
2.34 liter68.6 liter
rectangular
rectangular
32
228
LN2
refrigerator+LN2
up to 1.8 MeV up to 128 MeV

Final design
1000-liter∼800 liter
C-shape∼800
refrigerator+LN2
up to 128 MeV

CHAPTER 3. LIQUID XENON SCINTILLATION DETECTOR

34

Figure 3.4: Decay curves of scintillation signals from LXe measured for electrons, αparticles, and fission fragments. [60]The details of the 10-liter prototype are described in Appendix A. We constructed alarger prototype with 100-liter liquid xenon after the feasibility study with the 10-liter
prototype in order to evaluate the performance achievable in the final detector with more
realistic conditions. The details of the design and the performance of this larger prototype(100-liter prototype) are described in the following sections.

CHAPTER 3. LIQUID XENON SCINTILLATION DETECTOR

3.3

35

100-liter Prototype of LXe Scintillation Detector

The energy of γ-ray source used in the tests with the 10-liter prototype was limited up to∼1.8 MeV because of its small volume and the system such as cryostat and vessel, andPMT holding frame were simplified and specialized for the 10-liter prototype.
On the other hand the 100-liter prototype can be considered to be a detector with thesame scale as in the final detector except for its limited acceptance.
The purposes of the 100-liter prototype can be summarized as follows,• Evaluate detector performance with hinger-energy γ rays
• Introduce cryogenic system based on a mechanical refrigerator• Study the long term stability of the detector• Develop the slow control system for stable operation of the detector• Develop a purification system.
A schematic view of the 100-liter prototype detector is shown in Fig. 3.5. It has
an active volume of 372 × 372 × 496 mm3 (69 `) viewed from all sides by 228 PMTs
assembled into a rectangular shape (Fig. 3.6). The cryostat consists of thermal insulated
vessels equipped with a pulse tube refrigerator [61, 62] and a liquid nitrogen cooling pipe.
Several sensors are used inside the vessels for monitoring temperatures and pressures.
For avoiding interactions of γ-rays before the active volume of the detector the incidence face should not be massive. A thin aluminum plate and a honeycomb window madeof stainless steel are used as an entrance window. Only 0.01% of incident gamma-rays interact in this entrance window. Thickness of the material used in the front face including
the PMTs and the holder is as thin as 0.24 X0 within the entrance window as illustrated
at the bottom of Fig. 3.5.
The signals from the PMTs are taken out of the cryostat with a high-density feedthrough which was originally developed for the liquid argon calorimeter in ATLAS experiment [63].
In order to reduce the amount of the liquid the space outside the active volume isstuffed with hollow fillers made of SUS and aluminum plates.
The detector is equipped with 8 blue LEDs and four 241 Am α sources, two LEDs
and one α source on each lateral face, for PMT calibration. Three pairs of trigger counters (TC1, TC2, and TC3) are placed above and below the vessel to select cosmic raymuons traversing the LXe for various tests.

CHAPTER 3. LIQUID XENON SCINTILLATION DETECTOR

TC1

TC2

TC3

36

Upper Trigger Counters for cosmic rays

Signal Cables
Vacuum Pump
for Inner Chamber
Xenon
HV cables

Liquid Nitrogen
Pulse Tube
Refrigerator

Outer vessel
Vacuum Layer
for Thermal Insulation

Gas Xenon

Inner Vessel
Liquid Xenon
228 PMTs(R6041Q)

Xenon Level Meter

SUS
Honeycomb

Acrylic Filler

e / γ beam
Aluminum
Window

Vacuum Pump
for Outer Chamber

α source (241Am)
blue LEDs

Aluminum Filler

Aluminum Dummy PMTs

Aluminum Filler

Copper Heater
TC1

TC2

2

3

TC3

Lower Trigger Counters for cosmic rays
Materials

1A
0.24 X 0

B0.24 X 0

4
5

6

7

8

9

1. Aluminum Window
2. Vacuum
3. SUS Honeycomb
4. Acrylic Cover
5. PMT Tip Tube & Protecter
6. G10−base PCB
7. SUS Tube
8. Quartz Window
9. Liquid Xenon

thickness
0.1 mm
20 mm
16 mm
29 mm
30 mm
2.5 mmFigure 3.5: Schematic view of the 100-liter prototype of the LXe scintillation detector.

CHAPTER 3. LIQUID XENON SCINTILLATION DETECTOR

37372 mm
496 mmy

372 mm

(a)

z

x

(b)
Figure 3.6: (a) Schematic view of the PMT holder. (b) Picture of the PMT holder in the
100-liter prototype detector from the front. Front face structure is mainly made of G10
and acrylic.

CHAPTER 3. LIQUID XENON SCINTILLATION DETECTOR

3.4

38

Photomultiplier

Photomultiplier (PMT) is the most essential item in the LXe detector. The PMTs are
immersed in the LXe to collect as many scintillation photons as possible. The requirements
for the PMT in the LXe detector can be summarized as follows:• Operational at LXe temperature (165 K).
• VUV-sensitive photo-cathode.
• VUV-transparent window• Pressure-proof up to 3 atm.
• Compact• Low out-gassing.
We have been developing the PMT to meet these severe requirements in cooperation
with HAMAMATSU photonics. The properties of the PMT (HAMAMATSU R6041Q)
used in the 100-liter prototype are summarized in Table 3.5. Fig. 3.7 illustrates the charge
multiplication process in the metal channel dynode PMT. The voltage divider circuit of
the R6041Q is shown in Fig. 3.8.
Table 3.5: The properties of the PMT (R6041Q). These are typical values.
Properties
Size
Dynode type
Number of Dynodes
Photocathode material
Active Area Diameter
Window
Typical HV
Typical Gain
Dark Current
Rise Time
Transit Time
Transit Time Spread (TTS)
Cathode Radiant Sensitivity
Cathode Luminous Sensitivity
Anode Luminous Sensitivity

Value
2 inch (51 mm)
Metal channel
12
Rb-Cs-Sb
45 mm
Synthetic quartz
900 V
1 × 106
5nA
2 nsec12.5 nsec
0.75 nsec
74 mA/W
200 A/lm
70 A/lm

Since the LXe detector will be placed close to the magnet, the PMT used in the LXedetector have to work under the fringing field from the magnet.
Fig. 3.9 shows the relative output of the PMT as a function of the magnetic field [64]where the z-axis is defined by the PMT axis. The output degradation due to the magnetic
field strongly depends on the direction of the applied magnetic field with respect to theCHAPTER 3. LIQUID XENON SCINTILLATION DETECTOR

photon39

photonPhotocathodee"fly through"Focusing
Electrodes
e

0.8mm

DynodesFigure 3.7: Charge multiplication process in the metal channel dynode PMT. Some photons directly hit the first dynode.
K

DY1

DY2

DY3

DY4

DY5

DY6

DY7

DY8

DY9

DY10

DY11

P

DY12

C4

R16
R1

R2

R3

R4

R5

R6

R7

R8

R9

R10

R11

R12

R14

R13
C5

C1

R1:
11.2M 5%, 1/8W
R2-12: 5.6M Ω 5%, 1/8W
R13:
6.7M Ω 5%, 1/8W
R16:
200k Ω 5%, 1/8W
R14, R15: 10k Ω 5%, 1/8W
C1-C3: 0.01 µF, 500V
C4, C5: 0.0039µF, 2.5kV

C2

C3

R15

+HV
(RG-188A/U)

SignalOutput(RG-196A/U)

Figure 3.8: Voltage divider circuit of R6041Q.

tube axis. There is a strong dependence even on the direction on the photo-cathode plane
due to the structure of the dynodes. The maximum allowed strength of the magnetic
field is 150 Gauss and 50 Gauss for the perpendicular and parallel directions to the tube
axis, respectively. The maximum allowed strength is defined as the field strength which
reduces the relative gain of the PMT by 50%.
As mentioned in Sec. 2.3.2, we succeeded to reduce the fringing field from the magnet
down to 50 Gauss level in the LXe detector region by canceling the field using compensation coils.

Relative output [ %]CHAPTER 3. LIQUID XENON SCINTILLATION DETECTOR

140

x-axis

Y
Z

120

40

y-axisXz-axis

100
80
60
40
20
0
-300

-200

-100

0
100
200
300
Magnetic flux density [ Gauss]

Figure 3.9: Relative output of R6041Q to be used in the LXe detector as a function of
the applied magnetic field. The z-axis is defined by the PMT axis here.

3.5

Cryogenics

As described in Sec. 3.1.1, the temperature range of LXe at a reasonable pressure is rather
narrow. Stable and powerful cryogenic system is indispensable for the proper operationof the LXe detector.
As shown in Fig. 3.5, the 100-liter prototype has a cryostat composed of pulse tube
refrigerator, thermally insulated vessels, and cooling pipe for liquid nitrogen. The inner
vessel is isolated from outside by vacuum of 10−4 Pa ∼ 10−3 Pa for thermal insulation.
By using multi-layer super-insulation foils in the insulation vacuum, heat inflow due tothermal radiation is reduced down to 24 W which is well below the cooling power of thecooling system based on the refrigerator and the liquid nitrogen cooling pipe.
A new pulse tube refrigerator was developed for the 100-liter prototype [65] (Fig. 3.10).
The remarkable features of the refrigerator are summarized below.
• Easy to use• Effective direct re-condensing• Compact cooling part
• No cryogen required• No sub-cooling required

CHAPTER 3. LIQUID XENON SCINTILLATION DETECTOR

41• Quiet environment• Eco-friendly• Possibly long life
The refrigerator consists of two parts: helium compressor (LEYBOLD Coolpak series)
and cold head (developed in KEK). The compressor can be placed several meters awayfrom the cold head installed on the top flange of the cryostat. The refrigerator producesmuch less noise because there is no mechanical moving part around the cold head. The
specifications of the refrigerator are listed in Table 3.6. The refrigerator has a coolingpower of 70 W at 165 K which is well above the heat load in the cryostat of the 100-liter
prototype (Table 3.7).

Figure 3.10: Pulse tube used in the refrigerator of the LXe detector. The right is the pulse
tube for the 100-liter prototype with a cooling power of 70 W at 165 K. The left is thelatest version which will be used in the final detector and its cooling power is improved
up to 190 W at 165 K.
As shown in Fig. 3.5, the cryostat is also equipped with the cooling pipe in the inner
vessel where liquid nitrogen can flow. The liquid nitrogen cooling pipe is only used forthe liquefaction of xenon and also in case of emergency such as a power cut. During thenormal operation of the detector, the LXe is cooled only by the refrigerator.

CHAPTER 3. LIQUID XENON SCINTILLATION DETECTOR

42

Table 3.6: Refrigerator performance.
Cooling Power at 165 K
70 W
Surplus Power
20 W
Compressor Power
2.2 kW
Compression Cycle
2.2 HzCoefficient of Performance (COP)
3%

Table 3.7: Heat load in the cryostat of the 100-liter prototype.

heat Load [W]

3.5.1

Static PMT
24
16

Cable
10

Total
50

Operation

The vessel of the 100-liter prototype has to be filled with ∼120 liter LXe in total. Some
preparations are needed to bring the 100-liter prototype into operational conditions, andit normally takes half a month to complete all the processes of the preparation.
All the processes of the cryogenic operation are monitored and controlled by the slow
control system based on the MSCB [66]. The control software was developed with LabVIEW [67] as shown in Fig. 3.11.
Evacuation: Both the inner and outer vessels are initially evacuated. The best procedure for removing water adsorbed in the materials inside the vessel would be to bakethe inner vessel above 200 ◦ C. The baking temperature for the inner vessel is, however,limited up to 70 ◦ C because of the temperature tolerance of the PMTs and acrylics inside
the inner vessel. After the continuous evacuation for about ten days the inner pressure
reaches 10−3 Pa.
Pre-cooling: A pre-cooling phase then starts in order to cool the inner vessel down
to 165 K prior to liquefaction. The inner vessel is filled with gaseous xenon (GXe) of
0.2 MPa, and then cooled by both the liquid nitrogen cooling pipe and the refrigerator
for a whole day.
Liquefaction: Xe is liquefied by using the liquid nitrogen cooling pipe after the inner
vessel is sufficiently pre-cooled. The GXe is purified with a gas purifier (SAES Getter [68])and molecular filters (Oxisorbs [69]) before entering the inner vessel and getting liquefied.
The gas purifier can adsorb various contaminants in the GXe such as H2 O, O2 , CO2 , N2 ,and CH4 down to a ppb level. The molecular filter can adsorb oxygen. It usually takes
two days to complete the liquefaction. The vapor pressure is kept constant by controllingthe flow of the GXe and flow of of liquid nitrogen in the cooling pipe.
Keeping LXe: After the liquefaction, the LXe is maintained at 165 K and 1.3 atm
mainly by the pulse tube refrigerator.

CHAPTER 3. LIQUID XENON SCINTILLATION DETECTOR

43

During the beam tests at the AIST we kept the LXe stable over about 2000 hours.
Recovering and Warming-up: After the detector operation the LXe is recovered toa storage tank. The refrigerator is turned off and the outer vessel is filled with heatexchange gas (gaseous nitrogen) to accelerate the LXe evaporation, and a heater under
the PMT holder is switched on. The tank is cooled down by liquid nitrogen in orderto re-condense the xenon from the detector vessel. The recovery and warming-up of thecryostat take two and four days, respectively.

Figure 3.11: Control software of the cryogenic system of the 100-liter prototype developedwith LabVIEW.

CHAPTER 3. LIQUID XENON SCINTILLATION DETECTOR

3.6

44

Monte Carlo Simulation

The Monte Carlo (MC) simulation for the 100-liter prototype detector was coded basedon GEANT3 [70]. This simulation has run modes such as γ-rays, cosmic muon rays, andα particle in order to compare with measured data. Since GEANT3 can not simulatetransportation of scintillation photons, we coded a ray-tracing routine for scintillation
photons. The routine has some features. In the MC simulation, every scintillation photohas each wavelength which obeys a Gaussian distribution, and for each photon Rayleighscattering and absorption length in LXe, reflectance and transmittance to quartz are
defined according to the wavelength. Tab. 3.8 shows the parameters and their values
in the MC simulation. An example of simulation event for 40-MeV γ ray is shown in
Fig. 3.12. In this thesis the MC simulation was employed especially for estimation of QE.
Table 3.8: Parameters and values in the MC simulation for the 100-liter prototype detector.
Parameter
Wph(α) (LXe)
Wph(α) (GXe)
Wph(e) (LXe)
Scintillation Spectrum
Refractive index of xenon
Rayleigh Scattering Length
Absorption Length (LXe)
Quantum efficiency
Transmissivity of 2.5-mm Quartz
Refractive index of quartz
Absorption Coefficient on PMT holder

Value
18.1 eV18.1 eV21.6 eV
178 nm ± 2.1 nm (1σ)
1.62
45 cm
1m
5%
0.792
1.58
1.0 (no reflection)yConverted:

0.00

0.00

6.02

z

Figure 3.12: An example of MC simulation for 40 MeV γ ray. In this event the first
conversion depth is at 6 cm from the PMT surface of the incident face.

Chapter 4
Purification and Absorption Length
LXe should in principle be transparent to its own scintillation light thanks to the scintillation mechanism through the excimer state Xe∗2 [55] as mentioned in Sec. 3.1.3. However
possible contaminants in LXe, such as water and oxygen at ppm level, considerably absorb
scintillation light [71, 72]. Such contaminants have to be minimized in the LXe of our detector because the loss of the scintillation light will deteriorate the detector performance.
We, therefore, developed a circulation-purification system for the 100-liter prototype. In
this chapter we describe the performance of this purification system and discuss the impact of transparency of LXe on the expected performance of our detector for 52.8 MeV
γ-ray.

4.1

Optical Properties of LXeFirstly we discuss the optical properties of LXe that are of interest for a scintillation
detector. The main optical properties of LXe are listed in Table 4.1.
Table 4.1: Optical properties of LXe.
Material Properties
Value & Unit Ref.
Refractive index at scintillation wavelength 1.6 − 1.7[50, 53, 73]
Peak scintillation wavelength
178 nm[48, 49]
Scintillation spectral width (FWHM)∼ 14 nm[48, 49]
Absorption length λabs
> 100 cm
present work
Scattering length λsca
29 - 50 cm[53, 56–58, 73]
Light attenuation in LXe can be described by the attenuation length, λatt , as definedin the equation, I(x) = I0 e−x/λatt . The attenuation length consists of two separate
components, the absorption length, λabs , describing real absorption and loss of photons,
and the scattering length, λsca , that represents elastic scattering of photons without any
loss. For the elementary photon scattering they are related by: 1/λatt = 1/λabs +1/λsca .
For an actual photon beam one must take into account the fact that photons can be
forward scattered. In our case the elastic scattering is dominated by Rayleigh scattering,
therefore λsca may be regarded as the Rayleigh scattering length, λRay . The knowledge ofrefraction index n in the region of the xenon VUV light emission is also relevant.
45

CHAPTER 4. PURIFICATION AND ABSORPTION LENGTH

46

The most important among these parameters for the detector performance is theabsorption length λabs , since the energy measurement relies on the total number of scintillation photons detected by the PMTs that surround and view the LXe volume from all
sides and is therefore not affected by photon scattering.
The experimental knowledge of these quantities, λatt , λabs , λsca and n for pure LXe
is poor. Especially no measurement of λabs has been made before. There are also somediscrepancies among the available experimental data, which might partly be explained by
the degree of purity of the LXe. As we shall show later, small amounts of VUV absorbing
molecules like H2 O or O2 , at the level of a few parts per million, can dramatically change
LXe optical parameters. Thus a reliable determination of optical parameters necessarily
requires monitoring the level and the stability of the xenon purity. In addition a sizeof the LXe volume comparable to the absorption/scattering lengths is needed to make areasonable measurement of these lengths.
Considering the scintillation mechanism of LXe through the excimer state Xe∗2 [55],absorption in pure LXe is improbable, i.e. λabs ∼ ∞; any absorption is thus caused by
VUV absorbing impurities. In this paper we report the first measurement of λabs using
our prototype and present a significant lower limit.
In contrast to the situation for LXe, better information is available for gaseous xenon(GXe) at various pressures both for visible and VUV light [74–76]. One can then examine
if optical properties for LXe can be derived from those for GXe, although this might imply
a daring extrapolation in terms of density. For a non-polar gas like xenon, however, thisextrapolation proves to be valid [53]. One has to ascertain up to which value of photon
energies the extrapolation maintains its validity. This point was further investigated byus [77]; the extrapolation is reliable up to a photon energy of 8.1 eV. At higher energies
and closer to the first xenon absorption line at 8.3 eV the extrapolation is no longer
valid. Our prediction for the value of the LXe refractive index at its emission line (7 eV
corresponding to the wavelength of 178 nm) is n = 1.65 ± 0.03. Most of the information
obtained for GXe in various physical conditions can be used for reliably predicting other
LXe optical properties [77]. Here we restrict the discussion to the relation between two
quantities: n and λRay .
For a dense fluid like LXe λRay depends on density and temperature fluctuations of
the medium, according to the Einstein’s expression [78]:


1
ω4 
=
KT ρ2 κT
λR
6πc4

Ã

∂²
∂ρ

!2

KT 2
+
ρcv
T

Ã

∂²
∂T

!2 


(4.1)

ρ

where ² is the dielectric constant, κT is the isothermal compressibility, cv is the specificheat at constant volume and K is the Boltzmann’s constant.
Since xenon is a non-polar fluid, the second part of Eq. 4.1 comes out to be negligible[44, 53, 79]. The derivative appearing in the first part of Eq. 4.1 can be computed fromthe Clausius-Mossotti equation:
4π NA α(ω)ρ
²(ω) − 1=,²(ω) + 2
3
M

(4.2)

where NA is the Avogadro’s number, α(ω) is the molecular polarizability and M is themolecular weight. The Einstein’s equation reduces then to:"#ω4(n2 − 1)2 (n2 + 2)2
1
=
KT
κ
.
T
λR
6πc4
9

(4.3)

CHAPTER 4. PURIFICATION AND ABSORPTION LENGTH

47

This equation establishes therefore a useful relation between the index of refraction inpure LXe and the Rayleigh scattering length.

4.2

Xenon Purification

In Fig. 4.1 (a) the absorption coefficients for VUV light are shown for 1 ppm contaminationof water vapor [80] and oxygen [81]. The absorption spectra of water and oxygen largely
overlap with the xenon scintillation spectrum. Given these absorption coefficients andneglecting the scattering (λabs <λRay ), we calculated the light intensity as a function of the
distance from the light source for various concentrations of the contaminant. The resultis shown in Fig. 4.1 (b) and (c). Apparently water is the most dangerous contaminant.
Since water tends to absorb light with shorter wavelengths, only a component with longer
wavelengths survives for a long distance. This might explain the discrepancies among
the measurements of the LXe refractive index n, as n varies rapidly as a function of the
wavelength in the vicinity of the scintillation wavelength.
As we already noted in Sec. 3.5.1, xenon is well purified before filling the detector
vessel, but some inner components of the prototype are made of G10 and acrylic that are
known to absorb and desorb water. During the initial stage of the prototype operation,a strong absorption of scintillation light was observed.
We investigated on the residual gas in the inner vessel of the 100-liter prototype bymeans of mass spectroscopy. A quadrupole mass spectrometer [82] was used in this gas
analysis. The result is shown in Fig. 4.2. There are several peaks and they correspond to
He (mass number=4), H2 O (18), N2 (28), O2 (32), and CO2 (44). The peak at Mass = 65.5
corresponds to doubly ionized xenon Xe++ . It was found that water contamination was
the dominant in the vessel while the oxygen concentration was an order of magnitude
smaller. The level of other VUV absorbing contaminants such as hydrocarbons was morethan two orders of magnitude smaller. We concluded that water at the ppm level seemed
to be desorbed from the detector material into LXe.
We therefore introduced a circulation-purification system in the 100-liter prototype as
schematically shown in Fig. 4.3, to remove the water. In this system, xenon, taken fromthe bottom of the vessel through the Teflon tube and evaporated by the heat exchanger, ispumped by a diaphragm pump and circulated through the gas purifier and the molecularfilter, and is finally condensed back into the detector. The flow rate of GXe is about
500 cm3 /min, hence the whole volume could be circulated in a few month time. We also
carried out various tests to study the purification process, such as stopping or changing
the flow rate and bypassing the purifiers or the filters.

4.3

Absorption Length Estimate

Purification was continuously performed for over 1200 hours. To evaluate and monitor
light absorption in LXe separately from Rayleigh scattering during purification, we usedcosmic ray muons as well as the α sources.
The total number of photoelectrons collected by all the PMTs (Npe ) for each cosmic
ray event, being sensitive only to the loss of the scintillation photons, is a good measureof the light absorption. Note that cosmic rays triggered by pairs of scintillation counters
TC1, TC2 and TC3 (Fig. 3.5) traversed vertically the front, middle and back parts of theAbsorption Coefficient [m -1]

CHAPTER 4. PURIFICATION AND ABSORPTION LENGTH

Oxygen

1

48

Xe Scintillation Spectrum

0.1

Water Vapor

(a)

0.01
130

140

150

160

170

180

190

200

Wave Length [nm]I / I0Absorption in Xe + water vapor

Absorption in Xe + oxygen
100 ppb

1

1200 ppb
1 ppm

100 ppb

5 ppm

200 ppb
1010 ppm

10−1

−1

1 ppm
5 ppm

10

−2

0

10 ppm

(b)
10

−2

20

30

40

50

60

Distance [cm]

10

0

(c)
10

20

30

40

50

Distance [cm]Figure 4.1: (a) Absorption coefficient for VUV photons in 1 ppm water vapor and oxygen.
The Xe scintillation spectra is superimposed. (b) Light absorption calculated for various
concentrations of water in LXe, where the source of scintillation photons is placed at
d = 0, and I/I0 is relative intensity of scintillation photons at a distance from the source.
(c) Light absorption for oxygen.
detector. In Fig. 4.4 (c), the number of photoelectrons (Npe ) is plotted as a function oftime for the cosmic rays triggered by TC2. It increased by a factor of four in about one
month (700 hours) and almost saturated. Fig. 4.4 (a) and (b) show spectra of the total
Npe for cosmic rays before and after the purification, respectively. In a more careful study
the number of photoelectrons collected by the front (or back) PMTs were compared forIon Current [A]

CHAPTER 4. PURIFICATION AND ABSORPTION LENGTH

10

10

−5

−6

H 2O
CO/N2
H

CO2

O2

H2
10

49

−7

Xe
10

−8

0

10

20

30

40

50

60

70

80

Mass [amu]Figure 4.2: Mass spectrum obtained in the residual gas analysis. The multi-peak is caused
mainly by decomposition of the parent molecule or by recombination with ions generated
from the decomposition. For instance, the neighbors of H2 O(18) are H3 O+ (19), OH+ (17),
O+ (16), and so on.

Xe Tank

Gas Purifier

TeflonTube

Molecular
FilterHeat Exchanger

Diaphragm
Pump
Gas Xe flow

Figure 4.3: Setup for circulation and purification of xenon.
the events triggered by TC1, TC2 and TC3. A comparison with a Monte Carlo simulation
indicates that λabs increased from ∼ 10 cm to above 1 m.

CHAPTER 4. PURIFICATION AND ABSORPTION LENGTH

50

χ2 / ndf

35

Constant

30

25

Count

Count

Fig. 4.5 (a) shows spectra of the total Npe for α particle events before and after the
purification. In Fig. 4.5 (b) the relative changes in the α peaks of the PMTs located atcertain distances (7.6 cm and 11.6 cm) from the α sources are plotted. For the PMTs
at a longer distance, the PMT outputs increased much more significantly and saturated
slightly later, just as expected for the light absorption in LXe, e−x/λ with increasing λ.

55.6 / 55
163.1 ± 12.7

MPV

2.465e+04 ± 241

Sigma2100 ± 137.8

30
25

20

37.88 / 41

Constant

161 ± 12.4

MPV

8.521e+04 ± 614

Sigma

5198 ± 324.8

20

15

15

10

10

5

0
0

35

χ2 / ndf

5
0
0

10000 20000 30000 40000 50000 60000 70000 80000

2040

Total Number of Photoelectrons

60

Total Number of Photoelectrons

100 120140 160 180×103
200 220

Total Number of Photoelectrons(a)12000080(b)

TC2 trigger

10000080000(1)(2) (3)

(4)

60000
40000

(1) Molecular Filter Bypassed(2) Circulation Stop
(3) Circulation Restart

20000

0

(4) Circulation & LN2 Cooling Stop

0

200

400

600

800

1000 1200

Elapsed Time [hrs](c)Figure 4.4: (a) A number of photoelectrons before the purification and (b) after the
purification (c) Light yield transition for cosmic-ray muon events. The deposit energy forminimum ionizing particles (MIP) is approximately 155 MeV from the MC simulation.
We first made a crude estimate of the Rayleigh scattering length by using the PMTs

CHAPTER 4. PURIFICATION AND ABSORPTION LENGTH

51

1200

Before

1000

After

Relative Peak

Count

3.5

d = 11.6 cm
d = 7.6 cm

3

2.5
(1)

800

(2) (3)

(4)

2

600

400

1.5

(1) Molecular Filter Bypassed(2) Circulation Stop

200(3) Circulation Restart
1

0
0

200

400

600

0

800 1000 1200 1400 1600 1800 2000

(4) Circulation & LN2 Cooling Stop

0

200

400

600

800

1000 1200

Elapsed Time [hrs](b)Total Number of Photoelectrons(a)Figure 4.5: (a)Total Npe before and after the circulation. (b) Light yield transition for α
particle events, observed by one PMT.

data/MCdata(LXe)/data(GXe)located on the same face as the α source; these PMTs can not directly see the scintillation
light from the α particles but only the scattered light. Although ambiguities in reflectionof scintillation photons on the walls do not allow a more accurate estimate, our data prefervalues of λRay = 40 - 50 cm, which are consistent with the numbers currently available in
the literature [53, 56–58, 73].

1

1

10 -1

10 -1

(a)
10-2

0

100

200

300

400
500
600
α-PMT distance [mm]

(b)
10-2

0

100

200

300

400
500
600
α-PMT distance [mm]Figure 4.6: The PMT outputs normalized either to those in the GXe data (a) or to the MC
simulation without absorption (b) are plotted as a function of the source-PMT distanceat the beginning (open circle) and after purification (closed circle). The solid lines are
fitted results.
To evaluate the absorption length λabs , we compared the PMT outputs in the LXeto those in the GXe and to a Monte Carlo simulation with no absorption and a variable
λRay . Note that both absorption and scattering are negligible in the GXe. In Fig. 4.6 thePMT outputs normalized either to those in the GXe (a) or to the MC simulation with

CHAPTER 4. PURIFICATION AND ABSORPTION LENGTH

52

λRay = 45 cm (b) are plotted against the source-PMT distance. Here the distributions at
the beginning of purification (open circles) and after one month of purification (closed
circles) are compared. The evident exponential decline at the beginning almost vanishedafter purification. Note that the slopes are steeper in the GXe normalized plots because
they also contain the effect of scattering which is not canceled by normalizing to the GXe
data.
These distributions were then fitted with exponential functions. From the comparison
with the GXe data an effective attenuation length of 54+14−9 cm was obtained after the
purification. This effective length contains the effects of both the absorption and theRayleigh scattering. Since the scattered photons are not totally lost but may be detectedby other PMTs, the obtained effective attenuation length is longer than λatt and, especially
if λabs ÀλRay , it is longer than λRay . Note that the LXe/GXe ratio is larger than unity
since the ratio of the scintillation yields in LXe and GXe is approximately 2.7 [83].
The comparison with the simulation does not show a significant slope. We used thisresult to establish a lower limit on the absorption length λabs of 91 cm at 90% confidence
level or 80 cm at 95% confidence level, where λRay was varied from 30 cm to 50 cm in thesimulation. Before the purification λabs was 12.0 ± 1.8 cm. We conclude that the level ofwater content after the purification was much lower than 100 ppb.
After successful purification of LXe under the operational conditions, efforts have been
focused on reducing the initial amount of water contamination in the vessel. We replaced
most of the acrylic parts with Teflon to suppress out-gassing in the inner chamber, which
resulted in an initial absorption length λabs of 30 cm in the subsequent operation. A lower
limit on the absorption length λabs of 100 cm at 90% confidence level was then achievedin a much shorter time of xenon purification, in about 300 hours.
We are also developing a liquid-phase purification system with a fluid pump to increase
the purification efficiency. In such a system the circulation speed could be increased up
to 100 `/hour of LXe, more than 1000 times faster than the current system.

Chapter 5
Performance of the 100-liter
Prototype
5.1

Motivation

The γ-ray energy from the µ → eγ decay is just 52.8 MeV, whereas energy of γ rays ofbackgrounds in MEG experiment, for instance γ rays from the Michel decay, is never morethan 52.8 MeV. Therefore the LXe detector should have an excellent energy resolution in
the energy region of around 50 MeV. Moreover, good energy, position, and time resolutions
are required in order to recognize pile-up events of accidental backgrounds.
In order to verify the performance of the LXe detector, a beam test was carried out
with the 100-liter prototype by using γ-ray beam up to 40 MeV from a laser Compton
scattering (LCS) facility. Based on the obtained result we can estimate the expected
performance of the final LXe detector to be used in the MEG experiment. It is alsoquite important to develop Monte Carlo simulation by using measured data with a simple
configuration of PMTs, as employed in the 100-liter prototype, compared to the final
detector. Furthermore it is also possible to mimic the PMT configuration of the final
detector, curved C-shape geometry, by masking whole PMTs on certain plane of thedetector. Estimating the efficiency and evaluating how the detector performance deteriorates when we place additional material, in front of the entrance window, with equivalent
thickness to that of the COBRA magnet is another issue to be examined in this test.
These provide essential information to the design work of the final LXe detector.
It must be mentioned that another kind of beam test was performed later on this workby using γ rays from π 0 decays produced in the charge exchange process (π − +p→ π 0 +n) and from the radiative capture process (π − +p→ γ + n). In this test it is possible toevaluate the detector energy resolution by using almost monochromatic γ rays up to 129
MeV while in LCS beam the resolution has to be evaluated by the shape of the sharp edgeof γ-ray spectrum below 40 MeV. Nevertheless conducting the test by using the LCS beam
is significant because the detector can be radiated with pure γ-ray beam with reasonable
intensity necessary to evaluate position resolution with a collimator. Note that thanks tothe beam purity it is not necessary to consider the effect of possible background sources
like slow neutrons.
In this thesis the result from the π 0 beam test is not mentioned in detail. All performance evaluation and consideration on the final detector performance rely on the results
obtained in the LCS beam test.
53

CHAPTER 5. PERFORMANCE OF THE 100-LITER PROTOTYPE

5.2

54

Laser Compton Scattering beam test at AISTFor evaluating the performance of the LXe detector, a beam test was performed in April
2004 by using γ rays from laser Compton scattering (LCS) provided at the electron
storage ring, TERAS, at National Institute of Advanced Industrial Science and Technology (AIST) in Tsukuba, Japan. Fig. 5.1 shows a schematic view of TERAS. In the
TERAS facility, there are several beam lines to provide synchrotron radiation light andsoft X-ray. Among these there is a beam line, shown as LCS-1 in the figure, where highenergy γ-ray beam can be delivered.
In the TERAS facility electron acceleration and storage is done in the following way.
Electron beam of 310 MeV provided from a linear accelerator is injected into TERAS
up to 30 to 250 mA . Then injection is terminated and stored electrons in the ring arestarted to be accelerated to ∼800 MeV by RF powers. When electron energy reaches atarget value, the operation mode is switched from acceleration mode to storage mode.
It is possible to store electrons stably with a life time of 8 hours in normal operating
condition. Electron injection into TERAS is usually performed twice a day. The ringparameters for TERAS are summarized in Tab. 5.1. Electron energy in TERAS was set
to be 764 MeV in this test.
BL4

BL3−3

BL−Q2

BL3−2

RF cavity

BL2A

Kicker

BL2B
BL2C

QF
QD
QF
Injection BTS

Beam Position
MonitorVerticalCompensation
Magnet

DCCT

LCS−3

BL1−B

Septum
BL1−A

LCS−1

0 1 2 [m]Figure 5.1: Schematic view of TERAS.

In the LCS-1 beam line laser photons are generated by Nd:YAG pulse laser. Its
fundamental wavelength is 1064 nm and it can be converted to the second harmonic of
532 nm and the fourth harmonic of 266 nm for providing higher energy γ-ray beams.
The laser photons are guided to the collision point in the TERAS ring by a half-mirror
and collide head-on with electrons. Through Compton scatting on an electron, a laser
photon receives most part of the electron energy and boosted back in the direction of
initial electron beam. The energy of the LCS γ rays can be set up to 40 MeV by changing
the laser wavelength and/or the electron energy in TERAS. The properties of laser andCHAPTER 5. PERFORMANCE OF THE 100-LITER PROTOTYPE

55

Table 5.1: Ring parameter and laser properties for LCS beam.

Storage ring

Laser photon

Circumference
Bending radius
RF frequency
Max. stored current
Energy range
Energy in this test
Energy spread (σ)
Typ. storage time
Angular divergence (σ)
Horizontal bunch size (σ)
Vertical bunch size (σ)
Lasing wavelength
Energy spread (FWHM)
Angular divergence (σ)
Beam size

Compton edge energy(Error in σ)

31.45 m2.0 m
171.682 MHz
350 mA
200 MeV to 800 MeV
764 MeV
0.48% (3.7 MeV)
8 hours for 100 mA
0.115 mrad1.55 mm to 2.2 mm
1.0 mm
266 nm, 532 nm, 1064 nm
0.002%
0.5 mmrad
unknown
10.32±0.10 MeV
20.37±0.20 MeV
39.67±0.38 MeV

the LCS beam are also shown in Table 5.1. Fig. 5.2 shows a picture of the experimental
setup around the collision point.
It must be remarked that the LCS beam is not monochromatic but has an energy
spread determined by the scattering angle of photons (and by relative angle between thelaser photon and electron before collision). The energy spectrum of the LCS γ rays F (Eγ )can be approximately written as [84]:(µF (Eγ ) = N

EC
Eγ −
2

¶2

E2
+ C
4

)

,

(5.1)

where N is the normalization factor and Eγ is the γ-ray energy. This expression can be agood approximation if the energy of Compton edge EC is much smaller than the electronenergy. The EC is determined by the energy of laser photon El asEC =4γ 2 El
,
4γEl
1+
me

(5.2)

where γ is the relativistic factor of the incoming electron and me is the electron rest mass.
In this test, in order to define the incident spot on the detector and to select the γ-ray
energy two collimators were placed between the collision point and the LXe detector as
shown in Fig.5.3. They also served for excluding low energy γ rays from synchrotron
radiation that cannot be eliminated completely since the scattering point is set in abending section in the ring. The effect of the collimator on the incident γ-ray spectrum
is estimated by a simple Monte Carlo simulation as shown in Fig. 5.4. It can be seen that

CHAPTER 5. PERFORMANCE OF THE 100-LITER PROTOTYPE

56

by placing a smaller size collimator in front of the detector the spectrum given in Eq. 5.1
becomes narrower while the sharp Compton edge remains. In this thesis, the data withthe 1-mmφ collimator was used for analysis because no differences between results with
1-mmφ and 2-mmφ collimators were seen.

Figure 5.2: Setup for LCS beam. When the laser is green (532 nm), the energy of LCS γ
rays is 20 MeV.

TERASElectron storage Ring
764 MeV
50 mA ~ 300 mA

1st leadcollimator(2.8mm φ )2nd leadcollimator(1mm φ /2mm φ )γ beamLaser Photon
Laser-Electron
Collision point

266 nm532 nm1064 nm Nd:YAG
6205

150

200

LXe
Detector

Concrete Wall
4720

520

Figure 5.3: Experimental setup in TERAS beam test.

Intensity [a.u.]

CHAPTER 5. PERFORMANCE OF THE 100-LITER PROTOTYPE

57

1800
φ = 1mm2nd
φ = 2mm2nd
φ = 3mm2nd
φ = 5mm2nd
φ = infinity

1600
1400

2nd

1200
1000
800
600
400
200
0
0

5

10

15

20

25

30

35

40

45

Incident Energy [MeV]

Figure 5.4: Energy spectra depending on the diameter size of the 2nd collimator. Beamand laser properties listed in Table 5.1 are taken into account in this calculation.

CHAPTER 5. PERFORMANCE OF THE 100-LITER PROTOTYPE

5.3

58

Trigger and Data Acquisition

The data flow in the data acquisition is shown in Fig. 5.6. There were two groups of
PMT signals. The one is composed of signals from 128 PMTs located around the front
face of the detector. These PMT signals are recorded both in ADC and TDC. The otherconsists of signals from remaining 100 PMTs located rather back in the PMT supporting
holder. These PMT signals are recorded only in ADC. Signals from the 128 PMTs werealso utilized to provide trigger information for the acquisition system. Signal splitterswere prepared to split PMT signals to ADC and discriminators. Discriminator output
was utilized both for TDC input and trigger decision. The splitter is custom made for
the MACRO experiment and possible to pass analog signal with a bandwidth of 100MHz.
The threshold level for each channel in discriminators was set to be minimum, that is,-10 mV which is the minimum level in the discriminator. This discriminator module canprovide information about the number of hit channels (Nhit ) above the threshold. In thetrigger system another parameter Ndiscri was implemented. If Nhit of one discriminatoris 2 or more, the Ndiscri is incremented, enabling us to count the number of fired PMT
cluster. Cluster definition is illustrated in Fig. 5.6.
The TDC was operated in the common start mode. Timing jitter of the PMT signals
relative to the trigger start timing was typically 50 nsec, which could be handled with theelectronics time window without any significant problem.
Signals to ADC module were fed through 210-nsec cable delay so as to be entirely
included in 600-nsec ADC gate. The width of ADC gate was set to be 600 nsec in every
run mode to contain all signals fully. We prepared four kinds of trigger logics to dealvarious event types.
Pedestal and LED Run: In both run modes, the trigger is generated by NIM clock
generator at the rate of 100 Hz. Only when the run mode was LED (light-emitting diode)mode, the LED driver (CAEN C529, [85]) fed driving pulses to LEDs. In this test, it
was repeated several times a day for investigating the pedestal noise and stability of gain
adjustment.
LCS γ-ray Run: This trigger mode was activated by the coincidence between a trigger
from PMT outputs and a trigger from pulse laser. It allowed to veto the other sources
such as α-particle, cosmic-ray, and environmental backgrounds. The threshold of Nhit was
set to 2.
α-particle Run: The α sources was installed on each lateral face as shown in Fig. 5.5.
Since the light yield from α particles is not high, α-particle event fires mainly the nearest
cluster alone. When Nhit was 1, nearly 100% of those events was from α particle.
Cosmic-ray Muon Run: As shown in Fig. 3.5, three pairs of counters were set below
and over the LXe detector. Since trigger rate was very low (about 0.01 Hz), cosmic-ray
trigger was usually mixed with γ-ray trigger.
The data acquisition system consisted of mainly FASTBUS and partially CAMAC
standards. Due to the slow communication to the CAMAC system the data taking rate

CHAPTER 5. PERFORMANCE OF THE 100-LITER PROTOTYPE

59

was less than 200 Hz. The data acquisition system was driven by an online/offline software
package, MIDAS [66]. The MIDAS system managed also the slow control system including
all kinds of control and status monitoring such as xenon and purification system with helpof LabVIEW [67].

($( ** ,, .. 00)) '#$' )) ++ -"- //LED (x8)#  %&   !"!  blue
alpha source (x4){|yz{ u wx u opqrst       43875 12 43875 AB CD GHEFG
687 R 687 = ? KHN
|}~ v  v lmnopkl j
;
;
=
?
<
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@
L
9
9
K
J
I
:
:
i
O
Q
O

j
R
P
P
    k i W g <;OP Q <;OP > @ MNLM
UV\ XW^X ` b hdefgh STright[\ _ ]^YZ `_ ab cd front[ _] _ a c


top

cluster1
cluster2
cluster3

leftcluster4
cluster5(incident face)cluster6
cluster7

Outside View

bottomFigure 5.5: The clusters for generating trigger.

cluster8

Figure 5.6: Data flow diagram in LCS beam test.

Nd:YAG
Pulse Laser

228ch

HV module
LeCroyLRS1458, 1454

ORTEC 583B
CFD

Windows2000

LeCroy 365AL
4−Fold Logic Unit

LeCroy 365AL
4−Fold Logic Unit

LeCroy 3412
16ch 200MHz
Discriminator x8

PHILLIPS 708
Leading−edgeDiscriminator

PHILLIPS 708
Leading−edgeDiscriminator

PHILLIPS 708
Leading−edgeDiscriminatorBit3 PCI−VME
Model617

Technoland
Gate Gene.

FASTBUS MASTERSFI SIS4100

Technoland
N−TM 203
Clock generator

100Hz

CAEN C529
LED driver

SUHNER 6810.01.A−10dB attenuator

Blue LED x8
Toyoda Gosei
E1L49−3B1A−02

128ch

100ch

from MACRO exp.
8ch FAN−OUT x8

Technoland N−TM227
8ch Signal Dividerlow

Cosmic−ray
Trigger Counter
TC1, TC2, TC3

up

Technoland N−TM227
8ch Signal Divider

Electron Counter
ET1 − ET2
ET3 − ET4Delay
2.6 µ sec

LeCroy 622
Coincidence

LED, pedestal

LeCroy 622
Coincidence

LCS gamma

LeCroy 622
Coincidencealpha-particle

LeCroy 622
Coincidence

cosmic-ray

PHILLIPS 757
FAN−OUT

LeCroy 622
Coincidence

PHILLIPS 757
Logic Sum

PHILLIPS 757
Logic SumSTOPKAIZU 1500
Gate Gene.

START

Delay ~210 nsec

Delay ~210 nsec

600ns

KAIZU 1500
Gate Gene.

KAIZU 1500
Gate Gene.

LeCroy 1875A
64−Input TDC x2

PHILLIPS 757
FAN−OUTPHILLIPS 726
LEVEL
TRANSLATORECL STOPGATECIAFB x3

OPAL 96ch ADC

STOP

TDC

PHILLIPS 7186

CHAPTER 5. PERFORMANCE OF THE 100-LITER PROTOTYPE
60

CHAPTER 5. PERFORMANCE OF THE 100-LITER PROTOTYPE

5.4

61

PMT Calibration

A precise knowledge of PMT gains and quantum efficiency (QE) is necessary for reachingan excellent energy resolution and reconstruction accuracy of the first conversion point in
LXe.
The LXe detector is equipped with eight LEDs (two on each lateral face) to measuregains of each PMT and four 241 Am α sources (one on each lateral face) to measure QEs
as described in Chapter 3. Gain adjustment is for converting ADC count to the numberof photoelectrons (Npe ) and QE values of each PMTs are necessary for converting Npe tothe number of photons (Nph ) and, in particular, for position reconstruction.

5.4.1

Gain Adjustment

MethodPMT gains were adjusted to 1 × 106 in LXe (165 K and 1.3 atm). Blue LEDs [86] wereused to adjust and monitor PMT gains. A pair of LEDs facing each other on the lateraldetector side was flashed at 100 Hz by the LED driver. The gain for each PMT was set
to 1 × 106 . During data acquisition over two weeks all the gains were monitored several
times a day.
Since R6041Q is not good at single photon separation owing to its dynode structure,
the strategy of the gain adjustment is to observe plenty of photons and estimate PMT
gains from statistical fluctuation of them. In references of [87–89], the difficulty of single
photon separation and the way to adjust gains with multi-photons from LEDs are detailed.
Our model is simple. We assume that LED output is constant and the statistics of
Npe obeys Poisson distribution. Some of those photons reach the quartz window of a
PMT and transmit it, and photoelectrons are generated by photoelectric effect with acertain efficiency (QE), and hit the first dynode with a collection efficiency (CE). Bothobey binomial distribution. Then the photoelectrons are amplified by dynodes.
The distribution of Npe becomes a convolution of binomial distributions and Poisson
distribution. In that case, the upper tail is broader than lower tail. When Npe is large
enough (10 photoelectrons at least), the contribution of binomial distribution is negligible.
Therefore the spectrum after amplification can be Poisson distribution scaled by gain. The
gain can be given by the following equation:
cσ 2
,
(5.3)
eM
where g is the gain, c is the ADC least count (200 fC/ch), σ and M are the standard
deviation and the mean of ADC spectrum fitted with a Gaussian, respectively, and e is theelementary electric charge, assuming that the number of photoelectrons (Npe ) observed
on a PMT is so large that the ADC spectrum can be regarded as a Gaussian. In practice
we have to consider a contribution from the deviation of pedestal to it as the following
equation:g=e
σ 2 = g (M − M0 ) + σ02 ,
c

(5.4)

CHAPTER 5. PERFORMANCE OF THE 100-LITER PROTOTYPE

62

3500

σ2

Entries

where M0 and σ0 are the mean and the standard deviation of the pedestal spectrum,
respectively. The gain estimate becomes more reliable by using this equation. By changing
the intensity of the LED the PMT outputs vary as shown in Fig. 5.7 (a). Fig. 5.7 (b)shows an example of the linear relation between σ 2 and M . The gain of the PMT isevaluated by fitting the relation with Eq. 5.4. Thus the precision of gain determination
can improve by using data for various yield of photons.

(a)

(b)

10000

3000
8000
2500
6000

2000

1500
4000
1000
2000
500

0

0

500

1000

1500

ADC channel

2000

2500

0

0

500

1000

1500

2000

2500

ADC MeanFigure 5.7: (a) ADC spectra of a typical PMT in the gain adjustment. (b) The relation
between σ 2 s and the mean channels from (a), where σ 2 at ADC Mean = 0 corresponds withthe variance of the pedestal σ02 . In both figures the pedestal mean is already subtracted
from the ADC spectrum.
As shown in Fig. 5.8, after a few iteration of gain adjustment, the spread of all thegains became approximately 3% in sigma. This was limited by the minimum controllable
digit of the HV power supply. It is not so important to set them to the same gain. It isessential to determine the gains and keep them stable. Estimation of gain measurement
and monitoring accuracy will be discussed in the following.
Accuracy of the Method
As described above, this method requires stable light source. If the LED was unstable andits stability was worse than the random noise amplitude, the linearity in Eq. 5.4 would
be lost. Fig. 5.7, however, shows that the linearity is conserved during measurement.
The same pair of LEDs was always used out of 8 LEDs for calibration. In order tocheck the difference of the gain determination with the other pairs of LEDs, they were
flushed and the same procedure was repeated for each of them. Fig. 5.9 shows a relation
between σ 2 and ADC mean value for one PMT obtained by flushing different pairs ofLEDs. It can be seen that all points stay on a line, indicating that there is no difference
between selected pairs.
The LED calibration procedure was checked more systematically both by using different LED pairs and by using the same pair for several consecutive runs. It was found thatthe gain determination can be reproduced within an accuracy of 0.4% in sigma.

CountCHAPTER 5. PERFORMANCE OF THE 100-LITER PROTOTYPE

5040

χ2 / ndf

13.06 / 13

Constant

51.66 ± 4.68

Mean

6.004 ± 0.002

Sigma

0.0302 ± 0.0018

63

30

20

10

0
5.5

5.6

5.7

5.8

5.9

6

6.1

6.2

6.3

6.4

6.5

PMT Gain 10g

σ2

Figure 5.8: Gain distribution of 228 PMTs.
700

LED1+LED5600

LED2+LED6
LED3+LED7500

LED4+LED8
400
300
200
100
0

0

600

1200

1800

ADC MeanFigure 5.9: The relation between ADC mean and variance for 4 pairs of LEDs.
The stability of the gain adjustment for a particular LED pair was also checked bycomparing two consecutive runs, flashing the same LED pair. The ratio of the gain
obtained in two runs for each PMT was taken. Distribution of the ratios for all PMTs isshown in Fig. 5.10(a). It can be seen that the standard deviation is 1.6%. Since the PMT
gain is not probable to change in such short period, this can be regarded as reproducibilityof the procedure.
The long-term stability was also investigated as seen in Fig. 5.10(b). The data wastaken for about one month in another period of detector operation than the LCS beam
test. The gain variation is found to stay within 0.5% in sigma.

ID
Entries
Mean
RMS

50

Constant
Mean
Sigma

100
228
1.008
0.1641E−01
4.811 / 7
52.85
1.008
0.1612E−01

660

Gain (x 10 )Entries

CHAPTER 5. PERFORMANCE OF THE 100-LITER PROTOTYPE

5.022
0.1127E−02
0.1047E−02

40

30

64

1.6
1.4
1.2
1.0

20

0.8

10

0.6

0
0.75 0.8 0.85 0.9 0.95

11.05 1.1 1.15 1.2 1.25

2700

2800

2900 3000

(a)

3100

Run Number

Gain Ratio(b)

Figure 5.10: Short-term and long-term stability. (a) Ratio of the gain obtained in two
consecutive runs. Ratio of the gain obtained in two consecutive runs. (b) Long-term
stability of gain adjustment for a PMT.

5.4.2

QE Measurement

We must use same wavelength of light as Xe scintillation light for estimating QEs since
QEs highly depends on the wavelength. This is why LEDs are inappropriate as a lightsource for QE estimation. For that purpose α particle is the most appropriate as thelight source. Alpha-ray from 241 Am has an almost monochromatic energy spectrum(5.443 MeV (83%) and 5.443 MeV (15%)) with lower tail caused by energy loss in thesource material itself and its range in liquid xenon is beneficially short as 40 µm. In
addition it is very stable even at low temperature in LXe. The half life of 241 Am is longenough that the source intensity can be regarded to be constant. Therefore the α source
is a good point-like light source for estimating QEs.
There are two possibilities to estimate QEs at low temperature around operating
condition. One is to utilize cold gas xenon (GXe) and the other is just to measure the QEs
during operation i.e. in LXe. In GXe effects of scattering and absorption of scintillation
light is negligibly small while in LXe they are prominent. We tried both methods in thisanalysis.
We took α-particle data in such a condition that the inner vessel is filled with 1.3-atm
cold (170 K) GXe, whose scintillation spectrum is not so much different with that inliquid phase [90, 91]. The data was compared with a Monte Carlo simulation. In thissimulation, the scintillation efficiency (energy deposit required to emit one scintillation
photon, Wph (α)) of GXe was assumed to be 49.6 eV and the absorption and Rayleighscattering were switched off. As shown in Fig. 5.11, QE of each PMT was estimated bycomparing the measured spectrum to the one obtained in the simulation.
We took α-particle data in LXe also. Similarly as in GXe, QE of each PMT was
estimated, assuming Wph (α) to be 17.6 eV, absorption length to be 1 m, and Rayleighscattering length to be 45 cm. The QE distribution obtained by GXe data and LXe data
are compared in Fig. 5.12. Clear relation between two estimation methods can be seen

CHAPTER 5. PERFORMANCE OF THE 100-LITER PROTOTYPE

65

although the absolute value is different. This is most probably caused by ambiguity ofWph (α) in LXe and GXe. Although GXe data is easier to handle for avoiding problemsof the absorption and scattering, we employed the LXe data for QE estimation because
scintillation light yield is higher in LXe than in GXe and temperature uniformity in thecryostat is better in LXe than in GXe. Note that the newly installed purification systemenabled us to do in this way. It had been impossible to estimate QEs in LXe before we
succeeded in purifying xenon on site.
Fig. 5.12(b) shows the QE distribution estimated by using LXe data. The lower tailis attributed to the uncontrolled thickness of Mn-layer on the photo-cathode and to theinappropriate mixture of photo-cathode material resulting in resistivity increase at LXetemperature. The broad distribution is due to difficult evaporation technique for thephoto-cathode material.

700
600
500

Experimental data
MC simulation (Npe*1.42)

400
300
200
100
0
0

20

40

60

80

100

120

140

Number of Photoelectrons Npe

Figure 5.11: The Npe spectra observed by a PMT for α particle in LXe. The ratio ofexperimental data to the simulation data was about 1.4.

QE from LXe data [%]CHAPTER 5. PERFORMANCE OF THE 100-LITER PROTOTYPE

66

9
8

0.6683 ± 0.002927

Grad.

7
6
5
4
3
2
1
0
0

2

4

6

8

10

12

QE from GXe data [%]

Entry

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

1

2

3

4

5

6

7

8

Quantum Efficiency [%](b)
Figure 5.12: (a) QE estimated from GXe and LXe data. (b) Distribution of QE estimatedfrom LXe data.

CHAPTER 5. PERFORMANCE OF THE 100-LITER PROTOTYPE

5.4.3

67

Long-term Stability

1.2

Relative Npe

Relative Npe

The α-particle data in LXe are used for monitoring stability of the PMT outputs since
they are regarded as stable light sources. Fig. 5.13 shows that the PMT outputs stabilized
within 5%. This fluctuation includes the error of gain determination. The fluctuation of
the raw ADC data is less than 5%. Normally PMT output is unstable and high gain
just after completing liquefaction of xenon. As shown in Fig. 5.13 (b), the total Npe wasdecreasing in the early days. It took about 2 days for PMTs to be stable. After that, thelight yield was gradually increased by purification of LXe. If the effect of purification was
taken into account, the total Npe was able to be stable within 3%.

1.15

1.2

1.15

1.1

1.05

1.1

1.05

1

1

0.95

0.95

0.9

0.9

0.85

0.85

0.8
0

50

100

150

200

250

300

350

0.8
0

50

100

150

Elapsed Time [hrs]

200

250

300

350

Elapsed Time [hrs]

(a)

(b)

Figure 5.13: Long-term stability in α runs over the beam test for (a) Npe observed bya PMT and (b) a sum of Npe s by all PMTs. Elapsed time of zero corresponds to thebeginning time of the test.

5.4.4

Noise Estimate

As in any electronics system, noise is an important concern in the detector performance.
A typical distribution of the pedestal data is shown in Fig. 5.14(a). The distribution of
the pedestal after summing all 228 channels are shown in Fig 5.14(b). The width of thepedestal distribution corresponds to the electronics noise level.
The noise is comprised of both incoherent and coherent noise:
σT2 = σI2 + σC2 ,(5.5)

where σT2 stands for the total noise, σI2 the incoherent noise, and σC2 the coherent noise.
The incoherent noise can be thought of as random, whereas the coherent noise can bethought of as noise correlated between PMTs and channels in the ADC module. The
incoherent noise is defined as
σI2 =

n
X
i=i

σi2

σj2 ,

(5.6)


2

N
N
1 X

1 X
=
(qij − qi )2 − (qij − qi ) ,
N j=1
N j=1

(5.7)

CHAPTER 5. PERFORMANCE OF THE 100-LITER PROTOTYPE

2500

500

2000

400

1500

300

1000

200

500

100

0
-15

-10

-5

0

5

10

15

0
-300

-200

-100

0

100

68

200

300

Pedestal of one PMT [p.e.]

A Sum of Pedestals [p.e.]

(a)

(b)

Figure 5.14: Typical pedestal distribution of one channel (a) and a sum of 228 channels(b) after converting ADC channel to number of photoelectrons.
where qi is the average of ADC count(qij ) of j-th PMT over N events in the pedestal run.
The coherent and incoherent noise calculated by using these equations are summarized in
Tab.5.2
Table 5.2: Typical overall noise results.
Noise ADC count converted to Npe
σT
37.4
53.6
σI
31.7
46.5
σC
19.7
26.7

5.5

Incident Beam

In order to estimate the detector performance for γ rays of tens of MeV, the scale of theincident beam energy were 10 MeV, 20 MeV, and 40 MeV at Compton edge.
Moreover, we studied the position dependence of the detector performance by moving
the detector with respect to the beam. The impinging points are shown in Fig. 5.15.
The point P0 corresponded to the center of the impinging (front) face. The point P9
was shifted from the center of the PMT by +2 mm along x axis to avoid the edge of theentrance window of the cryostat. In this analysis the data from P1 to P8 was not used.

CHAPTER 5. PERFORMANCE OF THE 100-LITER PROTOTYPE

69

62 mm

Alminum beam window
PMT
45 mm
62 mm

The Centerof The Front FacePMT
P0
P0: (0, 0)
P1: (0, −10)
P2: (0, −20)
P3: (0, −31)
P4: (−10, −10)
P5: (−10, −20)
P6: (−10, −31)
P7: (−20, −20)
P8: (−20, −31)
P9: (−29, −31)
Unit: mm

P4
P1
P5 P7
P2
P6 P8

PMT

P3

P9

PMT
PMT Cathodex

Figure 5.15: Impinging points of γ rays in this test.

Table 5.3: Energy and position of impinging beam in this test.
γ-ray Energy at Compton edge
10 MeV
20 MeV
40 MeV

Impinging position
P0 and P9
P0 and P9
P0 ∼ P9yCHAPTER 5. PERFORMANCE OF THE 100-LITER PROTOTYPE

5.6

Position Resolution

5.6.1

Position Reconstruction in Simulation

70

The first conversion points of γ rays in LXe were reconstructed by using the spread ofcharge distribution on the front face. The point projected onto the front face can be
estimated as:
P36

X =
Qf =

i=1 qi Xi

Qf
36
X

,

(X = x, y)

qi ,

(5.8)
(5.9)

i=1

where qi is the number of photoelectrons observed by the i-th PMT located at Xi . We callthe X ”simple weighted mean”. This value tends to be pulled by qi far from the incident
position. For avoiding this problem, we newly devised a method to estimate the incident
position. In this method the following procedure was taken:
1. Calculate the simple weighted mean (x, y).
2. Make a 2-dimensional map with 6 × 6 blocks as Fig. 5.16. Each block has a circle
bin and it corresponds to a PMT photo-cathode with a diameter of 45 mm.
3. Fill the circle bin with PMT outputs like a histogram.
4. Draw a circle whose center is at (x, y). Define the radius Rf such that the sum of
qi inside the circle becomes a half of Qf .
5. Calculate the weighted mean of PMT outputs inside the circle. In this case, xi isthe center of overlap of the circle with i-th circle bin.
6. Iterate the 4 and 5 processes till the weighted mean converges.
In other words, the Rf is the radius of the circle such thatP36

i=1 qi Ci

Qf= 0.5,(5.10)

where Ci is an overlap ratio of the circle and i-th circle bin. If the circle includes the i-th
circle bin, Ci equals to 1. At this time we introduce a new variable:
Nf (0.5) =

36
X

Ci .

(5.11)

i=1

This parameter Nf is a number() of PMTs included in the circle Rf , and a function of theratio n for Qf . When the ratio n was changed from 0.1 to 0.9 every 0.1, it was found thatn of 0.5 was the best. This value Nf (0.5) can be a good measure of the first conversion
depth as described later.

CHAPTER 5. PERFORMANCE OF THE 100-LITER PROTOTYPE

17

41

46

53

33

18

77

105

38

112

220

201

85

34

95

80

222

820

710

199

69

50

221

857

757

219

54

94

202

186

83

15

Rf =6.37 cm

Nf (0.5)=3.84 PMT
42

52

58

37

71

116

95

86

66

148

172

186

126

82

120

180

279

236

205

100

70

106

162

263

267

165

111

34

81

135

178

178

126

86

15

52

(a) shallow event (4.4 cm)

Rf =11.51 cm

Nf (0.5)=11.63 PMT
82

94

91

73

59

(b) deep event (15.3 cm)

Figure 5.16: Schematic histograms of charge distribution on the front face. Each Npe isdrawn with gray scale and as a table in green. The radius of the red circle equals to Rf
and Nf (0.5) is the number of PMTs in the circle. Numbers on the circle are observed Npe .
Green crosses show true first conversion points. Red crosses show local weighted means.
Figure 5.17 shows a 2-dimensional distribution of differences between true and reconstructed positions obtained from MC simulation data. The data was generated under thefollowing conditions:• LCS beam with 40-MeV Compton edge.
• Impinging area was 124 mm×124 mm at the center of front face and the beam was
uniformly impinged.
• Events the first conversion occurred in the active volume.
The resolution of position reconstruction is estimated to be about 5.7 mm in σ byfitting the distribution with a 2-dimensional Gaussian function, where the sigma in x
direction equals to one in y direction.
In Fig. 5.18 a comparison between (a) local weighted mean and (b) simple weighted
mean is shown. It is clear that the local weighted mean is superior to the simple weighted
mean for deep events. The reconstructed position by the simple weighted mean tends tobe pulled to the centers of PMTs whereas the local weighted mean not. Thus we canconclude that the reconstruction of incident γ-ray positions can be done in a less biased
way with the local weighted mean.
Fig. 5.19 shows the relation between Nf (0.5) and local weighted mean in MC simulation. It can be seen that the position resolution for the shallow event (Nf (0.5) < 4)
deteriorates due to the bias by the nearest PMT. In the case of (b), the resolution wasvery high. In the region both are considered to be biased by the nearest PMT.

CHAPTER 5. PERFORMANCE OF THE 100-LITER PROTOTYPE
Entries
Mean xMean yRMS x
RMS yχ2 / ndf
const.
Mean xMean y
σx
σy

250
200
150

72

12305
0.0001362
0.008136
0.60560.618
647.2 / 377
211.1 ± 3.333
0.001711 ± 0.00548
0.01088 ± 0.005566
0.5653 ± 0.004555
0.575 ± 0.004765

100
50
0
2
1.5

y-y

0 [c

1
0.5

m] 0-0.5-1-1.5-2 -2 -1.5

-1 -0.5

0.5

0

1

1.5

2

cm]

x-x 0 [

X-X 0 [cm]Figure 5.17: Difference between true and reconstructed positions in simulation.
10

1600

8
6
4

1200

2

1000

0

800

-2

600

-4

400

-6

200

-8
-10
0

Entries
12305
Entries
12305
Mean
Mean
0.003951
0.008619
RMS
1.15
RMS
0.84042
175 // 47
χ 2 // ndf
ndf
601
Constant
881.5±± 19.2
10.5
Constant
1489
Mean
Mean
0.009863
0.01345 ±± 0.009919
0.00577
1.086
0.008
Sigma
Sigma
0.6189± ±0.0055

1400

5

10

15

20

25

30

35

40

45

50

0
-5

-4

-3

-2

-1

0

1

2

3

First Conversion Depth [cm]4

5

X-X 0 [cm]X-X 0 [cm](a) local weighted mean
10
8
6

900

Entries

12305

Mean

0.003951

800

RMS

700

χ / ndf
Constant

4
2

600

0

500

-2

400

-4

300

-6

200

175 / 47
881.5 ± 10.5

Mean

0.009863 ± 0.009919

Sigma

1.086 ± 0.008

100

-8
-10
0

1.15

2

5

10

15

20

25

30

35

40

45

50

0
-5

-4

-3

First Conversion Depth [cm]

-2

-1

0

1

2

3

4

5

X-X 0 [cm](b) simple weighted mean
Figure 5.18: Difference between the local weighted mean and simple weighted mean. Left
figures of (a) and (b) are the distributions of the residual between reconstructed and true
positions vs. the true first conversion depth in MC simulation. Right figures are theirprojections onto the x − x0 axis and fitting results with Gaussian.

15
10
5
0
-5
-10
-15
0

2

4

6

8

10

12

14

73

15

local weighted mean in x direction

local weighted mean in x direction

CHAPTER 5. PERFORMANCE OF THE 100-LITER PROTOTYPE

10
5
0
-5
-10
-15
0

16

2

4

6

8

10

12

14

Nf (0.5)

16

Nf (0.5)(a) impinged at P0(b) impinged at P9

Figure 5.19: The relation between Nf (0.5) and local weighted mean in MC simulation.

5.6.2

Depth Reconstruction in Simulation

The relations between Nf (0.5) and the first conversion depth in MC simulation are shownin Fig. 5.20. It is found that the reconstruction of the depth at P0 is better lower thanat P9 especially for the shallow event.

Nf (0.5)

16

Nf (0.5)

16
14

14

12

12

10

10

8

8

6

6

4

4

2

2

0
0

5

10

15

20

25

30

35

40

First converion Depth [cm]

(a)

0
0

5

10

15

20

25

30

35

40

First converion Depth [cm](b)

Figure 5.20: The relation between Nf (0.5) and the first conversion depth in MC simulation. The impinging point is P0 for (a) and P9 for (b).
For the same MC data as used in Fig. 5.17, the relation between Nf (0.5) and thefirst conversion depth was fitted with a second-order polynomial function to be correctedaccording to the first conversion depth. The result is shown in Fig. 5.21. In MC data,
the precision for reconstructing the first conversion depth was 8 mm.

Reconstructed Depth [cm]CHAPTER 5. PERFORMANCE OF THE 100-LITER PROTOTYPE

20

2500

18
16

74

Entries

12305

Mean

-0.2258

RMS

2000

1.771

χ / ndf
2

141293 / 40

Constant

12

1500

2068 ± 28.5

Mean

0.1854 ± 0.0081

Sigma

0.8415 ± 0.0084

10
8

1000

6
4

500

2
0
0

2

4

6

8

10

12

14

16

18

20

0
-10

-8

-6

-4

-2

0

2

4

6

8

10

Z-Z0 [cm]First Conversion Depth [cm]

(a)

(b)

Figure 5.21: (a) Scatter plot of reconstructed and the true first conversion depths. (b)Residual distribution after reconstruction.

5.6.3

Position Reconstruction

Position resolution was evaluated after correcting with QEs obtained in subsection 5.4.2.
qi0 = qi ×

Q,
Qi

(5.12)

where Qi means measured QE of i-th PMT, and Q is an average of all QEs. These
corrected charge qi0 was used in Eq. 5.9, 5.10 instead of qi .
Fig. 5.22 shows that local weighted mean and Nf (0.5) in experimental data. The behavior of reconstructed position was a bit different from one in MC simulation (Fig. 5.19).
As seen in (b.1) of Fig. 5.22, the obtained means are pulled by the center of the front
face. This phenomenon is considered to be caused by the miscalculation of QE. The position reconstruction depends on the accuracy of QE measurement. However the accuracy
method of QE has not established yet.

5.6.4

Depth Dependence

To evaluate the position resolution, the events in the range of 4.0 < Nf (0.5) < 12.0 was
selected at the cost of the efficiency because too shallow or deep events are highly biased.
This range corresponds to the actual first conversion depth from 4.5 cm to 18 cm, and theselection efficiency is about 35% from the MC simulation. More intelligent algorithm has
to be devised so as not to discard such events. The events were sliced every Nf (0.5) of 1.0
to fit with a 2-dimensional double Gaussian, which has four sigmas: narrow components
σx and σy , and broad components ρx and ρy , where x and y mean the direction. An
example of the fitting is shown in Fig. 5.23. All the results are shown in Fig. 5.24 for
10-MeV Compton edge, Fig. 5.25 for 20 MeV, and Fig. 5.26 for 40 MeV.

local weighted mean in x direction

CHAPTER 5. PERFORMANCE OF THE 100-LITER PROTOTYPE

75

15
10
5
0
-5
-10
-15
0

2

4

6

8

10

12

14

16

Nf (0.5)

15

local weighted mean in x direction

local weighted mean in x direction

(a)
10
5
0
-5
-10
-15
0

2

4

6

8

10

12

14

16

Nf (0.5)

15
10
5
0
-5
-10
-15
0

2

4

(b.1) before correction

6

8

10

12

14

16

Nf (0.5)(b.2) after correction

Figure 5.22: The relation between the depth parameter Nf and the local weighted mean.
Compton edge energy is 40 MeV, and the incident point is at P0 (a) and at P9 (b).

Entries
Mean xMean yχ2 / ndf
Const.
Mean xMean y
σx
σy
Ratio
ρx
ρy

500
400

14893
0.08632-0.002243
1132 / 609
465.3 ± 10.71
0.1292 ± 0.003342-0.002338 ± 0.00381
0.2842 ± 0.005949
0.3325 ± 0.007762
0.9248 ± 0.01092
0.6587 ± 0.03018
0.77 ± 0.03073

300

Entries
Mean xMean yχ2 / ndf
Const.
Mean xMean y
σx
σy
Ratio
ρx
ρy

300
250
200

18473
-2.794-3.1472889 / 752
266.6 ± 4.293-2.75 ± 0.005685-3.144 ± 0.005319
0.4565 ± 0.004731
0.4388 ± 0.004626
0.978 ± 0.002343
1.495 ± 0.09148
1.471 ± 0.08613

150
200

100

100

50

0
2
1.5

1
0.5

0
-1
-1.5
0
-0.5

-1
-1.5

-2
-2.5

0 0.5
-1 -0.5-2 -1.5

(a)

2 2.5
1 1.5

-2
-2.5

-3
-3.5

-4
-4.5

-5
-5.5

-4
-5 -4.5-3.5 -3-2.5 -2-0.5-1.5 -1(b)

Figure 5.23: Examples of the fitting result with a 2-dimensional double Gaussian for
EC = 40 MeV and Nf (0.5) > 4.0. The incident point is at P0 (a)and at P9 (b).

76narrow σx
narrow σy11# of Events

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

0
4

5

6

7

8

9

10

11

Number of Events (a.u.)

σ of local weighted mean [cm]CHAPTER 5. PERFORMANCE OF THE 100-LITER PROTOTYPE

012Depth Parameter Nf (0.5)

narrow σx
narrow σy11# of Events

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

0
4

5

6

7

8

9

10

11

Number of Events (a.u.)

σ of local weighted mean [cm](a) 10 MeV, at P0.

012Depth Parameter Nf (0.5)(b) 10 MeV, at P9
Figure 5.24: Position resolution as a function of Nf (0.5) for EC = 10 MeV, impinged at(a) P0 and (b) P9.

77

narrow σx
narrow σy11# of Events

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

0
4

5

6

7

8

9

10

11

Number of Events (a.u.)

σ of local weighted mean [cm]CHAPTER 5. PERFORMANCE OF THE 100-LITER PROTOTYPE

012Depth Parameter Nf (0.5)

narrow σx
narrow σy11# of Events

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

0
4

5

6

7

8

9

10

11

Number of Events (a.u.)

σ of local weighted mean [cm](a) 20 MeV, at P0.

012Depth Parameter Nf (0.5)(b) 20 MeV, at P9
Figure 5.25: Position resolution as a function of Nf (0.5) for EC = 20 MeV, impinged at(a) P0 and (b) P9.

78

narrow σx
narrow σy11# of Events

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

0
4

5

6

7

8

9

10

11

Number of Events (a.u.)

σ of local weighted mean [cm]CHAPTER 5. PERFORMANCE OF THE 100-LITER PROTOTYPE

012Depth Parameter Nf (0.5)

narrow σx
narrow σy11# of Events

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

0
4

5

6

7

8

9

10

11

Number of Events (a.u.)

σ of local weighted mean [cm](a) 40 MeV, at P0.

012Depth Parameter Nf (0.5)(b) 40 MeV, at P9.
Figure 5.26: Position resolution as a function of Nf (0.5) for EC = 40 MeV, impinged at(a) P0 and (b) P9.

CHAPTER 5. PERFORMANCE OF THE 100-LITER PROTOTYPE

5.6.5

79

Energy Dependence

The difference of the resolution according to the incident beam energy was investigated.
The range of Nf (0.5) was over 4.0. The events were sliced every Nf (0.5) of 1.0 to becorrected by shifting to the correct incident position (p0 or P9). The corrected events areshown in Fig. 5.22 (b.2). After the correction, the events were fitted with a 2-dimensional
double Gaussian. The position resolution from measured data and MC simulation are
shown in Tab. 5.4 and Tab. 5.5, respectively.
Table 5.4: Position resolution from measured data. Upper value in a column is narrowcomponent and lower value is broad one. Unit is cm. The percentage in a parenthesis isa fraction of each component.
Position\Energy
P0
P9
Position\Energy
P0
P9

position resolution in x direction
10 MeV
20 MeV
0.38 ± 0.01 (77.1%) 0.40 ± 0.01 (80.5%)
0.89 ± 0.02 (22.9%) 0.86 ± 0.05 (19.5%)
0.42 ± 0.01 (91.3%) 0.44 ± 0.00 (93.5%)
1.10 ± 0.07 (8.7%) 1.37 ± 0.10 (6.5%)
position resolution in y direction
10 MeV
20 MeV
0.35 ± 0.00 (77.1%) 0.36 ± 0.01 (80.5%)
0.85 ± 0.01 (22.9%) 0.88 ± 0.03 (19.5%)
0.49 ± 0.01 (91.3%) 0.48 ± 0.01 (93.5%)
1.18 ± 0.07 ( 8.7%) 1.52 ± 0.12 ( 6.5%)

40 MeV
0.42 ± 0.01 (83.8%)
1.10 ± 0.07 (16.2%)
0.43 ± 0.00 (95.3%)
1.90 ± 0.32 (4.7%)
40 MeV
0.39 ± 0.01 (83.8%)
0.81 ± 0.05 (16.2%)
0.47 ± 0.00 (95.3%)
1.95 ± 0.34 ( 4.7%)

Table 5.5: Position resolution from MC simulation. Upper value in a column is narrowcomponent and lower value is broad one. Unit is cm. The percentage in a parenthesis isa fraction of each component.
Position\Energy
P0
P9
Position\Energy
P0
P9

position resolution in x direction
10 MeV
20 MeV
40 MeV
0.37 ± 0.01 (82.7%) 0.47 ± 0.01 (90.1%) 0.41 ± 0.01 (87.9%)
1.12 ± 0.07 (11.3%) 1.66 ± 0.25 (9.9%) 1.51 ± 0.15 (12.1%)
0.50 ± 0.01 (90.2%) 0.44 ± 0.01 (87.6%) 0.49 ± 0.01 (89.3%)
2.64 ± 0.11 (9.8%) 1.66 ± 0.10 (12.4%) 2.15 ± 0.54 (10.7%)
position resolution in y direction
10 MeV
20 MeV
40 MeV
0.35 ± 0.01 (82.7%) 0.48 ± 0.01 (90.1%) 0.41 ± 0.01 (87.9%)
1.13 ± 0.06 (11.3%) 1.87 ± 0.33 (9.9%) 1.56 ± 0.17 (12.1%)
0.51 ± 0.01 (90.2%) 0.43 ± 0.01 (87.6%) 0.50 ± 0.01 (89.3%)
2.39 ± 0.11 (9.8%) 1.78 ± 0.10 (12.4%) 2.26 ± 0.68 (10.7%)

CHAPTER 5. PERFORMANCE OF THE 100-LITER PROTOTYPE

80

Position Resolution [cm]Fig. 5.27 shows the energy dependence of position resolutions.

broad σx at P0
broad σx at P9
broad σy at P0
broad σy at P9

1narrow σx at P0
narrow σx at P9
narrow σy at P0
narrow σy at P9

10-1
0

10

20

30

40

50

γ -ray Energy [MeV]

Position Resolution [cm](a) measured databroad σx at P0
broad σx at P9
broad σy at P0
broad σy at P9

1narrow σx at P0
narrow σx at P9
narrow σy at P0
narrow σy at P9

10-1
0

10

20

30

40

50

γ -ray Energy [MeV](b) MC simulation
Figure 5.27: The resolution of the local weighted mean in σ as a function of γ-ray energy.
Only the statistical errors in the fitting are presented as error bars.

CHAPTER 5. PERFORMANCE OF THE 100-LITER PROTOTYPE

5.6.6

81

Difference between the Data and the Simulation

It is found that the position resolution from the measured data is better than that from thesimulation. The position reconstruction in the measured data might be biased more thanthat in the MC and underestimated for some reasons. However it is appropriate that thediscrepancy comes from defectiveness of the modeling in the MC simulation, since bothresolutions were estimated by the same method. Indeed, the behavior of the scintillation
photons close to PMTs is not understood well. There remain some parameters to be
tuned: refractive index of xenon and PMT window for xenon scintillation photons, andreflectivity of PMT holders. If these parameters were tuned properly, the resolution in
the simulation should be coincident with the intrinsic position resolution, which will be
discussed in the next subsection.

5.6.7

Intrinsic Position Resolution

Here we will evaluate the intrinsic position resolution, which means the resolution concerning only the LXe scintillation process. The intrinsic resolution was expressed as:
2
2
2
2
σintr
= σx2 − (σnoise+ σbeam+ σcol),(5.13)

where σintr , σnoise , σbeam , and σcol are intrinsic position resolution, error sources frompedestal noise, the spread of the LCS beam, and the radius of the collimator, respectively.
After excluding those factors from the obtained resolution, the intrinsic resolution will be
evaluated.
Electronics NoiseThe electronics noise represents the pedestal noise. MC simulations for monochromatic
γ rays of 10 MeV, 20 MeV, and 40 MeV were performed. For those data, the incident
positions were reconstructed after taking account of coherent and incoherent noises obtained in Sec. 5.4.4. The result is shown in Tab. 5.6. In principle the coherent noise does
not affect the position resolution. The electronics noise was not dominant because thepedestal noise was small enough.
Table 5.6: Deterioration by electronics noise. Unit is cm.
Position \ Energy
P0
P9

10 MeV
0.02
0.05

20 MeV
0.02
0.04

40 MeV0.00
0.01

LCS beam
As shown in Tab. 5.1, the energy spread of the Compton edge is 1%. The deterioration of
position resolution was estimated by MC simulation. As shown in Tab. 5.7, little influence
was seen.

CHAPTER 5. PERFORMANCE OF THE 100-LITER PROTOTYPE

82

Table 5.7: The effect by fluctuation of LCS beam energy. Unit is cm.
Position \ Energy
P0
P9

10 MeV
0.02
0.01

20 MeV
0.00
0.01

40 MeV
0.01
0.00

Radius of Collimator
The diameter of the second collimator was 1 mmφ and 2 mmφ. The analysis in Sec. 5.6.5
was performed for events with the 1 mmφ collimator. We also analyzed events with
2 mmφ collimator. Comparing both results, no significant differences were seen. The
contribution to the error of the position resolution was considered to be negligible. It canbe guessed by the spectra in Fig. 5.4.
From these evaluations, we could obtain the intrinsic resolution. However the contribution of σnoise , σbeam , and σcol to the position resolution was negligible. Therefore theobtained resolution is considered to be almost intrinsic.

5.6.8

Systematic Error

Parameters in MC Simulation
The position resolution can be affected by the modeling in MC simulation because theposition reconstruction depends on the accuracy of QE determination. Some parameters
is not still fixed and have indefiniteness.
We examined whether the position resolution changed by varying each parameters ina certain range. The method was as follows:
1 Simulate α-particle events with a parameter set to a certain value.
2 Compare the Npe observed by a PMT in experimental data with one in the simulation to estimate the QE of the PMT.
3 Reconstruct the incident position on the basis of the obtained QEs.
4 Fit the the distribution of the reconstructed position.
5 Obtain the difference between this resolution and one in Tab. 5.4.
Parameters to be examined were refractive index of LXe (nXe ), Rayleigh scattering
length (λsca ), absorption length (λabs ), and reflection ratio on the lateral face. The range
of nXe was defined by Tab. 3.3, λsca λabs were by the result obtained in Chap. 4, andreflection ratio was from [92]. Tab. 5.8 shows the difference with position resolutions in
MC simulations. Those errors are added to position resolutions in Tab. 5.4 as systematic
errors.

CHAPTER 5. PERFORMANCE OF THE 100-LITER PROTOTYPE

83

Table 5.8: Difference of the position resolution by changing parameters in the MC simulation for QE estimate. Unit is cm.
range
Parameter
or
value
nXe
1.62
1.56 to 1.72
λsca
45 cm 40 cm to 50 cm
λabs
1m
90 cm to 3 m
Reflection
0%0% to 10%
Quadratic Sum
default
value

Incident energy & position
10 MeV 20 MeV 40 MeV
P0 P9 P0 P9 P0 P9
0.1 0.0 0.0 0.0 0.1 0.0
0.1 0.1 0.1 0.1 0.0 0.0
0.0 0.0 0.0 0.0 0.0 0.0
0.1 0.2 0.1 0.1 0.1 0.1
0.2 0.2 0.1 0.1 0.1 0.1

Consequently the difference between the resolutions from the data and simulations
was not understood completely. We should compare the position resolution with ones
from simulation samples obtained by changing values of those parameters.

5.6.9

Position Resolution

The position resolution does not always depend on γ-ray energy. It is difficult to extrapolate the position resolution to 52.8-MeV. From MC simulations, position resolution
for monochromatic 10-MeV γ rays is better than those for 20 MeV and 40 MeV. It isconsidered to be caused by electromagnetic shower because the critical energy of xenon
is 14.5 MeV. However the position resolution improves according to γ-ray energy over
20 MeV. Hence the position resolution for EC = 40 MeV is substituted for the resolution
in 52.8 MeV.

5.7

Energy Resolution

5.7.1

Compton Edge

The energy spectrum of the LCS beam has a sharp Compton edge and lower tail. In
order to evaluate the energy resolution, the shape of Compton edge was fitted with aconvolution of the Compton spectrum and a response function. The Compton spectrum
was simulated with parameters given in Tab. 5.1 and experimental setup shown in Fig. 5.3
on the basis of Klein-Nishina formula [84]. The spectra are shown in Fig. 5.28.
The amount of pile-ups depends on the beam current in TERAS. Fig. 5.29 shows pileups of multiple gamma rays when the beam current was about 120 mA. In this analysis
the data for low electron beam current (∼ 30 mA) were used to contamination of suppress
pile-ups events as shown in Fig. 5.30. Hence the subtraction of pile-up events was notdone in fitting procedure.
As seen in Fig. 5.30, the measured spectrum has a broader tail than the incident beam
spectrum. The lower tail comes from conversions in the front material (See Fig. 3.5) orin the second collimator made of lead. However the Compton edge is sharp enough toestimate the energy resolution. The lower tail was employed for that purpose.

Intensity (a.u.)

CHAPTER 5. PERFORMANCE OF THE 100-LITER PROTOTYPE

1.2

84

EC = 10.32 MeV
EC = 20.37 MeV
EC = 39.67 MeV

1
0.8
0.6
0.4
0.2
0
0

5

10

15

20

25

30

35

40

45

LCS Beam Energy [MeV]

Nf(0.5)Figure 5.28: LCS beam spectra in this test.

16
14

one photon

12

two photon

10

three photon

8
6
4
2
0
0

5000

10000

15000

20000

25000

30000

35000

40000

Total Number of Photoelectrons

Figure 5.29: Pile-up events in high beam current (EC =10 MeV).

5.7.2

Fitting Function

The response function was a Gaussian with lower tail as follows:
Ã

½
¾!

t t


,

 A exp σ 2 2 − (E − µ)uÃ!
f (E) =
(E − µ)2 A exp
,

2

−2σu

E ≤ µ + t,
(5.14)
E > µ + t,

where σu is the sigma in the upper part of the response function, E is the beam energy,µ is the peak of the response function, and t is the transition parameter which represents
the degree of the lower tail. For this function FWHM is written as:√
σ2t
FWHM = σu ln 4 + u ln 2 + .
t
2(5.15)

CHAPTER 5. PERFORMANCE OF THE 100-LITER PROTOTYPE

Nf (0.5)

1600
1400
1200

85

16
14
12

1000

10

800

8

600

6

400

4

200

2

0
0

5000

10000

15000

20000

25000

0
0

30000

5000

10000

Total Number of Photoelectrons

15000

20000

25000

30000

Total Number of Photoelectrons

Nf (0.5)(a)EC =40 MeV, impinged at P0
1600
1400

16
14

1200

12

1000

10

800

8

600

6

400

4

200

2

0
0

5000

10000

15000

20000

25000

0
0

30000

5000

10000

Total Number of Photoelectrons

15000

20000

25000

30000

Total Number of Photoelectrons(b)EC =40 MeV, impinged at P9
Figure 5.30: Measured energy spectrum for LCS beam.

5.7.3

Fitting Procedure

Energy resolution was evaluated using Qsum after QE correction, where Qsum means asum of Npe over all the 228 PMTs written as:
Qsum =

228
X

qi0 ,

(5.16)

i=1

where qi0 is the same as Eq. 5.12.
Parameters in the fitting with the convolution are normalization factor (A), upper
part of sigma (σu ), transition (t), and Compton edge parameter. The edge parameter is
Npe corresponding to the Compton edge in terms of MeV.
This fitting needed special care because the edge parameter tended to be ‘strong’ in thefitting procedure. That is, the other parameters strongly depends on the edge parameter.
The first step was to define the proper initial value of the edge parameter. For a start,some fittings were done in order to roughly obtain a fitting result. However it was possiblethat this result fell into a local minimum. As shown Fig. 5.31(a), the edge parameter wasscanned over the upper tail, fixed the other parameters. From this plot, the Comptonedge parameter such that chi-square was minimum was set to the initial value. The next
step was to define the fitting range. Since no pile-up events were seen in the spectrum asshown in Fig. 5.30, the upper limit of the fitting range was set to the bottom of the upper
tail. On the other hand, the lower limit had to be defined with chi-square as well as theCHAPTER 5. PERFORMANCE OF THE 100-LITER PROTOTYPE

86

χ 2/ndf

Compton edge parameter. In this analysis, it was important to fit the Compton edge toevaluate σu while it was not necessary to fit the full lower tail. The Npe where χ2 /ndf
became the minimum was selected as the lower limit. Because the lower limit could overthe peak of the fitting curve, it was set to −5σu from the peak at least. Fig. 5.31(b) is an
example of the fitting when the depth parameter Nf (0.5) is over 4.0.

102

27200

27300

27400

27500

27600

27700

27800

25000

30000

Compton edge parameter
(a)

450
400
350
300
250
200

Entries15961
Mean
2.175e+04
RMS
5090
χ2 / ndf
24 / 28
Constant 1.507e-05 ± 4.343e-07
σup
404.1 ± 14.1
transit-83.57 ± 5.12
C edge2.753e+04 ± 72

150
100
50
0
0

5000

10000

15000

20000

Total Number of Photoelectrons(b)
Figure 5.31: (a)The relation between χ2 /ndf as a function of the lower limit of the fitting
range. (b)An example of the fitting.

5.7.4

Depth Dependence

As done in the estimate of position resolution, Nf (0.5) was used to investigate the depth
dependence of energy resolution. The all results are shown in Fig. 5.32 for 10-MeV
Compton edge, Fig. 5.33 for 20 MeV, and Fig. 5.34 for 40 MeV.

87

20
σup

18

1

FWHM

16

Number of Events

0.8

14
12

0.6

10
8

0.4

Number of Events in ±3σ (a.u.)

Energy resolution [%]CHAPTER 5. PERFORMANCE OF THE 100-LITER PROTOTYPE

6
4

0.2

2
0
4

5

6

7

8

9

10

11

12

0
13

Depth Parameter Nf (0.5)

20
σup

18

1

FWHM

16

Number of Events

0.8

14
12

0.6

10
8

0.4

Number of Events in ±3σ (a.u.)

Energy resolution [%](a) 10 MeV, at P0.

6
4

0.2

2
0
4

5

6

7

8

9

10

11

12

0
13

Depth Parameter Nf (0.5)(b) 10 MeV, at P9.
Figure 5.32: Energy resolution as a function of Nf (0.5) for EC = 10 MeV, impinged at(a) P0 and (b) P9.

88

20
σup

18

1

FWHM

16

Number of Events

0.8

14
12

0.6

10
8

0.4

Number of Events in ±3σ (a.u.)

Energy resolution [%]CHAPTER 5. PERFORMANCE OF THE 100-LITER PROTOTYPE

6
4

0.2

2
0
4

5

6

7

8

9

10

11

12

0
13

Depth Parameter Nf (0.5)

20
σup

18

1

FWHM

16

Number of Events

0.8

14
12

0.6

10
8

0.4

Number of Events in ±3σ (a.u.)

Energy resolution [%](a) 20 MeV, at P0.

6
4

0.2

2
0
4

5

6

7

8

9

10

11

12

0
13

Depth Parameter Nf (0.5)(b) 20 MeV, at P9.
Figure 5.33: Energy resolution as a function of Nf (0.5) for EC = 20 MeV, impinged at(a) P0 and (b) P9.

89

20
σup

18

1

FWHM

16

Number of Events

0.8

14
12

0.6

10
8

0.4

Number of Events in ±3σ (a.u.)

Energy resolution [%]CHAPTER 5. PERFORMANCE OF THE 100-LITER PROTOTYPE

6
4

0.2

2
0
4

5

6

7

8

9

10

11

12

0
13

Depth Parameter Nf (0.5)

20
σup

18

1

FWHM

16

Number of Events

0.8

14
12

0.6

10
8

0.4

Number of Events in ±3σ (a.u.)

Energy resolution [%](a) 40 MeV, at P0.

6
4

0.2

2
0
4

5

6

7

8

9

10

11

12

0
13

Depth Parameter Nf (0.5)(b) 40 MeV, at P9.
Figure 5.34: Energy resolution as a function of Nf (0.5) for EC = 40 MeV, impinged at(a) P0 and (b) P9.

CHAPTER 5. PERFORMANCE OF THE 100-LITER PROTOTYPE

5.7.5

90

Energy Dependence

The energy resolution is expected to be improved according to increase in Npe . In order toverify the statistical energy dependence, the resolution for 10 MeV, 20 MeV, and 40 MeV
were evaluated with an event selection such that Nf (0.5) ≥ 4.0. The result is summarizedin Tab. 5.9(a). We also evaluated the energy dependence in MC simulation as shown in
Tab. 5.10(b). There are some differences between the results from measured data andMC simulation. In the later subsection, we will discuss the discrepancy.
Table 5.9: Energy resolution measured in LCS beam test. Unit is %.
Position\Energy
P0
P9

10 MeV
20 MeV
40 MeV
3.15 ± 0.04 2.12 ± 0.06 1.47 ± 0.05
3.06 ± 0.07 2.07 ± 0.01 1.47 ± 0.06

Table 5.10: Energy resolution in MC simulation. Unit is %.
Position\Energy
P0
P9

5.7.6

10 MeV
20 MeV
40 MeV
2.25 ± 0.04 1.60 ± 0.06 1.20 ± 0.04
2.03 ± 0.03 1.43 ± 0.10 1.09 ± 0.05

Intrinsic Resolution

The obtained resolution σE includes some factors to be worsened. The intrinsic resolution
was written as:
2
2
2
2
σintr
= σE2 − (σnoise+ σbeam+ σcol),(5.17)

where σintr , σnoise , σbeam , and σcol are intrinsic energy resolution, error sources frompedestal noise, spread of LCS beam energy, and the radius of the collimator, respectively.
Electronics Noise
The influence of the pedestal noise on the energy resolution was evaluated with MC
simulation as seen in Tab. 5.11.
Table 5.11: Deterioration of energy resolution by electronics noise. Unit is %.
Position \ Energy
P0
P9

10 MeV
0.2
0.1

20 MeV0.0
0.0

40 MeV
0.0
0.0

CHAPTER 5. PERFORMANCE OF THE 100-LITER PROTOTYPE

91

LCS beam
The fluctuation of the Compton edge energy is 1%. However the fluctuation was alreadyincluded the LCS spectrum to be convoluted. Therefore it may not be taken into account.
The horizontal size of electron bunch in TERAS is known to be from 1.55 mm to
2.2 mm. Fig. 5.35 shows the LCS beam spectra obtained by changing the bunch size.
The fitting was performed with these spectra again. However the differences were notseen.
Electron Bunch Size
2500

1.5mm
2.2mm
1.8mm

2000

1500

1000

500

0
30

32

34

36

38

40

42

44

Incident Energy [MeV]
Figure 5.35: LCS beam spectra with various horizontal electron bunch size in TERAS.

Radius of Collimator
The radius of the collimator does not affect the shape of the Compton edge. Hence theresolution does not include the effect of collimator radius.
From above evaluations, contribution from the electronics noise was the most dominant
for the energy resolution. The other sources σbeam and σcol were negligible. Because thesimilar noise is expected in the final detector, σnoise should be taken into account toevaluate the performance for 52.8-MeV γ rays.

5.7.7

Systematic Error

Displacement of the second collimator and the spread of the LCS beam and indefinitenessof parameters in the MC simulation are considered to be systematic errors in the obtainedenergy resolution.

CHAPTER 5. PERFORMANCE OF THE 100-LITER PROTOTYPE

92

Collimator Displacement

Intensity (a.u.)

The displacement of the second collimator can affect the energy resolution. Fig. 5.36
shows the LCS beam spectra for the collimator displacement ranging from 0 mm to 4 mmalong x direction. By comparison with the measured spectrum in Fig. 5.30, it is guessedthat the displacement should be 2.5 mm at most.

1

Displacement
0 mm
1 mm
2 mm
2.5 mm
3 mm
3.5 mm
4 mm

0.8

0.6

0.4

0.2

0
0

5

10

15

20

25

30

35

40

45

LCS Beam Energy [MeV]

Figure 5.36: LCS beam spectra for collimator displacement of 0 mm to 4 mm. Comptonedge energy is 40 MeV.
Assuming the true incident position was shifted by ±2.5 mm at most, the LCS spectrum was regenerated by the simulation to fit with the convolution again. The result isshown in Tab. 5.12.
In this beam test, whenever the energy of LCS beam was changed, the second collimator was rearranged. Therefore it is not possible that the collimator was shifted in every
run. If the collimator was shifted, the Compton edge of the incident beam tended to besmeared as shown in Fig. 5.36 and the resolution might be better.
Table 5.12: Difference in energy resolution between collimator displacement of 0 mm andone of 2.5 mm. Unit is %.
Position \ Energy
P0
P9

10 MeV−0.2−0.1

20 MeV−0.1−0.2

40 MeV−0.1−0.2

CHAPTER 5. PERFORMANCE OF THE 100-LITER PROTOTYPE

93

Parameters in MC simulation
Effects by the miscalculation of QEs was evaluated with MC simulation in the same way
as position resolution. The differences are shown in Tab. 5.13.
Table 5.13: Deterioration of the energy resolution by changing parameters in QE estimate.
Unit is %.
Parameter

default
value

nXe
λsca
λabs
Reflection

1.62
45 cm
90 cm
0%

range
or
value
1.56 to 1.72
40 cm to 50 cm
3m
10%Incident energy & position
10 MeV 20 MeV 40 MeV
P0 P9 P0 P9 P0 P9
0.1 0.0 0.0 0.0 0.1 0.0
0.1 0.1 0.1 0.1 0.0 0.0
0.2 0.2 0.1 0.1 0.1 0.1
0.2 0.2 0.2 0.2 0.1 0.2

From above evaluations, the combined errors are obtained as shown in Tab. 5.14.
Table 5.14: Combined systematic errors for energy resolution. Unit is %.
Position \ Energy

5.7.8

P0

10 MeV
+0.3
−0.4

P9

±0.3

20 MeV
+0.2
−0.3
+0.2
−0.3

40 MeV
±0.2
+0.2
−0.3

Energy Resolution

Taking systematic errors into account, we obtained the energy resolution as a function of
γ-ray energy as follows:
P0 :
P9 :

σ
(10.9 ± 0.6)√=
+ (−0.2 ± 0.6)
EE
(10.5 ± 0.7)σ√=+ (−0.1 ± 0.7)
E
E

(%),

(5.18)(%).

(5.19)

Fig. 5.37 shows the energy resolutions obtained in this section. For 52.8-MeV gamma
rays, the energy resolution is expected to be 1.30% at P0 and 1.35% at P9, that is, 3.1%
at P0 and 3.2% at P9 in FWHM. Those expected resolutions would be adequate when the
MEG experiment was performed with the 100-liter prototype. The performance expectedby the final detector will be discussed in the next chapter.

Energy Resolution [%]CHAPTER 5. PERFORMANCE OF THE 100-LITER PROTOTYPE

9410

σu at P0
σu at P9
FWHM at P0
FWHM at P9
σu/E=(10.9± 0.6)/ E+(-0.2± 0.6)
σu/E=( 10.5± 0.7)/ E+(-0.1± 0.7)

1

6

7

8 9 10

20

30

40

50

30

40

50

γ -ray Energy [MeV]

Energy Resolution [%](a) measured data

10

σu at P0
σu at P9
FWHM at P0
FWHM at P9
σup/E=( 6.9± 0.1)/ E+( 0.1± 0.1)
σup/E=( 6.2± 0.1)/ E+( 0.1± 0.1)

1

6

7

8 9 1020

γ -ray Energy [MeV](b) MC simulation
Figure 5.37: The energy resolution σu as a function of γ-ray energy.

CHAPTER 5. PERFORMANCE OF THE 100-LITER PROTOTYPE

5.7.9

95

Energy linearity

In order to verify the linearity of the detector response for γ rays from 10 MeV to 40 MeV,
we plotted the relation between the Compton edge parameters obtained in the previous
subsection and Compton edge energy estimated from ring and laser parameters. As shownin Fig. 5.38, the LXe detector has a good linearity. This is very strong point for γ-ray
detector, and it serves energy calibration with a high precision.
Linearity (CNpe-EC)/EC [%]Total Number of Photoelectrons Npe

40000
35000
30000
25000
20000
15000
10000

Compton edge (P0)Compton edge (P9)
Npe=(711±9)EC-(547±133) (P0)
Npe=(712±9)EC-(633±333) (P9)

5000
0
0

10

20

30

40

0.5
0.4

Compton edge (P0)Compton edge (P9)

0.3
0.2
0.1
-0
-0.1
-0.2
-0.3
-0.4
-0.5
0

50

10

20

Compton Edge Energy EC [MeV](a)measured data
Linearity (CNpe-EC)/EC [%]Total Number of Photoelectrons Npe

35000
30000
25000
20000
15000
Compton edge (P0)Compton edge (P9)
Npe=(711±9)EC-(547±133) (P0)
Npe=(712±9)EC-(633±333) (P9)

5000
0
0

10

20

30

40

50

Compton Edge Energy EC [MeV](c)MC simulation

4050(b)measured data

40000

10000

30

Compton Edge Energy EC [MeV]

0.5
0.4

Compton edge (P0)Compton edge (P9)

0.3
0.2
0.1
-0
-0.1
-0.2
-0.3
-0.4
-0.5
0

10

20

30

40

50

Compton Edge Energy EC [MeV](d)MC simulation

Figure 5.38: (a)(c) Incident LCS beam energy vs measured energy in Npe . (b)(d) Energy
linearity for data. C is a conversion factor from Npe to MeV obtained from the fitting
result of (a).

Chapter 6
Expected Performance
6.1

Expected Resolution

In this chapter we evaluate the performance of the final detector based on our analysis in
Chap. 5. Before that, it is necessary to understand the difference between the 100-liter
prototype and the final detector. The most different point in both detectors is the sizeand shape. Therefore the performance of the 100-liter prototype obtained in the LCS
beam test cannot be extrapolated straightforward to the final detector. We have to takethe difference into account. The criterion to connect with each other is considered to be
an absorption length.
We will explain the relation between absorption length and energy resolution, joinboth detectors together, and then evaluate the performance of the final detector.

6.1.1

Effect of Absorption Length

In this section we discuss the impact of the absorption length on the performance of the
LXe detector by estimating the energy resolution of the 100-liter prototype for 52.8 MeV
γ rays that are expected from the µ+ → e+ γ decays.
Simulations show that the determination of the incident positions of the γ rays is
only slightly affected by absorption and Rayleigh scattering. On the contrary the energy
resolution is heavily dependent on the absorption mainly because of fluctuations in lightcollection efficiency. For a short absorption length the total amount of light collected by
the PMTs changes according with the event-by-event shower fluctuations. In the following
we concentrate on energy measurement of γ rays.
For negligible absorption (i.e. λabs À the detector size) the γ ray energy may be simply
evaluated by the total sum of the photons collected by all the PMTs, possibly weighted by
the local density of the PMTs. For a finite absorption length, however, a better methodof summing the PMT outputs is necessary.
The γ ray energy E may be calculated as a linear sum of the PMT outputs qi with
arbitrary coefficients ci :X
E =c+
ci qi .
(6.1)
i

To optimize the coefficients we may use simulated events with the γ ray energy of Et andminimizeED(6.2)
χ2 = (E − Et )2 ,96

CHAPTER 6. EXPECTED PERFORMANCE

97

where hAi is the average of A over the simulated events. The minimization is straightforward and yields the following result:ci = M−1 (hEt qi i − hEt i hqi i) ,(6.3)

c = hEt i −

(6.4)

*
X

+

c j qj .

jHere M is just the covariance matrix of qi for the simulated events,
Mkl 'Nh(qk − hqk i)(ql − hql i)i .
N −1

(6.5)

This method is called “linear fit” and its validity is based on the principal component
analysis [93].

Number of Events

9000
8000
7000
6000
5000
4000
3000
2000
1000
0
0

10

20

30

40

50

60

Reconstructed Energy [MeV]
Figure 6.1: A reconstructed energy spectrum for 52.8-MeV γ rays by the linear fit.
Using the linear fit, a reconstructed energy spectrum for 52.8 MeV monochromatic γ
rays that uniformly irradiate the center of the detector face is shown in Fig. 6.1. The
spectrum has an asymmetric shape. The lower tail is caused by interactions of the γ raysin the materials before the LXe and by a leakage of shower components (mostly low energy
γ rays). We emphasize again that the most important for the µ+ → e+ γ experiment is
the resolution at the upper edge (σu ) to reject background events, while the lower tailconcerns the detection efficiency. The spectrum was fitted to Eq. 5.14.
The obtained resolutions in FWHM and σu for 52.8 MeV γ rays are plotted in Fig. 6.2
as a function of the absorption lengths assumed in the simulation. The resolutions for two

CHAPTER 6. EXPECTED PERFORMANCE

98

incident positions P0 and P9 described in the inset of Fig. 6.2 are similar, indicating asmall position dependence. The resolutions are also stable by changing λRay = 30 − 50 cm
and for n = 1.57 − 1.72 for LXe. Note that in the simulation refraction, reflection andabsorption of the scintillation light at the PMT quartz windows are taken into account.

Energy Resolution [%]

10
9
8

FWHM
upper sigma σ u

} P0
FWHM
upper sigma σ u } P9

P0
P9

7
6
5
4
3
2
1
0
10

100

1000

Absorption Length λ abs [cm]Figure 6.2: The expected energy resolutions for 52.8 MeV γ rays as a function of theabsorption length. Resolutions at two incident positions, P0 and P9.
With the achieved absorption length of λabs > 100 cm an energy resolution of 4%
FWHM and σu /E ∼ 1.2%, averaged over the detector acceptance, is expected from theMC simulation. The detection efficiency, if selected within ±4% around the energy peak,increases as λabs and for λabs > 50 cm it saturates at approximately 60%.

6.1.2

Energy Resolution

In order to evaluate the energy resolution for the final detector by using the energy
resolution obtained in the LCS beam test. we have to take the absorption length and thedetector shape into account.

CHAPTER 6. EXPECTED PERFORMANCE

99

Absorption Length

Energy Resolution (FWHM)

Fig. 6.3 shows the relation between the energy resolution and absorption length estimatedwith MC simulation for the final detector. Since the absorption length in the 100-liter
prototype was 1 m at least, the energy resolution in the final detector is expected to be
5.0% in FWHM. Taking the lower tail in the energy spectrum into account, it is reasonable that FWHM corresponds to about four times the upper sigma when the absorption
length is not so short as the depth of the detector. Furthermore we have to consider thedeterioration of the resolution by pedestal noise, PMT stability, and so on. Even if thedegree of the deterioration in the 100-liter prototype is scaled to the final detector, thedeterioration is negligible as mentioned in Sec. 5.7. Consequently it is appropriate thatthe intrinsic energy resolution in the final detector is 5% (FWHM).

14

Q sum
Linear Fit

12
10
8
6
4
2
0

0

100

200

300

400

500

600

Absorption Length [cm]Figure 6.3: The energy resolution vs. absorption length in the final detector by MC
simulation.
Curved Shape and Mask Analysis
The final detector has a different shape, a curved shape, from the 100-liter prototype.
Especially the PMTs on the front face are arranged in a convex shape. Because of thisit might not be appropriate to extend the obtained detector performance to estimate thefinal detector one. For studying this effect without relying on MC simulation but only
using real data other kinds of analysis have been performed by masking several PMTs in
the 100-liter prototype at the stage of data analysis by hand.
For simulating the convex shape, an analysis was done by using only 4×4 PMTs on
the front face and all PMTs on the other faces. Calibration and fitting procedures are

CHAPTER 6. EXPECTED PERFORMANCE

100

Energy Resolution [%]same as standard analysis. The result shows that the energy resolution does not change
significantly.
The curved shape effect was simulated by masking all PMTs on lateral face(s) similarly.
It was found that the observed number of photoelectrons decreases naturally and that theenergy resolution deteriorates accordingly up to 3% in sigma. However it is not statisticalbut seems to be position dependent on the first conversion point, indicating that we canrestore the resolution by applying certain intelligent algorithm. Note that this is reallyan extreme case and in the final detector those light discarded in this analysis can bedetected by some PMTs as far as the absorption length is long enough.
If the lateral faces are removed from the 100-liter prototype, it can be a simple simulation for the final detector. Actually the depth of the effective volume in both detectors
is about 50 cm. Therefore the 100-liter prototype such that the bottom and top face wasmasked is considered the final detector. The estimate of energy resolution with masked
faces is what we call “mask analysis”.
By fitting the data such that EC = 10 MeV−40 MeV and impinging position is P0
and P9, we estimated the energy resolution for the final detector. The fitting procedureis the same as done in Sec. 5.7. The result is shown in Fig. 6.4 and Tab. 6.1. From thisresult, the energy resolution for 52.8 MeV is estimated to be 2.2% in σu at both P0 and
P9.

10

σu at P0
σu at P9
FWHM at P0
FWHM at P9
σu/E=(10.3± 0.5)/ E+( 0.8± 0.5)
σu/E=( 9.5± 0.5)/ E+( 0.9± 0.5)

1

6

7

8 9 10

20

30

40

50

γ -ray Energy [MeV]

Figure 6.4: Energy resolution by mask analysis.
The frontage of the final detector is 2-PMT(= 12.4 cm) longer than one of the 100-liter

CHAPTER 6. EXPECTED PERFORMANCE

101

Table 6.1: Energy resolution by mask analysis. Error bars include only statistical errors.
Unit is %.
Position\Energy
P0
P9

10 MeV
20 MeV
40 MeV
3.98 ± 0.05 3.15 ± 0.06 2.42 ± 0.05
3.85 ± 0.08 3.03 ± 0.06 2.41 ± 0.01

prototype. In order to study the influence of the number of PMTs on the front face on
the energy resolution, we used only 4 × 4 PMTs as to the front face. The obtained energy
resolution was 1.9% in σu .
Thus the performance of the final detector is comparable to one of the 100-liter prototype and we can employ the result of the 100-liter prototype to evaluate the performanceof the final detector. The energy resolution in the final detector is expected to be 2.2%
in sigma, that is, 5.2% in FWHM.

6.1.3

Position Resolution

In the method with local weighted mean, the position reconstruction is performed withseveral PMTs(typically 4∼10 PMTs). The position reconstruction for the final detector
is in a similar situation. Therefore the position resolution is not different between the
100-liter prototype and the final detector. The position resolution in the final detector is
expected to be 9.9 mm to 11.0 mm for narrow components and 25.9 mm to 45.8 mm forbroad components in FWHM, which is conservatively from the worse result for 40-MeV
γ rays impinged at P0 and P9.

6.1.4

Timing Resolution

The timing resolution in the 100-liter prototype for 52.8 MeV γ rays was already estimatedto be 76 psec in sigma by a beam test with low energy electron beam [94]. Since it is only
measured value, we employ 76 psec as the timing resolution to evaluate the performanceof the final detector.

6.1.5

Efficiency

In the MEG experiment the COBRA magnet exists in front of the LXe detector andphotons have to traverse its wall. In order to simulate this situation, data was taken withseveral kinds of material located in front of the 100-liter prototype, just behind the 2ndcollimator. Five kinds of material were placed to study the effect systematically. They
were 5mm, 10mm, 15mm thick aluminum, 15mm thick aluminum with 4mm thick steel,and 5mm thick lead. The corresponding radiation lengths were 0.053X0 , 0.11X0 , 0.16X0 ,0.398X0 , and 0.89X0 respectively. As indicated by MC simulation study, the resolution
does not deteriorate but only efficiency is lost because of additional material. Actually
analysis was applied on these data and this point has been confirmed. Note that the
COBRA magnet thickness is 0.197X0 and material used in the 100-liter prototype forhoneycomb window and PMT holders and so on is close to those of the final detector.

CHAPTER 6. EXPECTED PERFORMANCE

102

Selection Efficiency [%]Fig. 6.5 shows the selection efficiency in the 100-liter prototype. It is found that the
selection efficiency is 44.6% for incidence at P0, 43.3% for incidence at P9, and 40.1%
for all over front face. Furthermore the efficiency becomes 30% with an energy selection
within ±4% around the energy peak by the linear fit.
100
90
80

all over front face

70

P0

60

P9

50
40
30
20
10
0
0

2

4

6

8

10

12

14

16

18

20

Threshold of Nf (0.5)

Figure 6.5: Selection efficiency as a function of Nf (0.5).

6.2

Backgrounds and Sensitivity

The following estimation is based on the assumption and calculation in [1, 2].
First we estimated the single event sensitivity. The detector acceptance defined by the
positron spectrometer and the LXe detector is 0.08 < | cos θ| < 0.35 and −60◦ < φ < 60◦ ,amounting to Ω/4π = 0.09. We assume a detection efficiency for the photon (εγ ) of
30%. For the positron we assume εe ∼ 90%. The single event sensitivity is defined as
the µ → eγ branching ratio for which the number of expected decays is equal to one.
Assuming a muon stop rate of Nµ = 5.8 × 107 /s, which is conducted in Subsec. 6.2.3,
and a total running time of the experiment T = 5.2 × 107 s (2 years). The single event
sensitivity for MEG experiment is calculated as
11×Nµ · T · (Ω/4π) εe · εγ · εsel
= 1.8 × 10−14 ,B(µ+ → e+ γ) =

(6.6)
(6.7)

where εsel is the efficiency of the event selection. Selection cuts covering 70% of the signal(1.4 FWHM for Gaussian distributions) are considered to be applied on the reconstructed
positron energy, on the e+ /γ relative angle and timing.

CHAPTER 6. EXPECTED PERFORMANCE

103

This sensitivity can be converted to 90% confidence level upper limits, in case of no
signal observed, by using the background rate estimates given in the following subsection.
In MEG experiment two major backgrounds are taken into account:(1) prompt background from radiative muon decays (µ+ → e+ νe ν µ γ ),(2) accidental background (µ → eνe ν µ + random γ).
In order to evaluate the number of background events, the detector performances wereassumed as seen in Tab. 6.2.
Table 6.2: Expected detector performances. Every values are in FWHM.

LXe detector
Resolution
EnergyTiming

unit
%
psec

Position(x)

mm

Value
5.2
179
9.9 ∼ 11.0 (narrow component)
25.9 ∼ 45.8 (broad component)

Positron Spectrometer
Resolution
EnergyTimingPosition

unit
%
psec
mrad

Value
0.8
100
10.5

Muon Beam
Resolution
Muon decay position

6.2.1

unit
mm

Value
2.1

Prompt Background

The prompt background was calculated using the formula given in [95, 96]. By numericalintegration over the selection cuts (1.4 FWHM for each selection variable) we find a background of 3.1 × 10−15 events per muon decay. As described in the following subsections,this rate is smaller than the accidental background rate. In this estimation the prompt
background is not considered.

6.2.2

Accidental BackgroundFor simplicity, the normalized e+ and photon energies, which are defined by x = 2Ee /mµ
and y = 2Eγ /mµ , will be used, where mµ is a muon mass. Further, it is assumed that δAand ∆A are taken to be a half width and a full width of the signal box for the observable
A respectively.
The effective branching ratio of the accidental background (Bacc ) can be derived. Firstof all, a number of the accidental background events (Nacc ) are given by

CHAPTER 6. EXPECTED PERFORMANCE

104

Ω
Ω
δω
· εe ) · (Nµ · fγ0 ·· εγ ) × ( ) · (2δt) · T · fPµ ,
(6.8)
4π
4π
Ω
where δt is a timing coincidence resolution. fe0 and fγ0 are the fractions of the spectrum
within the signal box of the e+ s in the Michel muon decay and photons in the radiative
muon decay respectively. They include their branching ratios. fPµ is a background suppression factor when a muon is polarized [97]. fPµ =1 is considered from now on. The
effective branching ratio for accidental background can be obtained by dividing Eq.(6.8)
by the product of a total number of muons and the detector acceptance given by
Nacc = (Nµ · fe0 ·Bacc =Nacc.
Nµ · T · (Ω/4π) · εe · εγ

(6.9)

For unpolarized muons, Bacc becomes
Bacc = Nµ · fe0 · fγ0 · (δω) · (2δt)
4π(6.10)

Estimation of fe0
fe0 is obtained for a given δx by integrating the Michel muon spectrum (Nmichel ) from1 − δx to 1.

fe =
=

Z 1
1−δx

Z 1

1−δx

dxNmichel"d(cos θe )2#³

dx 2x2 (3 − 2x) + 2x2 (2x − 1)Pµ cos θd(cos θe )2

≈ 2(δx)(6.11)

Estimation of fγ0
To estimate fγ0 , the radiative muon decay (µ+ → e+ νe ν µ γ ) is considered as a sourceof 52.8 MeV photon. The differential decay width is integrated over the e+ energy andthe angle between e+ and photon (θeγ ). After the integration of e+ energy and θeγ , thedifferential branching ratio for y ∼ 1 and any value of x is given by [97]dBacc (µ+ → e+ ννγ) ≈ J(y) · (1 + Pµ cos θγ )dyd cos θγ(6.12)

where J(y) is given byh (1 − y)α17 i(1 − y) ln−(6.13)
2πr
6The rate can be estimated by integrating the spectrum over the width of the signal
region. The partial branching ratio (denoted by fγ ) integrated over the signal region(1 − δy ≤ y ≤ 1) can be given from Eq.(6.12) byJ(y) =

fγ =
≈

Z 1
1−δy

³α´

2π

dy

dB(µ+ → e+ ννγ)dyhi(δy)2 ln(δy) + 7.33 (1 + Pµ cos θγ )d(cos θγ )2

(6.14)

CHAPTER 6. EXPECTED PERFORMANCE

105

From Eq.(6.14), it is shown that fγ is roughly proportional to (δy)2 . Now, fγ0 that does
not include the angular dependence is given by
³α´
h
i
fγ0 =
(δy)2 ln(δy) + 7.33
2πhi
= 1.16 × 10−3 (δy)2 ln(δy) + 7.33
(6.15)
Estimation of δωGiven the angular resolution δθeγ , the back-to-back resolution (δω) is presented byδω =π(δθeγ )2(δθeγ )2=.
4π
4(6.16)Net expression of accidental background
From the above, the effective branching ratio of accidental background is given by
Bacc = Rπ · (2δx) ·hαi(δy)2 (ln(δy) + 7.33) ×

2π∝ ·δEe · δteγ · (δEγ )2 · (δθeγ )2 ,³ δθ 2 ´

4· (2δt),(6.17)(6.18)

where only radiative muon decays are considered as a source of photons. The detailestimation of the accidental background including contributions from annihilations inflight and photon pile-ups by using the present apparatus will be given later.
Inclusive Photon Yield
The inclusive photon yield per muon decay gγ (y) (y ≡ 2Eγ /mµ ) was evaluated in [2] bytaking into account the following sources of photons:• photons from radiative muon decays;• photons from annihilation-in-flight;• photons from positron interactions with surrounding materials;• neutron induced background.
R

The integrated yield fγ (y) = y1 dy 0 gγ (y 0 ) is plotted in Fig. 6.6. The rate of two photon
pile-up can be written as:gγγ (y) =Z y0

dy 0 gγ (y 0 )gγ (y − y 0 )η(y 0 , y − y 0 ),(6.19)

where η(y1 , y2 ) is the pile-up rejection factor for two photons with energy fractions y1 andy2 , and 0 < y < 2. It depends on ∆Ωγγ and ∆tγγ which define the two-photon separation
power in solid angle and in time respectively, and are dependent on the energies of thephotons. They are evaluated by MC simulations [2].
The pile-up spectrum gγγ (y) is then integrated from (1 − δy) to (1 + δy), fγγ (y) =R 1+δy001−δy dy gγγ (y ), where y ≡ 1 − δy. The resulting integrated pile-up photon rate fγγ (y) isshown in Fig. 6.7.
The rate of accidental coincidences of Michel positrons with random photons given byfγ (y) + fγγ (y) is obtained by numerical integration over the selection cuts.

Photon Yield per Decay

CHAPTER 6. EXPECTED PERFORMANCE

10

10

10

106

-4

-5

Annihilation in Flight

All

-6

Radiative Decay

10

10

-7

-8

0.9

0.92

0.94

0.96

0.98

1
y Threshold

Photon Yield per Decay

Figure 6.6: Integrated photon yield per muon decay fγ (y).

10

10

10

10

10

-4

-5

-6

-7

-8

0.9

0.92

0.94

0.96

0.98

1
y Threshold

Figure 6.7: Integrated pile-up photon yield per muon decay fγγ (y).

CHAPTER 6. EXPECTED PERFORMANCE

6.2.3

107

90% C.L. Sensitivity

90% C.L. sensitivity

To simplify the calculation of Bacc , the accidental background rate estimated in [2] wasscaled by using Eq. 6.18 and Bacc ∝ Nµ2 . The muon stop rate should be optimized since
lower beam intensity reduces the accidental background rate. We obtain the relation
between the muon stop rate and 90% confidence level upper limit as shown in Fig. 6.8.
We find an accidental background of 8.9 × 10−14 events per muon decay with a stopping
muon rate of 5.8 × 107 /s. However it is expected that 4.9 accidental background eventsare found with a 90% C.L. sensitivity of 1.2 × 10−13 .
Practically the number of expected backgrounds should be set to 0.5. Then an accidental background of 2.6 × 10−14 events per muon decay with a stopping muon rate of
2.1 × 107 /s is obtained. The 90% confidence level upper limit becomes 1.5 × 10−13 . Since
this evaluation is based on the conservative values and some improvements in LXe detector are expected in the MEG experiment as described in later sections, the sensitivity
will achieve an order of 10−13 .
10-12

-13

1.5 × 10-13

10

1.2 × 10

-13

7

10-14

2.1 × 10
7

10

7

2×10

7

3×10

7

4.4 × 10

8

10

8

2×10

8

3×10

µ+ stop rate [1/s]Figure 6.8: The relation between the muon stop rate and the 90% C.L. sensitivity.

6.3

Decay Angular Measurement

If the µ → eγ events could be discovered, the MEG experiment would shift to the nextstage. The angular distribution of µ+ → e+ γ with respect to the muon-polarization
direction would give information to discriminate among various models, because different
theoretical models predict a different helicity of e+ in µ+ → e+ γ [95]. For polarizedCHAPTER 6. EXPECTED PERFORMANCE

108

muons, the angular distribution of positron from µ+ → e+ γ decay with respect to thedirection of µ+ spin direction is expressed bydN (µ+ → e+ γ)∝ Br(µ+ → e+ γ) × (1 + APµ cos θe )d cos θe(6.20)

where N is the number of observed µ+ → e+ γ events, Br is the branching ratio ofµ+ → e+ γ , Pµ is the muon-spin polarization, θe is the angle between the muon spin andthe positron, and A is asymmetric parameter as follows
A=|AL |2 − |AR |2,|AL |2 + |AR |2(6.21)AR and AL are coupling constants.
There are three SUSY models to be discriminated by measuring the angular distribution: The SU(5) SUSY-GUT model predicts A = +1, yielding a (1+Pµ cos θe ) distribution.
The SO(10) SUSY-GUT model predicts A ≈ 0, yielding an almost uniform angular distribution. Minimal Supersymmetric extension of the Standard Model (MSSM) with νRmodel predicts A = −1, yielding (1 − Pµ cos θe ) distribution. Hence it is possible thatthese models are clearly discriminated if the signals are observed.
The backgrounds for this measurement are the same as the µ → eγ decay search.
The prompt background obeys (1 + Pµ cos θe ) distribution and the accidental backgroundobeys (1 + Pµ2 cos2 θe ) distribution.
Here assuming that the Br(µ+ → e+ γ ) is 10−12 and A is +1, muon decay events weregenerated to count the number of backgrounds and µ+ → e+ γ signals. The detector
configurations and performances were set to the same values as those in Sec. 6.2. The
polarization Pµ was set to 97% as a realistic value although it could be 100% in principle.
The muon stop rate was set to a higher rate than the simple µ → eγ search, 3 × 108 ,because this measurement requires as many of statistics as possible.
There are two free parameter in this analysis: Asymmetry parameter ranging −1
to +1 and log10 Br ranging −13 to −11. The parameter space of A vs. log10 Br was
divided into 200 × 200 bins. In each bin, | cos θe | < 0.35 was divided into 4 bins to countthe number of backgrounds and signals observed there. For each 200 × 200 bin, χ2 for
Poisson-distributed data [98] was calculated.
2

χ =

4
X
i=1

Ã

"

2(Niobs − Niexp ) + Niobs ln

Niobs
Niexp

!#

,

(6.22)

where N obs and N exp are the observed and theoretical contents of the i-th bin.
Fig. 6.9 shows the 68%, 90%, and 95% C.L. sensitive region. It is found that A =−1, 0, +1 are distinguishable for Br(µ+ → e+ γ )> 10−12 with muon stop rate of 5.8 × 107
for 2 years. This measurement requires a large quantity of muon decay events. For that
purpose, raising the muon stop rate brings a significant result. Alternatively a spin rotator
might be introduced to enable us to select θe ± 1 according to the expected theoreticalmodel, although it requires re-arrangement of the beam line.

109

-11

10

log BRCHAPTER 6. EXPECTED PERFORMANCE

68% C.L.

-11.5

90% C.L.
95% C.L.

-12

-12.5

-13
-1

-0.5

0

0.5

1

Asymmetry

Figure 6.9: The sensitive region for the decay angular measurement with an assumptionof SU(5) SUSY-GUT and Br(µ+ → e+ γ )> 10−12 .

6.4

Prospects for Further Improvements of Performance

In this section we discuss prospects for further improvements of the performance of the
LXe detector.

6.4.1

New PMT

The PMTs (R6041Q) used in the 100-liter prototype have the low QE and the distributionof the values of QEs is rather broad as shown in Fig. 5.12.
In the R6041Q Rb-Cs-Sb is used as a photo-cathode material, but the cathode sensitivity of this material is not so high for Xe scintillation (178 nm). A Mn layer used
between the photo-cathode and the quartz window to keep the surface conductivity ofthe photo-cathode at low temperature may possibly absorb some part of the scintillation
photons before reaching photo-cathode layer. This might also be responsible for the low
QE of the R6041Q. Moreover, it is not so easy to control the thickness of the Rb-CsSb and the Mn layers due to technical difficulties in the evaporation procedure of thesematerials. This possibly cause the broad distribution of the QEs.
Recently new type of PMT (R9288) has been developed to overcome these problems in
the R6041Q (Fig. 6.10). More standard bi-alkali, K-Cs-Sb is used as photo-cathode in thismodel. K-Cs-Sb has a higher cathode sensitivity and it is easier to control the thickness
in the evaporation procedure as compared with Rb-Cs-Sb. Al strip pattern is coated on
the quartz window to keep the surface conductivity at low temperature instead of a Mn
layer. The strip pattern is designed to fit with the support structure of the dynodes tominimize the influence of the photon absorption in the Al strips.

CHAPTER 6. EXPECTED PERFORMANCE

110

Figure 6.10: Two types of PMTs: (a) R6041Q with Rb-Cs-Sb and Mn layers and (b) new
type (R9288) with K-Cs-Sb and Al strips.

The QEs of the R9288 have been recently measured. The preliminary results show that
their QEs are 3 − 4 times higher compared with the QEs of the R6041Q. We can expect
better energy resolution by using the R9288 in the LXe detector because the resolution isthought to be predominantly governed by the statistics of the number of photoelectrons.

6.4.2

Waveform Analysis

Capability of rejecting the pile-up background is quite essential for the γ-ray detector
in the MEG experiment. The distribution of the PMT outputs enables us to reject thepile-up of accidental γ rays that are well separated spatially. Even pile-ups that are notseparated spatially can be rejected by analyzing the waveforms of the PMT outputs. In
the 100-liter prototype, ADCs and TDCs were used to read the PMT outputs, while in
the final detector all the PMTs will be read with high-speed waveform digitizers. A fast
analog sampling chip based on a switched capacitor architecture is being developed at
PSI: The Domino Ring Sampling chip [99] for this experiment. The sampling speed isvariable between 0.5 GHz and 2.5 GHz. It will be implemented not only for the readoutof the LXe detector but also for the readout of the drift chamber system and the timing
counters.
The principle of the operation of the DRS is illustrated in Fig. 6.11. The sampling
frequency in the GHz range is generated with a series of inverters. A sampling signal
propagates through these inverters freely (domino principle). Additional AND gates allow
to stop the domino wave in any cell by an external trigger signal. The domino wave runs
continuously in a circular fashion. Once a signal is stored, it is read out by a shift registerat a clock speed of 40MHz and digitized externally by a flash ADC.
The prototype has been recently tested in the 100-liter prototype. The waveforms of
the PMT signals from about 50-MeV γ rays were successfully taken at s sampling speedof 2.5 GHz. The typical waveform is shown in Fig. 6.12. The performance of the pile-up

CHAPTER 6. EXPECTED PERFORMANCE

111

rejection is being investigated with these data.

Figure 6.11: The principle of the operation of the DRS chip.

χ2 / ndf

1200

43.3 / 499

Prob

1100

1

Baseline

1122 ± 2.5

Amplitude722.7 ± 31.5

t0

1.132e-07 ± 2.040e-10

Rise time 6.695e-09 ± 4.471e-10
Decay time 3.565e-08 ± 1.317e-09

1000

900

800

700
×10
0.35
0.4
[sec]

-6

0.05

0.1

0.15

0.2

0.25

0.3

[sec]

Figure 6.12: Typical waveform of PMT signal from about 50-MeV γ rays taken with theprototype of the DRS. A red curve is the best fit with two exponential function to the
waveform data.

CHAPTER 6. EXPECTED PERFORMANCE

6.5

112

Calibration Method

In principle, calibration of the PMTs in the final detector will be done by using thesame method employed in the prototype detector study. The gain will be periodicallymonitored and adjusted by using LEDs during the experiment. Individual PMTs will betested before installation by measuring their gain and QE in a test vessel. To measure
the resolution for a single photoelectron is essential to calibrate gain with precision. A
relative estimate of the QE under the influence of the magnetic field is as important thegain adjustment. It is planned to use α sources on wires in LXe for monitoring andmeasuring QE.
For absolute energy calibration, 55-MeV and 83-MeV γ rays from π 0 → γγ decays will
be employed. Fig. 6.13 shows the schematic drawing of the calibration procedure. The
γ-ray energy and the opening angle between two γ-rays have a correlation by the decay
kinematics. If we require the opening angle is more than 175· , the energy spread of γ-rays
is 0.3 MeV (FWHM), which is smaller than the energy resolution of LXe detector. In order
to select the opening angle, γ-ray counter on the opposite of the LXe detector is required.
NaI array counters are supposed to be used as the anti-counters. The anti-counters canface the target direction by moving to the upper and lower sides and tilting. If the π − rateis 1 × 107 , the trigger rate is estimated to be 10γ/s in the region of 2PMT×2PMTs (about
150cm2 ) on the incident face of the LXe detector. Assuming the number of PMTs on theincident face is 216, the calibration process takes one day if 30,000 events are required foreach region.
It is also planned to perform absolute position calibration by using the meshed collimator equipped inside the magnetic wall. For absolute timing calibration the radiative
muon decays will be used. At the early stage of the MEG experiment, absolute calibration
with beam should take some more weeks.
As mentioned in Sec 5.1, a beam test for the 100-liter prototype was performed in
πE1 area at PSI in 2004. In the LCS beam test the detector performance was evaluatedfor γ rays up to 40 MeV, whereas the CEX beam test employs monochromatic γ rays of
55 MeV, 83 MeV, 128 MeV to enable the performance evaluation for higher energy γ rays.
One of the principal purposes in the CEX beam test was to estimate timing resolution.
In the LCS beam test it was difficult to tag scattering electrons because there was little
place to be set the tagging counter.
In this test, we replaced most of R6041Q with R9288s. It is expected that the increaseof total number of photoelectrons improves the performance. Moreover some channels
were prepared for waveform analysis with DRS chip as shown in Fig. 6.12.
We are now analyzing data taken in the CEX beam test and the result will be reported
in 2005.

CHAPTER 6. EXPECTED PERFORMANCE

113

Anti Counter
55, 83 MeV

γ

tilt
up

LXe Detector

π0
Liq.Hydrogen
Targetdown

γ55, 83 MeV

tilt

Figure 6.13: Schematic view of calibration with CEX beam.

Chapter 7
Conclusion
The 1000-liter liquid xenon scintillation detector is a key to the MEG experiment aiming
at verifying theories beyond the SM like SUSY-GUT through searching for a lepton flavor
violation signal, µ → eγ decay. Since such a large detector has never been built before,
we constructed a 100-liter prototype of the LXe detector to establish a stable operationand to evaluate the practical performance for 52.8-MeV γ rays.
One of the strong points of LXe as a scintillator medium is high light yield. However
the contaminant in xenon such as water and oxygen causes the deterioration of the detector
performance. By introducing a purification system for liquid xenon, an absorption length
longer than 100 cm at 90% C.L. has been achieved. Thanks to the purification system
LXe is kept pure enough to maintain the high performance of the LXe detector at any
time. Moreover we established the stable operation of the LXe cryostat and the calibration
method. The stability of the LXe detector was assured by such a stable system.
In order to evaluate the performance of the LXe detector for γ rays of tens of MeV,
we carried out a beam test by using LCS beam at AIST in April, 2003. For 10-MeV to
40-MeV γrays, the energy resolution was estimated to be 3.2% to 1.5%, and the position
resolution of about 9.9 mm−11 mm (FWHM) was obtained.
Based on the result from the LCS beam test, we estimated the performance for the
1000-liter LXe detector. It is expected that the energy resolution is 5.2% (FWHM) andthe position resolution is the same as one for 40 MeV. The results from the various tests
with the 100-liter prototype and systematic studies with MC simulation show that a 90%
C.L. sensitivity in the MEG experiment reaches 1.5 × 10−13 to enable the new search forµ → eγ decay.

114

Appendix A
10-liter prototype of Liquid Xenon
Scintillation Detector
In 1998 the first prototype of LXe scintillation detector was constructed [100]. It has anactive volume of 2.34 liter surrounded by 32 PMTs. Those PMTs and their holder were
immersed in about 10-liter LXe as shown in Fig. A.1.
Gas XeLiquid Nitrogen

CoolingPipevacuum forthermal insuration
Gas Xe~ 1atmLiquid Xe

Figure A.1: Cross-sectional view of 10-liter prototype of LXe scintillation detector andits vessel.

115

APPENDIX A. 10-LITER PROTOTYPE OF LIQUID XENON SCINTILLATION DETECTOR116
The features of the 10-liter LXe detector were as follows:• Photomultipliers immersed in LXe to catch LXe scintillation photons directly.
• LXe operation by using LN2 .
• LEDs for adjusting PMT gains.
• α source (241 Am) for monitoring the stability of PMTs and adjusting relative PMT
gains.
• γ-ray sources for performance evaluation.
• Less out-gassing material, such as Teflon, Aluminum, and SUS.
• Double-layer vessel for thermal isolation.

Entries/(1 mm)

13.86

200

Constant
Mean
Sigma

Cs
z1-z 2

/ 18
203.7
.8638
6.213

100

0

Entries/(1 mm)

It was very first time for us to treat the LXe detector. One of the purposes was toestablish the stable and secure operation of LXe. Those days it was already known wellthat the purity of LXe at ppb level was essential for high light yield. We payed attention
to sufficient evacuation of vessels before liquefaction of xenon. It took 20 days to bakeand evacuate the vessel. The refrigerator was not used, cooling pipe of LN2 was adopted.
It was controlled according to the inner pressure with an electromagnetic valve. The
running time amounted to 1000 hours. No serious trouble happened over a series of thetests. Everything worked stable and well. The PMT output was stable within 0.5%. This
was also an evidence of the stable operation.
The other purpose in the test with 10-liter LXe detector was to examine the responsefor γ rays because we had never seen any signals in LXe detectors. Tests began with low
energy sources. We selected γ-ray sources from 320 keV to 1.836 MeV. The results areshown in Fig. A.3, A.2, and A.4. In the case of low energy γ rays, Compton scattering
is dominant and electron shower cannot occur. Therefore it is nonsense to extrapolatethese results to higher energy like 52.8 MeV straightforward. However this test was greatsignificance in the history of R&D on the LXe detector.
100
75

-20

0

20
40
∆ z (mm)Mn
z1-z 250

18.74 / 18
83.87
1.981
5.383

25
0

-40

Constant
Mean
Sigma

-40

-20

0

20
40
∆ z (mm)Figure A.2: The position resolution with the 10-liter prototype detector.

APPENDIX A. 10-LITER PROTOTYPE OF LIQUID XENON SCINTILLATION DETECTOR117

Energy Resolution (%)

20

18

16

14

12
51

10

Cr
137

8

Cs
54

6

Mn
88

Y

4

2

0 -1
10

1

Energy (MeV)σ [psec]

Figure A.3: The energy resolution with 10-liter prototype detector. If theses results are
extrapolated to 52.8MeV, the expected energy resolution is less than 2%.
600
500

2 PMTs
4 PMTs
6 PMTs
8 PMTs10 PMTs
12 PMTs

400

300

200

100
200

500

1000

2000

Total Number of Photoelectron

Figure A.4: The timing resolution with the 10-liter prototype detector. The resolution is
expected to be about 50 psec for over 20, 000 photoelectrons.

Bibliography[1] S. Korenchenko et al., “ Letter of Intent for an experiment at PSI”, R-98-05.0 (1998),
available at http://meg.web.psi.ch/docs/loi/loi.ps[2] T. Mori et al., “Search for µ → eγ down to 10−14 branching ratio”, Research Proposal
to PSI, May 1999.
[3] A. Baldini et al., “The MEG experiment: search for the µ+ → e+ γ decay at PSI”,
Research Proposal to INFN, Sep. 2002.
[4] G.W. Bennet et al., Phys. Rev. Lett. 89 (2002), hep-ex/0208001v2 (2002).
[5] J. Hisano and K. Tobe, Phys. Lett. B510 (2001) 1997.
[6] L.J. Hall and Y. Nomura, hep-ph/0205067 (2002).
[7] L.J. Hall, V.A. Kostelechy and S. Raby, Nucl. Phys. B267 (1986) 415.
[8] R. Barbieri and L.J. Hall, Phys. Lett. B338 (1994) 212;
R. Barbieri, L.J. Hall, and A. Strumia, Nucl. Phys. B445 (1995) 219.
[9] J. Hisano et al., Phys. Lett. B391 (1997) 341;
Erratum, Phys. Lett. B391 (1997) 357.
[10] The ALEPH, DELPHI, L3 and OPAL Collaborations, and the LEP Higgs Working
Group, LHWG Note/2001-04, hep-ex/0107030, July 2001.
[11] Super-Kamiokande Collaboration, Y. Fukuda et al., Phys. Rev. Lett. 81 (1998) 1562;
Super-Kamiokande Collaboration, Y. Fukuda et al., Phys. Lett. B433 (1998) 9;
Super-Kamiokande Collaboration, Y. Fukuda et al., Phys. Lett. B436 (1998) 33;
Super-Kamiokande Collaboration, Y. Fukuda et al., Phys. Rev. Lett. 82 (1999) 2644;
Super-Kamiokande Collaboration, S. Fukuda et al., Phys. Rev. Lett. 85 (2000) 3999.
[12] MACRO Collaboration, Phys. Lett. B434 (1998) 451.
[13] Soudan Collaboration, Phys. Lett. B391 (1997) 491.
[14] Super-Kamiokande Collaboration, Y. Fukuda et al., Phys. Rev. Lett. 81 (1998) 1158;
Super-Kamiokande Collaboration, S. Fukuda et al., Phys. Rev. Lett. 86 (2001) 5651;
Super-Kamiokande Collaboration, S. Fukuda et al., Phys. Rev. Lett. 86 (2001) 5656.
[15] SNO Collaboration, Q. R. Ahmad et al., Phys. Rev. Lett. 87 (2001) 071301;
SNO Collaboration, Q. R. Ahmad et al., Phys. Rev. Lett. 89 (2002) 011301;
SNO Collaboration, Q. R. Ahmad et al., Phys. Rev. Lett. 89 (2002) 011302.
118

BIBLIOGRAPHY

119[16] R. Davis Jr., D.S. Harmer, and K.C. Hoffman, Phys. Rev. Lett. 20 (1968) 1205;
B. Cleveland et al., Ap. J. 496 (1998) 505.
[17] Gallex Collaboration, Phys. Lett. B285 (1992) 376;
Gallex Collaboration, Phys. Lett. B357 (1995) 237;
Gallex Collaboration, Phys. Lett. B388 (1996) 384;
Gallex Collaboration, Phys. Lett. B447 (1999) 127.
[18] SAGE Collaboration, Phys. Rev. Lett. 83 (1999) 4686.
[19] GNO Collaboration, Phys. Lett. B490 (2000) 16.
[20] Kamiokande Collaboration, K.S. Hirata et al., Phys. Rev. Lett. 63 (1989) 16;
Kamiokande Collaboration, K.S. Hirata et al., Phys. Rev. Lett. 65 (1990) 1297.
[21] J. Hisano, T. Moroi, K. Tobe, M. Yamaguchi and T. Yanagida, Phys. Lett. B357
(1995) 579.
[22] J. Hisano, D. Nomura, Y. Okada, Y. Shimizu, M. Tanaka, Phys. Rev. D58 (1998)
116010.
[23] J. Hisano and D. Nomura, Phys. Rev. D59 (1999) 116005 and references therein.
[24] A. van der Schaaf et al., Nucl. Phys. A 340 (1980) 249.
[25] H.P. Povel et al., Phys. Lett. B 72 (1977) 183.
[26] P. Depommier et al., Phys. Rev. Lett. 39 (1977) 1113.
[27] W.W. Kinnison et al., Phys. Rev. D 25 (1982) 2846.
[28] J.D. Bowman et al., Phys. Rev. Lett. 42 (1979) 556.
[29] R.D. Bolton et al., Phys. Rev. D 38 (1988) 2077.
[30] M.L. Brooks et al., Phys. Rev. Lett. 83(1999) 1521.
[31] MECO Collaboration, W. Molzon et al., BNL AGS proposal P940 (1997);
the updated information are available at http://meco.ps.uci.edu/.
[32] R.M. Djilkibaev and V.M. Lobashev, Sov. J. Nucl. Phys. 49(2), (1989) 384; “MELC
Experiment to Search for the µ− A → e− A Process,” V.S. Abadjev et al., INR preprint
786/92, November 1992.
[33] Letters of Intent for PRISM and PRIME are available at
http://www-ps.kek.jp/jhf-np/LOIlist/LOIlist.html.
[34] A. Badertscher, D. Renker and L. Simons, PSI internal report (1989); PSI Users’
Guide, Accelarater Facilities.
[35] PSI-Scientific Report 2002, 2003/Volume I.
[36] MEG technical note TN015, June 2002. (http://meg.psi.ch/docs/index.html).

BIBLIOGRAPHY

120[37] W. Ootani et al., IEEE in Transactions on Applied Superconductivity. 14 (2004)
568-571.
[38] A. Yamamoto et al., Nucl. Phys. B78 (1999) 565.
[39] A. Yamamoto, Y. Makida et al., IEEE Trans. Applied Superconductivity 12, 438(2002).
[40] BELLE Collaboration, BELLE Progress Report, KEK Report 97-1, April 1997;
BELLE Collaboration, BELLE Technical Design Report, KEK Report 95-1, April
1995.
[41] BaBar Collaboration, Technical Design Report, March 1995.
[42] O. Nitoh et al. , Jpn. J. Appl. Phys. 33 (1994) 5929.
[43] M.I. Lopes and V.Chepel, D. Lide ed., “Handbook of Chemistry & Physics”, 76th
edition (1995), Chemical Rubber.
[44] A.C. Sinnock and B.L. Smith, Phys. Rev. 181 (1969) 1297.
[45] F. Sauli ed., “Instrumentation in High Energy Physics”, Advanced Series on Directions in High Energy Pysics Vol.9, World Scientific, 1992.
[46] Particle Data Book.
[47] C. W. Fabjan and F. Gianotti, “Calorimetry of particle physics”, Rev. Mod. Phys.
75 (2003) 1243
[48] J. Jortner et al., J. Chem. Phys. 42(1965) 4250.
[49] N. Schwenter, E.-E. Koch and J. Jortner, “Electronic Excitations in Condensed Rare
Gases”, Springer-Verlag, Berlin 1985.
[50] L. M. Barkov et al., Nucl. Instr. and Meth A379 (1996) 482.
[51] V. N. Solovov, V. Chepel et al., Nucl. Instr. and Meth. A516 (2004) 462.
[52] S. Nakamura: private communication.
[53] G.M. Seidel, R.E. Lanou, W. Yao, Nucl. Instr. and Meth A489 (2002) 189.
[54] T. Doke et al., Jpn. J. Appl. Phys. 41(2002) 1538.
[55] T. Doke, Portugal Phys. 12(1981) 9.
[56] A. Braem et al., Nucl. Instr. and Meth. A320(1992) 228.
[57] V. Y. Chepel et al., Nucl. Instr. and Meth. A349(1994) 500.
[58] N. Ishida et al., Nucl. Instr. and Meth. A384(1997) 380.
[59] G. M. Seidel et al., Nucl. Instr. and Meth. A489(2002) 189.

BIBLIOGRAPHY

121[60] T. Doke et al., Nucl. Instr. and Meth. A420(1999) 62.
[61] T. Haruyama et al., KEK Preprint 2002-102, Sep 2002.
[62] GM pulse tube refrigerator, Aisin Seiki Co., Ltd., 2-1 Kariya, Asahi, Aichi 448-8650,
Japan.
[63] ATLAS Liquid Argon Calorimeter Technical Design Report, CERN/LHCC/96-41,
ATLAS TDR2, December 15, 1996;
D. Axen et al., ATL-LARG-2003-007.
[64] The tolerance against the magnetic field was measured by the Hamamatsu Photonics.
[65] T. Haruyama et al., KEK preprint 2002-102.
[66] Data acquisition system, MIDAS, http://midas.psi.ch/[67] LabVIEW, http://www.ni.com/[68] MONO TORR PS15 Series, SAES Pure Gas, Inc. 4175 Santa Fe Road San Luis
Obispo, California, 93401 USA.
[69] Oxisorb, Messer Griesheim GmbH, Dusseldorf, Germany.
[70] GEANT, Detector Description Simulation Tool, CERN Program Library.
[71] K. Watanabe et al., J. Opt. Soc. Am. 43 (1953) 753.
[72] K. Watanabe et al., J. Chem. Phys. 21 (1953) 1026.
[73] V.N. Solovov, V. Chepel, M.I. Lopes and A. Hitachi, Nucl. Instr. and Meth. A516
(2004) 462.
[74] U. Hohm, Molecular Physics 81 (1994) 157.
[75] A. C. Sinnock, J. Phys. C: Sol. St. Phys. 13 (1980) 2375.
[76] A. Bideau-Mehu et al., J. Quant. Spectrosc. Radiat. Transfer 25 (1981) 395.
[77] A. Baldini et al., arXiv:physics/041072v1 15 Jan 2004.
[78] Landau, Lifshitz. Electrodynamics of continuous media, Pergamon Press.
[79] U. Hohm, K. Kerl, Molecular Physics, 69 (1990) 803.
[80] Y. Yoshino et al. “Absorption cross section measurement of water vapor in the wavelength region 120 to 188 nm” Chem. Phys. 211 (1996) 387.
Tabulated data available at
http://cfa-www.harvard.edu/amdata/ampdata/VUV H2O/
[81] The tabulated data ‘GG O2x.txt’ are taken fromhttp://uvisun.msfc.nasa.gov/GG/GG34-ECHAR/oldhome.html

BIBLIOGRAPHY

122[82] Prisma QMS200, Pfeiffer Vacuum Technology AG, Berliner Str. 43 35614 Asslar,
Germany.
[83] M. Miyajima et al., Nucl. Instr. and Meth. B63 (1992) 297.
[84] F. R. Arutyunian and V. A. Tumanian, Phys. Lett. 4(1963) 176.
[85] LED driver C529, CAEN S.p.A., Via Vetraia 11 55049 Viareggio (LU), Italy.
[86] Mono-Color Lamps/φ4 Series E1L49-3B1A-02, Toyoda Gosei Co., Ltd., Aichi, Japan
452-8564.
[87] S. Tokár et al., ATL-TILECAL-99-005.
[88] E.H. Bellamy et al., Nucl. Instr. and Meth. A339 (1994) 468.
[89] P. Hanlet et al., Nucl. Instr. and Meth. A521 (2004) 343.
[90] E. Morikawa et al., J. Chem. Phys. 91 (1989) 1469.
[91] J. Jortner et al., J. Chem. Phys. 42 (1965) 4250.
[92] Roger H. French, Harald Müllejans, and David J. Jones, J. Am. Ceram. Soc. 81(1998) 2549.
[93] S. Belforte et al., SVT Technical Design Report, CDF note 3108 (1994); CERN EP
report 81-12/Rev.
[94] T. Mitsuhashi, Master thesis of Univ. of Tokyo (2003), unpublished in Japanese.
[95] Y. Kuno and Y. Okada, Phys. Rev. Lett. 77 (1996) 434.
[96] C. Fronsdal and H. Überall, Phys. Rev. 113 (1959) 654;
S. G. Eckstein and R. H. Pratt, Ann. of Phys. 8 (1959) 297.
[97] Y. Kuno, A. Maki, and Y. Okada, Phys. Rev. D55 (1997) 2517.
[98] S. Baker and R. Cousins, Nucl. Instr. and Meth. 221 (1983) 437.
[99] N. Ishida et al., Nucl. Instr. and Meth. A518 (2004) 470.
[100] T. Miyazawa, Master thesis of Univ. of Tokyo (1999), unpublished in Japanese.