Ph. D. Thesis

A Search for the Decay µ+ → e +γ
Using a High-Resolution Liquid Xenon
Gamma-Ray Detector

Yasuhiro NISHIMURA
Department of Physics, School of Science,
the University of Tokyo

December 2010

Abstract
Recent observations of neutrino oscillation indicated a lepton ﬂavor mixing in neutrino
sector, whereas charged lepton ﬂavor violation has not been observed so far in past experiments. A rare decay with charged lepton ﬂavor mixing, µ → eγ, is sensitive to new
physics beyond the standard model. Many new physics models, which explain the hierarchy problem naturally, predict µ → eγ in achievable branching-ratio region with ameasurement.
The MEG experiment searches for µ+ → e+ γ at Paul Sherrer Institut (PSI) in Switzerland. Innovative detector technology was developed for the experiment, such as a liquid
xenon gamma-ray detector, a positron spectrometer with a special gradient magnetic ﬁeld
for a high-rate positron measurement and a fast waveform sampler chip. In 2008 the ﬁrst
physics data was taken for three months. After upgrade for the detector, the data wastaken for two months in year 2009.
The liquid xenon detector plays the most important role to suppress background eventsand showed excellent resolutions with a proper calibration. The light yield of liquid xenon
greatly improved by a puriﬁcation and was stable over the physics run in 2009. During
the physics run in 2009, the detector was monitored with various calibration sources andoperated stably.
The sensitivity of upper limit on the branching ratio at 90% conﬁdence level (C.L.) isestimated in 2009 data to be
S2009 = 6.1 × 10−12 .
On the 2009 data, a likelihood analysis was performed to set the upper limit on the
branching ratio,
Br(µ+ → e+ γ) < 1.5 × 10−11 at 90% C.L.
The MEG experiment is currently running toward a 10−13 branching-ratio region for anext few years.

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CONTENTS

Contents
Introduction

1

I

2

Lepton Flavor

1 Lepton Flavor Physics and µ → eγ
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Lepton ﬂavor mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 Neutrino and the see-saw mechanism . . . . . . . . . . . . . . . . . . . . .
1.4 Motivation of µ+ → e+ γ search . . . . . . . . . . . . . . . . . . . . . . . .
1.5 Physics of the µ+ → e+ γ decay . . . . . . . . . . . . . . . . . . . . . . . .

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4

II

8

MEG Experiment2 Principle and Overview of the MEG Experiment
2.1 Signal and background of µ → eγ . . . . . . . . . . . . . . . . . . . . . . .
2.1.1 Signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.2 Backgrounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Strategy of the MEG experiment . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Requirement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.2 Muon source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.3 Positron tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.4 Scintillator for a gamma-ray measurement . . . . . . . . . . . . . .
2.3 Sensitivity and goal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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3 Detector and Setup
3.1 Detectors overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1 MEG detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.2 MEG coordinate system . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Beamline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Proton accelerators at PSI . . . . . . . . . . . . . . . . . . . . . . .
3.2.2 Proton target and surface muon . . . . . . . . . . . . . . . . . . . .
3.2.3 Area πE5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.4 Beam transport system . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.5 Muon stopping target . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 COBRA magnet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.2 Magnetic ﬁeld . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4 Drift chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.1 Required performance . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.2 Design of chamber . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.3 Readout electronics . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5 Timing counter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5.1 Design of timing counter . . . . . . . . . . . . . . . . . . . . . . . .
3.5.2 Timing ϕ-counter . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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CONTENTS

iii

3.5.3 Timing z-counter . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Liquid xenon detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6.1 Property of liquid xenon scintillator . . . . . . . . . . . . . . . . . .
3.6.2 Liquid xenon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6.3 Photo-multiplier tube . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6.4 The 900-liter liquid xenon detector . . . . . . . . . . . . . . . . . .
3.6.5 Constant calibration source in detector . . . . . . . . . . . . . . . .
3.6.6 Cryogenics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6.7 Puriﬁcation system . . . . . . . . . . . . . . . . . . . . . . . . . . .
Setup for π 0 run . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.7.1 Purpose and principle . . . . . . . . . . . . . . . . . . . . . . . . .
3.7.2 Negative pion beam . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.7.3 Liquid hydrogen target . . . . . . . . . . . . . . . . . . . . . . . . .
3.7.4 NaI tagging detector . . . . . . . . . . . . . . . . . . . . . . . . . .
3.7.5 Pre-shower counter in front of the NaI . . . . . . . . . . . . . . . .
Cockcroft-Walton proton accelerator . . . . . . . . . . . . . . . . . . . . .
3.8.1 Purpose and principle . . . . . . . . . . . . . . . . . . . . . . . . .
3.8.2 Cockcroft-Walton accelerator . . . . . . . . . . . . . . . . . . . . .
3.8.3 Beamline and target . . . . . . . . . . . . . . . . . . . . . . . . . .
Electronics and data acquisition . . . . . . . . . . . . . . . . . . . . . . . .
3.9.1 MIDAS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.9.2 Slow control system . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.9.3 Data acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.9.4 Trigger system . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.9.5 Waveform digitizer . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.9.6 Computer resource and online frontend . . . . . . . . . . . . . . . .
3.9.7 Monitor and analysis with ROME framework . . . . . . . . . . . .
3.9.8 Monte Carlo simulation . . . . . . . . . . . . . . . . . . . . . . . .

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4 Method of Event Reconstruction
4.1 Waveform analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.1 Drift chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.2 Timing ϕ-counter . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.3 Liquid xenon detector . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.4 NaI detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Gamma-ray reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.1 Scintillation photons . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.2 Position reconstruction . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.3 Timing reconstruction . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.4 Energy reconstruction . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.5 Non-uniformity correction . . . . . . . . . . . . . . . . . . . . . . .
4.2.6 Pileup search and correction . . . . . . . . . . . . . . . . . . . . . .
4.3 Positron reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.1 Strategy of position reconstruction . . . . . . . . . . . . . . . . . .
4.3.2 Hit z-position reconstruction in drift chamber . . . . . . . . . . . .
4.3.3 Hit-timing reconstruction in timing-counter bar . . . . . . . . . . .
4.3.4 Track ﬁnding and ﬁtting . . . . . . . . . . . . . . . . . . . . . . . .

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3.6

3.7

3.8

3.9

iv

CONTENTS

5 Run
5.1 First MEG physics run in 2008 . . . . . . . . . . . . . . . . . . . . . . . .
5.1.1 Overview of 2008 run . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.2 Run . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.3 Detector status . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 MEG run in 2009 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.1 Overview of 2009 run . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.2 Degrader setting . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.3 Run . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.4 Detector status . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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III

78

The Liquid Xenon Gamma-Ray Detector

6 Calibration and Monitor of the Liquid Xenon Detector
6.1 Outlook of calibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2 Gain of PMTs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.1 Gain calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.2 Gain shift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.3 Gain adjustment . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.4 Monitor of gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3 Alpha sources and quantum eﬃciency . . . . . . . . . . . . . . . . . . . . .
6.3.1 Quantum eﬃciency . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3.2 Absorption and scattering . . . . . . . . . . . . . . . . . . . . . . .
6.3.3 Particle discrimination . . . . . . . . . . . . . . . . . . . . . . . . .
6.4 Light yield . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4.1 Light-yield monitor . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4.2 Monitor during π 0 run . . . . . . . . . . . . . . . . . . . . . . . . .
6.4.3 Monitor with the CW accelerator . . . . . . . . . . . . . . . . . . .
6.4.4 Cosmic-ray monitor . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4.5 AmBe monitor . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4.6 Alpha monitor . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4.7 Monitor during muon beam . . . . . . . . . . . . . . . . . . . . . .
6.4.8 Combined monitor of the light yield in 2008 . . . . . . . . . . . . .
6.5 Uniformity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.5.1 Non-uniformity correction . . . . . . . . . . . . . . . . . . . . . . .

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7 Performance of the Liquid Xenon Detector
99
7.1 Position . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
7.1.1 Collimator run in 2008 . . . . . . . . . . . . . . . . . . . . . . . . . 99
7.1.2 Collimator run in 2009 . . . . . . . . . . . . . . . . . . . . . . . . . 101
7.2 Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
7.2.1 Intrinsic time resolution . . . . . . . . . . . . . . . . . . . . . . . . 102
7.2.2 Absolute time resolution . . . . . . . . . . . . . . . . . . . . . . . . 104
7.3 Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
7.3.1 Energy resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
7.3.2 Uniformity of reconstructed energy . . . . . . . . . . . . . . . . . . 107

CONTENTSv

7.3.3 Linearity of reconstructed energy . . . . . . . . . . . . . . . . . . . 108
7.3.4 Energy dependence of energy resolution . . . . . . . . . . . . . . . . 108
7.3.5 Position dependence of energy resolution . . . . . . . . . . . . . . . 109
7.3.6 Systematic uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . 112
7.4 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
7.4.1 Cosmic ray . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
7.4.2 Background distribution . . . . . . . . . . . . . . . . . . . . . . . . 115
7.5 Eﬃciency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
7.5.1 Detection eﬃciency . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
7.5.2 Measurement of two-gamma decay . . . . . . . . . . . . . . . . . . 118
7.5.3 Eﬃciency for analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 119

IV

Combined Analysis and Performance121

8 Performance of Positron Detector
121
8.1 Time resolution of timing counter bars . . . . . . . . . . . . . . . . . . . . 121
8.2 Quality of positron reconstruction . . . . . . . . . . . . . . . . . . . . . . . 122
8.3 Positron energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
8.4 Positron angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
8.5 Decay vertex resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
9 Combined analysis of a Gamma ray and a Positron125
9.1 Relative angle, θeγ and ϕeγ . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
9.2 Relative timing teγ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
9.3 Normalization factor for µ+ → e+ γ . . . . . . . . . . . . . . . . . . . . . . 126
9.3.1 Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
9.3.2 Counting the Michel decay, µ+ → e+ νe ν µ . . . . . . . . . . . . . . 127
9.4 Systematic uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

V

Physics Analysis on 2009 Data

130

10 Analysis for the µ+ → e+ γ Search
13010.1 Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
10.1.1 Event selection and blinding . . . . . . . . . . . . . . . . . . . . . . 131
10.1.2 Analysis region and acceptance cut . . . . . . . . . . . . . . . . . . 132
10.1.3 Experiments simulation . . . . . . . . . . . . . . . . . . . . . . . . 133
10.1.4 Conﬁdence region . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
10.1.5 Eﬀect of systematic uncertainty . . . . . . . . . . . . . . . . . . . . 134
10.2 Maximum likelihood analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 135
10.2.1 Deﬁnition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
10.2.2 Observables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
10.3 Probability density function . . . . . . . . . . . . . . . . . . . . . . . . . . 137
10.3.1 Signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
10.3.2 Radiative decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
10.3.3 Accidental background . . . . . . . . . . . . . . . . . . . . . . . . . 139
10.4 Result of the maximum likelihood ﬁt . . . . . . . . . . . . . . . . . . . . . 140

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CONTENTS
10.5 Sensitivity of Run 2009 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
10.6 Upper limit of µ+ → e+ γ branching ratio . . . . . . . . . . . . . . . . . . . 140
10.7 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
10.7.1 Event distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
10.7.2 Highly-ranked events . . . . . . . . . . . . . . . . . . . . . . . . . . 142
10.7.3 Result in sideband data . . . . . . . . . . . . . . . . . . . . . . . . 143
10.7.4 Eﬀect of the systematic uncertainty . . . . . . . . . . . . . . . . . . 144
10.7.5 Future prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

VI

Conclusion

Appendix

148
150

A Radiative decay
150
A.1 Radiative-decay diﬀerential branching ratio . . . . . . . . . . . . . . . . . . 150
B Engineering run in 2007
151
B.1 Overview of 2007 run . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
B.2 The LXe detector status . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
B.3 MEG engineering run in 2007 . . . . . . . . . . . . . . . . . . . . . . . . . 151
B.4 π 0 run in 2007 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
C Calibration of the NaI detector
152
C.1 Gain adjustment of APDs . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
C.2 Performance of the NaI detector . . . . . . . . . . . . . . . . . . . . . . . . 153
C.3 Gain adjustment of pre-shower counter . . . . . . . . . . . . . . . . . . . . 155
Acknowledgment

157

INTRODUCTION

1Introduction
Lepton is known to have three generations of particles. Charged leptons are classiﬁed aselectron, muon and tauon with diﬀerent masses, and corresponding electron-, muon- andtau-neutrino are known in neutrino sector. Quark also has three generations of particles
and these is a mixing between generations. For a long time there had been no observation of lepton mixing, thus the lepton ﬂavor number had been regarded as preserved.
However, in neutrino sector, a mixing of lepton ﬂavor was implied from atmospheric neutrino oscillation in 1998 at Super-Kamiokande, Japan [1]. There is still no observation of
lepton-ﬂavor mixing in charged lepton sector so far.
The Standard Model (SM) in particle physics can describe phenomena of particles
well but a new physics beyond the SM is desired to overcome artiﬁcial features of the SM.
Some new physics predict charged-lepton-ﬂavor violation (cLFV) around an observablelevel.
The rare muon decay, µ+ → e+ γ, is sensitive to new models of the SM extension
around the current upper limit of branching ratio Br(µ+ → e+ γ) < 1.2 × 10−11 (90%C.L.) given by MEGA experiment in 1999 [2]. The MEG experiment aims to search forµ+ → e+ γ at a sensitivity better than the current limit by two orders of magnitude [3].
We started physics data taking in 2008 and reported the ﬁrst physics result with threemonth data, Br(µ+ → e+ γ) < 2.8 × 10−11 (90% C.L.) [4]. There were some updates of
hardware before the 2009 run started, then the data was taken for two months in 2009.
This thesis will describe the results from the run in year 2009.
Chapter I introduces the physics motivation of the MEG experiment. Then the detail of the MEG experiment and the MEG detectors are described in Chapter II. The
calibration and the performance of the liquid xenon gamma-ray detector are described in
Chapter III. The performance of the other detectors are shown in Chapter IV. In Chapter
V the analysis and the result of µ+ → e+ γ search using 2009 data are shown.

2

1. Lepton Flavor Physics and µ → eγPart I

Lepton Flavor
1

Lepton Flavor Physics and µ → eγ

1.1

Introduction

The behavior of fermions and gauge bosons are well described in the Standard Model(SM). A lot of evidence supports the SM, but it was mainly conﬁrmed under TeV-scaleenergy and the hierarchy problem remains. The hierarchy implies that a ﬁne tuning with
cut-oﬀ energy or some extensions of the theory are needed. In addition, many parameterssuch as masses, mixing angles and the number of generation in the SM are determinedby experimental observations without predictions from the SM. Therefore people tend to
consider that the SM is localized up to GeV scale and is an approximation of a global
theory.
Many extended models from the SM are proposed, such as supersymmetry or extra
dimensions. One way to verify these models is a higher energy collisions of particles. In
the near future the Large Hadron Collider (LHC) will operate at a collision energy of
14 TeV energy region. Another powerful approach to go beyond the SM is a search forrare mixings of lepton ﬂavor, which is sensitive to many new physics models depending
on ﬂavors to be mixed. High-energy frontier and rare decays with lepton-ﬂavor mixings
are complementary to verify predictions in new models with diﬀerent sensitivities forparameters such as energy scale, therefore both approaches are desired.

1.2

Lepton ﬂavor mixing

The quarks and leptons are classiﬁed into three generations. The mixing of mass eigenstates in quark sector with Cabibbo-Kobayashi-Maskawa (CKM or KM) matrix is wellknown, while there had been no observation between leptons. However, if neutrinos have
non-zero masses and mixing angles, neutrino oscillation appears with mixing lepton ﬂavors. The oscillation was observed ﬁrst at Super-Kamiokande and it proves lepton ﬂavor
violation (LFV) occurs in neutrino sector. So far, however, there is still no observation of
charged-lepton-ﬂavor violation (cLFV).
The cLFV process can occur in any weakly decaying particles of µ, τ and also π, K,
B, D, W and Z particles. Because parameters of new physics models aﬀect each decaying
channel with diﬀerent tendencies depending on its models, the multifaceted research of
the cLFV with many channels would help a discrimination of the models.
Muon decay channels enable to search for the cLFV physics under less backgrounds
than those of tauon decays. Some theories predict that rare muon decays are enhanced
than other ﬂavors by those mass ratio. In many popular theories, the decay, µ → eγ,
tends to appear more frequently than other modes of µ → eee and µ − e conversion.
At the muon side current ongoing project is only the MEG experiment to search forµ → eγ at Paul Sherrer Institut (PSI). A possibility of the Coherent Muon to ElectronTransition (COMET) experiment to search for the µ−e conversion at the Japanese Proton
Accelerator Research Complex (J-PARC) is under study. Intense source of B mesons
provides many clues of lepton physics and B factory at High Energy Accelerator Research1.3

Neutrino and the see-saw mechanism

3

Organization (KEK) has a plan to upgrade luminosity in future such as SuperKEKB,
which has 40 times higher intensity than the current world most intense KEKB. The
parallel search of ﬂavor mixing in diﬀerent sectors has diﬀerent sensitivity to discriminate
various extensions.

1.3

Neutrino and the see-saw mechanism

In order to describe too small masses of neutrinos some theories are suggested, for example
Zee-mechanism, which produces radiative mass from one-loop radiative correction, allows
a nonzero mass of the left-handed neutrino introducing one extra Higgs doublet and one
charged singlet. Another strong candidate is the seesaw model.
The right-handed neutrino, which is a singlet of SU(2)L and noted as νR , can exist
in the Lagrangian of the SM as a Yukawa coupling term, then it can obtain a mass
with Higgs mechanism. The Majorana mass term is also added in the Lagrangian. The
sea-saw mechanism can naturally explain the small masses of neutrinos such that theright-handed Majorana mass matrix, MR , is much larger than the Dirac mass matrix,
MD and the left-handed Majorana mass is set to zero. One obtains the mass matrix ofthe light neutrinos,((Mν = −MDT MR−1 MD + O
mν ≃

mD
mR

)2 )
,

m2D
,
mR

(1)
(2)

where mD,R is a scale of MD,R respectively and mν is that of neutrinos. For example
an electroweak scale of mD ≃ 100 GeV and an GUT scale of mR ≃ 1015 GeV gives areasonable mass of neutrinomν , to be O(10−2 ) eV. On the other hand an assumption of√mD ∼ mµ,τ and mν ∼ ∆m2atm ∼ 0.05 eV suggests mR in a range of 108 -1011 GeV.
The mixing in neutrino sector also suggests the cLFV decay. For example a µ+ →e+ γ decay arises when radiative neutrino mixing occurs with a weak interaction involving
W boson while the lepton ﬂavor changes between neutrinos (Figure 1.1). In such a casethe branching ratio of µ+ → e+ γ is determined by a mass ratio of the mass diﬀerence of
2 2),muon and positron to W boson mass, (∆m221 /MW
3α ∑ ∗∆m221
Uµi Uei
2
32π i
MW
(
)2
∆m221
α
2
sin 2θ12≈< 10−54 ,
2
128π
MW
2

B(µ → eγ) =

(3)
(4)

where U is the Pontecorvo-Maki-Nakagawa-Sakaga (PMNS or MNS) matrix, sin2 2θ12 =0.86 and ∆m221 ∼ 8 × 10−5 eV 2 are assumed. The branching ratio in the SM with massive
neutrinos is too low to be reached experimentally. In other words, the signal of cLFV is
deﬁnitely the evidence of the new physics beyond the SM. Many extensions of the SMenhance the mixing of lepton ﬂavor and predict the existence of µ → eγ near to thecurrent upper limit of Br(µ → eγ).

4

1. Lepton Flavor Physics and µ → eγ
W+

+



e

e+

Figure 1.1: Feynman diagram for the µ+ → e+ γ in the Standard Model.

1.4

Motivation of µ+ → e+ γ search

The advantage of using muons to search for new physics is absence of strong interactions.
Further, a low energy muon produces only electron, positron, gamma ray and neutrinos
with only a few decay modes. Therefore only two types of detectors for positrons andgamma rays are required. A µ+ → e+ γ has a clear two-body decay and there is no missing
particle in signal.
For µ − e conversion the branching ratio is about hundred times lower than that ofµ+ → e+ γ in major cases of extended theories. Furthermore the observed number ofmuons limits the achievable branching ratio rather than the performance of a detector.
Thus to be comparable with µ+ → e+ γ , an intense muon source is required. On the other
hand, because a µ+ → e+ γ search, as well as µ+ → e+ e− e+ , is limited by a resolution of
detectors and pileup, an innovative upgrade of a detector enables to give a strict upper
limit of the branching ratio.
The observation of LFV events should be the evidence of extended theories of theSM. Even though there is no LFV observed, the lower limit of branching ratio is able
to distinguish a possible model and its parameters. The LFV search with τ lepton is
also needed for a discrimination of models because the sensitivity of the LFV between
diﬀerent pairs of lepton family depend on models. However, the angular distribution fromµ+ → e+ γ with polarized muons is also dependent on models, thus there is a possibility
to discriminate models only in the µ+ → e+ γ search. Regarding the region aroundcurrent upper limits of rare muon or tau lepton decays and other cLFV, the search forµ+ → e+ γ has a powerful ability to discriminate various models for new physics beyond
the SM. If µ+ → e+ γ is discovered, it is the evidence of new physics because the SM does
not predict it in the reachable region.

1.5

Physics of the µ+ → e+ γ decay

General SUSY The supersymmetric (SUSY) scenarios enhance LFV because of themisalignment between fermion and sfermion mass eigenstates. The LFV would occur by
one-loop diagrams with the exchange of gauginos and sleptons, thus the branching ratioof µ → eγ is determined by the ratio of corresponding elements in slepton mass matrix,
a SUSY mass running in the loop and tan β that is the ratio of the two MSSM-Higgs
vacuum expectation values (VEVs).
SUSY GUT SU(5) In the grand-uniﬁed theory (GUT), the electroweak interaction
and the strong interaction are globally treated in a group, such as SU(5), SO(10) orE6,7,8 (E series of Lie groups). The SU(5) is a minimal expression but can not unify the1.5

Physics of the µ+ → e+ γ decay

5gauge couplings of the SM and it was excluded by the longer proton decay time thanits expectation as experimentally proved at KAMIOKANDE [5]. However, the minimum
SUSY extension of the SM (MSSM) solves the hierarchy problem and agrees with allobservations. Figure 1.2 shows the relation of branching ratio [6]. The possibility ofµ → eγ discovery in this model is low but exists only in the case of light SUSY particles
and large values of tan β and A0 . The input parameters are given as m0 , M1/2 < 1 TeV,
|A0 | < 3 m0 , 3 < tan β < 50 and µ > 0. For the neutrino sectors, we assume a hierarchicalspectrum for both light and heavy neutrinos and we take mν3 = 0.05 eV, 1010 < M3 <1015 GeV. The gray regions are excluded by the current experimental upper bounds on
Br(µ → eγ).
With right-handed neutrinos of singlet (SU(5)RN ), SU(5) model gets a natural enhancement of the branching ratio due to the left-handed sleptons mass matrix. Figure
1.3 shows the correlation between branching ratios between µ → eγ and τ → µγ for three
diﬀerent values of Ue3 = (0.001, 0.01, 0.1), which is the element of the MNS matrix and a
crucial parameter to determine Br(µ → eγ ).

Figure 1.2: Branching ratios of µ →eγ and τ → µγ in SU(5) SUSY
GUT without right-handed neutrinos.
Red and green dots satisfy the B →Xs γ constraints at the 99% C.L. limit
while black dots do not. Green dots
additionally satisfy mh0 > 111.4 GeV.
≤ 5×
All the points satisfy ∆aSUSY
µ
−9
10 .

Figure 1.3: Branching ratios of µ →eγ and τ → µγ in the SU(5)RN model.
The input parameters are given as
m0 , M1/2 < 1 TeV, |A0 | < 3 m0 ,3 < tan β < 50 and µ > 0, andfor both light and heavy neutrinos,mν3 = 0.05 eV and 1010 < M3 < 1015
GeV are set.

Gray regions are excluded by the experimental upper limit.

SUSY GUT SO(10) Compared to the minimal SU(5) SUSY GUT, naturally a large
mixing of lepton ﬂavor is introduced in SO(10) with see-saw mechanism, because Yukawa

6

1. Lepton Flavor Physics and µ → eγ

couplings of neutrino relates with those in quark sector and both the left-handed andright-handed sleptons receive LFV eﬀects. For example, the branching ratio of µ → eγ isenhanced by (mτ /mµ )2 compared to the minimal SU(5) SUSY GUT. The correlation of
branching ratio between µ → eγ , τ → µγ and µT i → eT i are described with A0 = 0 in
Figure 1.4, by various ﬁve models of diﬀerent higgs content, ﬂavor symmetry and diﬀerent
MR hierarchy [7]. The assumption for each model on SO(10) for (tan β, sin θ13 ) is that
Albright - Barr (AB)[8], Chen - Mahanthappa (CM)[9], Cai - Yu (CY)[10], Dermisek Raby (DR)[11] and Grimus - Kuhbock (GK)[12] have (5, 0.002), (10, 0.013), (10, 0.0029),(50, 0.0024) and (10, 0.00059), respectively.

10

-06

10
10

BR( τ −> e + γ )

10
10

-07
-08

-10

10
10

AB modelCM modelCY modelDR modelGK model-09(A0 = 0)

-11

-12

10
10

-14

10
10

-13

-15

-16

10
10

-17
-18

10

-19

10

-18

-17

10

10

-16

10

-15

-14

-13

-12

-14

-13

-12

10
10
10
BR( µ −> e + γ )

10

-11

10

-10

10

-09

10

-08

(a) µ → eγ and τ → eγ

10

-06

10
10

BR( τ −> µ + γ )

10
10

-07

-08

-10

10
10

AB modelCM modelCY modelDR modelGK model-09(A0 = 0)

-11

-12

10
10

-14

10
10

-13

-15

-16

10

-19

10

-18

-17

10

10

-16

10

-15

10
10
10
BR( µ −> e + γ )(b) µ → eγ and τ → µγ

10

-11

10

-10

10

-09

10

-08

1.5

Physics of the µ+ → e+ γ decay

7

-10

10

-11

10

-12

BR( µ + Ti -> e + Ti )10

AB modelCM modelCY modelDR modelGK model-13

10(A0 = 0)

-14

10

-15

10

-16

10

-17

10

-18

10

10

-18

-17

10

-16

10

-15

10

-14

-13

10
10
BR( µ −> e + γ )

10

-12

10

-11

10

-10

-09

10

(c) µ → eγ and µ + T i → e+ + T i
Figure 1.4: Relation between branching ratios of muon rare decays in SO(10) SUSY GUT.
The present experimental constraints are indicated by the dashed lines [7].

8

2. Principle and Overview of the MEG ExperimentPart IIMEG ExperimentThis part introduces a principle and an apparatus of the MEG experiment with its advantages. Details of expected signal and background, detectors and the status are described.
Recent experiments to search for the µ+ → e+ γ are shown in Table 1. The previous
experiment by MEGA gave the limit of Br(µ+ → e+ γ) < 1.2 × 10−11 (90% C.L.) in 1999
[2]. The parameters in the table determine the ability to search µ → eγ , and suggest apossibility to reach unexplored region with new experiments. The MEG experiment aims
at two orders of magnitude lower than the limit with innovative detectors and a highly
eﬃcient measurement.
Table 1: Progress of 90 % C.L. upper limits of Br(µ+ → e+ γ ) and performance in full
width at half maximum (FWHM).
Year

Site

1977 TRIUMF
1980
SIN
1979 LAMPF
1986 LAMPF
1999 LAMPF
2008
PSI
1

Beam rate ∆Ee(sec−1 ) (%)
2 × 105 π + 8.7
5 × 105 µ+ 10
2.4 × 106 µ+ 8.8
4 × 105 µ+ 8
1.3 × 107 µ+ 1.2
3 × 107 µ+ 1.6

∆Eγ
(%)
9.3
8.7
8
8
4.5
4.7 1

∆teγ
∆Θeγ
(nsec) (mrad)
1.4
6.7
1.9
37
1.8
87
1.6
15
0.35

Upper Limit
Br(µ → eγ)
3.6 × 10−9
1.0 × 10−9
1.7 × 10−10
4.9 × 10−11
1.2 × 10−11
2.8 × 10−11

Ref.
[13]
[14]
[15]
[16]
[2]
[4]

FWHM from upper part of sigma.

2

Principle and Overview of the MEG Experiment

2.1

Signal and background of µ → eγ

2.1.1

SignalThe MEG experiment utilizes positive muons in order to avoid a formation of a muonic
atom and a process such as µ − e conversion. The µ+ → e+ γ signal is a clear two-bodydecay from a positive muon at rest on a stopping target and decays to back-to-backdirection at a coincident time. Both a positron and a gamma ray have energies at a half
muon mass, mµ /2 = 52.8 MeV/c2 . Therefore observed parameters of a time diﬀerence, teγ ,an opening angle, Θeγ , and each energy from half muon mass, mµ /2−Ee and mµ /2−Eγ candistinguish a signal from backgrounds by selecting events with these parameters aroundzero. The distinctive signal is an advantage to detect the µ → eγ decay.
2.1.2

Backgrounds

Even though a pure positive muon beam is introduced into the target, there are several
backgrounds from muon decay by itself. Figure 2.1 shows energy spectra of positrons andSignal and background of µ → eγ

2.1

9Differential Branching Ratio (dB/dE)

gamma rays from muon decays. The most dominant muon decay mode is µ+ → e+ νe ν µ ,which is called Michel decay (MD) named after Louis Michel, and it produces many
positrons around the signal energy region. The positron itself and the gamma ray fromradiative muon decays or annihilation of positrons make a source of µ+ → e+ γ backgroundwhen a positron and a gamma ray get accidentally coincident with back-to-back direction
around the signal energy region, 52.8 MeV. For a µ+ → e+ γ searching experiment there
are two main backgrounds and this accidental background is the most dominant.
Second one is a prompt background from a physical decay µ+ → e+ νe ν µ γ . Anotherdecay mode of radiative muon decay (RD, RMD), µ+ → e+ νe ν µ γ , emits both a positron
and a gamma ray at coincident time with a branching ratio Br(µ+ → e+ νe ν µ γ) = (1.4 ±0.4)% (Eγ > 10 MeV). This forms a coincident background of back-to-back positron andgamma ray if two neutrinos get less energies.
10-1
10-2
10-3
10-4
10-5

γ from µ → e ν ν γ
e from µ → e ν ν

10-6
10-7

0

10

20

30

40
50
Energy (MeV)

Figure 2.1: Energy spectra of a positron from µ+ → e+ νe ν µ [17] and a gamma ray fromµ+ → e+ νe ν µ γ [18]. Other variables are integrated.

Prompt background The diﬀerential branching ratio of the radiative muon decay wascalculated at the rest frame of a muon,
dBRD (µ → eν ν̄γ) =αdy
βdx dΩe dΩγ
364πy[F (x, y, d) − βPµ · pˆe G(x, y, d) − Pµ · pˆγ H(x, y, d)],|p⃗e |, d = 1 − β pˆe · pˆγ ,
Ee
2Eγ
2Ee
, y=
,
x =
mµ
mµ

β =

(5)

(6)
(7)

where Pµ is a polarization vector of a muon and functions of F (x, y, d), G(x, y, d) andH(x, y, d) are described in Appendix A.1 ([19, 20, 21]).
Our interest is a background around the µ+ → e+ γ signal region, therefore the dBRD
is integrated in ranges of 1 − δx ≤ x ≤ 1, 1 − δy ≤ y ≤ 1 and 0 ≤ z ≤ δz, where
the parameter z is deﬁned as z = π − Θeγ and δx, δy and δz mean detector resolutions

10

2. Principle and Overview of the MEG Experiment

for the signal discrimination. There is an assumption of uniform performance about any
directions, δz = δzϕ = δzθ . The partial branching ratio is expressed as,∫ 1
dBRD (µ → eν ν̄γ) =∫ min[δz,2√(1−x)(1−y)]

∫ 1
dx

1−δx

dz

dy
1−δy

0

dB(µ+ → e+ ν ν̄γ)
dxdydzα=[J1 (1 − |Pµ | cos θ) + J2 (1 + |Pµ | cos θ)]d(cos θ),
16π

J1
J2

)2
( )4
( )8
1 1
δz
δz
δz
2
− (δx)+,22
2
3 (δy)
2
( )2
( )4
( )6
8 δz
δz
δz
2
2
= 8(δx) (δy)− 8(δx)(δy)
+
,
2
2
3 2

8
=
(δx)3 (δy)
3

(8)

(

(9)

where θ is the angle between the muon spin and the positron direction [22].

Accidental background With a realistic muon rate and detector’s resolution, theaccidental background is the most dominant as a background of µ+ → e+ γ decay. The
positrons come from normal Michel decay, while the gamma rays from the radiative muon
decays, annihilation in ﬂight (AIF) of positrons or external bremsstrahlung.
With taking each detection probability of a positron and a gamma ray in the µ+ →+e γ signal region into account, the ratio of the accidental background (Bacc ) over total
muons, by integrating a muon rate Rµ , is(∫Nacc =dTΩe
Rµ · fe0 · ηe ·
· ϵe

DAQ

4π

) (
)
Ωγ
δωeγ
0
· Rµ · fγ · ηγ ·· ϵγ ·· (2δteγ ),(10)
4π
Ωeγ

Nacc
dT (Rµ · (Ωeγ /4π) · ηeγ · ϵe · ϵγ )
DAQ
(
)
δωeγ
0
0
= Rµ · fe · fγ ·· (2δteγ ) · η,
4π

Bacc = ∫

(11)
(12)

where the eﬀect of polarization determined by detector’s acceptance is included in η as
the suppression factor by a muon polarization. It is maximized to η = 1 in the case of
100% depolarized muon. The fraction of energy spectrum around µ+ → e+ γ signal region
is expressed as fe0 and fγ0 for positrons and gamma rays, respectively.
In order to consider the fγ0 , in a theoretical aspect, the diﬀerential branching ratio of
the radiative muon decay is considered after the integration of the positron energy andthe opening angle [23],dBRD (µ → eν ν̄γ) ≃dyd(cos θ)[J+ (y)(1 + |Pµ | cos θ) + J− (y)(1 − |Pµ | cos θ)], (13)
y

2.2

11

Strategy of the MEG experiment√r ≡ me /mµ is neglected and J+ (y) and J− (y) are deﬁned by[()α
1 − y 17
J+ (y) =(1 − y) 3 ln
−
6π
r
2
]
(
)
(
)
1−y
1 − y 132
+ − 3 ln
+ 7 (1 − y) + 2 ln−
(1 − y) ,
(14)
r
r
3
[(
)
α
1 − y 932
J− (y) =(1 − y)
3 ln
−
6π
r
12
(
)
(
)
]
1 − y 29
1 − y 55
2
+ − 4 ln+
(1 − y) + 2 ln−
(1 − y) .
(15)
r
3
r
12

where the term of orderWith using above relations, the fractions are estimated as∫ 1−r
dBRD (µ+ → e+ ν ν̄γ)
α
0
fγ =
dy
≈
(δy)2 [ln(δy) + 7.33],
dy
2π
1−δy
∫ 1+r
dBM D (µ+ → e+ ν ν̄)
0
fe =
dx
≈ 2(δx),
dx
1−δx

(16)
(17)

thus the eﬀective branching ratio of accidental background is approximately given by
[

]
α
(δz)2
2
Bacc ≈ Rµ · (2δx) ·(δy) (ln(δy) + 7.33) ·· (2δteγ ) · η.
2π
4

2.2

Strategy of the MEG experiment

2.2.1

Requirement(18)

A search for a rare decay of muons requires an intense muon beam and an excellent
performance of detectors for both a gamma ray and a positron in order to avoid pileup
and reach the interesting region. As described in Section 2.1, the better resolution of thedetector can suppress main backgrounds from accidental pileup, which would limit thesensitivity of the search.
2.2.2

Muon source

Because muons are ﬁnally stopped on a target without including a beam momentum into
decay products, a low-energy muon beam is allowed. A direct current (DC) of a muon
beam is eﬃcient to suppress the accidental background compared to alternating current(AC) muons, because the accidental background depends on eﬀective beam rate in abunch and the observed number is accumulated by averaged rate.
We select the world’s most intense DC muon beam from 590 MeV proton ring cyclotron
facility of ∼2 mA intensity at Paul Sherrer Institut in Switzerland.
2.2.3

Positron tracking

Many positrons are produced from Michel decays around a signal energy, thus pileup is a
critical problem. Therefore, in the positron detector, it is desired to avoid too long tracking
time and to select only the interesting signal region. In addition, a material thorough12

2. Principle and Overview of the MEG Experiment

tracking should be as less as possible to avoid scattering, energy loss or annihilation of
low positron momentum, around 52.8 MeV.
As a solution, we developed a special magnet with a gradient magnetic ﬁeld, whichenables a momentum cut with its geometry and a suitable tracking length. Undesired low
momentum positrons is outside the detector, then eﬀective measurement is possible. To
detect positrons low mass drift chambers are also developed and plastic-scintillator bars
support a timing determination.
2.2.4

Scintillator for a gamma-ray measurement

Equation 18 suggests that the energy resolution for a gamma ray (δy) is crucial to suppress
the background level. Thus, the gamma-ray detector is the most important part todetermine a ﬁnal sensitivity.
The gamma-ray measurement in the MEGA experiment has a good energy performance but a low detection eﬃciency of photon spectrometer about 2.4%, because it detects a photon via charged particles [2]. It is considered that the performance of photon
detector could improve from the list in Table 1, with a proper selection of scintillators,
especially as timing and eﬃciency.
Performance of various scintillators is shown in Table 2. Some crystals with goodtiming performance are typically small size and not suitable for a large detector to measureten-MeV scale. We adopt a xenon in a liquid state with a fast signal and a high density.
It is a new frontier with a use of a large 900-liter (2.7-ton) liquid xenon as a detector, sothat innovative liquid xenon gamma-ray detector was developed for the MEG experimentas later described in Section 3.6.
Table 2: Comparison of various scintillators.
LXe
Density (g/cm3 )Radiation length (cm)Mollier radius (cm)Decay time (ns)
Emission peak (nm)
Relative output
1

2.98
2.77
4.2
45
178
75

LAr

NaI CsI BGO(Tl) (Tl)
1.40 3.67 4.51 7.13
14 2.59 1.86 1.12
7.2 4.13 3.57 2.23
1620 230 1300 300
127 410 560
480
90
100 165
21

LSO
(Ce)
7.40
1.14
2.07
40
420
83

LaBr3
(Ce)
5.29
2.1
2.85
25
380
130

PbWO4
8.3
0.89
2.00
30/101425/4201
0.083/0.291

slow/fast component

2.3

Sensitivity and goal

Although we would estimate a sensitivity of the MEG experiment with a measured performance and a likelihood method later, it makes a sense to obtain an overview of timescale toward our goal beforehand. The single event sensitivity (SES) of µ+ → e+ γ ,deﬁned in Equation 19, is a sensitivity of background-less single-signal discovery,
SES(µ+ → e+ γ) =1,
Rµ · T · (Ωeγ /4π) · ϵe · ϵγ · ϵeγ

(19)

2.3

13

Sensitivity and goal

where Rµ is the muon stopping rate, T is the total eﬀective run time, Ωeγ is the detector
acceptance with considering a muon polarization, ϵγ and ϵeγ are detection eﬃciencies ofa gamma-ray and positron detector and ϵeγ is the total eﬃciency to select back-to-backeγ of trigger, analysis and selection.
Actual branching-ratio sensitivity of null-signal observation starts a saturation when atotal time reaches a region that SES becomes comparable with the dominant backgroundof Bacc . As a function of total time T , Bacc /SES can be regarded as the number ofaccidental backgrounds in a certain signal window for Bacc . Around the region of thecurrent limit, an achievable region in µ+ → e+ γ search is limited by Bacc , not by statistics.
There are shown estimation of backgrounds approximately by assuming a detector
performance. In the case of MEGA experiment, Table 1 givesδx = 0.0084, δy = 0.032, δz = 0.02, δteγ = 1.12 ns,
Rµ = 1.3 × 107 (DC rate for SES), Rµ = 2.6 × 108 (for Bacc ),(Ωeγ /4π) · ϵe · ϵγ · ϵeγ = 0.003,(20)

where AC beam rate with 6-7% duty cycle is considered in Rµ only for Bacc but not for
SES and we assume 1.4 FWHM region as 90% region. Then each background is estimatedto be
BRD = 9.1 × 10−15 , Bacc = 4.4 × 10−12 , SES(T = 1 year) = 8.1 × 10−13 .

(21)On the other hand, the current performance of the MEG experiment are typicallyδx = 0.012, δy = 0.033, δz = 0.02, δteγ = 0.25 ns,
Rµ = 3 × 107 , (Ωeγ /4π) · ϵe · ϵγ · ϵeγ = 0.017,(22)

where we assume the same δz as the MEGA because a comparison is diﬃcult and these
are not so diﬀerent each other. The backgrounds and SES are calculated as
BRD = 9.2 × 10−15 , Bacc = 4.4 × 10−14 , SES(T = 1 year) = 6.0 × 10−14 .

(23)

Although the deﬁnition of resolutions slightly diﬀers between two experiments, we cansee lower accidental backgrounds for the MEG experiment by two order of magnitude
thanks to the intense DC muon beam and the high resolution of timing. The energy
resolutions are comparable each other, but detection eﬃciencies of the MEG detector are
much better. Especially, the gamma-ray detector in MEGA detects charged particles fromconverted gamma rays, thus the eﬃciency is low.
The SES and Bacc in Equation 23 indicate that the MEG experiment needs a few
years run, considering available beam time of nine months per year, eﬀective DAQ time,a calibration and a maintenance. The upper-limit sensitivity for null signal obtained in2009 analysis will be shown later in Section 10.5 by our analysis method. The strategy
to acquire the suﬃcient performance in MEG will be shown in next section.

14

3. Detector and Setup

3

Detector and Setup

3.1

Detectors overview

3.1.1

MEG detector

Detectors consist of the positron spectrometer inside the magnet and the liquid xenon(LXe) gamma-ray detector. The C-shaped LXe detector is located outside the magnet
and the positron detectors, which consist of a drift chamber (DCH) and a scintillation
timing counter (TIC), are mounted around a lower position from a target as shown in
Figure 3.1. Two sets of TIC are located at the upstream and downstream side, each ofwhich consists of two layers of arrays along the beam axis and the azimuthal axis.

Figure 3.1: Overview of detectors in the MEG experiment.

3.1.2

MEG coordinate system

We deﬁne an orthogonal coordinate system by (x, y, z) as a global coordinate system of
the MEG (Figure 3.2). The origin is deﬁned as the center of COBRA magnet and also at
the central position of the MEG target. The z-axis is parallel to the muon beam with thebeam direction. The y-axis is vertical so the x-axis penetrates perpendicularly the central
detection face of the LXe detector at negative x. The θ parameter is deﬁned as the polar
angle from the z-axis, that means the beam direction is presented with θ = 0. The ϕ isan azimuth of the z-axis and takes zero on the positive x-axis. For example, a direction
from the target to the center of the LXe detector is (ϕ, θ) = (π, π2 ). The spherical polar
coordinates and the cylindrical polar coordinates are deﬁned by θ and ϕ.

3.2

Beamline

γ

e

15

1m
COBRA Magnete+Muon Beam
Stopping Target

Drift chamber

Figure 3.2: Layout of detectors in the MEG experiment.

3.2

Beamline

3.2.1

Proton accelerators at PSI

The facility to provide protons at PSI consists of three accelerators (Figure 3.3). At ﬁrst
the PSI Cockcroft-Walton Pre-Injector generates 870 keV protons from a source made upof hydrogen atoms. Then PSI Injector 2 cyclotron with four spectromagnets provides 72
MeV protons with 0.2% FWHM spread, 50.63 MHz frequency (19.75 ns interval) and 0.3
ns width of a bunch from the 870 keV injector.
Finally the Proton Ring Cyclotron with a diameter of approximately 15 meters, which
consists of eight sector magnets and four accelerator cavities (Figure 3.4), accelerates the
72 MeV proton beam up to 590 MeV kinetic energy. The accelerator normally delivers 2.0
or 2.2 mA protons, sometimes 1.8 mA. With some resonators’ upgrades for the Injector
2 and cyclotron, the operational current is planned to be increased to 2.6 mA and ﬁnallyto 3.0 mA within a few years [24].
Table 3: Characteristics of 590 MeV Ring Cyclotron [25].
Injection Energy
72 MeV
Extraction Energy
590 MeV
Extraction Momentum
1.2 Gev/c
Energy spread (FWHM)
ca. 0.2 %Beam Emittanceca. 2 π mm × mrad
Beam Current
2.0 - 2.2 mA (in DC)
Accelerator Frequency
50.63 MHzTime Between Pulses
19.75 ns
Bunch Width
ca. 0.3 ns
Extraction Losses
ca. 0.03 %16

3. Detector and Setup

Figure 3.3: Proton Accelerators at PSI. Injector 1 is Figure 3.4: The 590 MeV Ring
Cyclotron of PSI.
unused.

3.2.2

Proton target and surface muon

The proton beam reaches the target station M and E, then the Spallation Neutron Source(SINQ) target or a beam dump. The E target has a 1 Hz rotating truncated cone ofpolycrystalline graphite. Its length along beam direction is 40 mm (Figure 3.5). The
rotation is to avoid a heat and the graphite is replaced by a few months.
A lifetime of charged pion at rest is about 26 ns, which is comparable with the time
between beam pulse of 19.75 ns. A muon is produced by a charged pion decay, π ± → µ± νµ ,with a muon neutrino, thus these two are polarized by opposite direction each other. The
momentum of µ± from π ± decay at rest is Eµ ∼ Eν = (m2π± + m2νµ − m2µ )c/2mπ± =29.8 MeV/c. The muons from stopped pions around a surface of the target within a fewµm is called surface muon, which has a low energy loss and a trivial depolarization during
a short pass length in a target and has an upper edge at 29.8 MeV/c. Sub-surface muons,
which come from pions in the bulk of the target, are also generated with lower momentum
and cloud muons with higher momentum originate from pions outside the target. The
intense surface muons are used for the MEG experiment.

3.2
3.2.3

Beamline

17

Area πE5

The MEG experiment uses πE5 area, which is one of ﬁve branches from target E. By
viewing the target E at 175◦ with respect to the primary proton beam, positive or negative
pions, muons and electrons or positrons are provided with a lower momentum 10-120
MeV/c. The πE5 area has a suitable channel to obtain surface muons. Figure 3.6 showsthe πE5 branch, which has two subbranches U and Z to switch the beam for two setupsin πE5 area by a bending magnet. The Z branch of the left-hand side in the ﬁgure has
the last bending magnet and the ﬁrst degrader in it. MEG uses Z branch to extract thesurface positive muon beam.

Figure3.5:
Target E (40 mm
thickness).

Figure 3.6: Branch to the πE5 area.

The πE5 beam line in Figure 3.6 consists of bending, quadrupole, hexapole magnets
and slits, and it can transfer pions and muons with ﬂuxes shown in Figure 3.7. Especiallysurface muons make a peak around 28 MeV/c down to 10 MeV/c. In the middle ofthe beam line, three sets of horizontal and one set of vertical slits can determine themomentum and the acceptance of beam.
3.2.4

Beam transport system

Figures 3.8 and 3.9 show the MEG beam transport system in the πE5 area to bringthe muon beam to stopping target. It consists of a quadrupole triplet (Triplet I), a
velocity separator using a Wien ﬁlter, a second quadrupole triplet (Triplet II) and abeam transport solenoid (BTS) with superconducting magnet from a view of the beam

18

3. Detector and Setup
10 11
10 10

-1 -1

N (mA s )

10 9
10 8
π+
πmeasured pointsµ+µmeasured points

10 7
10 6
10 5
10 4
0

20

40

60

80

100

120

140

160

P (MeV/c)

Figure 3.7: Pion and muon beam intensity at πE5 beam line.

direction. The purpose of the system is to focus positive surface muons at the centerof the muon stopping target with selecting and degrading momentum and to suppress
other particles. A momentum degrader at the center of the BTS is made of Mylar with athickness between 200 and 450 µm which can be optimized to maximize stopping eﬃciency
with less backgrounds.
With a horizontal magnetic ﬁeld of 133 Gauss and a vertical electric ﬁeld of 195 kV,
the Wien ﬁlter separates positive muons from positron contamination by 7.5 σ and also
from others. The beam spot size at the center of the target is σx = 9.5 mm and σy = 10.2mm.

Figure 3.8: Schematic view of MEG beam transport system.

3.2

Beamline

19

Figure 3.9: Beam transport solenoid (BTS).

3.2.5

Muon stopping target

The target has to eﬃciently stop the muon. On the other hand it should be as thinas possible in order to avoid scattering, annihilation and energy loss of positrons in thetarget. Thus an elliptical shaped plane with a large slant angle from a vertical planeof muon beam direction is suitable to have a enough thickness for a muon stopping aswell as a less thickness for positrons’ emission to the detector. In addition, inside of the
COBRA magnet, except for around the detectors, is ﬁlled with helium and a few percent
air for that. A narrow spread of positron momentum by the Wien ﬁlter allows to control
a precise stopping point with using a degrader at the center of BTS.
The dimension of the target is 79.8 mm along vertical axis and 200.5 mm along thelong axis (Figure 3.10). The target is slanted with 20.5◦ relative to the beam axis. The
target has six holes of 10 mm diameter to align the target and to estimate the resolutionof the vertex position reconstructed with the positron tracking.
The target is made of a material with light Z, that is a sheet of polyethylene andpolyester with a 205 µm thickness corresponding to 18 mg/cm2 on plane and gives an
82% stopping eﬃciency. The target is supported with a frame made of Rohacell (0.895
g/cm3 ) and is remotely operated with an insertion system to move between the mounted
position and a stay position apart from the center. Figure 3.11 shows the location of thetarget and the insertion bar around an upper position.
This insertion system of the muon target allows a background study without the target
and another target or another beam line from down stream side. The other insertion
systems are equipped at the down stream side, which allow a beam scanning at the centerwith using APD, a proton beam line and a target insertion of a proton accelerator for a
photon calibration and a hydrogen target for a pion charge exchange run.

20

3. Detector and Setup

Figure 3.10: Muon stopping target.

Figure 3.11: Mounting position of the target.

3.3

COBRA magnet

3.3.1

DesignThe positron spectrometer consists of drift chamber, two types of timing counter and a
special superconducting magnet with a gradient magnetic ﬁeld dedicated to the MEG
experiment. The magnet is called COBRA (COnstant-Bending-RAdius) (Figure 3.12)[26]. All the positron detectors are mounted in the magnet and the LXe detector is put
outside. Thus a window for a gamma ray on COBRA wall should be very thin for a
gamma-ray transmission.
The most important issue is a reduction of high-rate positrons around 108 sec−1 rate.
An optimization of a geometry and an alignment of positron detectors make it possible toselect a high energy region around the 52.8 MeV signal from high-rate positrons. However,
because the dominant muon decay, µ+ → e+ νe ν µ , emits a positron largely in a high energy

3.3

COBRA magnet

21

Figure 3.12: The COBRA magnet.

region near the signal, an additional idea is desired.
There are two solutions to avoid high-rate hits in the COBRA magnet. Figure 3.13
illustrates a diﬀerence between a simple solenoid (a, b) and the solenoid with gradientﬁeld in the MEG experiment (c, d). In a uniform solenoidal magnetic ﬁeld, there is noforce along a cylindrical axis therefore a helical trajectory has a constant pitch, whichmakes many pileups (Figure 3.13 a). While a non-zero radial component of the magnetic
ﬁeld forces to sweep positrons away quickly (Figure 3.13 c).
In a normal solenoidal magnetic ﬁeld, the radius of a charged particle’s trajectory
relates to its momentum. However, the momentum selection is poor in the ﬁeld because
the radius depends on its emission angle, too. Second advantage of the COBRA gradientﬁeld is that tracks of the same momentum have the same radius and are independentof emission angles (Figure 3.13 d), which enables a precise and strict momentum cut asshown in Figure 3.14. In usual solenoidal magnet, radii of tracks depend on a momentum
component on a vertical plane of cylinder. The radius of the same momentum is therefore
not constant by emission angles (Figure 3.13 b).
Superconducting solenoidal magnet with step structure of diﬀerent radii forms thegradient magnetic ﬁeld. Mainly the COBRA consists of one central coil, two gradientcoils and two end coils shown in Figure 3.15. At the both ends of the COBRA, a pair of
two large resistive coils cancel the stray ﬁeld from the COBRA magnet around the photomultiplier tubes (PMTs) of the LXe detector less than 50 Gauss as shown in Figure 3.16.
The superconducting cable is made of NbTi multiﬁlament embedded in copper matrix
with a 0.59 mm diameter and covered with high-strength aluminum stabilizer with a 0.8
× 1.1 mm2 dimension, which is insulated with a Kapton polyimide. The overall crosssection is 0.9 × 1.2 mm2 .
The central coil and the gradient coils have four layers and the end coils have three.
The high-strength cable allows a thin support structure and total thickness of the magnet
including its cryostat is estimated to be 0.197 X0 , corresponding to 85% transmission
eﬃciency of gamma-rays at the signal energy (52.8 MeV).

22

3. Detector and Setup

rate(Hz/cm2 )Figure 3.13: Principle of COBRA magnet.

5

10

104

3

10

Uniform B-field

102
COBRA B-field

10

1
0

DC region

5

10

15

20

25

30
radius(cm)Figure 3.14: Positron rate on drift chamber in COBRA magnetic ﬁeld.

3.3.2

Magnetic ﬁeld

In a normal operation at 360 A current (about half of critical current of the superconducting cable) the central ﬁeld is 1.27 T at z = 0 and slowly decreasing, as |z| increases,
to 0.49 T at edge (Figure 3.17). Figure 3.18 shows the magnetic ﬁeld of Bz and |Br | inside
the COBRA magnet.

3.4

Drift chamber

23�����������������

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

���������������
��

Bz (T)

Figure 3.15: Design of the COBRA magnet [26].

Stray field measured here

26.5mT11.5mT

Photon detector(LXe)

1.2
1.1

5mT

1
Compensationcoil

60.8mT

0.9

0.14T

0.8
0.32T
1.7T

End coil
Gradient coil
Central coil

0.7
0.6
0.5
0

0.2

0.4

0.6

0.8
1
1.2
Distance along axis (m)Figure 3.16: Map of COBRA magnetic ﬁeld
Figure 3.17: Magnetic ﬁeld (Bz ) along[26].
beam axis (x = y = 0).

3.4

Drift chamber

3.4.1

Required performance

The drift chamber (DCH) measures a momentum, a decay vertex and an emission angleof a positron. A time property of a positron is determined by the timing counter at theend of its track. The main purpose of DCH is to obtain the track of a positron. We
require following items for the MEG positron tracker:
1. Low mass structure to avoid positron energy loss and multiple scattering
2. High rate tolerance for high rate positron hit, up to ∼10 kHz/cm2
3. Selection over 40 MeV/c to µ+ → e+ γ signal positron momentum

3. Detector and Setup
R (cm)

24

30
25

1.5
1.4
1.3
1.2
1.1
1
0.9
0.8
0.7
0.6

Drift chamber

20
15
10
5

R (cm)

0
0

20

40

60

80

100 |z| (cm)Bz (T)

30
25

0.3
Drift chamber

0.25

20

0.2

15

0.15

10
5

0.1

0
0

0.05

20

40

60

80

0
100 |z| (cm) |B | (T)R

Figure 3.18: Map of COBRA magnetic ﬁeld (Bz , Br ) on r − |z| plane.

4. Sensitive for both along transverse and longitudinal directions
Thanks to highly eﬃcient selection of positron momentum by the COBRA, we canselect momenta by simply optimizing a geometry of DCH. Even after a reduction by
momentum, coming positrons still have a high rate. The material of DCH makes boththe eﬃciency and the resolution worse, thus it should be as less as possible. The designof DCH is specially optimized for the MEG experiment.
3.4.2

Design of chamber

The drift chambers consist of 16 modules radially aligned with 10.5◦ intervals in theazimuthal angle. The radius is from 19.3 cm to 27.9 cm in order to select only positrons
around the signal region. In helium gas inside the COBRA magnet, all modules are
installed at a lower part (Figure 3.2).
Each module consists of a support frame, a foil with a cathode pattern and anodewires as shown in Figure 3.19, and is composed of two layers with isolated by the cathodefoil with 3.0 mm gap enough to suppress a cross talk. The layers contains nine axial sense
wires, ten grounded potential wires and nine drift cells (Figure 3.20). The two types ofwires are shifted each other between the two layers in order to resolve ambiguity along aradial direction. The ﬁeld map and drift lines are calculated by a GARFIELD simulation(Figures 3.21 and 3.22) [27].
With a 4.5 mm pitch, a carbon-ﬁber frame stretches sense wires by 50 g tension andpotential wires by 120 g alternately (Figure 3.23) [28]. The sense wire, with positive highvoltage, and the potential wire have a 25 µm diameter made of Ni/Cr (80:20) and 50 µm
of Be/Cu (2:98) respectively. The wires are surrounded with a cathode pad made of thin
12.5 µm-thickness polyimide with aluminum deposition (Figure 3.24).
For a chamber active gas, the helium based gas mixture, He:C2 H6 = 50:50, is adopted.
The mean of total radiation length inside the tracking volume for a signal positron isabout 2 × 10−3 X0 . It mainly comes from a material of chambers such as cathode foil

3.4

Drift chamber

Figure 3.19: Element of a drift chamber module.

y−Axis [cm]y−Axis [cm]Figure 3.20: Section of wires in two layers.

x−Axis [cm]x−Axis [cm]Figure 3.21: Contour line of the po- Figure 3.22: Particle drift line to eachwire.
tential.

25

26

3. Detector and Setup

Figure 3.23: Stretched wires on a drift chamber module (mm). Thereis no support frame at the target side.

Figure 3.24: Cell and support of drift chamber.

and wires (1.9 × 10−3 X0 ) and other little contribution is from the helium atmosphereand the chamber gas (0.26 × 10−3 X0 ).
The drift chamber measures two-dimensional hit positions along z and ϕ direction
and rough hit timings. For the geometrical reason, all wires are aligned in parallel withz axis and there is no crossing wire. To reconstruct two-dimensional positions, a special
periodical shape of cathode named ‘Vernier Pad’ is adopted with the same direction ofwires for z measurement. Figure 3.25 shows a schematic view of the vernier-pad method
on cathode using a ‘zig-zag’ shape strip.

Figure 3.25: View of vernier pad.

There are four cathode channels to be read out per one anode sense wire. The isolationof cathodes is formed by etching on two cathode foils at both upper and lower side. At
ﬁrst the hit wire with a resistance, 2200 Ω/m, tells the z position by the ratio of thecharges at both ends of the wire with an accuracy of 1 cm. Further the vernier structureof a 5 cm zig-zag period determines a more accurate z position within that period becauseof diﬀerent phases of verniers at both sides. The layers are shifted each other by one-half3.5

Timing counter

27

cell along a longitudinal direction in order to resolve ambiguity. Section 4.3.2 explains
the details of the reconstruction.
3.4.3

Readout electronics

For the readout at the pre-ampliﬁers, the anode wire is decoupled with 2.7 nF capacitor
with biased by typically 1850 V through 1 MΩ protection resistance. Because a waveform
sampler for the DCH accepts only a positive signal, two diﬀerent ampliﬁers of invertingand non-inverting types are developed for anode and cathode output respectively. The
ampliﬁer is fabricated on a 20.5 mm × 30.5 mm mini card with three input channels andeach consists of two operational ampliﬁers, OPA691 (current-feedback type, 190 MHz
bandwidth, Texas Instruments Inc.). The ampliﬁer has a gain of 52 and works under ±6
V.
In a chamber with double layers, read channels of anode at both sides of nine wires
needs totally 36 inputs, corresponding to 12 inverting mini-cards and decoupling capacitors. On the other hand four cathodes per a wire require 24 non-inverting mini-cards,
therefore totally 18 cards are mounted at one side (Figure 3.26).

Figure 3.26: Preampliﬁer cards at one side of drift chamber.

3.5

Timing counter

3.5.1

Design of timing counter

Timing counter (TIC) arrays detect a positron in the angular range of 0.08 < | cos θ| <0.35 after hitting the drift chamber (Figure 3.1). The arrays consist of two layers of
diﬀerent plastic scintillators along z direction and ϕ direction. The inner layer along ϕdirection is made of a ﬁne bending scintillation ﬁber and an avalanche photo diode (APD)
in order to tag z position with a precision of its pitch, thus it is called timing counter28

3. Detector and Setupz (TICZ). The outer layer along z direction gives the timing information of the ﬁnal hitof the positron from the drift chamber and also ϕ positions, therefore it is called timing
counter ϕ (TICP). TICP takes an important role to determine positron timing and TICZ
contributes for an eﬃcient trigger and a z determination, while TICP can also measure z
position roughly. The two sets of timing counter arrays are installed at down stream andup stream outside the drift chamber. In the 2009 run timing z counter was not used. A
plastic bag surrounds whole TIC detector and is ﬁlled with nitrogen gas to protect PMTs
of TICP from the helium gas.
3.5.2

Timing ϕ-counter

The ϕ counter is an array of 15 plastic scintillation bars, each of which is made of BC-404
by BICRON (SAINT-GOBAIN), with a 4 × 4 × 80 cm3 dimension. Figure 3.27 showsthat the bars are aligned with the same angular pitch as the DCH (10.5◦ ) along ϕ from−150◦ to 10◦ at a radius of 32 cm. It covers 160◦ ϕ-acceptance between −150◦ and 10◦ .
To make path lengths of positrons uniform, the bars are mounted with slant angle of 20◦
and formed into a hexagonal shape so that positrons do not graze the edge of bars asshown in Figure 3.28.
At both side of the bar, ﬁne-mesh PMTs of 2 inches, R5294 made by Hamamatsu
Photonics with an active area of 39 mm diameter, are attached with a tilting angle of 10◦
such that the angle between the PMT axis and the magnetic ﬁeld is 30◦ where the PMT
gain is maximized.

Figure 3.27: Picture of timing ϕ counter.

3.5.3

Timing z-counter

Bending 128 scintillating ﬁbers of 6 × 6 BCF-20 by BICRON (SAINT-GOBAIN) form
the z counter as shown in Figure 3.29. At both end of the ﬁber, 5 × 5 mm2 silicon

3.6

Liquid xenon detector

29

Figure 3.28: Design of timing ϕ counter.

avalanche photo-diodes, S8664-55 by Hamamatsu Photonics, are attached. The ﬁber is
optically separated at a center.

3.6

Liquid xenon detector

3.6.1

Property of liquid xenon scintillator

For the MEG experiment we constructed the world’s largest liquid xenon detector of 900liter volume (2.7 tons in weight) by developing innovative technologies. That allows theexcellent sensitivity for a µ → eγ search.
The use of liquid xenon as a scintillator has many advantages compared with otherscintillators. Its excellent property takes important roles on various ongoing projects suchas a dark matter search, a neutrinoless double beta decay search, a gamma ray astronomy,
medical applications such as positron emission tomography (PET) and so on. A shortsummary of the advantage is listed as follows:• High density 2.95 g/cm3 and short radiation length X0 = 2.77 (cm)• High light yield, 80% of NaI(Tl)• Fast response of 45 ns for gamma rays
• No absorption of scintillation light in liquid xenon

30

3. Detector and Setup

Figure 3.29: Timing z counter and 1 cm × 1 cm APD for scintillation ﬁbers. The ﬁbers
are mounted on timing ϕ bars.

• Uniform because of liquid• Particle discrimination
There are, however, some diﬃculties for the following reasons:• Expensive• Stable cooling in liquid phase at low temperature• High purity to avoid absorption of the scintillation light by contaminations• Detection of vacuum ultraviolet (VUV) scintillation lightThanks to various studies with prototype detectors, all concerning were solved in the
MEG LXe detector [29, 30].
3.6.2

Liquid xenon

The scintillation light in noble gases is attributed to the decay of excited dimers (Xe∗2 ), or
excimers in other words, but not a excited atoms (Xe∗ ) to the ground state, thus there is
no absorption by itself. For argon, krypton and xenon, the luminescence emission bands,

3.6

31

Liquid xenon detector

that is scintillation wavelength, are almost identical between liquid, solid, and gas phases,
except for neon. The characteristics of liquid rare gases are listed in Table 4 and liquid
xenon shows the highest stopping power and shortest decay time with high scintillation
light yield, however the scintillation light with a short wave length (VUV, λ = 175 nm)
is diﬃcult to detect. The property of xenon is summarized in Table 5.
Table 4: The main characteristics of Ar, Kr and Xe as scintillators.

3ρ (g/cm )Z
λ (nm)
Boiling T(K)dE/dx (m.i.p.) (MeV/cm)
X0 (cm)Moliere radius (cm)τ (ns)

Ar
1.39
18
128
87.3
2.11
14.0
7.3
6 / 1000

Kr
2.45
36
147
119.9
3.45
4.76
4.7
2 / 91

Xe
2.98
54
178
167.1
3.89
2.87
4.1
4 / 22 / 45

Scintillation process Injection of ionizing radiation into xenon produces excited atoms(Xe∗ ) or ions (Xe+ ). Accordingly, there are two types of scintillation processes with adiﬀerent W value and decay time. The ratio of two is determined by a deposited energy
density, thus it depends on injected particles. The scintillation pulse from alpha particles
is faster than that from gamma rays or electrons because of its large dE/dx, and thisproperty is useful to discriminate particles.
At ﬁnal stage, however, the scintillation light is emitted from a decay of the excimer,∗
Xe2 → 2Xe + hν, for all the scintillation processes. The excimer has mainly two excited
3 +molecular state of singlet 1 Σ+u and triplet Σu . The decay time of singlet state has much
shorter than triplet state, therefore two diﬀerent time constants appear depending on theprocess. In the case of alpha particle, singlet state has 4.2 ns decay time and triplet has
22 ns, while these depends on excited species.
The faster scintillation process occurs in such a way that excited atoms instantly form
excimers and then emit photons,
Xe∗ + Xe + Xe → Xe∗2 + Xe,
Xe∗2 → 2Xe + hν.

(24)
(25)

Another electron-ion recombination process from Xe+ is slower than direct excitation,
Xe+ + Xe
−
Xe+
2 +e
Xe∗∗
Xe∗ + Xe + Xe
Xe∗2

→
→
→
→
→

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

(26)
(27)
(28)
(29)
(30)

3. Detector and Setup
Table 5: Properties of LXe.
Material Properties
Atomic Number
Atomic Weight
Density at 161.4 K
Boiling point
Melting point
Triple point (temperature)
Triple point (pressure)
Radiation length
Critical Energy
Mollier radius
Scinti. wavelength (peak±FWHM)
Refractive index at 175 nm
Wph for electron
Wph for α particles
Decay time (recombination)
Decay time (fast components)
Decay time (slow components)
Absorption length
Scattering length

Value & Unit54
131.2932.978 g/cm3
165.1 K
161.4 K
161.3 K
0.805 atm
2.77 cm
14.5 MeV
4.2 cm(178 ± 14) nm
1.57 to 1.72
21.6 eV17.9 eV
45 ns
4.2 ns22 ns> 100 cm
29 cm to 50 cm

Ref.
[31]
[32]
[31]
[31]
[33]
[33]
[31]
[34]
[34]
[35]
[36, 37, 40]
[38]
[38]
[39]
[39]
[39]
[40, 41, 42, 43]2

Attenuation Coefficients [cm / g]32

Total Attenuation

Photoelectric Absorption

Scattering

Pair
Production

Photon Energy [MeV]

Figure 3.30: Photon reaction in liquid xenon.

3.6

Liquid xenon detector

33

The recombination process with 45 ns slower decay component is dominant in scintillation
light from electrons and also from gamma rays. For gamma rays the pair production occurs
around MeV scale as shown in Figure 3.30.
The liquid state has the beneﬁt of homogeneity, however, to keep liquid state needs
special technique because of its narrow temperature range. Figure 3.31 shows phase
diagram of xenon and liquid phase should be kept between 161 and 165 K at 1 atom.

Pressure [atm. absolute]

102liquid

10

solid

gas

1

10

−1

120

140

160

180

200

220

240

260

Temperature [K]Figure 3.31: Xenon phase diagram.

The eﬀect of radioisotope of xenon is negligible in our case from the viewpoint of
the rate and the energy. The impurities in the liquid xenon should be removed with apuriﬁcation system not to lose a xenon scintillation light by absorption. There is no self
absorption in xenon, but contaminations such as oxygen, nitrogen and water decreasea light yield of short-wavelength scintillation light (Figures 3.32 and 3.33). Not only a
puriﬁcation system but also a light yield monitor is needed for a stable operation of theliquid xenon detector.
3.6.3

Photo-multiplier tube

Under 50 Gauss magnetic ﬁeld the PMT for the LXe detector has to work in the 165 K
liquid xenon up to absolute pressure of 0.3 MPa and also has to detect high-rate VUV (λ ∼178 nm) photons. Materials of PMTs should be low because the gamma-ray has to traverse
the PMTs on the gamma-ray entrance face. Furthermore the MEG experiment requires a
low current operation because a heat generation accumulated by many 846 PMTs makes
it hard to cool xenon. A new PMT with metal channel dynodes was developed for the
MEG experiment in collaboration with Hamamatsu Photonics (Table 6, Figure 3.34).

3. Detector and Setup
Absorption coefficient (m-1 )34

Oxygen1

Xe scintillation spectrum

0.1

Water vapor

0.01
130

140

150

160

170

180

190

200

Wave length (nm)Absorption in H 2 O-doped Xe

Absorption in O 2 -doped Xe
I / I0I / I0Figure 3.32: Absorption spectrum by each contamination in liquid xenon [44].

1

100 ppb

1

200 ppb
1 ppm

100 ppb

5 ppm

200 ppb
1010 ppm

10−1

−1

1 ppm
5 ppm
10 ppm

−2

10

0

−2

10

20

30

40

50

60

10

0

10

20

30

40

50

Distance [cm]Distance [cm]Figure 3.33: Absorption by distance and contamination.

The window of the PMT is made of synthetic quartz glass, which is transparent between 160 and a few thousands nano-meter wavelength, with a 80% transparency aroundλ ∼ 178 nm without using a wavelength shifter. The photo-cathode material is bi-alkali
K-Cs-Sb, which has better sensitivity than Rb-Cs-Sb adopted in the initial version of
PMT. Bialkali has a high resistance and its large dependence by temperature. To makea uniform response for temperature and on cathode, aluminum stripes of 4% area aredeposited on the photo-cathode to avoid the resistivity of bialkali (Figure 3.35). The QE
is estimated to be about 15%.
High-resistance resistors are used in the voltage divider of the PMT in order to minimize the heat dissipation (Figure 3.36). In order to avoid the problem of the over-linearity
at high-rate environment, Zener diodes are inserted in parallel to the last two stages of
the resistive divider for twelve-step dynodes and keep a voltage around 85 V.
Thanks to the compensation coils of the COBRA the magnetic ﬁeld becomes weakunder 50 Gauss around the LXe detector as shown in Figure 3.16. The eﬀect of magnetic

3.6

Liquid xenon detector

35

Table 6: Properties of the PMT (R9869). These are typical values.
Size
Active area size
PMT length
Photo-cathode material
Dynode type
Number of dynode
Typical HV
Typical gain
Typical QE
Rise time
Typical Transit time
Typical Transit Time Spread

57 mm ϕ45 mm ϕ32 mm
K-Cs-Sb
Metal channel
12900 V
1 × 106
15 %2 nsec12.5 nsec
0.75 nsec

Figure 3.34: Schematic view of PMT R9288.

Figure 3.35: Photo-multiplier tube for the LXe detector. Aluminum stripe makes a ﬂat
response.

36

3. Detector and Setup

K

DY1

R1

DY2

R2

DY3

R3

DY4

R4

DY5

R5

DY6

R6

DY7

R7

DY8

R8

DY9

R9

DY10

R10

DY11

P

DY12

R17

R14

R15

R16

R11

R12

R13

R20

Z1

C4

R21

R19

Z2
C5

C1

R1,R12,R13 : 2MΩ 1%, 1/8W
R2-11 :
1MΩ 1%, 1/8W
R14-R16 :51Ω 1%, 1/8W
R17 :10kΩ 1%, 1/8W
R18 :10kΩ 1%, 1/4W
R19-R21 :100kΩ 1%, 1/8W

C1-C3 :
C4, C5 :
Z1 :
Z2 :

C2

0.022µF, 1kV
0.01µF, 2kV

C3

R18

+HV
(RG-188A/U)

RD68S
RD82S

SignalOutput(RG-196A/U)

Figure 3.36: Divider circuit of photo-multiplier tube.

Relative output [%]ﬁeld was measured by three directions shown in Figure 3.37, because the PMTs aremounted on six diﬀerent faces. There are larger decreases on lateral faces than others but
no signiﬁcant change on inner face as displayed in Figure 3.38. The measured decrease ofgains from COBRA oﬀ to on is about 10% on average and suﬃciently small.
140

x-axisYZy-axis120

z-axis

X

50

100

Entries
846
Mean
0.911
RMS
0.1009Underflow
6
Overflow2

all PMTs

40
80

30
PMTs (Inner face)

60

20
40

10

20

0
-300

0
-200

-100

0

100
200
300
Magnetic flux density [ Gauss]

Figure 3.37: Response of PMT against magnetic ﬁeld. Relative gain decrease is shownby three axes with diﬀerent magnetic ﬂux
densities.

0.5

0.6

0.7
0.8
0.9
1
1.1
1.2
Gain (COBRA ON) / Gain (COBRA Off)

Figure 3.38: PMT gain ratios for COBRA magnetic ﬁeld on / oﬀ. The ratio
is measured with LEDs and shown by all
PMTs. The gains of PMTs in the innerface have small changes as shown by asuperimposed distribution around 1.

3.6
3.6.4

Liquid xenon detector

37

The 900-liter liquid xenon detector

The LXe detector uses liquid xenon of 900 liter volume (∼800 liter in active volume). In
the liquid xenon 846 PMTs are mounted on all the six faces in liquid xenon. Figure 3.39
shows the C-shaped detector, which is mounted outside the magnet and covers 11% of
the solid angle.

Inside of the liquid xenon detector shows
the inner face on the left hand side andthe outer face on the right.
Figure 3.39: The liquid xenon detector.

Figure 3.40 shows schematic view of the LXe detector. The inner face and the outerface are in a cylindrical shape with a radius of 67.85 cm and 106.35 cm respectively, while
top and bottom face are on the planes of ϕ = ±60◦ and lateral down stream and up
stream face are on θ = (±30 + 90)◦ . The 38.5 cm depth of liquid xenon is corresponding
to 14 X0 . Development view of all faces is shown in Figure 3.41, where it can be seenthat PMTs on the detection inner face are arrayed most densely. A special coordinate (u,v, w) based on the inner face is deﬁned to describe a position of gamma-ray vertex in thedetector.

Rinner = 67.85 (cm)u = z
v = Rinner × arctan(y/x)√
w =x2 + y 2 − Rinner

(31)
(32)
(33)
(34)

38

3. Detector and Setup

Figure 3.40: Schematic view of the liquid xenon detector.

outer

top

100

downstream

upstream

80
60
40
20

v-axis148.6cm0

w-axis
inner

cm

.5

38

58cm

z

u-axisbottom96cm

Figure 3.41: Development view of the faces of liquid xenon detector. Each face is equippedwith 216, 234, 144 × 2 and 54 × 2 PMTs for inner, outer, lateral and top or bottom.

3.6
3.6.5

Liquid xenon detector

39

Constant calibration source in detector

The detector is equipped with LEDs and alpha sources in liquid xenon. The picture andlocation are shown in Figures 3.42 and 3.43.
241

Am source The point-like source of radioactive 241 Am had been developed for the
MEG experiment [45]. It emits alpha ray at 5.485 MeV (84.5%) and 5.443 MeV (13.0%).
The long 432-year life time is suitable for a year-long operation. Each source is optimized
to be ≈ 200 Bq activity. Backgrounds from sources are negligible because we are measuring the events at the energy above a few tens of MeV. Five alpha sources are attached ona thin tungsten wire of 100 µm diameter with 12.4 cm interval as shown in Figure 3.44,
and ﬁve wires are stretched from both lateral sides.
LED The blue-light LEDs with 470 nm wavelength are installed for the PMT gain
calibration. They are ﬂashed at 100 Hz for the gain measurement and constantly ﬂashedat 1 Hz during the physics data taking for the gain monitoring. The light from LEDs is
attenuated with pin hole and Teﬂon to illuminate PMTs more uniformly and to operate
stable voltage with suppressing light intensity. Each lateral face has six mounted positions
and ﬁve are in normal use for a constant calibration as shown in Figure 3.43.
3.6.6

Cryogenics

The cryostat of the MEG LXe detector requires thin window for the gamma-ray detection, non-magnetic materials, good thermal insulation and cooling system. The cryostat
consists of two diﬀerent inner and outer vessels to keep xenon cooling in liquid state. The
insulation layer between two vessels is in vacuum state and super insulation sheets are
installed to prevent a radiant heat from coming.
The entrance window for the gamma ray is made as thin as possible to suppress
gamma-ray conversion inside. Thanks to aluminum honeycomb panel covered with carbon
ﬁber plate at the inner vessel, the stainless steel part of the window is a thin of only 0.4mm at the inner vessel with a high-pressure tolerance up to 0.5 MPa, the entrance windowat the outer vessel is made of 0.7 mm-thick stainless steel. Its total thickness is 0.075 X0 .
Aluminum spacers are installed outside the PMT arrays to avoid scintillation light fromthe outside of the active volume and to save expensive xenon. A capacitance level meteris installed along outer face and 27 resistances of Pt-100 temperature sensors are attached
to monitor the xenon temperature. All cables for HVs, signals, sensors and LEDs, with
Teﬂon isolation to keep xenon clean, come out of the cryostat through the feedthroughs
at the top of the detector. A 200 W pulse-tube refrigerator, a turbo molecular pump
and a cryo-pumps are mounted at the top chimney of the detector [46]. The refrigerator
shown in Figure 3.45 was specially developed for the liquid xenon cooling in the MEG. It
enables to stably keep xenon in liquid with a help of the heater in the detector. In order
to cool down the vessels quickly for a transportation of xenon or to help the refrigerator
in normal operation, cooling pipes with liquid nitrogen are attached outside the outerand the lateral faces. In actual operation pipes on lateral side are sometimes used to cool
down xenon in addition to constant cooling of refrigerator.
The detector has two storages to keep whole amount of xenon outside the detector
for a maintenance or repair of the detector (Figure 3.46). One of the storages is a 1000-

3. Detector and Setupv (cm)

40

100

α source
LED

50

0

-50

-100
-100

Figure 3.42: Inside view ofthe detector shows 241 Am
source on wire and LED
on wall. Three LEDs with
diﬀerent attenuations aremounted by each points onlateral faces.

0

100

200
-u (cm)Figure 3.43: Projection view of 25 alpha sources on 5 wires andLEDs at 20 positions on the wall in the LXe detector. Filled 10
squares as LEDs are constantly used for a gain measurement
and others are not used.

Figure 3.44: Close-up view of 241 Am source on tensioned wire along beam axis. Diameteris 100 µm and longitudinal dimension is about 2 mm.

liter dewar in Figure 3.47 to keep xenon as a liquid with a refrigerator [47]. The quicktransfer and recovery is possible thanks to the liquid transportation and storage with aliquid pump. Another storage system consists of eight high-pressure gas tanks as shownin Figure 3.48 to store high-pressure gas of xenon stably for a long maintenance.
3.6.7

Puriﬁcation system

In order to purify xenon, two types of puriﬁcation system in liquid and gaseous phasewere developed [48]. The liquid puriﬁer system has oxidization-reduction ﬁlter made ofcopper and molecular sieves, which removes oxygen and water with 180 liter/h circulation
by piston-type liquid pump. The system was installed at the back side of the detector(Figure 3.49). Another puriﬁcation system in gas phase uses metal-heated getter to remove3.7

Setup for π 0 run

41

Figure 3.45: Pulse tube refrigerator for liquid xenon.

Figure 3.46: Cryogenics of the liquid xenon detector.

H2 O, O2 , CO, CO2 , N2 , H2 and hydro-carbon molecules from gaseous xenon down to 1.0
ppb level with slow circulation speed lower than 100 cm3 /hour in liquid.

3.7

Setup for π 0 run

3.7.1

Purpose and principle

The gamma ray from π 0 decay is the most important calibration source for the energy,
timing and positron with the LXe detector. The PSI beam facility can supply charged
pions as well as muons and electrons or positrons to the πE5 area. The π − beam isintroduced to the center of the MEG detector with the same beam line and there are42

3. Detector and Setup

Figure 3.47: Liquid xenon tank andgaseous puriﬁcation system.

Figure 3.48:
tank.

Gas xenon storage

two processes occurred. One is the charge exchange reaction (π − p → π 0 n → 2γn) andanother is the radiative capture reaction (π − p → γn). The energy region from π 0 decays
is between 54.9 MeV and 82.9 MeV, while a 129.4 MeV monochromatic gamma ray anda 8.9 MeV neutron are produced from the radiative capture. In addition the Dalitz decayof neutral pion (π 0 → γe+ e− ) is a coincident event of a gamma ray and a positron or anelectron. Thus it is useful to calibrate the drift chamber, too.
The energy range of the gamma-ray from the π 0 decay arises from the momentumof 28 MeV/c at the decay of the π 0 in the laboratory frame, after the charged pion π −exchanges a charge with a proton of a hydrogen at rest. It is interested that the energies
of generated two gamma rays from the π 0 decay are determined by the opening angle of
θγγ between two gammas,
m2π0,
2Eγ (Eπ0 − Eγ )(mπ− + mp )2 + m2π0 − m2n= 137.85 (MeV),=
2(mπ− + mp )cos θγγ =

(35)

Eπ 0

(36)

(mπ− , mπ0 , mp , mn ) = (139.57, 134.97, 938.27, 939.57) (MeV/c2 ),(37)

where Eγ is the energy of the gamma rays (Figure 3.51). Equation 37 shows masses ofcharged pion, neutral pion, proton and neutron respectively. Monochromatic gamma-rays

3.7

Setup for π 0 run

43

Figure 3.49: Liquid puriﬁer in 2009.

of 54.9 MeV and 82.9 MeV are obtained by selecting back-to-back events (Figure 3.52).
The lower peak of 54.9 MeV is very near to the signal energy from µ+ → e+ γ, that is why
we use it for the performance evaluation.
Because the LXe detector has a 2/3π acceptance along a ϕ direction, we need a tagging
detector with the same coverage at opposite side in order to detect the back-to-back twogamma-ray decay (Figure 3.50). A liquid hydrogen target placed at the center of the
MEG detector instead of a muon stopping target.

Figure 3.50: Overview of the setup in π 0 run.

3.7.2

Negative pion beam

In π 0 run a charged pion, π 0 , decays into two gamma rays from after a single-charge
exchange reaction of a negative charged pion and a proton. To obtain a monochromaticE γ (NaI(Tl)) (MeV)

3. Detector and Setup

Eγ (MeV)

44

90
85
80
75
70
65
60
55
50
45
40
150

155

160

165

170 175 180
Opening Angle

Figure 3.51: Gamma-ray energy
and opening angle of two gamma
rays in 2009 π 0 run at the LXe detector.

110
100

400

90

350

80

300

70

250

60

200

50

150

40

100

30

50

20

20

40

60
80
100
E γ (Liquid Xenon) (MeV)

0

Figure 3.52: Energy distribution of two
gamma rays from a π 0 decay with selecting
back-to-back decays in the LXe detector andin the NaI detector.

π 0 momentum of 28 MeV/c, we select a liquid hydrogen as a stopping target from the atrest charge exchange reaction (CEX) reaction, 1 H(π − , π 0 )n. The π − p system also results
in a radiative capture to a neutron and a gamma ray, nγ.
The ratio of two channels is known as Panofsky ratio,
P =σ(π − p → π 0 n),σ(π − p → γn)(38)which was measured in the previous experiments to be 1.5 [49, 50].
By a diﬀerent conﬁguration of BTS magnet and turning oﬀ the Wien ﬁlter, the negative
pion beam is tuned to have a 70.5 MeV/c momentum and the measured spot size at thehydrogen target of σx ∼ 8.5 mm and σy ∼ 7.5 mm. Because negative pions come from abunch of the pulse beam with many contaminations of electrons and cloud muons, morebackgrounds are observed than in the muon beam. We optimized the beam intensity
testing several conditions of the beam slits to consider some eﬀects in the LXe detector
such as a pileup.
3.7.3

Liquid hydrogen target

The liquid hydrogen (LH2 ) target has a cylindrical cell of a 50 mm diameter with a 75
mm length ﬁlled with ∼150 cc LH2 in 20 K cooling (Figure 3.53). The window of thetarget cell is made of a thin 135 µm mylar window. The target is inserted from down
stream side with a two meter long pipe.
A hydrogen buﬀer of two bottles with 47 liters each is connected to the LH2 cell
constantly with 2.5 bar in gas or 1.2 bar after the liquefaction. A ﬂow of the liquid helium
from the 250 liter dewars enables liquefaction of hydrogen with a pressure control.
The setup of the LH2 target takes about three days to remove the proton beam lineof Cockcroft-Walton accelerator, assemble the target system and cool a hydrogen. One

3.7

Setup for π 0 run

45

Figure 3.53: Liquid hydrogen target.

helium dewar is exhausted per a few days during π 0 run with a decrease of about 2.4%
per hour and the exchange of the dewar needs for a few hours. The π 0 run is usuallyplanned less than a few times per year because of its long running time about one or two
weeks.
3.7.4

NaI tagging detector

Because the LXe detector has the acceptance with 120◦ along ϕ direction and ±30◦ along
θ, it detects only one gamma ray from a back-to-back decay of π 0 . In order to obtain
monochromatic gamma-rays from the back-to-back decays, another calorimeter is required
at opposite side of the LXe detector. It allows the LXe detector to measure a lower
gamma-ray energy near to µ → eγ signal. The selection of opening angle depends on thegeometry of the detectors’ setup and it determines the energies of two gamma rays (Figure3.51). Therefore the only important issue for the tagging detector is to identify higher
energy of two gamma rays in a certain precision at the back-to-back position opposite toa measured position of the LXe detector and a high performance of the tagging detector
does not required. We adopted the movable NaI detector for that.
The tagging detector for one of two gamma rays consists of nine crystals of NaI(Tl)scintillator and two layers of plastic scintillator for the timing measurement. In order toscan the whole acceptance of the LXe detector, the NaI detector is mounted on a moverthat can get the same coverage of the LXe detector. The NaI mover has three movements
along ϕ direction from −57◦ to 57◦ , z direction from −350 mm to 350 mm correspondingθ direction from −24◦ to 24◦ and θ-rotation from −22◦ to 22◦ to always face the target.
Figure 3.54 (a) shows a picture of the mover. The array of the 3 × 3 NaIs is put on thestage and the plastic timing counter is attached in front of the central NaI.
There are some diﬃculties in the readout of the scintillation photons from the NaI
crystal by a PMT. The PMT gain varies depending on the position of the NaI due to themagnetic ﬁeld and it is diﬃcult to mount PMTs due to the limited space. Therefore, forthe detection of the scintillation photons, APDs and charge ampliﬁers are adopted. On
the other hand for the plastic scintillator, ﬁne-mesh PMTs are used for a photon detection
because there is no need of a severe energy selection for the plastic scintillators from a
trigger point of view.
Each NaI crystal has a size of 62.5 mm × 62.5 mm × 305 mm (11.8 X0 ) and its
acceptance of 6◦ or 0.07% solid angle per crystal is almost the same as the 1 PMT sizeon the inner face of the LXe detector. For the timing measurement the two plastic
scintillators of 60 mm × 60 mm × 7 mm are attached in front of the central NaI crystal.
A lead converter of 50 mm × 50 mm × 5 mm is put on the plastic with 2.2 X0 . About

46

3. Detector and Setup(b) NaI back plane.

(a) NaI mover.

(c) APDs alignment.

(d) Ampliﬁers and APD.

Figure 3.54: Apparatus of the NaI detector for π 0 decay run.

40% of gamma rays are counted in plastic scintillator. However, for the eﬃcient energy
measurement it can be removed if there is no need to measure timing.
We use the APD (H8664-1010, Hamamatsu Photonics) with a 10 mm × 10 mm active
area and 2 mm thickness. It works with 410 V and 50 gain typically and detects scintillation photons from the NaI crystal without shifting wavelength. One primary ampliﬁer
integrates charges and converts its to amplitude, then shaping ampliﬁer forms and ampliﬁes the signal. The charge ampliﬁer is gn0261 (GNomes Design co.,ltd.) developed by
Hiroshima University with a 19 mm × 19 mm size and 0.8 V/pC gain. On the other handthe shaping ampliﬁer is a small handmade ampliﬁer with a size of 13 mm × 18 mm andhas two outputs (Figures 3.54 (d) and 3.55). The waveform is analyzed in two diﬀerent
waveform sampler, both a DRS chip and a digitizer in the trigger board as later describedin Sections 3.9.4 and 3.9.5, then the pulse height is estimated. Figure 3.56 shows a sample
of a waveform obtained from the DRS with enough time window for a peak estimation.
The design principle of the APD module is the following.
• Detect photons in APD with light guide.
• Amplify and shape signal from APD.
• The temperature of APD is controlled with a Pt-100 temperature sensor and a
Peltier device.
• Heat radiator made of copper and fan to ventilate air inside module.
• Optical contact to lead laser (not used).

Setup for π 0 run

3.7
0

Amplitude (mV)

0
+12V
C6

C4

6.8u

0.1u

R2

C3

100

180p

220

2
R5

LM6172

4

R3

3

TRG OUT

-1200

-1000

-800

-600

-400

47

-200
0
Time (nsec)

47

U1A

ENE OUT

0

U2A

C7

C5

6.8u

0

0

R6
1

8

4

0

C2
1

8

3

+

56

-

4.7n

50

1k

+

2

LM6172

-

R1

200
150

R4

C1

250

27p

560

IN

47

0.1u
-12V

0

Figure 3.55: Shaping ampliﬁer.

Figure 3.56: Sample ofwaveform from NaI+APD
signal and a ﬁt with dottedline.

• Blue LED (Surface Mount Device type) coupled to NaI for a APD monitor.
• Both charge ampliﬁer and shaping ampliﬁer and easily replaceable.
Beside the optical window of the NaI, all the electronic parts are housed in a small spaceof cylindrical shape, 52 mm diameter with 10mm thickness. The module is attached at
the back plane of the NaI crystal with a total module size of 64 mm × 64 mm × 10 mmexcept for screw and fan as shown in Figure 3.57.

Acrylic light guide
andReflector (Al)Radiatior plane(Copper)
Fan
Cable
thru.

APD
Window

Peltier
deviceAPD

Conductor(Copper)

Chargeamp.

Shaperamp.

Light pulse
window

LED/Laser guide(a) APD module(b) Light guide

Figure 3.57: Layout of the APD module.

The APD can get less noise at low temperature, however, it is diﬃcult enough to cool
the all detector down because the APD shares a heat capacity with the NaI crystal. The
purpose of thermal control is to keep the gain of APD constant by cooling only around the
APD. With a help of the slow control system of SCS-2000, very precise thermal control
is enabled within 0.08% stability with the cooling ability of the 10 ◦ C lower than room
temperature. Figure 3.58 shows the stability of the controlled temperature around the

48

3. Detector and Setup

Voltage of Peltier

1.82
1.8
1.78
1.76
1.74
1.72
1.7
1.68
1.66
1.64
23-15h23-21h24-03h24-09h24-15h24-21h25-03h23-15h23-21h24-03h24-09h24-15h24-21h25-03h25-09h25-15h25-09h25-15hRadiator Temperature
Room Temperature

26.5
26
25.5
25
24.5
24
23.5
23
22.5

APD Temperature°

Temperature ( C)°

Temperature ( C)

Voltage (V)APD for two days in the lowest graph and the active voltage control for the Peltier device
in the top graph, and the thermal monitor of backplane and room temperature in the
middle graph. The details of the calibration and performance are given in Appendix C.1.

18.2

°

0.014 C σ

18.1
18
17.9
17.8

23-15h23-21h24-03h24-09h24-15h24-21h25-03h25-09h25-15hFigure 3.58: Thermal control and monitor of the central NaI crystal.

3.7.5

Pre-shower counter in front of the NaI

In front of the central NaI crystal, two layers of plastic scintillators are put for a timing
measurement (Figure 3.59). A lead converter of 5 mm thickness is put in the front to makea shower of charged particles into the plastic scintillator. The converter or the countercan be removed in case of unnecessary to measure timing and the eﬃciency of the energy
measurement accordingly increases. The scintillation is read out by two PMTs at bothsides of the scintillator with a light guide along the ϕ-direction. The PMTs are H6152
made by Hamamatsu Photonics with photocathode of 17.5 mm ϕ and ﬁne mesh dynodeto work in the magnetic ﬁeld.

3.8

Cockcroft-Walton proton accelerator

3.8.1

Purpose and principle

A Cockcroft-Walton (CW) proton accelerator dedicated for the MEG experiment is installed at the downstream side of the MEG detector for the calibration of the LXe detector.
Gamma rays from nuclear reaction of the proton in various targets are very useful for theconstant and frequent monitor of the scintillation light yield of the LXe detector, as wellas the estimation of energy response of whole detector. The normal target for the muon
beam can be replaced by the target for the CW. The replacement can automatically bedone by inserting the beam pipe with the CW target from the downstream side using abellows system. Frequent calibration is possible because the target exchange needs only
a few minutes, on the other hand it is absent during the π 0 run because the downstreamside is occupied with the hydrogen target.

3.8

Cockcroft-Walton proton accelerator

49

PMT

PMT

Plastic
scintillators

gamma ray

NaI

(60x60x7mm)

Lead converter(50x50x5mm)

NaI
PMT
Light guide

Figure 3.59: Timing counters in front of the NaI (Front view, side view and a picture).

Number of events

The normal target made of lithium tetraborate (Li2 B4 O7 ) provides reactions froma lithium and a boron. The most useful energy peak at 17.7 MeV is obtained fromthe resonant reaction in lithium, 73 Li(p,γ)84 Be with a resonance energy at Tp = 440 keV(ΓR ≃ 12.5 keV). The 17.7 MeV clear peaks can be a source of precise light yield monitor
within 1% and allows to estimate a correction factor to make the detector response uniform
over whole acceptance of the detector.
Another gamma-ray peaks from boron are coincidently given by the nuclear reaction,
1112
5 B(p,γ)6 C with a resonance at Tp = 163 keV (ΓR ≃ 5.3 keV). Available energies are
11.7 MeV depending on the incident proton energy and another 4.44 MeV from 12 C∗ atcoincident time, therefore it allows the timing measurement between timing counter andthe LXe detector, as well as the conﬁrmation of the energy scale or the light-yield monitor.
Figure 3.60 shows peaks in the LXe detector obtained in CW run.

1200

12

*

C → 12 C + γ

1000
800
19

F(p, α γ ) 16 O

B(p, γ )12 C

11

*

7

Li(p, γ ) 8 Be

600
400
200
0
0

5

10

15

20
Eγ [MeV]Figure 3.60: Energy peaks in the LXe detector with a use of the CW accelerator.

50

3. Detector and Setup

3.8.2

Cockcroft-Walton accelerator

For the calibration of the LXe detector, the CW accelerator for the MEG experimentproduces the proton beam up to 1 MeV with a intensity of 1012 sec−1 . Detailed property
is noted in Table 7 and Figure 3.61 shows the inside of the accelerator. The acceleratoris placed at the small separated area beside the πE5 area. From the downstream side
the accelerated protons are transported to the center of the MEG detector and the beam
direction is opposite and parallel to the muon beam line (Figure 3.62). The gamma rays
are produced at the center of the COBRA magnet as well as the gamma rays from RD,
therefore we can calibrate the LXe detector at the same condition as in the muon datataking.
Table 7: Properties of MEG CW accelerator.
Terminal energy range (keV)
Energy ripple (RMS eV)
Angular divergence (mrad×mrad)
Spot size at 3 m (cm×cm)
Energy setting reproducibility (%)
Energy stability (FWHM %)Range of current (µA)
Current stability (%)
Current reproducibility (%)
Duty cycle (%)
Start-up time (min)Figure 3.61: Electrode cascade inside
the CW accelerator.

Nominal300 − 900
< 500
5×5
<3×3
0.1
0.1
1 − 100
3
10
100
< 20

Measured at PSI
200 − 1100
< 50
∼4×4
<1
OK
OK
0.1 − 135
OK
OK
OK
< 15

Figure 3.62: CW beamline installed at
the down stream side of the MEG detector.

3.9
3.8.3

Electronics and data acquisition

51

Beamline and targeta.u.

We had tested various targets with changing proton energy. The current target made ofa thick lithium tetraborate (Li2 B4 O7 ) crystal disk is mounted at the end of the proton
12
beam line. We can select the reaction of 73 Li(p,γ)84 Be or 11
5 B(p,γ)6 C with the same target
by setting the proton kinematic energy to 500 or 700 keV, respectively.
Figure 3.63 shows a resonance of lithium and excitation curve for a thick target. The
right side peak of the proton beam in the ﬁgure is higher but it can interact with a thicklithium target on a ﬂat resonance. The emitted gamma-ray energy depends on both aproton energy and an emitted angle from proton, thus the lithium peak energy and thehigher energy of the boron peaks should be calculated. The peak energy from lithium isestimated to be 17.7 MeV with a 0.8% width in sigma in the case of our usual setup (500keV and FWHM < 0.5 keV), on the other hand the higher peak from boron gets 12.0
MeV energy.
Lithium ResonanceThick target excitation curve
Protron energy from CW

0.3

0.35

0.4

0.45

0.5

0.55

0.6
E (MeV)

Figure 3.63: Energy spectrum and resonance of the lithium target.

3.9

Electronics and data acquisition

3.9.1

MIDAS

The MEG experiment uses MIDAS (Maximum Integration Data Acquisition System)
developed at PSI as a DAQ system [51]. MIDAS works on many platforms and provides
a graphical interface with a full control on a web browser as a HTML format from a
HTTP server. The parameters of setup are written in the online database (ODB) andsome parameters can be shown in graphical history plots for a monitor. After front-end
programs running on diﬀerent machines collect data, event builder generates events frombuﬀers and logger system writes data. Thanks to the independent treatment of hardwares,
any access to speciﬁc hardware are possible with user’s implementation, though drivers
for typical DAQ hardware such as CAMAC, FASTBUS and VME are already available.
3.9.2

Slow control system

To control all hardwares remotely in the same way, most of modules for the control have acommunication based on the Midas Slow Control Bus (MSCB) developed at PSI. Modules
are grouped by purpose or physical location in the area and internally synchronized via
the MSCB bus, then each group has an external access with USB or Ethernet adapter.

52

3. Detector and Setup

A slow control frontend program runs in one of the online machines for the DAQ andall groups are centralized in it to be operated by the DAQ system. In addition, both amanual control with Character-based User Interface (CUI) and a control with a GraphicalUser-Interface (GUI) programs such as LabVIEW (by National Instruments) are remotely
possible.
One of the main purpose to use the slow control systems (SCS) is to store a log ofvarious monitors. The log is recored by external programs such as the MIDAS DAQ
system or LabVIEW. All measured values are stored in MIDAS at beginning of eachtaken run. Some of them are also recorded in MIDAS during a run with a constant slow
rate of 0.1 Hz independently from normal DAQ.
There are various modules of the SCS developed for the MEG experiment. The mostmodules can be operated under a stand-alone control with a programmable ﬁrmware
even if these lose commands from an external system, which allows the safe control andminimizes traﬃc. For example, all HV dividers in the MEG are based on the systemand control HV under speciﬁed limit of voltage and current, ramp it up gradually, equipwith auto-recovery and provide measured voltages and currents to the DAQ. For the mostcontrols we use SCS-2000 device with many functions. It accepts up to eight daughter
cards and a back panel to supply input or output channels up to 64, eight channels per
a card, is attached. The various cards such as ADC, DAC, some kinds of relays, current
source, voltage meter, capacitance meter, LED pulser are available. The systems in the
MEG experiment are listed in Table 8.
Table 8: Running systems based on SCS for the MEG experiment.
COBRA and BTS monitor, Beam status,
HV of LXe, TIC, DCH and NaI, Environment monitor such as temperature,
VME crate monitor, Gas system for DCH, Puriﬁer of xenon,
Control of 1000L LXe tank, Operation of LXe, LED pulser for LXe,CW accelerator and beam line, Operation of AmBe source (since 2010),
Operation of the liquid hydrogen target,
NaI mover system, NaI thermal control

3.9.3

Data acquisition

Because plenty of data mainly from over a thousand waveforms is recorded, there are a
few separated stages on DAQ for a reduction of data. At early stage in frontends before
data are concentrated to MIDAS, some data reductions for waveforms are performedby suppressing zero-signal waveform or re-binning uninteresting region except for peaks
or a baseline, which can be customized by run or event type. All events both fromtriggered data and periodical monitor are stored in a special data format for MIDAS, thencompressed and transferred to a archive system and also to a storage system of analysis
clusters. The data transfered to cluster are analyzed immediately and various plots are
generated to show data quality. The analyzed result is stored as a ROOT format in a few
separated ﬁles for the result of the reconstruction and for the raw data such as waveformor temperatures. The information of run is recorded in MySQL database commonly used

3.9Electronics and data acquisition

53

in whole MEG analysis. During data taking, a display to monitor a quality of a real-timedata is provided by the same analyzer program.
3.9.4

Trigger system

Except for the timing ﬁber z-counter, all signal waveforms from detectors are taken,
while signals for a trigger are arranged by each detector. The DCH does not take partin a µ+ → e+ γ trigger because of a slow signal and a necessity of a complex analysis toreconstruct events. Therefore the trigger for the muon decay is based on fast PMT signals
from the LXe detector and timing counter, which allows to acquire high-rate muons withless dead time. With a help of a late readout of capacitor buﬀer arrays in the waveform
digitizer (DRS), the trigger system also has an ability to take coincident π 0 -decay events
between fast PMT signals from the LXe detector and slow APD signals from the NaI
detector arriving a hundred nano seconds later. The topology of the trigger system hasa tree structure with triple layers and roughly selects kinematics of the gamma energy
and time diﬀerence and opening angle. Because the timing z-counter was absent in 2008
and 2009 run, the positron information only from the timing ϕ-counter determines thetrigger without precise direction match between a positron and a gamma. Nevertheless,the system shows enough trigger performance.
Trigger structure The following signals are formed for the trigger system.
• LXe inner face (216 PMTs, 1 channel per PMT)
• LXe lateral faces (288 PMTs, 1 channel per 4 PMTs)• LXe back+up+down faces (342 PMTs, 1 channel per 4 PMTs except one case with
1 channel per 2 PMTs)• TICP bars (60 PMTs, 1 channel per PMT)
• TICZ ﬁbers• DCH wires (64 wires, 1 channel per wire)• Auxiliary channels (NaI, LED, Beam)• Cosmic ray counters for DCH calibration
Two types of trigger boards make a tree structure with three layers and branches areclassiﬁed by a part of the detectors. At the ﬁrst stage seen by incoming signals, trigger
boards of VME 6U named Type1 accept signals in ﬂash analog to digital converters(FADC, AD9218, Analog Devices) and digitizes it at 100 MHz with 10 bits bin resolution
to acquire waveforms. Type2 trigger boards of VME9U at the second layer collect outputs
from Type1 boards with ﬁve boards and ﬁnally into one Type2 board and it makes a
trigger for DRS.

54

3. Detector and Setup

Figure 3.64: Flow of signal processing from detectors to the trigger and the waveform
digitizer (DRS).

Signal from gamma ray to trigger The signal from the LXe detector and the timing
ϕ-counter goes into active splitter boards, each with 16 input channels, to split the signal
for the waveform digitizer (DRS) and the trigger. The ampliﬁers with a high 1900 MHz
bandwidth (THS4509, Texas Instruments) of the active splitters send one of split signals
to DRS with inverting its polarity from negative to positive. Another split signals fromthe ampliﬁers with a 320 MHz bandwidth (AD8138, Analog Devices) are brought into
the trigger with summing a part of them. Figure 3.64 shows the signal ﬂow from thedetectors to the trigger system and the waveforms digitizer. From the inner face of the
LXe detector all the 216 channels go to the trigger, while outputs from 288 PMTs on
lateral faces and 342 PMTs on other faces are grouped every four PMTs.
Signal from positron to trigger The each signal from 60 PMTs of timing ϕ-counteris split to three in a passive splitter with a ratio of 8:1:1. The output of ten percent
is for a current monitor to check the lifetime of PMTs. Another ten percent goes toactive splitter, which is split to two signals with the same amplitude as the input. Oneof them is sent to a trigger board and the amplitude drops by 30% due to the limited
bandwidth. Another is acquired with DRS to determine the charge and the amplitude
but the timing. The largest 80% signals are shaped with double-threshold discriminator(DTD) which generates output of NIM signal. The lower threshold (25 mV) allows agood timing performance with a less eﬀect of a time walk as possible, while the higher
threshold prevents a fake signal due to noise or delta-ray hits. The output of 50ns-width
NIM signal is acquired also by the DRS.

3.9

Electronics and data acquisition

55

Other signals to trigger For various calibrations other detectors such as the NaI
detector, cosmic-ray telescope counters for DCH calibration and neutron generator canparticipate in trigger. Other trigger signals from pedestal, LED, laser and proton current
are also fed to the trigger system. Although the information of the primary proton current
provided at PSI is not currently used for triggers, it is useful to monitor beam status andcan optionally treat triggers depending on beam status if it were necessary.

Rate (Hz)

Trigger algorithm Trigger algorithm is programmable on FPGA (XILINX VirtexIIpro) and we deﬁne up to 32 trigger types as listed in Table 9. By each trigger type wecount the number of triggered events and record live and dead time for each trigger type.
Rate of each trigger can be adjusted by a pre-scale factor for each trigger type. Thesefacility enables to count intrinsic triggered events as well as DAQ events.
106
105
104
103
102
10
1
1
9
3
2
22
12
31 P
2
1
1
4
EG MEG QMEG ∆MEG ∆RAD LXe SeAlpha4 LED 8 DCH TICφ 7 LXe C
ed
Self SelfΘ
osm estaltW NARR lf Q in LX
Low
Wid
ics
id
OW Higheee0MCount / Run

Figure 3.65: Trigger rate by each trigger type in the µ+ → e+ γ taking run.

103

102

10
9
1
3
2
1
2
31 P
2
1
1
4
EG MEG QMEG ∆MEG ∆RAD LXe S2eAlpha4 LED 8 DCH2 TICφ 7 LXe C
ed
Self SelfΘ
osm estaltW NARR lf Q in LX
Low
Wid
ics
id
O
e
e
e
W High0M

Figure 3.66: Taken events by each trigger type with pre-scaled in the µ+ → e+ γ taking
run.

Thanks to the customized program and waveforms in trigger boards, ﬂexible andcomplicated trigger are possible. For example, it is possible to select alpha events in thetrigger under high-rate gamma-ray background by using information of waveform.
The DAQ has typically 84% live time and the triggered event rate of µ+ → e+ γ candidate was 5 Hz and total DAQ rate is 6.5 Hz.

56

3. Detector and Setup

Table 9: Trigger deﬁnition and pre-scaling factor (Prsc) in the MEG 2009 run. Approximately Qlow ∼ 30 MeV, Qhigh ∼ 40 MeV, TN ∼ 20 ns, Twide ∼ 40 ns and T0 ∼ 100 ns are
adopted.

Id
0
1
2
3
4
5
6

7
8
9
10
12
14
16
17
18
19
20
21
22
23
24
27
28
31

Trigger typeµ+ → e+ γµ+ → e+ γ , low energyµ+ → e+ γ , wide angleµ+ → e+ γ , wide Tµ+ → e+ νe ν µ γ narrow/ Dalitz decay in π 0µ+ → e+ νe ν µ γ wide T/ CW-B
π 0 with NaI

Prsc.
1
50
500
200
1000

π 0 w/o pre-shower
NaI alone
LXe alone HighLXe alone Low/ CW-Li / α
α selection
LED

20000
-

Michel DCH track+ TC hit
DCH track w/o outer
DCH track
Cosmic DCH
DCH single chamber
Cosmic Counter alone
TC alone w/ bar mult.
CR counter coinc.
TC Pair
LXe Cosmic
NaI counter alone
Pedestal

Logic(QLXe > Qhigh ) ∧ (|Teγ | < TN ) ∧ (Θeγ < ΘN )(QLXe > Qlow ) ∧ (|Teγ | < TN ) ∧ (Θeγ < ΘN )(QLXe > Qhigh ) ∧ (|Teγ | < TN ) ∧ (Θeγ < Θwide )(QLXe > Qhigh ) ∧ (|Teγ | < Twide ) ∧ (Θeγ < ΘN )(QLXe > Qlow ) ∧ (|Teγ | < TN )-(QLXe > Qlow ) ∧ (|Teγ | < Twide )-(QLXe > Qhigh ) ∧ (QN aI > Qthr )∧i (QN aI,4 > QN aI,i ) ∧ (|Tγγ | < T0 )∧ PMT patch on LXe ∧ !(Id=7)(QLXe > Qhigh ) ∧ (QN aIT C > Qthr ) ∧ (|Tγγ | < TN )(QN aI > Qthr )(QLXe > Qhigh )(QLXe > Qlow )

22000
10
7

10

107
2500
20000

(QLXe > Q0 ) ∧ α selection
100 Hz pulse from LED module(1 Hz in the physics run)
DCH hits ∧ TIC hits
DCH self
DCH self
Outer tagging CR counters
DCH single self
Cosmic-ray on TIC

Clock for pedestal

3.9
3.9.5

Electronics and data acquisition57

Waveform digitizer

We have two diﬀerent waveform samplers. One is for the trigger purpose and anotherfor the analysis. The slower FADC of 10 ns width/bin described in Section 3.9.4 is used
for the trigger and the faster Domino Ring Sampler (DRS) chip with gigahertz samplingis adopted for the analysis. Compared with conventional ADC or TDC, the shape ofwaveform gives more useful information such as pileup events, timing, noise, saturationand time constant to be used for particle identiﬁcation.
The fast waveform digitizer with switched capacitor arrays, DRS, is developed at PSI[52]. Since 2009 the MEG experiment has been using the fourth version of DRS (DRS4)
for the LXe detector, PMTs of the timing counter and the drift chambers. The DRS4
has 950 MHz bandwidth at a variable sampling rate up to 6 GHz with 1024 cells, eachwith more than 11 bits resolution. The charge in the cells is slowly read out later withcommercial FADC and each bin is digitized by 30 ns read-out time, that is totally a few
kHz in one chip. New feature of on-chip Phase Locked Loop (PLL) is implemented forsampling frequency, which allows sampling speed in a range from hundreds MHz to 6
GHz. Each chip has nine channels and ninth channel can be used to record the external
clock to synchronize all the DRS chips. If all the eight channels read the same signal, thenumber of cells increased up to 8192 or if half of the channels are used as a buﬀer, thedead time can be reduced.
Four DRS4 chips are mounted on the cards with 16 channels and two cards are inserted
on VME board. Each card receives a 20 MHz global clock signal from master quartz anddivides it to four DRSs with 0.78 MHz clock. In 2009 the four out of eight channels in
DRS4 are used to record four signals of the LXe detector at 1.6 GHz sampling. Thatmeans that there is possibility by using four spare channels to improve internal timing
accuracy with by doubling the sampling speed up to 3.2 GHz or to reduce dead time byusing spare as a buﬀer. These features can be switched on only with a ﬁrmware upgrade.
For drift chambers and APDs of the NaI detector sampling rate is set to 800 MHz (500
MHz in 2008) thanks to 500 ns delay in trigger.
3.9.6

Computer resource and online frontend

In the MEG experiment four frontends for the trigger and ﬁve frontends for the waveform
acquisition with DRS are running. The frontends are running on diﬀerent online computers. The online computers with DRS frontends are connected to each VME crate with an
optical ﬁber. One of the trigger frontends sends command to start or stop run with run
information as a master. The event builder on a powerful online computer accumulates
information from all frontends and constructs an event, then logger system stores each
event as data. In parallel, a slow control frontend collects information such as high voltages, temperatures and pressures from each slow control system, then the event builder
constructs these as a diﬀerent event type. Online computer provides DAQ interface via
HTTP protocol and ODB database. The run information is stored in ODB and SQL
database, and a header of run data.
When each run is ﬁnished, the data are transfered to oﬄine cluster, in order to analyze
the data, and also stored in an archive system with compressed in a GZIP format. The
plots to check the data quality are automatically generated and the analyzed data are
stored on oﬄine clusters for further analysis.

58

3. Detector and Setup

In 2009 it took ﬁve minutes to take 2000 events, which is the typical number of eventsfor each run. The data rate is 16.6 MB/s or 1.4 TB/day and the data is compressed bya factor of two. The total data size was 38 TB in 2009.
3.9.7

Monitor and analysis with ROME framework

Analysis and monitor framework in the MEG experiment base on the Root based Object oriented Midas Extension (ROME) developed at PSI [53]. The analyzer is called‘MEGAnalyzer’ and provides an event display in both online and oﬄine analysis. The
MEGAnalyzer reads raw data in the MIDAS format or analyzed data in the ROOT format
and writes the analysis results in ROOT format.
The ROME is a source code generator to provide a basic framework of analysis as
an extension of ROOT library for a general purpose. A C++ class is automaticallycreated according to a XML ﬁle that describes input and output parameters or tasks fora data analysis. Created framework can read conﬁguration parameters from XML ﬁle ordatabases such as MySQL or sqlite. The ROME also provides remote connection for adisplay or a remote access to ﬁles. The user can just insert analysis code in the skeletonclass generated by ROME. The online analysis allows a real time monitor of DAQ withanalyzing data even though data is not recorded. The tasks or outputs can be disabled
by ﬂags in conﬁguration XML ﬁle.
The monitor of the MEGAnalyzer can display a positron tracking and scintillation
light distribution of a gamma ray, waveforms, trigger information such as trigger rate,
hit map in timing counter and drift chambers and histograms of various results. The
MEGAnalyzer plays a major part of the analysis such as calibrations, event reconstruction
and selection, physics analysis and toy MC simulation with PDFs and also works in aninteractive mode.
3.9.8

Monte Carlo simulation

The Monte Carlo simulation comprises two parts. One is the detector simulation andanother is for the electronics simulation and event mixing.
The simulation of the detectors and kinematics of particles is based on GEANT3.21[54]. The beam transportation can also be simulated, however normally events start fromthe target at the center of the MEG detector. Both calculated and measured magnetic
ﬁeld for the COBRA magnet and BTS are available. A drift of electrons or ions canbe simulated with energy loss in gases or materials and drift according to an electricalﬁeld in a drift-chamber cell calculated with GARFIELD [27]. The scintillation photons
in the scintillation bars of the timing counter are determined by taking attenuation andreﬂection into account, and ﬁnally detected with a ﬂuctuation of the Poisson statistics.
The scintillation photons in the liquid xenon are generated in each energy deposit basedon W values depending on particle type. The propagation of scintillation light is simulatedwith various parameters such as reﬂections, absorption, Rayleigh scattering, transmissionof quartz PMT window and light speed. The event can be generated for the signal, Michel
decay, radiative muon decay and separated positron or gamma ray of each decay as wellas other backgrounds such as annihilation in ﬂight of positron. Various calibration events
such as cosmic ray, 241 Am alpha source, LED and π 0 decay or a beam transportation are
also simulated.

3.9

Electronics and data acquisition

59

After all event kinematics and response of the detector are simulated, the MEGBartender, which is based also on the ROME framework, can simulate electronics andwaveform and also mix simulated events. The MEGBartender generates raw data suchas waveform in the same format as in the data. To generate waveforms of the DCH
and the LXe detector, actual measured response is used. The 5.4 keV soft X-ray from54
Mn source causes a single-electron avalanche in drift chamber and its signal can be an
impulse response. For the LXe detector measured average waveform is used to obtainan impulse response. The signal is synthesized by convoluting hit information with theimpulse response. The signal in timing counter is generated with digital ﬁlters in softwareand random ﬂuctuations. The output data from the MEGBartender can be analyzed in
the MEGAnalyzer in the same way as for the real data.

60

4. Method of Event Reconstruction

4

Method of Event Reconstruction

4.1

Waveform analysis

4.1.1

Drift chamber

The drift chamber has the largest number of channels, with two channels from anodes
and four channels from cathode per each chamber cell. However, the number of hit wires
is limited and the most channels are quiet. In order to reduce data size, online frontend
of DRS can discard zero-signal waveform without recording. Common HV, circuit andground may bring a common-mode noise on the DCH ampliﬁers. Although recording thechannel with null signal is sometimes useful to subtract common noise from the signal
waveform on an event basis, we do not use it currently. At the beginning of 2009 run we
optimized the method of the zero-signal suppression.
Even for hit channels we can reduce data size by rebinning the part of the waveform
outside the region around the baseline and the signal peak. Because of ionization clusters
in single particle track, multiple peaks can appear. The following procedure is repeatedto ﬁnd the signal and obtain its charge. The maximum peaks in anode waveform overa certain threshold is recognized as a peak, then the width is taken by a full width atanother threshold and that region is masked for next peak search. Time of each peak istaken at single threshold and charge is integrated in optimized 50 ns window, which iscommon for six channels in the same cell.
4.1.2

Timing ϕ-counter

There are two signal outputs from each PMT of the timing ϕ counter; a squared NIM
pulse and raw PMT signal as described in Section 3.9.4. The PMT time is obtained bya template ﬁt with NIM pulse. The template is formed from the averaged signal. The
leading edge position and baseline are free parameters in the ﬁt, while the scale should beconstant because the pulse is the NIM standard. The NIM pulse delayed from a raw PMT
signal by about 20 ns and the integrated window for the raw signal is 30 ns wide. From
the raw signal the charge and the amplitude between estimated baseline and peak arecalculated. The charge is for the gain equalization and the amplitude is for the time-walkcorrection because NIM pulse is made at a certain threshold as described in Section 3.9.4.
4.1.3

Liquid xenon detector

In the online frontend the data size of the waveform of the LXe detector is reduced withrebinning by merging eight bins of the waveform histogram except for the important partof the waveform such as baseline, leading edge and peak. The rebinning suppression isenabled by threshold or event type, for example in pedestal trigger there is no suppression.
We applied some types of shaping for the waveform.
• The summed waveform over the PMTs with a charge above a certain threshold isused for the determination of the time window for the charge integration, a particle
discrimination and a pileup identiﬁcation.
• The high-pass ﬁltered waveform suppresses pileup since the signal with narrow width(48 ns) allows a short integrated region. The advantage of high pass ﬁlter is thatthe baseline is set to zero and the ﬂuctuation of the baseline calculation disappears.

4.1

Waveform analysis

61• The low-pass ﬁltered waveform, in a way of moving average, allows to reduce highfrequency noise, spikes and the ﬂuctuation of DRS cells, thus the waveform issmoothed.
• Template of noise for each DRS channel reduces biases around starting point oftrigger, which appeared in new version, DRS4.
• Template subtraction of the cell pedestal for each DRS channel is eﬀective.
• Correction of saturation is performed by scaling the template waveform according
to the time-over-threshold (ToT).
The following methods are tried, but these are not applied in current normal analysis.
• The Fast Fourier Transform (FFT).
• The diﬀerential waveform indicates the peak time of the raw signal at zero-crossing
time even if pileup exists.
• Event-by-event common noise reduction is implemented to compensate coherent
noise of low frequency.
• Fit with a waveform template or a function are not used because it takes a lot oftime.
The optimization of the shaping parameters was performed regarding the noise of
DRS, the pile up and the ﬂuctuation of the baseline. The gamma-ray reconstruction uses
a high-pass (HP) ﬁltered charge to reduce a pileup easily. For the calibration of the PMTs
we use a normal-integrated (NI) charge without high-pass ﬁlter because the waveform in
the LED run diﬀers from that of gamma rays.
Timing calculation uses raw waveform without any ﬁlters and shaping not to distortleading-edge shape. To determine the PMT time independently of pulse height, we estimate the leading timing at 30% of its amplitude. Because the ﬂuctuation of charge is lessthan that of amplitude, in fact, the timing is determined by charge corresponding to 30%
height with using the known relation between charge and amplitude.
4.1.4

NaI detector

Due to a trigger arrangement of both slow NaI signals and fast counter signals to be taken
at diﬀerent sampling speeds, some unused channels exist. The ﬂow of each input channel
is shown at the bottom in Figure 3.64. Each signal from four PMTs of the two timing
counters in front of the NaI and is taken by both 800 MHz (or 500 MHz in 2008) and 1.6
GHz DRS. For the analysis only 1.6 GHz DRS is used.
The ampliﬁer of APD has two output channels. The faster waveform sampled by 1.6
GHz DRS did not join in both analysis and trigger. It is noisy but provides optional use
of a fast trigger because of the fast leading edge. Another channel is taken by both 800
MHz DRS (Figure 3.56) and 1.6 GHz DRS (not used at all) and also by trigger waveform
digitizer. For the analysis the low-pass ﬁltered waveform of 800 MHz DRS or trigger
waveform can be used. The charge from APD is integrated in the charge ampliﬁer, thus
the amplitude of the waveform determines the energy. Hence, it is no problem that the62

4. Method of Event Reconstruction

tail of the waveform is out of range even in 800 MHz sampling as long as the peak can be
estimated. Finally, the amplitude is taken from trigger waveform in 2009 analysis because
spikes sometimes appear around a peak in DRS waveform.

4.2

Gamma-ray reconstruction

4.2.1

Scintillation photons

Scintillation photons in the liquid xenon are detected by 846 PMTs in the LXe detector.
The distribution of the PMT outputs allows to reconstruct the timing, the position andthe energy. Generally the number of scintillation photons in each PMT is obtained fromthe integrated charge of PMT with taking the quantum eﬃciency (QE), the collection
eﬃciency (CE) and the gain into account. We reconstruct the number of photo-electrons,
Npe,i = C × Qi /(Gi × CEi × e),(39)

and the number of scintillation photons,
Npho,i = Npe,i /(QEi ),(40)

where i means the index of PMTs, Gi is the gain of PMT, e is the elementary electriccharge, C is a constant factor from an attenuation related with electronics, QEi is a QE
and CEi is a CE of PMT. The calculation of those parameters using LEDs and alphasources in the detector are described in Section 6.2 and 6.3. Separate treatment of QE andgain is sometimes useful because QE depends on temperature while gains are sensitive
to magnetic ﬁeld and decrease by aging eﬀect. The Npe,i is used to determine statisticalerror and the Npho,i is an important parameter to reconstruct events in the LXe detector.
4.2.2

Position reconstruction

The position of the event vertex can be estimated from the light distribution on PMTs.
The position is necessary also for the timing and the energy reconstructions in the LXedetector. The incident angle or direction are diﬃcult to be reconstructed because agamma ray around signal energy region 52.8 MeV forms an electro-magnetic shower.
The direction of the gamma-ray is, therefore, determined by the line connecting thereconstructed position of the gamma-ray and the vertex position on the target, which isreconstructed by the positron tracking. Especially a performance near the inner face isimportant since the gamma ray around signal energy is converted within a few centimeter
after entering the liquid xenon. The main reconstruction methods tried in the MEG
experiment are the followings:• Method i) Weighted mean of PMT’s position• Method ii) Linear ﬁt with Monte Carlo simulation• Method iii) Fit with light distribution on a face
• Method iv) Least squares method

4.2

Gamma-ray reconstruction

63

The method i) is an useful way for the fast check or for the calibration such as an
identiﬁcation of alpha sources in the LXe detector or cosmic ray. The deeper eventfrom the inner face shows a better performance because many PMTs can detect photons.
However the shower development or the event at the detector edge give a bias for thereconstruction.
The second method is not currently applied because the parameters for the scintillation
light propagation in the Monte Carlo simulation is not well tuned.
The third method is to ﬁt a light distribution along the inner face and its peak indicatesthe position of u and v [55]. The depth from the inner face, w, is determined by the widthof ﬁtted distribution so that the wider distribution indicates the deeper depth.
The approach iv) is the current best way and is adopted for the MEG analysis in 2008
and 2009. This method is optimized for gamma rays from the target and uses some local
PMTs on the inner face near the incident position. The reconstruction using only the
inner face is due to the following reasons:
1. Most events are close to the inner face.
2. To avoid the shower ﬂuctuation in the outer face.
3. The densest area of PMTs with the closest distance each other.
The position (u, v, w) is determined by minimizing χ2position deﬁned as
χ2position =

P∑
MT
i

Npho,i − c × Ωi (u, v, w),
σpho,i (Npho,i )(41)

where c is the free parameter for ﬁtting as well as (u, v, w) and Ωi (u, v, w) is the solid
angle subtended by the photo-cathode of the i-th PMT, which is calculated numerically.
The statistical uncertainty of the number of√
scintillation photons, σpho,i (Npho,i ), is deﬁned
from that of photo electrons, σpe,i (Npe,i ) = Npe,i , as
(
)
Npe,i
σpho,i (Npho,i ) = σ
(42)
QEi
√
2
Npe,i
1
2+
=
(σ(QE
))
(σpe,i (Npe,i ))2 .
(43)
i
QEi4
QEi2
√
We assume that σ(QEi ) = 0 for simplicity, then σpho,i (Npho,i ) = Npho,i /QEi is obtained.
To avoid the shower ﬂuctuation and pile-up gamma-ray, χ2position (u, v, w) is minimizedin the ﬁt around the limited number of PMTs. After the ﬁrst ﬁt with a selection of
typically 45 PMTs around the PMT observing the largest number of photons, the second
ﬁt in a more restricted area with about 15 PMTs is performed. Then biases along u andw axis, which are observed in the MC, are corrected with the correlation estimated by
MC simulation. These biases are caused by the slant incidence of the gamma-ray on the
inner face, therefore there is no similar bias for v direction. The ﬂuctuation of the shower
development is also considered with a diﬀerence of χ2position as two ﬁtting results from
diﬀerent PMT selections. A correction is applied by the diﬀerence with comparing to the
MC. The performance including these correction is evaluated with actual measurement
later in Section 7.1.

64

4. Method of Event Reconstruction

4.2.3

Timing reconstruction

The timing of the gamma-ray hit is calculated from the arrival time of photons at each
PMT,
thit,i = tpmt,i − tdelay,i − tof f set,i ,(44)
where thit,i is the timing at vertex position, tpmt,i is the timing from the waveform analysis
and tof f set,i is the oﬀset of each channel.
The delay time tdelay,i occurs by a propagation time tprop (d, vef f ) in the liquid xenon
estimated from the distance d between PMTs and the vertex position and the eﬀective
velocity of scintillation light vef f , then we can obtaintdelay = tprop (d, vef f ) − tindir (η) − twalk (Npe ),(45)

where tindir (η) is a correction for the eﬀect of the indirect photons using the incident angle
η between the vertical axis of PMT surface and vertex position, which is caused by thereﬂection and the scatter at a large η.
Current estimation of tpmt,i is done at 30% of the peak height of the waveform insteadof at a ﬁxed threshold. The time-walk correction twalk (Npe ) is nevertheless introduced asa function of Npe , but the eﬀect is usually tiny except when a large pulse appears.
Finally we can determine the hit time tLXe with minimizing χ2time deﬁned as
χ2time =∑ (thit,i − tLXe )2i(σt,i (Npe ))2

(46)

,

where σt,i (Npe ) is time resolution of each PMT as a function of the number of photoelectrons [56].
4.2.4Energy reconstruction

For the reconstruction of the gamma-ray energy, a simple sum of all the number of photons
with a ﬁxed weight is the current best estimation. The weight is determined as thereciprocal of the coverage of the photo-cathode of the PMT on the face of the detector.
The weight is constant and independent of the reconstructed position and the charge.
The energy is then calculated from the sum of the number of photons after corrections
related to the solid angle for shallow events (w < 3 cm), the reconstructed position andthe measured light yield. Therefore the conversion formula can be described as below:
Energy = F (u, v, w) × S(u, v, w) × T (t) × C ×

846∑(Npho,i × Wi ),

(47)

i

where (u, v, w) is the coordinates in the liquid xenon detector deﬁned in Equations 32,
33, 34. F (u, v, w) is a non-uniformity correction factor by the reconstructed position,S(u, v, w) is a correction factor by the solid angle, T (t) is a correction to compensate thechange of light yield, C is conversion factor from the number of photons to energy, Wi is
the constant weight and Npho,i is the number of photon (Section 4.2.1) of the i-th PMT.

4.2
4.2.5

Gamma-ray reconstruction

65

Non-uniformity correction

For convenience we introduced the coordinates of u, v, w based on the geometry of themost illuminated inner face as described in Section 3.6.4. The faces are located in the (u,v, w)-coordinates (Figure 3.41) as:• inner : u-v plane, w = 0 (cm),• outer : u-v plane, w = 38.4 (cm),• top : w-u plane, v = 74.3 (cm),• bottom : w-u plane, v = −74.3 (cm),• up : upstream side,• down : downstream side.
Current energy reconstruction has a dependence along u, v and w and six faces of detector
have a diﬀerent behavior. This is because the vertex position is not taken into account in
the reconstructed number of photons with constant weights. The non-uniformity in thecurrent method is discussed here to know what kind of a position dependence exists.
The non-uniformity of the detector response projected to each face can be explainedroughly with a simpliﬁed model. For example the solid angle of each detector face, withignoring the ϕ-curvature of detector, is described as below,
AF aceΩF ace (x, y, z) =4π{(
arctan(+ arctan(+ arctanzz√(XM ax − x)2 + (YM ax − y)2 + z 2(XM ax − x)(YM ax + y)zz(
+ arctan(XM ax − x)(YM ax − y)√
(XM ax − x)2 + (YM ax + y)2 + z 2√√(XM ax + x)(YM ax + y))))

(XM ax + x)2 + (YM ax + y)2 + z 2)}(XM ax + x)(YM ax − y)

(XM ax + x)2 + (YM ax − y)2 + z 2

,

(48)

where x and y are the axes parallel to the face with a range of [−XM ax , XM ax ], [−YM ax , YM ax ],respectively, while z-axis is vertical to the face, which is located at z = 0. A factor AF ace
is an eﬀective area of the face for the photon detection.
For the signal MC the detected total number of photons on the inner face is ﬁtted
with this function as shown in Figures 4.1 (a), (b), (c) along u, v and w, respectively,
which shows a good agreement. In the total number of photons of all faces, a horizontal
dependence of u, v shows double peaks in a shape of ‘M’ as shown in Figure 4.1 (d), or fourpeaks in u-v plane, which is also described by summing the functions over the six faces.
Double peaks along parallel axes come from the dependence of vertical faces at both sides
as shown in Figure 4.1 (c). This model implies that the non-uniformity exists intrinsicallyby the geometry and the three-dimensional correction is required. Actual non-uniformity
is, however, more complicated due to the reﬂection, the curvature, the attenuation and4. Method of Event Reconstruction
×10

3

×103

χ2 / ndf
1280 / 26
Scale
3.262e+05 ± 7.488e+03
U edge(cm)25.88 ± 0.10
V edge(cm)54.84 ± 46.98
Depth(cm)5.668 ± 0.170

220
200
180
160
140
120
100
80
60
40

-30

-20

-10

0

10

20

30
u (cm)The number of photons on inner face

The number of photons on inner face66

χ2 / ndf
610.8 / 31
Scale
3.202e+05 ± 1.480e+03
V edge(cm)74.4 ± 0.0
U edge(cm)27.9 ± 1.9
Depth(cm)6.97 ± 0.14

220
200
180
160
140
120
100
80
60
40

-80

-60

(a) Along beam axis (u).
×10

-40

-20

0

20

40

60

80

v (cm)(b) Along vertical ϕ (v).

χ2 / ndf
447.9 / 14
Scale
3.249e+05 ± 4.083e+02
V edge(cm)28.57 ± 1.09
U edge(cm)28.57 ± 1.09

240
220
200
180
160
140
120
100
80
60

The number of photons on all faces

The number of photons on inner face

3

×10

3

440

420

400

380

360

40

0

5

10

15

20

25
w (cm)(c) Along depth (w).

-30

-20

-10

0

10

20

30
u (cm)(d) Total photons in all faces, along u.

Figure 4.1: Position dependence of the reconstructed scintillation photons only in the
inner face on (a) u, (b) v and (c) w. The red plots are the peaks scanning along axis andthe blue line is the function of the opening angle (Equation 48). Position dependence ofthe reconstructed scintillation photons along u is shown in (d), where two peaks appear
compared to (a) because of the photons from side walls.

the global bias of the calibration. Thus we ﬁnally use actual measurement of the nonuniformity for the correction, which will be shown in Section 6.5.1.
This model also suggests that the (u, v) dependence depends on gamma-ray energy
because the event distribution along depth and the shower development depends on theenergy. The diﬀerence is actually observed in 17.7, 54.9 and 82.9 MeV peaks. However,
if we correct the three-dimensional dependence, the eﬀect should become smaller.
The non-uniformity is intrinsic in our current reconstruction method, but there isa slight diﬀerence between the measurement and the MC in the asymmetry or in theposition of the double peaks. These can arise from biased estimation of QE or imperfectknowledge of the scintillation photon propagation in the liquid xenon. However, thediscrepancy between the data and the MC is not an issue for the energy reconstruction if
the non-uniformity is corrected by the measured dependence.
4.2.6

Pileup search and correction

Pileup in muon beam The LXe detector has no segmentation with homogeneous
liquid xenon. Pileup of the background gamma-ray occurs frequently according to theacceptance of the detector with 10% solid angle, a DC muon beam rate, typically about

4.2

Gamma-ray reconstruction

67

3×107 Hz and waveform time window of 640 ns or 48 ns integrated region. Possible sourcesof the gamma-ray background are, however, not only direct gamma rays from radiative
muon decay, but also annihilation in ﬂight (AIF) of positrons and bremsstrahlung of
positrons and so on. Therefore it is considered that low energy gamma rays are piled up
with a large energy deposit to be able to make a trigger. The MC simulation roughly
estimated that gamma rays above 0.5 MeV are piled up around the signal energy region
with around 0.1 probability in the case of 3×107 Hz muon intensity.

102

200 µm degrader

10-1

300 µm degrader

10

10-2

1

10-3

10-1
10-2

a.u.

(%)

Pileup identiﬁcation There are implemented two simple ways to identify pileup events.
One is to look for peaks in the light distribution observed by PMTs on the inner face.
The number of the identiﬁed peaks during the muon decay run is shown in Figure 4.2(a). Another method is to ﬁnd the pileup in the time-domain. This method is complementary to the previous spatial method because the timing diﬀerence can discriminate
pileups even if gamma rays arrive at the similar position with a diﬀerent time. Thanks tothe all waveforms taken, it is one possibility to ﬁnd multiple peaks in each waveform or
partially summed one. The other possibility is to ﬁnd the event with a large χ2 /NDF in
the ﬁtting of the time reconstruction described in Equation 46. The threshold of χ2 /NDF
to reject pileups is adjusted to 3 as shown in Figure 4.2 (b). This method is eﬀective
only to identify pileups. Unfolding the pile-up is done in the same way as in the spatial
method, as described in next paragraph.

10-4

1

2

3

4
5
6
The number of peaks

0

5

10

15
χ2/NDF(a) Distribution of the number of (b) Distribution of χ2 /NDF of thepeaks in the spatial light distribu- time reconstruction. Dotted plotstion.
show that of data and solid line
shows that of signal MC without
pileups.
Figure 4.2: Pileup discrimination by spatial or timing selection.

Pileup elimination It is quite important to correctly reconstruct the pileup event
instead of just discarding it since the probability of the pileup is as large as 7%. We
eliminate a small pileup by comparing the distribution of the PMT outputs with the
expected distribution. A look-up table of the expected PMT outputs is prepared withthe measured distribution with 17.7 MeV gamma-ray in the CW run. The table contains

68

4. Method of Event Reconstruction

average output of each PMT for each mesh (1.55 × 1.55 × 1.55 cm3 ) for the reconstructed
position. If the pileup is found, the elimination is performed in the following procedure.
1. Reconstruct energy in the usual way.
2. Fit PMT scintillation-photon distribution with the expected distribution stored in
the table except for pileup region.
3. Calculate the expectation of outputs around pileup region based on the ﬁrst reconstructed energy.
4. Replace photons of some PMTs around pileup region with those of the expectation.
5. Reconstruct energy again with replaced outputs of PMTs.
The light distribution in Figure 4.3 shows the elimination eﬀect on 2D PMT development
view.
100
80

21999

100

100

21999

80

100

60

80

40

60

20

40

0

20

6304
60

80

40

60

20

40

1806

6304

1806

517
0

20
0

148

-20

517

0

148

-20
42

-40

42

-40

-60

12

-80

-60

12

-80
3

-100
-100
z

-50

0

50

100

150

200

250

300
1

3

-100
-100
z

-50

0

50

100

150

200

250

300
1

(a) Before pileup elimination.
(b) After pileup elimination.
Figure 4.3: Photon distribution in PMTs with eliminating pileup.

With using the same table, dead PMT channels are also recovered. Replaced the number of scintillation photons of the dead channel are estimated from the photon averaged
over the three PMTs at the symmetric locations along u and v direction.
The replacement depends on the table, and it is not appropriate for cosmic ray, 241 Amalpha sources on wires and LED runs. This is because the light distribution of gamma
rays from central targets, such as muon or proton target, diﬀers from that for the special
calibration sources. The monitor of the light yield is performed without the elimination to
avoid uncertainties such as the diﬀerent energy region and light distribution by calibrationand the change of non-uniformity.
Diﬀerent pileup depending on beam status The probability density function (PDF)
of gamma-ray energy for the accidental background is prepared for pile-up and non-pileup
events separately.
In the case of π 0 run, the source of pileup is diﬀerent from that for the muons because
there are many high energy and low energy backgrounds. The background in the π 0
run comes from the π 0 decay (a ﬂat distribution between 54.9 and 82.9 MeV) and fromthe radiative capture of the charged pion (129 MeV gamma-ray and 8.9 MeV neutron).
Additionally many positrons, electrons and muons are also expected because the Wienﬁlter is not used in π 0 run. The diﬀerence of the background condition between the pionand the muon beam is taken into account in the estimation of the energy resolution in π 0
run.

4.3

4.3

Positron reconstruction

4.3.1

Strategy of position reconstruction

Positron reconstruction

69

In the positron spectrometer, positron tracks are reconstructed by drift chamber andtiming z-counter with combined analysis. Although there is no vertex detector, the extrapolation of positron tracks gives vertex position. The analysis ﬂow for the positron is
the following.
1. Reconstruct positron timing and position in the TICP
2. Reconstruct timing from the leading edge of anode-wire waveform and z position of
the hit by the vernier method for each wire in DCH
3. Cluster ﬁnding
4. Track ﬁnding
5. Track ﬁtting with the Kalman ﬁlter
The positron track is reconstructed by using the Kalman ﬁlter in order to include themultiple Coulomb scattering, the energy losses and the magnetic ﬁeld eﬀectively.
4.3.2

Hit z-position reconstruction in drift chamber

At ﬁrst we compute asymmetries of charges for anode wires and for vernier pads. On theanode wire the asymmetry between both ends is estimated. One of cathodes in the vernier
structure is read out at one side of down stream or up stream, while another cathode atanother side as shown in Figure 3.25 and we take the asymmetry between these for bothinner and outer foils. These asymmetries denoted as ϵa for anode wires, ϵ1 and ϵ2 forcathode pads, are calculated from a general equation,ϵ=

QU − QD,
QU + QD(49)

where QU is the charge read out at the upstream side and QD at the downstream side.
The parameter ϵa gives a rough z position with considering load impedance r and theresistance on wire, ρ = 2200 Ω/m as
(
)
r L
z=−
+
(50)
· ϵa ,
ρ 2
where the length of wire L depending on the wires.
In the vernier pads the precise z position in a zig-zag period is obtained from theangle α = arctan(ϵ2 /ϵ1 ). Because of the phase diﬀerence of π between upstream anddownstream readout on the plane and the phase diﬀerence of π/2 between inner andouter pad, the hits on a ϵ1 - ϵ2 plane shows a circle with phase of α corresponding to the
5 cm zig-zag period. Figure 4.4 shows the vernier α-circle. Finally the combination of the
global reconstruction from the wires and the local position in the vernier period gives theprecise z-position. Each line in Figure 4.5 indicates the n-th vernier periods on α-charge
division plane. Position is described from equation z = l · (α/2π + n − n0 ), where n0 is
the count of the central vernier and n is the vernier turn from down stream side, and l isthe 5 cm period of vernier.

70

4. Method of Event Reconstruction

Figure 4.5: Phase on vernier circle and anode charge
division.

Figure 4.4: Vernier circle.

4.3.3

Hit-timing reconstruction in timing-counter bar

The timing measured in the timing z-counter, TT C , is deﬁned as the timing at the ﬁrst
hit on the counter. The hit time on the k-th scintillator bar (k = 0-29), TT C,k is obtained
from measured time at PMTs at both ends, ti,k and to,k , with correcting time walk eﬀect
by using pulse height Ai,k and Ao,k from inner PMT close to target and outer PMT aroundthe edge of detector, respectively. With the factor of the time walk correction, fj,k (Aj,k ),distance from the hit point to the PMT, dk,j=i,o , the longitudinal length of bar L and theeﬀective velocity vT C in the bar (14.5 cm/ns), there is a relation asdk,j+ fj,k (Aj,k ) (j = i, o),vT C
L = dk,i + dk,o ,tj,k = TT C,k +

(51)
(52)

therefore with using the number of scintillation photons in each PMT, Ni,k and No,k , thereconstruction of zT C,k and TT C,k is obtained asvT C · |to,k − ti,k | L
+ ,
2
2
√
∑
Nj,k · (tj,k − fj,k (Aj,k ) − dk,j )
j=i,o
√
.
=
∑
Nj,k
j=i,o

|zT C,k − zof f set,k | =TT C,kIn 2008 we assume a model of time walk correction,1
fj,k (Aj,k ) = bj,k + cj,k √(j = i, o),
Aj,k

(53)
(54)

(55)

where bj,k and cj,k can be determined by a least χ2 method with collecting triple hits inadjacent three bars (k − 1, k, k + 1) as()2∑(tj,k−1 + tj,k+1 )2χ ≡tj,k −|dk =dk−1 =dk+1 ,Tk =Tk−1 =Tk+1 .
(56)
2
all triple events

4.3

Positron reconstruction

71

This correction improves the time resolution at least by a factor two. Additional logarithmic term is introduced in 2009 and the time walk correction of Equation 55 is replaced.
With a lower threshold Dj,k in DTD (described in Section 3.9.4) the correction factor in2009 is described as
√
(
)
Dj,k
Dj,k
′
fj,k (Aj,k ) = bj,k + c0,j,k+ c1,j,k log(j = i, o).
(57)
Aj,k
Aj,k
The unknown factors, b′j,k , c0,j,k , c1,j,k , are evaluated from the averaged waveform shape.
4.3.4

Track ﬁnding and ﬁtting

After all hits information are constructed both in drift chamber and in timing counter,reconstruction of positron tracking can proceed. Rough principle is described here to ﬁnd
positron tracking and ﬁt it with considering a loss of energy and the magnetic ﬁeld to
extract momentum.
Cluster ﬁnding A cluster means a collection of hits in single module by a single charged
particle. Separately from each cluster of each chamber, another larger cluster among
several modules is called a ‘track candidate’, which is a collection of previous clusters bya single track to be recognized by track ﬁnding in next step. Each drift chamber module
consists of two layers with shifting radially by a half size of the cell each other, thus
typically a minimum of two hits is found from a positron track in a chamber. Single hit
in a chamber is also recognized as a cluster if it is ﬁnally alone. Each layer has nine cells
along R, then at ﬁrst we cluster hits along R, then along z.
In each module, hits within three radially adjacent cells are clustered temporarily,then split if more than a few centimeter deviation along z from average in a category
is observed. The z average depends on the selection into a category, thus reﬁnement
proceeds by removing and reassembling hits with many iterations. Next we connect
clusters between modules.
Track ﬁnding In order to connect modules, at ﬁrst step we search for tracking seeds
with three clusters in modules. The search requests a radius larger than 24 cm, that is
because there are possibilities that• clusters existing at both side,• many clusters in the same track,• high momentum,• less hits than inside R.
What we know is the distance from the wire but not the direction from wire, namely acircle from the wire with free angle in x-y plane and we have to solve so called ‘left-rightambiguity’. The seeds of three clusters enable to suggest possible tracks with connecting
hits on the circles.
At ﬁrst we look for clusters with a radius larger than 24 cm except for modules at bothends along ϕ. The seed requires that the cluster radius at the middle module of the threeZ (cm)4. Method of Event Reconstruction

Y (cm)

72

0

30
20
10

-10

0
-10

-20
-20
-30

-30
-30

-20

-10

0

10

20

30
X (cm)

-30

-20

-10

0

10

20
30
X (cm)(a) x − y view(b) x − z view
Figure 4.6: Event display of positron tracking. Fitting with Kalman ﬁlter is performed
for clusters in a track candidate.

is shortest, diﬀerence of the radius is smaller than 2 cm and at least one cluster must
contain multi-hit cluster. Three modules must be adjacent within one skipped moduleand the diﬀerence of z must be within 4 cm per one interval of modules. If the seed isfound, rough track time is estimated.
Then we extract seeds at both side and ﬁnd connection to other clusters in othermodules. Finally we reconstruct the tracking time in DCH from all hits on the track andsearch for matched hit on the timing counter. The tracking time is extrapolated fromtiming counter with considering a propagation time and a momentum, which is estimatedby track ﬁtting described in the next section.
Track ﬁtting To obtain both a momentum and a precise track, track ﬁtting is performed for the found track. Our analysis method relies on the Kalman ﬁlter, which isbased on linear dynamic systems of a Bayesian model [57, 58]. It is eﬀective for tracks
with small number of hits or noise by environment, thus suitable for the positron tracking
in MEG experiment.
The features of the Kalman ﬁlter are• include eﬀects of multiple scattering, energy loss and non-uniform magnetic ﬁeld,• three-dimensional and complex trajectory can be reconstructed,• error propagation is taken into account.
The Kalman ﬁlter recursively estimates parameters set by each measurement in order.
For the ﬁt there are ﬁve free parameters, namely two position, two direction and one momentum of positron with in advance provided magnetic ﬁeld and materials. Fit example
is shown in Figure 4.6.

5. Run

5

73

Run

Since in 1999 the MEG experiment was approved at Paul Sherrer Institut there was along-term development such as the liquid xenon gamma-ray detector and the positron
spectrometer. At the end of 2007 we ﬁnished the construction of the detector and successfully performed an engineering run where we estimated the detector performance andtested the µ+ → e+ γ trigger as well. In 2008 we successfully took the ﬁrst physics data
for three months. With some improvements for the detectors the stable data acquisition
was carried out for two months in 2009.

5.1

First MEG physics run in 2008

5.1.1

Overview of 2008 run

The MEG experiment started the ﬁrst physics data taking on 12 September, 2008 andit continued for three months. During the run, the drift chamber was suﬀered from adischarge problem. Thanks to the puriﬁcation, the light yield of xenon was improving.
Two π 0 decay runs were performed to measure the performance of the LXe detector in
its all acceptance. The ﬁrst π 0 run in 2008 started at the end of July and ended on 1
September before the MEG physics data taking to evaluate all the performance. The
second π 0 data was taken for a short days period 18 to 23 in December to conﬁrm theperformance partially after the light yield increased. The regular shutdown period forthree months at PSI started at the end of December, then for next 2009 run we ﬁxed
problems of the drift chambers, the LXe detector and so on.
5.1.2

Run

Physics run During the physics run in 2008, 9.5 × 1013 muons stopped on the target in
total. For the purpose of the monitoring, calibrations and normalization eleven diﬀerent
trigger types were mixed in the run. The live time was 85% amounted to 3.3 Msec in total.
The dedicated run for the radiative decay (RD) events were performed under the lower
beam rate by a factor 25 and lower gamma-ray energy threshold of 25 MeV, although
RD trigger was mixed also in the physics run. The RD data mixed in the physics run areuseful for the normalization of muons and the background estimation, while the successful
observation of RD enables the estimation of the detector performance such as the relative
timing and the positron energy.
π 0 run In 2008 the performance was evaluated in all the acceptance of the LXe detector
by moving the NaI detector on 3 × 8 meshes, each with 3 × 3 PMT size on the innerface of the LXe detector. At each position 200-300k events were taken and took six hours
at each position. Every day during π 0 run, calibration data using LEDs, alpha sources
and cosmic rays were taken for three hours. The lead collimator in 2008 had vertical or
horizontal slits of 1 cm width with 1.8 cm thickness and 1.1M events were taken in total.
There was the second π 0 run with changing beam rate, to evaluate the performanceafter the improvement of the light yield by 40% and to measure the dependence of theperformance or backgrounds on the beam rate.

74

5. Run5.1.3

Detector status

Drift chamber The drift chamber system suﬀered from a discharged problem in 2008.
Because of a frequent discharge, the HV applied to the drift chambers were unstable forsome channels and some were out of operation, thus the detection eﬃciency was much
lower than expected especially at the end of 2008 run. The frequency of the discharge
gradually increased, and ﬁnally in all 32 planes of 16 modules, only 12 planes worked at
a nominal voltage (1850 V) and other 6 channels at a lower voltage. Figure 5.2 (a) shows
the history of the biased HV for each cells.
The discharge was caused by the helium gas at the end of the plane where HV wasbiased. To avoid an annihilation of positrons there is a helium in the COBRA magnet
except for around timing counters and 50% helium in drift chambers. To avoid themultiple scattering of the muon and positron, the inner bore of the COBRA is ﬁlled withhelium gas. The chamber gas is the mixture of helium and ethane. The helium gas
permeated to the weak part in the PCB little by little during the 2008 run.
Timing ϕ counter Till the end of October there was one broken channel on trigger
side and it was ﬁxed.
Timing z counter Timing z counter for z tagging of positron was not ready and not
used. Nevertheless the 2008 run could be performed with a reasonable trigger eﬃciency
even without the z-counter since the timing ϕ counter can also estimate z position in thetrigger by using the time diﬀerence between the PMTs at both ends.
LXe detector Three dead channels of PMTs existed with problems about one of signal
cables and two of HV lines. Additionally one strange shape of waveform and one unstable
gain of the PMT were also found. During the run other two PMTs got a large decreaseof the gain. However, it is not severe because these all were apart from a detection face.

5.2

MEG run in 2009

5.2.1

Overview of 2009 run

Before the 2009 physics run started the discharge problem of drift chamber was investigated and ﬁxed. The drift chamber was stably operated in whole 2009 run as shown in the
HV history in Figure 5.2. Additionally, the waveform digitizer chip (DRS) was upgraded
and the yield of liquid xenon scintillation light recovered before the 2009 run started.
Because other project using the same beam channel the MEG experiment got muons in
the later half of the year. The physics data taking was performed for two months in 2009,
which is 55% shorter than three-month run in 2008. The produced protons during the
MEG physics run is shown in Figure 5.1. Thanks to the improvement of the positroneﬃciency, the observed number of muon decays increased by a factor of two comparedto the run 2008. There were two setups of muon momentum degrader. A 200 µm thickdegrader was used at the ﬁrst half of runs, then 300 µm-thick degrader was used for thesecond half.

Integrated primary proton charge (C)5.2

MEG run in 2009

75

7000

2008

6000
5000
4000

2009

3000
2000
1000
0
03/09

14/09

26/09

07/10

19/10

30/10

11/11

22/11

04/12

16/12

27/12
Date

Figure 5.1: Integrated muons at PSI during the MEG data taking.

5.2.2

Degrader setting

In 2008 the Mylar degrader had 300 µm thickness at the center of BTS magnet outside
the COBRA magnet. The 2009 physics run started with 200 µm degrader to shift the
stopping distribution inside of target to the center. This was estimated in the Monte
Carlo simulation but it was not totally optimized. At the end of November 2010, thedegrader thickness was reverted to 300 µm because it was found that in 200 µm degrader
the event distribution had a larger asymmetry along beam axis and the positron hits inthe timing counter at the down stream side four times larger compared with up streamside. The stopping eﬃciency of the muon target is estimated to be about 56% and 82%
for 200 µm and 300 µm degrader, respectively. There were diﬀerent background and event
distribution between 200 µm and 300 µm degraders, which is taken into account in thephysics analysis.
5.2.3

Run

Physics run Delivered muon rate at the primary proton current of 2 mA is shown in
Table 10. For example stopping rate in 300 µm degrader at 2.2 mA is 2.9 × 107 µ+ · s−1 .
The muon rate was optimized with the beam slits by considering the background. Twelve
types of the trigger are mixed in the physics run as shown in Figures 3.65 and 3.66. The
200 µm degrader run started at the end of October and ran for 18 days with 10 Hz DAQ
rate and 75% live time, while the 300 µm degrader run was taken for 26 days with 6Hz
DAQ rate and 84% live time. LED monitoring run was performed everyday during thephysics data taking. Full sets of calibration data were taken three times a week, which
includes LED data with beam on and oﬀ, LED gain calibration, alpha source data andthe CW data. In total 94 TB data was collected and run ﬁnished at the end of December.
π 0 run The period of π 0 run is shorter than 2008 π 0 run and statistics for one measurement at the region in 3 × 3 PMT size also reduced from 300k to 200k events. The
run was performed for twelve days from the middle of October. Diﬀerent lead collimatorswith long slits along beam axis are prepared for the position measurement at two diﬀerent
positions on the inner face.

76

5. RunTable 10: Muon rate delivered at the center of the detector in 2 mA primary proton
current.
Beam tuning
2008 setup
2009 setup

5.2.4

200 µm Degrader(4.3 ×107 µ+ · s−1 )3.7 ×107 µ+ · s−1

300 µm Degrader
3.7 ×107 µ+ · s−1
3.2 ×107 µ+ · s−1

Detector status

Recovery of the positron eﬃciency In 2008 discharge on drift chambers frequently
happened as noted in Section 5.1.3. Figure 5.2 (b) shows history of the HV applied for
all cells in 2009 run. Compared with previous 2008 (a) it is quite stable during physics
data taking. Accordingly positron eﬃciency recovered.

Plane ID

(V)

1900

30

1850

25

1800

20

1750

15

1700
1650

10

1600

5
0

1550

18/09 25/09 02/10 09/10 16/10 23/10 30/10 06/11 13/11 20/11 27/11 04/12 11/12
Date / 2008

1500

Plane ID(a) HV history in 2008.
1900

30

(V)

1850

25

1800

20

1750

15

1700
1650

10

1600

5
0

1550

12/11

19/11

26/11

03/12

10/12

17/12
Date / 2009

1500(b) HV history in 2009.
Figure 5.2: HV history applied for each drift chamber cell in 2008 (a) and 2009 (b).

The LXe detector A new liquid puriﬁcation system of O2 getter was installed, which
can remove oxygen and also water. The liquid xenon circulated through the puriﬁer at
180 liter/h transfer speed with new pump, then about 8k liters liquid xenon was circulated
corresponding to nine times volume of the LXe detector. Before the 2009 run, the lightyield increased about 2.5 times from the lowest in 2008 or 1.6 times from the end of 2008by the puriﬁcation.
Some bad channels of PMTs were ﬁxed and some PMTs with larger gain shift, which
is described later in Section 6.2.2, were replaced. Evacuation pump and cooling pipe werealso updated.

5.2

MEG run in 200977

New version of DRS waveform digitizer For the LXe detector and the drift chamber
the DRS was upgraded from version 2 to 4, while the timing ϕ-counter used the sameversion of DRS (version 3). New version of DRS has less eﬀect of temperature drifts, agood linearity up to 1 Volt, no ghost pulses due to residual charge, better timing accuracy
with 20 MHz global synchronization between boards and ability of faster sampling up to
6 GHz, though the sampling rate and bins were kept at the same as 2008 setup of 1.6
GHz and 1024 cells. Cross talks with a clock signal disappeared in new version. Other
small problems occurred in 2009 that the baseline got some biases around starting cellsof triggered point and a few spike structure. It was, however, not a big issue since it canbe solved in oﬄine analysis by means of the templates of cell pedestals and baselines.
Trigger The signal received at the trigger board is three times larger compared with
DRS boards because of the attenuation register 1/3 at the input of DRS. Sometimes thetrigger suﬀered from the saturation, for instance, for the shallow event where the the some
PMTs in the inner face receive larger amount of light. The dynamic range of the trigger
improved from 1 to 2 Volt by replacing frontend cards for a part of PMTs of the LXedetector. Thanks to the improved discrimination of the waveform shape at the trigger
side because of the improved light yield, alpha particles were able to be separated fromgamma rays in online (Figure 5.3). It allows to mix the trigger for the alpha events inthe physics run in order to monitor the detector performance.

98% α

103

102

γ

10

1
4

6
8
10
12
Charge / Height of sum waveform

Figure 5.3: Triggered events as alpha particles with a selection eﬃciency of 98% in muon
beam. Horizontal axis shows a ratio of charge to height for a precise discrimination in
oﬄine analysis as described later in Section 6.3.3.

78

6. Calibration and Monitor of the Liquid Xenon Detector

Part IIIThe Liquid Xenon Gamma-Ray
Detector
6

Calibration and Monitor of the Liquid Xenon Detector

6.1

Outlook of calibrations

For a long-time run, it is very important to keep a quality of a gamma-ray measurement
by a monitor and a calibration. First concern is the light yield of scintillation photons inliquid xenon, which depends on a purity and it might change. Second concern is an aging
eﬀect of PMTs due to the high-rate environment. However, these can be overcome by aprecise and frequent monitor. One of the important purposes in this section is to ensure
the stability or to trace the change.
The excellent detector performance is important for the MEG experiment to achieve agood sensitivity of µ → eγ , such as the better timing resolution thanks to the fast responseof the liquid xenon scintillation. Especially, the energy calibration is the most important.
As indicated by Equation 18, the number of accidental background is proportional to asquare of a gamma-ray energy resolution and it is a dominant factor. Therefore the energy
reconstruction with a good resolution, long-term stability, and uniform response for all
gamma-ray interaction points is crucial to suppress backgrounds of the µ → eγ decay.
In order to calibrate and monitor the LXe detector, various methods are prepared for
the MEG experiment. For a frequent monitor and calibration of PMTs, alpha sources andLEDs are used. The nuclear reaction of protons, 73 Li(p,γ)84 Be, by using Cockcroft-Walton(CW) accelerator with the lithium target enables to trace a light yield of a scintillation
light by gamma rays at 17.7 MeV. The π 0 run to measure two gamma rays from a neutralpion decay is the most powerful way to know the detector performance about the energy,
the timing and the position around a µ → eγ signal region in the whole acceptance of thedetector. Before moving on the explanation of each method, all calibration sources are
summarized in Table 11 with its characteristics and purposes.

6.2

Gain of PMTs

6.2.1

Gain calculation

The LEDs attached on the lateral faces of the LXe detector are useful light sources tomonitor and estimate gains of all PMTs. The gain calculation by LEDs is based on
statistics of the collected number of photo-electron, Npe , which is independent of theamount of photons and the wavelength. Observed charge, q, from PMT output is given
by gain, G, and a conversion constant, e, as an equation, q = G · e · Npe , where the gain
does not include a collection eﬃciency of the ﬁrst dynode from cathode. By counting
many LED events, the mean of the charge and the number of photoelectrons obey an6.2

Gain of PMTs

79

Table 11: Calibration sources for the LXe detector.

Type
LED
241
Am
Cosmic ray241
Am 9 Be
CW proton
π − beam

Thermalneutron capture

PurposePMT gain, timing
QE, Xe property
light-yield monitor
light-yield monitor
light-yield monitor
energy and timing
energy, timing,
position,
detection eﬃciency,
light-yield monitor
light-yield monitor

Sourceblue light
α
µ
γ
γ
γ,
neutron,eγ

Energy∼470 nm λ5.5 MeVa hundred MeV
4.4 MeV
4.4, 12.0,
17.7 MeV
54.9-82.9,
129.4 MeV
8.9 MeVInterval
a few days/mixed
a few days/mixed
dedicated/mixed
dedicateda few days

9 MeV

(under testing)a yearequation,q = G · e · N pe .

(58)

The variation of the observed charge contains a noise from electronics or charge calculation
as σ0 , a ﬂuctuation of a photon propagation before reaching a PMT and a power of LED
2
pulser as σLED and a resolution on the single photoelectron as σG, by an equation,222
σq2 = (G2 + σG
) · e2 · (σpe
+ σLED) + σ02(59)

We assume that the intensity of photons from LEDs is constant and the number of photoelectrons obeys Poisson statistics when the photons are converted to photoelectrons at
the photocathode. The Poisson distribution gives a relation between the deviation and2
the mean of photoelectrons, σpe= N pe . By Equations 58 and 59, we obtain a relation
between the mean and variance of charge and the gain,22+ σ0′2) × e2 × σpe
σq2 = (G2 + σG2
= (G2 + σG
) × e2 × N pe + σ0′22(G2 + σG)×e=× q + σ0′2 ,
G

(60)
(61)
(62)

where σ0′ is a constant term and diﬀers from a pedestal of σ0 because it contains σLEDand the gain. The number of photons coming into PMT, Npho , is calculated by a relationof Npho = Npe /QE, where a quantum eﬃciency, QE, is described later in Section 6.3.1.
We took nine steps with diﬀerent LED intensities in beam oﬀ condition as shown incharge distributions of Figure 6.1. Each step contains 3000 events and in total it took
half an hour for one gain measurement. We can obtain a relation between charge q̄ andvariation σq2 as shown in Figure 6.2, and then the slope of plots is regarded as the gain.
Figure 6.3 shows a charge map of PMTs when one LED ﬂashing, while Figure 6.4 showsthat of ten LEDs ﬂashing which can illuminate all the PMTs at the same. Figure 6.5

σ2

6. Calibration and Monitor of the Liquid Xenon Detector
Counts

80

500

×10-3
2
0.12 χ / ndf

400

3.493 / 7

p0

1.756e-06 ± 4.529e-07

0.1 p10.0004981 ± 8.829e-06

0.08
300
0.06
200

0.04
Gain = 1.49 x 106

100
0

0.02
0

0.05

0.1

0.15

0
0

0.2
0.25
-Charge (e+)

0.05

0.1

0.15

0.2
Q meanFigure 6.1: Nine LED peaks by various Figure 6.2: Gain estimation from theintensities.
slope on charge mean and variance(σ 2 ) plane.

V (cm)V (cm)

shows the relation of the mean and the variance of charge from each LED and all LEDs
on upper ﬁgure and the slopes of those in lower ﬁgure, which suggests that calculated
gains are independent of a light intensity and a LED.

30

0.2

LED

100

0.7

LED

100

30

31

50

31

25

50

0.15

32

26

0.5

27

0.4

26

32

0

0.1

0

27

-50

0.6

25

28

34

0.05

-50

29

35

28

34

0.3

-100
-100

0

100

200
-Z (cm)

0

29

35

-100

0.2
-100

0

100

200
-Z (cm)Figure 6.3: Charge map of PMTs
from one LED. The number shows
id of each LED and LED of id=30 Figure 6.4: Charge map of PMTs from nine LEDs.
All PMTs obtain enough charges at the same time.
illuminate the detector.

Usual gain calibration was taken everyday or three times per week depending on thedetector situation. Additionally the most intense step was taken everyday and every time
when we start or stop using beam to monitor the variation of PMT gains relatively. LEDs
are ﬂashed with 100 Hz during the usual calibration and LED data with 1 Hz are mixed
in MEG physics data taking.
6.2.2

Gain shift

By means of PMT calibration methods described above, a long-term stability of all PMTs
were checked. However, temporally there was the PMT gain increase or decrease depend-

6.2

Gain of PMTs

0.12 ×10

81

σ2

-3

Fit with normal LED run

χ2 / ndf
p0
p1

0.1

Normal LED run

3.493 / 7
1.756e-06 ± 4.529e-07
0.0004981 ± 8.829e-06

XEC LED 25
XEC LED 26

Fit with all LEDs

0.08

χ2 / ndf
p0
p1

0.06

XEC LED 27

122.3 / 97
1.274e-06 ± 7.63e-09
0.0005039 ± 2.733e-06

XEC LED 28
XEC LED 29
XEC LED 30

0.04

XEC LED 31
XEC LED 32

0.02

XEC LED 34
XEC LED 35

0

0.05

0.1

0.15

0.2

Q mean×10

Gain by each LED

3

2500
2000
1500
1000
500
10-4

10-3

10-2

10-1 Q mean

Figure 6.5: Relation between the slope on charge mean and variance (σ 2 ) by each LED
light.

ing on the beam intensity when we started using the beam as shown in Figure 6.6, whichis named ‘gain shift’. This was conﬁrmed by diﬀerent methods such as LED peaks, alphapeaks, and gain calculation by means of LEDs. This gain shift is not coming from thepileup eﬀect but the PMT itself since the gain calculation relies on the statistics of photoelectrons which is independent of the beam intensity. A monitor with constant LED
light in Figure 6.6 shows a gradual increase clearly after starting a delivery of muons into
the target. The contribution of beam switching time is a small, about ten seconds. As
shown in Figure 6.7, gain shift factors depend on individual PMTs and the mean value isabout 2%. Some PMTs have a larger gain increase, while several PMTs has less eﬀect ornothing.
We know that it is related with a manufacturing process and indirectly with a cathodeblue sensitivity (SKB). As shown in Figure 6.8 larger gain shifts are observed by PMTs
which have larger serial number than 1000.
The shift is correlated with a beam intensity so that we can correct it with monitoring
constantly. In order to correct this gain shift, LED data such as shown in Figure 6.6 areused. Exponential function with three time constants describes the gain shift well. Fit
results indicate that the transition is faster in opening the beam blocker than in closing
the blocker and it takes 5 minutes for the gain shift to be stabilized within 10% whenbeam blocker is opened and 20 minutes when the beam blocker is closed. Therefore after
the beam blocker is opened or closed we wait 15 minutes before starting physics datataking and wait 30 minutes before starting a regular calibration, respectively. During thewaiting time, LED ﬂashing runs are taken to monitor and correct the shift.
We prepare diﬀerent functions for each PMT, for diﬀerent beam condition of muonsand pions, and for both the beam blocker opened and closed, and shape of the transition
seems to be no change for each prepared set. Typical shift of total number of photons is6. Calibration and Monitor of the Liquid Xenon Detector

Beam-off gain / Beam-on gain

Beam-on gain / Beam-off gain

82

1.4

Physics run

1.35

Beam on

1.3
1.25

τ0 (s)
15.82
Factor 00.1783τ1 (s)
223.4
Factor 1
0.09465
τ2 (s)
9.522e+009
Gain shift factor
1.275

1.2
1.15
1.1
1.05
1
0.95

0

500

1.05

1000

1500

τ0 (s)
Factor 0
τ1 (s)
Factor 1
τ2 (s)
1/Gain shift factor

1
0.95
0.9
0.85
0.8

Time (s)58.39-0.11041050-0.081017098
0.7835γ calibration run

Beam off

0.75

0

500

1000

1500 Time (s)Figure 6.6: Gain shift of a worst PMT after beam blocker opened in upper ﬁgure andclosed in lower.

220
200
180
160
140
120
100
80
60
40
20
0

0.9
1
1.1
1.2
Gain-shift correction factor from beam off to on

Figure 6.7: Gain shift factor from beam oﬀ to on of all PMTs.

about 2%. Because the most scintillation light is detected on the inner face, the larger
gain shifts appears on the inner face. The larger shift is observed in a π − beam because
we do not use the Wien separator in the π − beam and many electrons and muons exist.
6.2.3

Gain adjustment

Before physics data taking started, gains were adjusted by following reasons:• Equalize each PMT performance such as timing response.
• Keep a pulse height within a dynamic range of waveform sampling boards

6.2

Gain of PMTs

83

1.2
1.15
1.1
1.05
1
0.95
0.9
Gain shift factor beam off /on

0.85
0Cathode Blue Sensitivity(Skb)/20+0.8

200 400 600 800 1000 1200 1400 1600 1800
PMT serial ID TCxxxx

Figure 6.8: Gain shift factor (Beam oﬀ / Beam on) and Cathode blue sensitivity by PMT
serial number, plotted by red circles and blue dots, respectively. Both values shifted by
the serial number according to the change of manufacturing plant.

Normally a gain of a PMT with same resistive divider is in proportion to V kn , where
V is a bias voltage, n is the number of dynode stage and k is a factor determined by amaterial of dynodes. However, the PMTs for the MEG experiment use two Zener diodes
in the last two stages shown in Figure 3.36, thus the equation is approximately modiﬁed,
Gain ∝ (V − 0.95Z − V0 )11k ,Z = Z1 + Z2 = 130 (Volt.),

(63)
(64)

where Z is the total voltage at two Zener diodes and V0 is an oﬀset by a loss in cables.
Figure 6.9 shows the relation between HV and gain of a PMT as well as a ﬁt result with
Equation 63.
In 2008 and 2009 we adjusted all gains to 1.8 ×106 , without considering QE values ina simple way, by a few iteration for a determination of HV set with using the relation.
Applied HV in 2009 is shown in Figure 6.10, which is enough lower than maximum bias
voltage of PMTs about 1200 V. That allows a large increase of gain even if it decreases,
for example, a shift of 200 V higher voltage from the 2009 set brings ten times larger gain.
6.2.4

Monitor of gain

Figure 6.11 shows calculated gains and LED peaks of a certain PMT on inner face, inwhich the values of LED peaks are scaled to the gain value of the right-most point. We cansee a decrease of gains for a long time scale and it depends on a beam rate and particle.
This aging eﬀect can be seen in all PMTs especially on the inner face of the detector,
shown in Figure 6.12. The decrease is independent of the gain shift eﬀect. Figure 6.13
shows that the gain dropped to 90% in average during 2009 run. However, we can keep
the gain for next several years by increasing HV because this drop is recovered by only
about 5 V increase of HV and applied HV is suﬃciently lower than maximum HV (Figure6.10).
One can see more stable monitor result with LED peaks than with the gain calculation
although those tendencies are the same as shown in Figure 6.11. Therefore we calculated
the absolute gain by averaging some sets of LED calibrations at a stable condition without

84

6. Calibration and Monitor of the Liquid Xenon Detector
×10

3500
3000
2500
2000

χ2 / ndf

19.65 / 5Prob0.001453

Factor

1.128e-021 ± 5.102e-022

Power

9.422 ± 0.06221

80
70
60

0

50

98.19 ± 7.491

400±Const.
ZenerV+V0

PMTs

Gain

3

30

1500

20
10

1000

0

700

500
0

720 740 760 780 800 820 840 860 880 900 920 940

Bias HV (V)

800

900
1000
1100
High voltage of PMTs (V)Figure 6.10: Determined HV
set in 2009. Maximum voltage
rating is 1200 V.

Figure 6.9: Gain - HV curve and ﬁt.

×103
1850

π0 runPhysics run

LED peak
Gain

1800
1750
1700
1650
1600
1550
46000 48000 50000 52000 54000 56000 58000 60000 62000 64000

Run number

Figure 6.11: History of gain and scaled LED peak of a certain PMT. The shift just afterthe π 0 run is due to a diﬀerent magnetic ﬁeld of BTS. The red square dots from LED are
scaled to the gain value adjusted by the absolute gain of blue dots and enable the gain
monitoring stably.

the beam for a few days. After that the gain is traced relatively by means of LED peaks.
A simple linear interpolation is applied for the MEG run only in 2009 and for the π 0 run
in both 2008 and 2009, between each measurement point. The peak of LED contains not
only a gain but also CE, QE for blue-light LED and a digitizer, and these are corrected.
The gain calculation is still continued to avoid a disagreement from an aging of LED or the
LED pulser. Thanks to the faster LED one-step run for a peak estimation than nine-step
LED calibration set, the LED one-step run is frequently taken during the calibration set
and in beam on. After all the gain calibration are applied, LED peaks mixed in physics
data taking show a stability in Figure 6.14, which is within about 1% in sigma (Figure6.15).

85

Alpha sources and quantum efficiency

1
0.99
0.98

PMTs

Relative gain

6.3

0.97
0.96
0.95
0.94
0.93

70
60
50

All
Inner
Outer
Up
Down
Top
Bottom

0.92
29/10

05/11

40

Entries

842

Mean

89.88

χ2 / ndf

39.51 / 39

Constant

55.82 ± 2.46

Mean

90.13 ± 0.17

Sigma

4.785 ± 0.128

30
20
10
0

12/11

19/11

26/11

03/12

10/12

20 30 40 50 60 70 80 90 100 110 120[%]

17/12 24/12
Date 2009

LED peakFigure 6.12: Relative change of averaged gains on Figure 6.13: Relative gain dePMTs by each face in muon beam (2009).
crease of PMTs in all the 2009
runs. There were gains of two
PMTs decreasing largely.

1.03

LED

1.02

50

1.01

40

1

30

0.99

1463

Mean

0.9999RMS

0.001576

χ2 / ndf

275.4 / 143

Constant

37.05 ± 1.64

Mean

1 ± 0.0

Sigma

0.0008719 ± 0.0000292

20

0.98
0.97

Entries

10

12/11

19/11

26/11

03/12

10/12

17/12
Date

Figure 6.14: LED peaks mixed in the MEG
2009 run. Some lower points come from abeam break, a wrong gain interpolation anda low proton current.

00.992 0.994 0.996 0.998

1

1.002 1.004 1.006 1.008
LED peaks (a.u.)

Figure 6.15: LED peaks in the MEG
2009 run within 0.09% in σ.

6.3

Alpha sources and quantum eﬃciency

6.3.1

Quantum eﬃciency

A QE of a PMT can be estimated by point-like alpha sources. Since we know the installedalpha positions, we can estimate the photoelectrons observed by each PMT by meansof MC simulation. Then, QE is extracted from the comparison between the measured
photoelectrons and estimated ones by the MC, with considering the calculated gain by
LED. This method enables the estimation of QE times gain, and we can separate QEfrom the gain. The collection eﬃciency is included in the QE, while the transmittance of

86

6. Calibration and Monitor of the Liquid Xenon Detector

the quartz PMT window is not in the QE because the MC simulation calculates it. The
wavelength of scintillation light from alpha particles is the same as that from gamma rays,
thus the estimated QE from alpha sources can be applied for the gamma-ray detection.
In liquid xenon phase the reconstructed positions from alpha sources make rings aroundalpha wires because a range of scintillation photons about 40 µm from the wire is nearcompared with a 100 µm diameter of the wire and the wire makes a shadow, while ingaseous state the reconstructed shape is like a point because of suﬃciently far generation of
scintillation photons from the wire in the range of about 7 mm. The MC-data correlationof peaks from observed photons by each source are shown in Figure 6.16 and its slope
indicates a QE as a diﬀerence from MC. The events are selected for each PMT to avoid
shadow positions behind wire and sources which has a large incident angle to the PMT.
The QE is obtained by averaging some sets of estimations to reduce statistical ﬂuctuations.
The obtained QE is normalized in such a way that the mean of all QEs takes 0.16 to avoid
the change of other properties such as the light yield. It is possible to calculate QE bothin liquid and gas where the wavelength of scintillation is the same. The QE in gas
is less inﬂuenced by absorption and scattering in xenon but is inﬂuenced by the eﬀectof reﬂection on the wall and on the PMT window, and by a possible eﬀect caused bytemperature gradient in the detector. Therefore the QE set to be used in the 2009 data
is estimated in liquid phase.
A ﬁne tuning for the MC such as reﬂection, attenuation lengths and light speed improved agreement with actual data, however the MC for the QE estimation is sensitive tothese parameters and a small remained discrepancy between the data and the MC makes
it diﬃcult to estimate QE. For instance, on a photo-cathode, diﬀerent incident angles ofphotons from sources at diﬀerent positions with respect to a PMT direction bring a bias
even if disagreement of a reﬂection, a photon polarization or a response of photo-cathodefor a slant injection is small between data and the MC. We could not overcome a small
disagreement in a large incident angle between data and MC, thus we correct it by theangle in the QE calculation. In addition, a global bias is observed as a diﬀerence of
non-uniformity of reconstructed scintillation photons between the data and the MC. The
QE is corrected globally by using 17.7 MeV gamma ray from 73 Li(p,γ)84 Be to eliminate
asymmetries of peaks between PMTs at symmetric positions on each face of the detector.
Figure 6.17 shows the QE distribution of all PMTs which is applied for all 2009 data.
6.3.2

Absorption and scattering

The scintillation light from excimers (Xe∗2 ) is not absorbed by a liquid xenon in itself,
but is absorbed by a contamination in xenon and causes Rayleigh scattering that is themost dominant. In general the attenuation factor I(x) and attenuation length λatt aredescribed with absorption length λabs and diﬀusion length λdif ,I(x) = I0 e−x/λatt ,
1
1
1
=
+
.
λatt
λabs λdif
The inversed scattering length, h, is described by
[
( )
(
)]
1
ω4
δϵ
kT 2 δϵ4h==kT ρ κT
+
,
λR
6πc4
δρ T
ρcv δT ρ

(65)
(66)

(67)

6.3

Alpha sources and quantum efficiency

87

90
80

PMTs

Data mean

PMT
PMT609.
609.QE=9.56607
QE=9.56607%,%,(Uncert.
(Uncert.2.27392
2.27392%)
%)

70

50

19 : 81.34
18 : 39.76
17 : 21.17
23 : 18.35
24 : 15.84
22 : 12.15
16 : 10.04
21 : 8.50
15 : 6.06
20 : 5.91
12 : 3.81
11 : 3.52
13 : 3.51
10 : 3.02

40
30
20
10
0
0

35
30

60

20

40

60

80

100

120

140
MC mean

25
20
15
10
5
0

0.1

0.15

0.2

0.25

Quantum efficiency (Normalized to 0.16)

Figure 6.16: Comparison of alpha peaks between con- Figure 6.17: Estimated QE ofstant QE (16%) in MC and data.
all PMTs.

PMT charge in liquid / gas

where ω is the angular frequency, c is the velocity of light, k is Boltzmann constant, T
is the temperature, ρ is the liquid density, κT is the isothermal compressibility, cv is theheat capacity at constant volume, and ϵ is the dielectric constant.
The optical properties of liquid xenon are poorly known and it is the most diﬃcult
point to reproduce events in the MC. The pairs of alpha source and PMT have exactly
known distances and it is useful to estimate the attenuation length or the light speed inxenon. To obtain those we compare the charges in liquid xenon with those in gas xenon orin the MC. Since the attenuation in gas phase is long enough because of the low density,
we can estimate attenuation length in liquid by taking the ratio of charges. Figure 6.18
shows the relation between the ratio of liquid to gaseous xenon and distance, and 65 cm
attenuation is observed in 2009 data. Another way is to use the MC instead of gas. It
allows us to check each optical parameter of MC such as attenuation, scattering lengthor reﬂection in the MC.

χ2 / ndf
Prob
Constant
Slope

9
8
7

94.82 / 37
5.685e-007
1.709 ± 0.009-0.01539 ± 0.00020

λ = (65 ± 0.9) (cm)

6
5
4
3
2
1
0

10

20

30 40 50 60 70 80 90 100
Distance between α source and PMT (cm)Figure 6.18: Attenuation length by charge ratio in liquid / gas from α source and distance
between source and PMT in 2009 run.

88

6. Calibration and Monitor of the Liquid Xenon Detector

6.3.3

Particle discrimination

Amplitude (a.u.)

Since there is a diﬀerent density of energy deposit between alpha and gamma ray, thedominant scintillation process of fast or slow time components diﬀer. Using all waveform
information from PMTs, we can recognize the diﬀerence of time components clearly.
Figure 6.19 shows averaged and normalized waveforms from alpha and gamma-ray events.
We have two ways to distinguish particles by estimating time constants as a result of aﬁt with a function model, or by using a charge-height ratio. The charge over heightratio of summed waveform has an suﬃcient ability to separate alpha events from gamma
ray, which is the simplest and fastest method. The discrimination is useful to estimate
gamma-ray peaks in similar energy region of alpha or to take alpha events eﬃciently. As
shown in Figures 6.20 and 6.21, the separation improved with the increase of the lightyield by the puriﬁcation.

0
-0.2
-0.4
-0.6

γ ray

-0.8

Am α

241

×10
0.5
(sec)

-6

-1

0

0.1

0.2

0.3

0.4

α

Sep 2008
Dec 2008
2009

γ

2008
2009

4

6

8
10
12
14
Charge / Height of sum waveform

Charge / Height of sum waveform

Figure 6.19: Averaged waveform from alpha events and gamma-ray events.

11

γ ray
Am α

241

10
9

2008

2009

8
7
6
31/08/08 31/10/08 31/12/08 02/03/09 02/05/09 02/07/09
Date

Figure 6.20: Alpha-gamma identiﬁcation Figure 6.21: History of a charge-height ratiowith puriﬁcation.
by a charge-height ratio.

6.4

6.4

Light yield

6.4.1

Light-yield monitor

Light yield89

The monitor of the light yield is crucial because the light yield directly relates with theenergy scale that is determined at 54.9 MeV peak in a certain period of π 0 run. We
had a precise light-yield monitor during beam-oﬀ periods by various sources. In 2008 we
performed puriﬁcation even during physics data taking, then in 2009 the puriﬁcation was
stopped before physics run started because the increase of the light yield seemed to besaturated. That indicates that the 2008 data needs a correction for the light yield, andwe have to conﬁrm a long-term stability in 2009.
It is the most precise method to use 17.7 MeV gamma-ray peaks from lithium target
by the CW proton accelerator. However, the CW beamline can not be used during π 0
run because it must be removed to install the hydrogen target. Instead, during π 0 run,peaks of 54.9 and 82.9 MeV gamma rays from π 0 decay can be used for the monitor.
For the monitor during a few days to change the beamline from π − to muon beam andCW proton beam, other sources of gamma rays from americium-beryllium (AmBe) andcosmic rays are useful. In order to combine the time-dependent transitions from diﬀerent
energies and periods, we took several types of monitoring runs with overlapping periods
because a linear response of reconstructed scintillation photons is not ensured.
Other sources are sometimes used to support the monitor. Monitoring by alpha sources
is not always the same as that by gamma rays. That is because the dominant scintillation
process diﬀers between alpha particles and gamma rays. A degree of suppression in eachprocess depends on particles contaminating xenon. Thus, events from alpha sources are
not suitable to monitor the gamma-ray energy, but can be used to check the stability ofthe detector. For a consistency check, an edge of gamma rays from radiative muon decays
can be used for the monitor in the muon beam. The edge includes the energy resolutionthat might change by time, thus it is not used for the calibration or the precise monitor.
Monitoring sources mixed in physics data taking, such as cosmic rays or alpha particles,
do not have enough statistics to perform a precise calibration or a monitor but enable tocheck a long-term stability.
Following sections from 6.4.2 to 6.4.7 show the stable light yield in 2009 monitored byeach calibration source. Even if there is a light-yield change, it can be corrected by themonitor as shown in Section 6.4.8 that describes a light-yield correction in 2008.
6.4.2

Monitor during π 0 run

The π 0 run plays an important role in a performance evaluation of the LXe detector. Oneof the important purposes is to determine the energy scale by a 54.9 MeV peak near thesignal energy of 52.8 MeV. Therefore the energy scale obtained in the π 0 run ought to be
extrapolated to the MEG run exactly.
As shown in Figure 6.22, the inner face is divided into 24 patch positions, and data
are taken for each patch position separately to select back-to-back two gammas from π 0
decay. The NaI detector is moved to the opposite side of each patch during calibration.
Each patch consists of 3 × 3 PMTs. In a speciﬁed patch, a special trigger to select a
gamma direction is issued if the maximum charge in inner face is observed in one of thenine PMTs. For the back-to-back selection of two gammas, the trigger also requires the
maximum signal at central crystal among nine crystals, or hits in pre-shower counter in

90

6. Calibration and Monitor of the Liquid Xenon Detector

Figure 6.22: Software-collimator patches on the inner face for π 0 run. Circles show thelocation of PMTs and are divided into 3 × 8 patches by 3 × 3 PMTs region (∆u × ∆v =18.6 × 18.6 (cm2 )). The collimator patch #8 in dotted red box is used for the light-yieldmonitor and the determination of the energy scale.

front of the central NaI. The former is used for the energy measurement and later is forthe timing measurement. The interaction of gamma rays in lead converter worses energy
resolution, thus these are separately used by purpose. The online selection of maximum
deposit in central NaI makes analysis eﬀective because it is hard to use the events witha gamma ray entering the surrounding eight NaIs due to worse resolution by gammaray leaks. The distribution of triggered opening angle is shown in Figure 6.23, where
the events with the opening angle larger than 170◦ are selected. It agrees well with the
expectation of the angle 11◦ , which is the size of a patch viewed from the target. In orderto acquire better resolution of the NaI, we also apply a cut by an energy ratio of thecentral NaI to the all NaIs, to be larger than 0.6.
Reconstructed scintillation photons of 54.9 MeV energies at 24 patches diﬀer becauseof the position-dependent response as described in Section 4.2.5. Therefore we select oneof the divisions for a constant monitor to be taken frequently. The central upper position,‘patch #8’ of dotted box in Figure 6.22, is frequently taken for the monitor. It enables
to monitor the change of the light yield independently of the position dependence.
The opening angle is calculated from the reconstructed position of the LXe and thecentral position of the NaI. This opening angle information is used to correct the expectedenergy using the theoretical correlation between energy and opening angle. The two
gamma rays around edge of the patch makes higher 54.9 MeV-like peak or lower 82.9
MeV-like peak, thus it is corrected by theoretical energy dependence of opening angle.
Figure 6.24 shows the correction factor for each energy and it is eﬀective for edge events.
To avoid a shift of opening angle by a misalignment of the NaI position, both peaks
at 54.9 and 82.9 MeV in the LXe detector and also the other gamma-ray peak at the6.4

Light yield

91

Correction factor

NaI detector are monitored because the change of peaks by the shift of opening angle
is opposite between two gamma rays, and thus it can be separated from the light-yieldchange.
The runs at patch #8 were taken everyday just after or before the calibration set ofLED, alpha and cosmic ray run. Typically it takes for half an hour to complete the runwith 50k events for each calibration. Figure 6.25 shows the monitor of the light yield atpatch #8 position as blue circles, while peaks from other patches are red plots. The peaks
from patch #8 agree with others and show the stable operation in π 0 run.
1
0.8
0.6
0.4

1.04
83MeV

1.02
1
0.98
55MeV

0.2

0.96

0
165

0.94
165

170
175
180
Opening angle (degree)

170

175
180
Opening angle (degree)

55 MeV peak [a.u.]

Figure 6.23: Opening angle dis- Figure 6.24: Correction factor
tribution triggered by 3 × 3 by opening angle for 82.9 MeV
PMTs region.
and 54.9 MeV.

1.02
1.015
1.01
1.005
1
0.995
0.99
0.985
0.98
22/10

23/10

24/10

25/10

26/10
Date / 2009

Figure 6.25: 54.9 MeV peak history in 2009 π 0 run. Blue circle plots show the monitoringat patch #8.

6.4.3

Monitor with the CW accelerator

The CW calibration run around 30k events was taken to collect 17.7 MeV lithium peaks
once per a few days during physics run. Figure 6.26 shows 4.4 MeV and 12.0 MeV peaks
from boron and Figure 6.27 shows 17.7 MeV and broad 14.6 MeV peaks.
The light-yield stability during 2009 run is ensured with 17.7 MeV lithium peaks asshown in Figure 6.28, and its projection in Figure 6.29 shows the stability within 0.25%

2400
2200
2000
1800
1600
1400
1200
1000
800
600
400
200
0

Events

6. Calibration and Monitor of the Liquid Xenon Detector
Events / 467

92

1200

1000

Entries45518

χ2 / ndf

108.3 / 81

Scale1097 ± 10.7

Peak

1.808e+005 ± 6.433e+001

σup1

800

5198 ± 57.5
-4662 ± 178.2

Transition
Ratio
σup2

600

0.3263 ± 0.0047
1.314e+004 ± 2.992e+002

400

200

50

100

150

×103

0

The number of scintillation photons

Figure 6.26: Boron peaks of gamma
rays in CW run.

80

100

120
140
160
180
200
The number of scintillation photons

×103

Figure 6.27: Lithium peaks of
gamma rays in CW run.

18MeV Lithium peak [a.u.]in σ. Thus, we concluded that the light-yield in 2009 was stable within 0.25% precisionby the lithium peak monitor. The resolution was also stable as shown in Figure 6.30.

CWLiPeak

1.02

10

1.015
8

1.01
1.005

6

Entries

27

Mean

17.68

RMS

0.05521

χ2 / ndf

1.927 / 4

Constant

9.914 ± 2.812

Mean

17.68 ± 0.01

Sigma

0.04215 ± 0.00870

1
4

0.995
2

0.99
0.985
0.98

0
29/10

05/11

12/11

19/11

26/11

03/12

10/12

17/12

17.45 17.5 17.55 17.6 17.65 17.7 17.75 17.8 17.85 17.9
Li peak [MeV]

24/12
Date

Energy resolution σupper (%)

Figure 6.29: 17.7MeV Lithium
Figure 6.28: Monitor with 17.7 MeV peaks in 2009
peaks in 2009 within 0.25% staCW run.
bility.

3.05
3
2.95
2.9
2.85
2.8
2.75
2.7
2.65
29/10

05/11

12/11

19/11

26/11

03/12

10/12

17/12

24/12
Date / 2009

Figure 6.30: Stability of energy resolution at 17.7
MeV in 2009 CW run.

6.4
6.4.4

Light yield

93

Cosmic-ray monitor

EventsThe Landau distribution from cosmic rays is obtained by selecting muons penetratingouter face and inner face, as shown in Figure 6.31. The beneﬁt of the cosmic-ray monitor
is that it is always available and it is mixed in the physics run.
120
100

χ2 / ndf

730.2 / 77

Constant

475.8 ± 14.0

MPV

1.727e+006 ± 9.574e+003

Sigma

2.287e+005 ± 6.612e+003

80
60
40
20
500

1000

1500

2000

2500

3000

×103

The number of scintillation photons

Figure 6.31: Landau peak of cosmic ray.

6.4.5

AmBe monitor

The americium-beryllium source, 241 Am-9 Be, provides a 4.4 MeV gamma ray from the∗bound-excited state of 12 C∗ , which is produced in the 94 Be(α, n)126 C nuclear reaction after
241
Am emits 5.5 MeV alpha particle [59]. Another reaction of 94 Be(α, n)12
6 C emits a 8
MeV neutron.
There are two major backgrounds; alpha and neutron backgrounds. The alpha contamination from 241 Am immersed in liquid xenon can be easily separated by the particle
identiﬁcation using pulse shape. The neutron background originates from the source itself.
In the case of the monitor during π 0 run, it comes also from the π − beam, and thus thisbackground could change as a function of time. It is diﬃcult to estimate the backgroundshape and rate with a dedicated diﬀerent run without the source. Therefore, we estimate
the background spectrum using the AmBe run data itself as shown as a light blue line in
Figure 6.32 [60]. By subtracting the estimated background, the peak of 4.4 MeV gamma
ray clearly appears as shown as a gray ﬁlled histogram in the ﬁgure. Estimated energy
resolution agrees with an expectation from other calibration runs but its precision is low
because of the background, thus the same 4.4 MeV peak from the lower boron peak in
CW run is suitable to see an energy dependence of energy resolutions.
The connection between π 0 and physics run is important because the energy scale isestimated in π 0 run. The monitor with both AmBe source and cosmic ray conﬁrms thestability of the light yield in 2009 between 54.9 MeV π 0 and 17.7 MeV CW monitor.
6.4.6

Alpha monitor

The alpha peaks are constantly taken with LED run to estimate QE, but it is not used fora light yield monitor of ‘gamma ray’ because of the diﬀerent scintillation process described6. Calibration and Monitor of the Liquid Xenon Detector

Events / 540

94

AmBe

6000

All
γ spectrum
α spectrum

5000

Sginal with BG subtraction
BG estimated by self
Fit with γ spectrum

4000

Fit with signal spectrum

3000

Entries400

χ2 / ndf

10.12 / 101244 ± 15.7

Constant

2000

Mean

4.87e+04 ± 3.45e+01

Sigma

2569 ± 47.9

1000
0

20

40

60

80

100

×103
120

The number of scintillation photons
Figure 6.32: 4.4 MeV gamma-ray peak from AmBe source.

Eventsin Section 3.6.2. The monitor of alpha peaks is still signiﬁcant to monitor the purity ofxenon by alpha particles and stability of the detector including the waveform digitizationand the gain calculation. Figure 6.33 shows the summed peak over all 25 sources, whichenables more precise monitor than using peaks from each source.
80
70
60

χ2 / ndf

177.5 / 144

Scale

62.32 ± 1.53

Peak
σup

5.54e+004 ± 2.81e+002
4576 ± 206.9

Transition-2088 ± 231.4

50
40
30
20
10
0

10000

20000

30000

40000

50000

60000

70000

80000

The number of scintillation photons

Figure 6.33: Alpha peak of all sources.

6.4.7

Monitor during muon beam

The stability of the LXe detector could be conﬁrmed by beam-oﬀ calibration set. Then,
it is important to check the stability in physics run when the muon beam is used. The
mixed events of alpha sources in physics data taking allow the monitor once per day, while
those of cosmic rays two in a week. The monitors are shown in Figure 6.34 and the peaks
from alpha sources and cosmic rays seem to be stable within each precision of monitors.

Peak [a.u.]

6.4

1.03

95

Light yieldLED
α 241Am
Cosmic ray

1.02
1.01
1
0.99
0.98
0.97
29/10

05/11

12/11

19/11

26/11

03/12

10/12

17/12
24/12
Date / 2009

Figure 6.34: Peak of alpha, cosmic ray and LED in muon beam (The same LED peaks as
in Figure 6.14).

6.4.8

Combined monitor of the light yield in 2008

270
260
250
240
230
220
210
200

07/08

14/08

21/08

28/08
Date

30500
30000
29500
29000
28500
28000
27500
27/11

(a) 54.9 MeV in August.

04/12

115
110
105
100
95
90
85
08/10/08

07/11/08

18/12

07/12/08

1150

376
374
372
370
368
366
18/12

25/12
Date

(b) 4.4 MeV AmBe.

×103

08/09/08

11/12

The number of scintillation photons

The number of scintillation photons

×103

3

The number of scintillation photons

×10
280

The number of scintillation photons

The number of scintillation photons

In 2008, to trace the change of the light yield, the peak of 54.9 MeV at patch #8 and 17.7
MeV peak from lithium were combined with the help of cosmic rays and AmBe source(Figure 6.35). Instead of using the number of photons per energy, we obtain the relativechange of the light yield by scaling each peak history in such a way that the average ofpeaks during overlap period are the same values between histories. This method reduces
the uncertainties such as a linearity of energy response and unknown cosmic-ray peakenergy.

19/12

20/12

21/12

×103

1100
1050
1000
950
900
850
800
08/09/08

08/10/08

07/11/08

07/12/08
Date(d) Cosmic ray (Beam oﬀ).

Figure 6.35: Peak history in 2008.

23/12
Date

(c) 54.9 MeV in December.

Date(d) 17.7 MeV CW Lithium.

22/12

6. Calibration and Monitor of the Liquid Xenon Detector

Light yield [a.u.]

96

1.4
Gaseous purification

1.3
Liquid purification

1.2
1.1
1

0.9
Physics run

0.8
π0 runπ 0 run0.7
09/08/2008 08/09/2008 08/10/2008 07/11/2008 07/12/2008
Date
Figure 6.36: Combined history in 2008.

Figure 6.36 shows the change of the light yield in 2008. It was constructed withlight-yield histories shown in Figure 6.35. To make a smooth history, points taken neareach other were merged with taking average. After that a simple linear interpolation isapplied. We conﬁrmed that the peaks from alpha sources stayed constant during 2008
data taking, which diﬀered from the other results from gammas. This can be explainedby the diﬀerent contribution of the scintillation process described in Section 3.6.2, andthe history of alpha peaks was not used for the light yield correction. The constructed
light yield history was used in 2008 to extrapolate the energy scale that was obtained at
the end of August in π 0 run.
Figure 6.37 shows the light yield from 2008 to 2009. The red plots shows the peaksof 17.7 MeV by CW calibration and blue plots are taken from cosmic-ray Landau peaks.
Before physics run in 2009 we performed a puriﬁcation for xenon and the light yield wasmuch improved. We conﬁrmed the stable light yield in all monitors, therefore we do not
apply the light yield correction for 2009 data.

6.5

Uniformity

6.5.1

Non-uniformity correction

Although the reconstructed scintillation photons has the non-uniformity response, theuniform energy response is available by the non-uniformity correction based on actual
measurement in calibration runs. We made correction factors along u and v by 17.7
MeV peaks in CW run and depth correction functions by 54.9 MeV peaks in π 0 run in2009 (by 17.7 MeV in 2008). In 2008 we observed the change of non-uniformity with the6.5

Uniformity

97

Figure 6.37: Light yield history from 2008 to 2009. The 17.7 MeV peak in CW run (redplots) and cosmic-ray Landau peak (blue plots) show the consistent improvement.

improvement of light yield, therefore we prepared two sets of correction tables before andafter the puriﬁcation started. Thanks to the stable light yield we prepared only one setof non-uniformity correction in 2009.
The correction factor is estimated with both two dimensional relation on u-v planeand one dimensional relation along depth, w. In particular, the peak transition along
depth depends on both the energy scale and the position on u, v. Therefore the depth
correction in 2009 is made from 54.9 MeV peak in π 0 run with separated three u positions,while only one u-division in 2008. The lateral walls are near each other than the top andbottom faces, thus peaks have larger dependence along u direction than v direction. Thisis the reason why we separate depth correction along u direction rather than v direction.
Figure 6.38 shows factors of depth correction in 2008 and 2009.
The remained u-v correction is estimated after the depth dependence is corrected.
Ideally the use of 54.9 MeV peaks is the best way to observe 52.8 MeV signal, however
π 0 run are taken separately by 24 patches, and those may contain additional uncertainty
coming from time-dependent variation. In addition, the larger gain decrease in π − beam
than that in muon beam makes it diﬃcult to trace gain correctly, which may also bringgaps between patches. On the other hand 17.7 MeV gamma rays are available for thewhole region of inner face at the same time which avoid any time-dependent variation.
Thus we adopted lithium peaks for u-v non-uniformity correction. We estimate peaks
by one PMT size window (6.2 cm × 6.2 cm) for w deeper than 2 cm with shifting by
1/3 PMT width along u and v to make a smooth peak transition. Thus the windows
are overlapped and 24 selection windows are deﬁned along u and 72 along v. Figure 6.39
shows the correction factor on u-v plane, which is inversed non-uniformity response.

98

6. Calibration and Monitor of the Liquid Xenon Detector

1.2

1.1

2008 before purification

U (center)U (up stream)

1.08

2008 after purification

1.15

U (down stream)

1.06
1.1

1.04
1.02

1.05

1

1

0.98
5

10

15

20

25

5

30
Depth [cm]

10

15

20

25

Depth [cm](a) Reciprocal of CW peaks in 2008.
(b) Reciprocal of 54.9 MeV peaks in 2009.
Figure 6.38: Correction factor along depth (w). In 2009 factors are separately estimatedalong the beam axis u by three sets.

60

60

1.06
40

40

1.04

1.04
20
1.02
0

1

-20

0.98

-40

-60

0.96

-20

-10

0

10

20
u (cm)

1.04
20

1.02
0

1.06

1.06
40

20

1.08

v (cm)60

1.08

v (cm)v (cm)

1.08

1.02
0

1

-20

-40

0.98

-60

0.96

-20

-10

0

10

20
u (cm)

1

-20

-40

0.98

-60

0.96

-20

-10

0

10

20
u (cm)(a) Before puriﬁcation in (b) After puriﬁcation in (c) In 2009.
2008.
2008.
Figure 6.39: Correction factor on u-v plane (as the reciprocal of the peak). Acceptanceregion is shown in black dotted box and white circles indicate PMTs. QE set is the same
between (a) and (b), but diﬀerent between 2008 and 2009. The light yield improved between the sets. The factor in 2009 is calculated after the depth dependence is compensatedby the factor in Figure 6.38 (b).

7. Performance of the Liquid Xenon Detector

7

Performance of the Liquid Xenon Detector

7.1

Position99

The position resolution of the liquid xenon detector along two directions, (u, v), is evaluated in a dedicated π 0 run at a certain part of the inner face. Lead collimators withslits were mounted in front of the gamma-ray window. Resolutions are measured by anevent distribution of reconstructed positions around the slits. Because it takes too muchtime to measure position resolutions at all positions in the acceptance region, position
dependence was estimated from the MC and the comparison with data was done at limited positions. In 2008 π 0 run, the agreement of position resolution between the data andthe MC was checked. A QE estimation with a displacement of alpha source wires or unexpected errors from optical properties in MC such as the reﬂection and the attenuation
length could make a global bias in the position reconstruction. In 2009, a global bias of
the reconstructed position along beam axis z was measured in addition to the position
resolution.
7.1.1

Collimator run in 2008

The lead collimators with slits which were used in 2008 measurement are shown in Figure7.1. Each width of the slit is 1 cm, and the thickness of the lead collimator is 1.8 cm.
Figure 7.2 (a) shows a reconstructed event distribution along u axis taken with the leadcollimator that is shown in the Figure 7.1 (right one). Three peaks and two inner edges
come from three horizontal slits and both sides of lead. The outer edges out of the leadcollimator come from a bias on trigger, which selects collimator regions in 2 × 3 PMTsize. A ﬁtted red line is a combination of triple Gaussians for slits and two Error functions
for edges with a ﬂoor. Figure 7.2 (b) is the same setup in the π 0 MC.

Figure 7.1: Lead collimator with 1.8 cm thickness in 2008 (a 2-inch PMT is shown for areference). The lead on the left side has vertical slits of 1 cm width and the two leads on
the right side have a 13 cm-length horizontal slit. Between two leads with the horizontal
slit, another collimation is possible by these gap as shown in picture. The lead withhorizontal slits in 2009 has a three times longer length.

Table 12 shows the sigmas from the ﬁtting, which includes the width of slits and thebeam spread in the hydrogen target of σx = σy = 8 mm and σz = 25 mm. The averageof σv in slits is 6.9 mm in data and 6.5 mm in MC, and then the diﬀerence between data
and MC is estimated to be 1.8 mm. The diﬀerence is added to the position dependent
resolution map obtained from the signal MC. The diﬀerence probably originates from a
precision of the PMT calibration, which is not included in the MC. The standard deviationof the diﬀerence between measured and expected mean of v position is 0.7 mm.

100

7. Performance of the Liquid Xenon Detector

500
450
400
350
300
250
200
150
100
50
-15

-10

-5

0

5

10

15

Vertical axis on the detection face (v) [cm](a) Data in 2008 π 0 run.
(b) MC simulation.
Figure 7.2: Event distribution through slits sliced along v. The selection is applied for allenergy regions from two gammas, w deeper than 2 cm and a range of −15 cm < u < 5cm.
Table 12: Sigmas ﬁtted in slits and edges along v (w >2 cm). Central slit in MC isomitted due to a diﬀerence of the geometry between data and MC.

σv in 2008 Data (mm)σv in MC (mm)σv in MC truth (mm)slit1 slit2
7.2
6.8
6.8
4.7
-

slit3
6.7
6.5
4.9

edge1
4.7
3.9
2.3

edge2
4.2
4.2
2.8

The resolution along u direction can be also estimated with vertical slits as shown in
Figure7.3. However, it is more complicated for the following reasons:• Slant angle of incident gamma rays makes a diﬀerent response by u due to thecylindrical shape of the detector.
• Not independent from the depth resolution σw .
• The faces of the slits are perpendicular to the inner face, and are not parallel togamma rays.
• Beam spread along z is wider (σz = 25 mm) than along ϕ (σx = σy = 8 mm) andits projection along u on the inner face is about 5.8 mm.
• The length of a gamma-ray shower is projected on u, especially around large |u|.
Figure 7.3 shows an event distribution through vertical slits along u direction. The averageof σz in six points is 6.1 mm with about 1 mm bias around center and those are comparablewith the result along v.
The reconstruction method is the same for u and v, thus in principle the resolutions are
similar to each other except for depth contribution. The position resolution along u and v
strongly depends on the depth, which can not be seen in data but can be estimated in the7.1

Position

101

500
450
400
350
300
250
200
150
100

∆ Z (Reconstructed - Expected) [cm]

-10

0

10

20

z [cm]

0

10

20

z [cm]

0.2
0.1
0
-0.1
-0.2
-0.3
-0.4
-0.5
-0.6

Figure 7.3: Event distribution through slits sliced along u (z) in 2008 π 0 run. The upper
distribution is ﬁt by six Gaussians with a ﬂoor as a continuous line and the expectationof slit positions is marked on the top of peaks. The plots in the lower shows the diﬀerence
between the reconstruction and the expectation of u by the u position of slits.

MC. The diﬀerence between the data and the MC is applied to the position dependent
resolution on u, v and w obtained in the MC.
7.1.2

Collimator run in 2009

In 2009 we prepared two collimators with long horizontal slits and 18 mm thickness. Twocollimators have the same dimension except for the width of slits, 10 mm and 5 mm,
and each has a long slit and three short ones to cover the entire z position at diﬀerent v
positions. The 10 mm-slits collimator was put at the v center of the detector as shown in
Figure 7.4 and another with 5 mm slits at the lower part of the detector.
v (cm)

50

4
2
0

45
40
35
30

-2
-4
-6
-8
-10
-12

25
20
15
10
5

-20

-10

0

10

20

z (cm)

0

Figure 7.4: Event distribution of 10 mm slits in 2009 π 0 run. Circle plots show peaks inslits ﬁtted by scanning along u. Large white circles indicate the active area of PMTs.

Figure 7.5 shows a double Gaussian ﬁt of projection for v with 2.1 cm width cut alongu. Figure 7.6 is projection for u by each three short-length slit with 10 mm width cut

102

7. Performance of the Liquid Xenon Detector

Entries / 0.12cm

for v around the slits. These are ﬁtted with an error function on a ﬂat ﬂoor. The peak
positions are shown in black circles in Figures 7.7 (a) and (c) for 10 mm and 5 mm slits,
respectively. The sigmas are shown in Figure 7.8 for 10 mm slits and Figure 7.9 for 5 mm
slits. Average of sigmas on the 10 mm and 5 mm slits data are 6.8 mm and 6.5 mm in σv(Figure 7.10), respectively, and it agrees with 2008 result.
240200

χ2 / ndf
Scale0
mean0

180

σ0

220

117.6 / 121
119.9 ± 4.9-5.706 ± 0.027
0.6592 ± 0.0271

160

Scale1
mean1

140

σ1

120

Floor

130.1 ± 5.0
0.05354 ± 0.02542
0.6748 ± 0.0274
60.4 ± 0.9

100
80
60
40
20
0

-15

-10

-5

0

5

v (cm)

100

191.4 / 112-9.797 ± 0.173
49.61 ± 1.65
41.53 ± 0.81
0.4913 ± 0.2513

80

140

χ2 / ndf

290 / 140

Mean

-0.186 ± 0.069

Width17.86 ± 0.14

120

Scale

58.47 ± 1.48

100

UpperSigma 0.6676 ± 0.1643

Floor

LowerSigma

Entries / 0.3cm

χ2 / ndf
Mean
Scale
Floor
Sigma

120

Entries / 0.3cm

Entries / 0.3cm

Figure 7.5: Cross section along vertical v (w > 2 cm).

100

36.54 ± 0.68

80

χ2 / ndf
Mean
Scale
Floor
Sigma

132.6 / 112
8.956 ± 0.139
39.21 ± 1.42
33.57 ± 0.76
0.6829 ± 0.2865

0.703 ± 0.142

60

80

60
60

40

0

20

20

20

-30

40

40

0

-20

-10

0

10

20

30
z (cm)

-30

-20

-10

0

10

20

30

z (cm)

0

-30

-20

-10

0

10

20

Figure 7.6: Longitudinal cross section of three slits along z (w >2 cm).

7.2

Time

The timing performance of the MEG detector is evaluated with a coincident radiative
muon decay as a time diﬀerence between the LXe detector and the positron spectrometer.
The single timing performance of the LXe detector was estimated by the measurement of
two gamma rays of π 0 decay using the opposite plastic counters in front of the NaI as areference. Another method was performed to measure an intrinsic time resolution, where
the diﬀerence of reconstructed times by subdividing PMTs in the LXe detector into twogroups were compared.
7.2.1

30

z (cm)

Intrinsic time resolution

The diﬀerence of reconstructed time from two divided groups of PMTs indicates theintrinsic time resolution. We performed the estimation on π 0 -decay data near the signal

Entries / 0.02cm

v (cm)

7.2

0.2

5
4

24

Mean

0.05218RMS

0.06442χ2 / ndf

5.497 / 8

Constant

103

0.1

0.3

2.274 ± 0.733

Mean 0.05079 ± 0.03103

3

Sigma 0.09465 ± 0.04149

0.15
0.1

Entries

Time

2

0.05
0

1

-0.05
-0.1
-20

0

20

0
-0.3

z (cm)

-35.9
-36

4
3.5
3
2.5

0

0.2

v (cm)

Entries24

Mean-36.13RMS
χ2 / ndf

2.844 / 9

0.0723

Constant 2.343 ± 0.806
Mean-36.11 ± 0.04

Sigma

0.111± 0.062

2

-36.1

1.5

-36.2

1

-36.3

0.5

-36.4

-0.1

(b) Projection of (a) on v.
Entries / 0.02cm

v (cm)(a) 10 mm vertical slit.

-0.2

-20

0

(c) 5 mm vertical slit.

20

z (cm)

0
-36.4

-36.3

-36.2

-36.1

-36

-35.9

-35.8

v (cm)(d) Projection of (c) on v.

Figure 7.7: Peaks on the long slit by scanning along z with width of ∆z = 2.1 cm.

energy. The word ‘intrinsic’ means that it includes a precision of timing estimation at each
PMT and electronics such as cable or synchronization but no ﬂuctuation of scintillation
light in the detector from a reﬂection or per-event shower development. It gives some
useful information such as position or the number of photons dependence of timing andthe diﬀerence between data and MC. PMTs are subdivided into two groups (odd andeven index number group) as shown in Figure 7.11. Its uniform and symmetric division
allows the same treatment with the same statistics of photons each other. The normal
time reconstruction is performed for each group and two obtained timings are compared.
The statistics of photons becomes half by two divisions, but that eﬀect for the intrinsic
time resolution is canceled out after the time diﬀerence is divided by two. Half of thetime diﬀerence between the odd-number and even-number group of PMTs is regarded as
the intrinsic time resolution, deﬁned as σ((teven − todd )/2). It resulted in 37.5 ps at 54.9
MeV and 30.5 ps at 82.9
√ MeV. Figure 7.17 shows that the dependence of the resolution
on energy is ﬁt with 1/ Eγ .
The dependence on position is also checked. Figure 7.12 shows a map of the intrinsic
time resolution of two groups. In the ﬁgure the u-v window for the scan is set to 1 × 1
PMT size and energy ranges around 54.9 MeV (40 MeV < Eγ < 60 MeV) and 82.9 MeV(70 MeV < Eγ < 90 MeV) are selected. Figures 7.13, 7.14 and 7.15 show the resolution
along depth w, u and v.

7. Performance of the Liquid Xenon Detector

0.85
0.8
0.75

Entries/(∆z = 2.1cm)

σv (cm)104

10mm slit

10

0.7
0.65
0.6
0.55
-20

0

20 z (cm)

5mm slitχ2 / ndf

8

Constant
Mean

0.6792 ± 0.0102

Sigma

0.05523 ± 0.00958

χ2 / ndf

6

7.766 / 95.456 ± 1.187

Constant
Mean
Sigma

4

6.502 / 14
3.086 ± 0.711
0.6475 ± 0.0272
0.1138 ± 0.0344

σv (cm)Figure 7.8: σv in 10 mm slits.
2
0.9
0.8

0

0.4

0.5

0.6

0.7

0.7

0.8

0.9
1
σv (cm)

0.6
0.5
-20

0

20 z (cm)Figure 7.10: Distribution of the position resolution σv in 5 mm and 10 mm slits (Fittings on
slices in z with 1/3 PMT width).

Figure 7.9: σv in 5 mm slits.

z

Figure 7.11: PMT grouping scheme forthe intrinsic time resolution study. PMTs
shown in blue circles belong to odd group,and those in orange circles belong to evengroup.

7.2.2

Absolute time resolution

The coincident time of two gamma rays are measured with scanning the whole acceptanceby moving the NaI detector at 24 positions (Figure 6.22). At each scanning position 50k
events were taken with using the plastic scintillators and the lead converter in front of the
NaI. Absolute time resolution was measured from the time diﬀerence between the LXeand pre-shower detectors.
Figure 7.16 shows the time diﬀerence between two detectors, which is estimated to be

v (cm)

7.2

Time

105

55

60
50

40

0

40

-20

35

-40

σ (teven - todd) / 2 (ps)

45

20

55

55 MeV50

83 MeV

45
40

30
35

-60
25

-20

-10

0

10

30

(ps)
20
u (cm)

1

10

w (cm)55

σ (teven - todd) / 2 (ps)σ (teven - todd ) / 2 (ps)Figure 7.12: u-v map of intrin- Figure 7.13: Intrinsic time resolution as
a function of depth.
sic time resolution.

55MeV

50

83MeV

45
40
35

55

40
35
30

25

25

-20

0

20

20
u (cm)

83MeV

45

30

20

55MeV

50

-50

0

50

v (cm)

Figure 7.14: Intrinsic time resolution as a Figure 7.15: Intrinsic time resolution as afunction of v (at u-center).
function of u (at v-center).

171 ps in sigma of Gaussian distribution at 54.9 MeV and 163 ps at 82.9 MeV. In this
distribution, main three components are considered,• Resolution of the reference pre-shower counter : 72 ps in σ,• Contribution from beam spread : (58 ± 2) ps in σ,• Time resolution of the LXe detector : to be estimated,
therefore time resolution of the LXe detector is calculated by subtracting contributionsof reference pre-shower counter and the beam spread to be 144 ps at 54.9 MeV and 134

106

7. Performance of the Liquid Xenon Detector

Number of events /(0.03 nsec)

ps at 82.9 MeV, respectively. √A dependence of the resolution on the energy was shown in
Figure 7.18, which results in 6592 (MeV)/Eγ + 1462 ps with a ﬁt.

700
600
500
400
300
200
100
0
-1.5

-1

-0.5

0

0.5
1
1.5
tXEC - tref (nsec)

50

200

Sigma of ∆ t/2 (psec)

Sigma of ∆ t/2 (psec)

Figure 7.16: Time diﬀerence between the LXe detector and pre-shower timing counter infront of the NaI.

45

180

40

160

35

140

30

120

25

100

20
σ = 277.8 / E

15
10

60
40

5
0
40

σ = 6592 / E + 1462

80

20
50

60

70

80

90
100
Eγ (MeV)Figure 7.17: Intrinsic time resolution as a function of the energy.

7.3

Energy7.3.1

Energy resolution

0
40

50

60

70

80

90
100
Eγ (MeV)Figure 7.18: Absolute time resolution as a function of the energy.

The energy resolution and scale of the gamma-ray detector are determined at 54.9 MeV
peak in π 0 run. Precise determination of the energy scale and measurement of the resolution are quite important to improve sensitivity of the experiment.
The energy peak is estimated with a combination of Gaussian function for higher energy part and exponential function for a tail. These two functions are smoothly connected
at transition point lower than the peak energy. Only in π 0 run, the pile-up elimination

7.3

Energy107

is not applied. Instead of that, to obtain the energy resolution in π 0 run, we considered a diﬀerence of pedestal between muon beam and charged pion beam by a following
procedure.
1. Prepare two pedestal distributions of the number of scintillation photons mixed
in a corresponding π 0 runs and also in physics run (200 µm or 300 µm degrader
separately).
2. The histograms prepared in the ﬁrst step are scaled by averaged non-uniformity
correction factor at each position.
3. Fit 54.9 MeV peak at the position by Exponential-Gaussian function convolved withthe pedestal histogram in the π 0 runs.
4. The Exponential-Gaussian component in the previous ﬁtting function is a intrinsic
resolution excluding a contribution of the pedestal distribution. Generate peak
distribution from the Exponential-Gaussian function with convolving the pedestal
histogram in the physics run, which is corresponding to the distribution duringphysics data taking without pileup elimination.
5. Fit the constructed 54.9 MeV peak with Exponential-Gaussian function.

Number of events / (0.64 MeV)

Figure 7.19 shows the energy peak at 54.9 MeV ﬁt with the function at 3 × 3 PMTs
region of upper central part (patch #8). The selection is applied for events deeper than
2 cm, opening angle larger than 175◦ and around 82.9 MeV peak at the NaI.

250
200
150
100
50
0

25

30

35

40

45

50

55

60
65
Eγ (MeV)Figure 7.19: Energy peak of 54.9 MeV in π 0 run.

7.3.2

Uniformity of reconstructed energy

The non-uniformity correction factors of energy scale are estimated using 17.7 MeV peaks
as described in Section 6.5.1. Figure 7.20 shows the distribution of peaks at various
positions by scanning the inner face with selections of one PMT size at 17.7 MeV or 1.5 ×
1.5 PMT size at 54.9 MeV. The broad distribution of 17.7 MeV peaks becomes sharp by

108

7. Performance of the Liquid Xenon Detector

the correction with 0.1% width in sigma. Although the correction factors were estimatedat 17.7 MeV, we have also conﬁrmed the factors by 54.9 MeV mean distribution, whichis as narrow as 0.28% in sigma.

U-V scan

18MeV peaks without correction
18MeV peaks with correction
55MeV peaks with correction

102

10

1
0.94

0.96

0.98

1

1.02

1.04
1.06
Peak / Energy

Figure 7.20: Peak distribution at 17.7 and 54.9 MeV by u-v scan. The non-uniformity
correction is not applied for broad distribution by 17.7 MeV peaks, and it gets sharp
after the correction. Peak at 54.9 MeV becomes also sharp with the same non-uniformity
correction.

7.3.3

Linearity of reconstructed energy

The linearity of the energy scale is checked using gamma rays from 4 to 129 MeV. Because
we determine the energy scale at 54.9 MeV, which is close to 52.8 MeV signal energy, theexistence of non-linearity is not severe and it can be corrected even if it exists. Within a
10-102 MeV region, we conﬁrmed a good linearity shown in Figure 7.21, and a correction of
non-linearity in the reconstruction is not necessary. The 5.5 MeV peak of alpha particles
is not on the line because the dominant scintillation process diﬀers from that of gamma
rays and W value is also diﬀerent.
7.3.4

Energy dependence of energy resolution

The energy resolutions in Figure 7.22 are estimated by means of gamma rays of 4.4 MeV
and 12.0 MeV from boron and of 17.7 MeV from lithium in CW run, and of 54.9, 82.9
and 129 MeV in π 0 run at patch #8 position of 3 × 3 PMT size. The resolution of 4.4
MeV AmBe peak is not shown here because it is not so reliable when subtracting neutron
backgrounds and its origin is the same as the reaction of the lower boron peak. At patch#8 of the energy determined position, the energy resolution as a function of energy is
obtained by ﬁt in Equation 68,()
10.4
σupper√ ⊕ 1.2 (%) (at patch #8, w > 2 cm).
=
(68)
E
E

Reconstructed Energy (MeV)

7.3

Energy

109

140
120
100
80
60
40
20
0
0

20

40

60

80

100 120 140
Truth Energy (MeV)

σupper (%)

Figure 7.21: Linearity of reconstructed energy in 4.4, 12.0, 17.7, 54.9, 82.9 and 129 MeV.

6

χ2 / ndf
p0
p1

5
4

2.945 / 4
10.41 ± 0.1766
1.201 ± 0.03842

10.42+1.22
Eγ

3
2
1
0
0

20

40

60

80

100 120 140
Energy (MeV)

Figure 7.22: Energy resolution at 4.4, 12.0, 17.7, 54.9, 82.9 and 129 MeV. The lower line
shows the contribution of pedestal.

7.3.5

Position dependence of energy resolution

Energy resolution in CW run and π 0 run The energy resolution depends on areconstructed position largely. The dependence is investigated in CW Lithium run andπ 0 run as shown in Figure 7.23. Resolution is worse in the shallow part and around theedge of the acceptance. The dependence is taken into account in the physics analysis.
Figure 7.24 shows energy resolutions. Each entry is taken by a window of one PMT size
at 17.7 MeV or 2 × 2 PMT size on the inner face. In the ﬁgure, the energy resolution in

110

7. Performance of the Liquid Xenon Detector

5.5

FWHM (%)

σupper (%)

sigma at 17.7, 54.9 and 82.9 MeV is simply averaged to be 2.8, 2.2 and 2.0 %, respectively.
In both ﬁgures peaks in π 0 run are raw without pedestal subtraction. Following section
shows a estimation of the energy resolution at 52.8 MeV µ+ → e+ γ signal.
18MeV Lithium peak

5

55MeV 2γ peak

4.5
4

18
55MeV 2γ peak

14

3.5

12

3

10

2.5

18MeV Lithium peak

16

8

2
6

1.5
1

1

1

10
Depth (cm)10Depth (cm)

5.5
5
4.5
4
3.5
3
2.5
2
1.5

FWHM by w.
FWHM (%)

σupper (%)σupper by w.
18MeV Lithium peak
55MeV 2γ peak

18MeV Lithium peak

11

55MeV 2γ peak

10
9
8
7
6
5

-20

0

20

-20

u (cm)

σupper by u (w > 2cm).
18MeV Lithium peak

3.5

0

20

u (cm)

FWHM by u (w > 2cm).

4

FWHM (%)

σupper (%)

12

55MeV 2γ peak

3

11

18MeV Lithium peak

10

55MeV 2γ peak

9
8

2.5

7
6

2

5
1.5

-50

0

50

σupper by v (w > 2cm).

v (cm)-50

0

50

v (cm)

FWHM by v (w > 2cm).

Figure 7.23: Energy resolution in σupper and in FWHM along (u, v, w) - directions. Bluedotted lines show the acceptance edges. FWHM at 17.7 MeV is derived from only thehigher peak in the ﬁtted function.

The energy resolution at diﬀerent u and v positions are evaluated by a window of
PMT-unit size, therefore a ratio of active to inactive area of inner-face PMTs is same inany scanning points. That means no resolution dependence on position within a PMT
appears. In order to look at a ﬁne structure of the energy resolution correlated with theoptical window of the PMT, a narrow window of 5 mm × 186 mm size, corresponding
to 0.08 × 3 PMT size, is selected for events at patch #8 position. Figure 7.25 shows
resolutions in sigma or FWHM as a function of u and v at 54.9 MeV. There may be
a little correlation with center of PMTs, however it is a trivial and there is no strongu-v divisions

7.3

Energy111

18MeV Lithium peak

90

55MeV 2 γ peak

80

83MeV 2 γ peak

70
60
50
40
30
20
10
0

1

2

3

4
5
σupper (%)

Figure 7.24: Energy resolution in σupper at 17.7, 54.9 and 82.9 MeV by u-v divisions.

FWHM (%)

σupper (%)

dependence. Therefore the ﬁne structure of energy resolutions within one PMT on the
inner face is averaged.
2.2
2.1
2

1.9
1.8
1.7
1.6

PMT
-10

-5

0

5

6.4
6.2
6
5.8
5.6
5.4
5.2
5
4.8
4.6
4.4

10
u (cm)

PMT
-10

-5

5

10
u (cm)(b) FWHM by u.
FWHM (%)

σupper (%)(a) σupper by u.
2.4
2.3
2.2
2.1
2
1.9
1.8
1.7
1.6

0

6.5
6
5.5
5

PMT

20

25

30

4.5
35 v (cm)

PMT

20

25

30

35 v (cm)(c) σupper by v.
(d) FWHM by v.
Figure 7.25: Energy resolution at 3 × 3 PMTs region of patch #8 position with a ﬁnescan. Events are selected by 5 mm × 186 mm window to check the resolution structure
within a 1-PMT size window. Arrows show the center of PMTs.

Signal PDF of gamma-ray energy in 2009 The signal-energy PDF is based on 54.9
MeV resolution in π 0 run and expressed by the Exponential-Gaussian function. Parameters are prepared for each three dimensional position. The PDF is estimated by one
PMT-size step in u and v directions with selecting 2 × 2 PMTs region within the acceptance, and w is divided into ﬁve windows, [0, 0.5], [0.5, 1], [1, 2], [2, 12] and [12, 38.6]
(cm).

112

7. Performance of the Liquid Xenon Detector

The procedure to obtain position dependent PDF at 52.8 MeV signal is described
below:
1. The energy resolutions on the inner face are measured at 9 × 24 positions with 2
× 2 PMT size window selection in one-PMT size step (w > 2 cm). The obtained
resolutions are shown in Figure 7.26.
2. In ﬁve depth divisions and wide range of w > 2 cm for the normalization, the resolution is also estimated by three divisions along u axis. The ﬁve depth-dependence
resolutions are normalized with that in the wide range.
3. The energy dependence of sigma and transition point is estimated from 4.4, 12.0,
17.7, 54.9, 82.9 and 129 MeV peaks at patch #8 position. From the relations ofsigma and transition as shown in Figures 7.27 and 7.28, respectively, conversion
factors into the signal energy are calculated.
4. The resolutions obtained at the ﬁrst step are scaled to take into account dependence
on depth and energy using factors estimated at the second and the third steps.
The eﬀect of the energy dependence is trivial for the resolution about 1% relatively.
On the other hand the eﬀect of the depth dependence is large particularly for a lower
tail in shallow depth. Figure 7.29 shows a function obtained from a ﬁtting on the 54.9
MeV data, and PDFs for signal at diﬀerent depths. Averaged resolutions of sigmas in thewhole acceptance are 2.1% (2 cm ≤ w < 38 cm), 2.8% (1 cm ≤ w < 2 cm) and 3.3% (0cm ≤ w <1 cm).
7.3.6

Systematic uncertainty

The candidates of uncertainties, which are related with gamma-ray energy scale, are listed
below,• Diﬀerence between expectations and other peaks of 82.9 MeV and 129 MeV : 0.3%,• Uniformity at 54.9 MeV energy in the whole acceptance : 0.3% (in Section 7.20),• Uncertainty of light yield monitor : 0.3% (in Section 7.3.2),• Uncertainty of gain : 0.09% (in Section 6.2.4, Figure 6.15),• Statistical uncertainty of ﬁtting 54.9 MeV peak : 0.05%.
The ﬁrst listed uncertainty includes the uncertainties of the non-linearity, the peakcorrection by the opening angle and the peak estimation by the ﬁt. The non-linearity ofenergy is not an issue because the 54.9 MeV peak for the energy determination is near tothe signal 52.8 MeV energy. The shift of the opening angle from the back-to-back angle,
however, brings higher shift of 54.9 MeV-like peak and lower shift of 82.9 MeV-like peakby the correction, while a 129 MeV peak is not corrected by the angle. The second term
indicates that the discrepancy of non-uniformity between 17.7 MeV peak used to makethe u-v correction and 54.9 MeV peak for the conﬁrmation is within its range. We do
not observe jumps or a gradient decrease in the light-yield monitor, then the stabilityof the light yield in third, which includes the precision of the monitor in CW run andEntries / (6.2 × 6.2 cm2) in acceptance

35
30
25
20
15
10
5
0
0

1

2

3

v (cm)(a) Distribution of upper σ in acceptance
(%)
4
60
3.5

40

20

3

0

113

Energy

40
35
30
25
20
15
10
5
0
0

4
5
σup (%)

2

4

6

8

10
12
FWHM (%)(b) Distribution of FWHM in acceptance (%)
v (cm)

Entries / (6.2 × 6.2 cm2) in acceptance

7.3

10
60
9
40
8

20

7

0
2.5

-20

-20

-40

2

-60

6

-40
5
-60

1.5
-20

-10

0

10

20
u (cm)

4
-20

-10

0

10

20

u (cm)(c) Map of upper σ (%)(d) Map of FWHM (%)
Figure 7.26: Energy resolutions at 54.9 MeV on inner face (w > 2 cm). The diﬀerence ofpedestal between π − and µ+ beam is considered in the ﬁt.

gain calibrations, is not used. The gain uncertainty is taken from the conﬁrmation of
the stability by the LED peaks in beam, therefore it includes all about the PMT gainsuch as gain calculation, shift and the stability of electronics. Final uncertainty of peak

2
1.8

χ2 / ndf

Transition [MeV]7. Performance of the Liquid Xenon Detector

σ [MeV]114-0.2

2.204 / 4

p0

0.09929 ± 0.001739

p1

0.01232 ± 0.0003982

-0.3

1.6
1.4

-0.4
1.2
1
-0.5
0.8
0.6
-0.6
0.4
0.2
0

20

40

60

80

100 120 140
Truth Energy [MeV]

Figure 7.27: Energy dependence ofenergy resolution σupper .

0

20

40

60

80

100 120 140
Truth Energy [MeV]

Figure 7.28: Energy dependence oftransition point from Exponential
to Gaussian in PDF.

U[-3.10,3.10] V[0.00,6.19]
1

0.8

W[0.0, 0.5] σ2.84 FWHM14.03
W[0.5, 1.0] σ2.73 FWHM9.45
W[1.0, 2.0] σ2.46 FWHM7.47
W[2.0, 12.0] σ1.85 FWHM5.04
W[12.0, 38.6] σ1.99 FWHM6.61
W[2, 40] σ1.86 FWHM5.19 (Original)

0.6

0.4

0.2

0

25

30

35

40

45

50

55

60
Eγ (MeV)Figure 7.29: Signal energy PDF of gamma rays normalized by height instead of area.
Conversion is applied with the energy correction, then the depth correction.

determination by the ﬁt is doubly counted, thus the uncertainty of the energy scale is∆Eγ = (0.3 ⊕ 0.3 ⊕ 0.09 ⊖ 0.05)% = 0.43%.

7.4

Background

7.4.1

Cosmic ray(69)

Cosmic ray background can contaminate physics data. The ratio of collected photons byouter face to inner face is an eﬀective parameter to discriminate cosmic rays from gamma
rays. This is because most cosmic muons penetrate the detector with a long path andilluminate many PMTs on several faces, while gamma rays from the target are mostly
converted near the inner face and the inner face detects many scintillation photons from

7.4

Background115

gamma rays. In addition to that, the depth from inner face is introduced to improve theselection eﬃciency. The cosmic-ray cut is performed on depth(w)-ratio(R) plane as shownin Figure 7.30 to reject deep events and to keep middle depth events,(w < a1 × R + b1 ) ∧ (w > a2 × R + b2 ),(70)

w (cm)

where parameter is optimized to be (a1 , b1 , a2 , b2 ) = (15, 22, −400, 120) after a ﬁne adjustment of b1 with considering the eﬃciency. This selection has 56% rejection power ofcosmic rays with 99% gamma-ray eﬃciency. It is applied for physics analysis.

35

Cosmic
ray

30
25
20
15
10
5
0
0.5
1
1.5
R (Inner / Outer ratio of the number of photons)

Figure 7.30: Depth and photons ratio of inner and outer face. Black square is cosmic ray
and red plot is gamma rays in the signal MC.

7.4.2

Background distribution

We prepared following inputs to extract position-dependent background PDF of gammaray energy,• A histogram of energy deposit in radiative muon decay (RD) in MC,• A histogram of energy deposit in annihilation in ﬂight (AIF) in MC,• Pedestal distribution of energy mixed in physics data with 200 or 300 µm degrader
separately,• Comic ray spectrum in real data,• Trigger eﬃciency for higher veto threshold to avoid cosmic rays,• Trigger eﬃciency for threshold around lower energy.
All estimation of background distributions can be done at teγ sideband before opening
blind region. Data periods with 200 µm or 300 µm degrader are separately treated withcorresponding pedestal data because of diﬀerent event distributions. Two types of trigger
eﬃciency curves are considered for cosmic-ray veto and the threshold at the low energy.

116

7. Performance of the Liquid Xenon Detector

Veto energy threshold for cosmic ray is around 63-64 MeV, and lower energy thresholdaround 42-44 MeV.
The cosmic-ray spectrum in physics data has a higher edge because of a veto thresholdin trigger. In cosmic-ray run with no beam, this veto eﬃciency can be checked by an event
ratio of cosmic rays with veto to that without veto as shown in Figure 7.31. Higher cut
oﬀ has about 9% resolution in σ. It is worse than expectation (about 3%) because somesignal heights from PMTs are saturated on the trigger board. The veto threshold relatively
diﬀers by reconstructed position because of the non-uniformity eﬀect of the reconstructed
number of photons. Thus, the estimation is performed by diﬀerent depth divided at 2 cm
and also by three (w ≤ 2 cm) or four (w > 2 cm) divisions along v direction to separately
treat around top and bottom faces within 1.5-PMT region along v from v edge. Insteadof the using veto eﬃciency curve directly, the cosmic ray with veto and without beam is
ﬁtted by polynomial function and used for the background component.

χ2 / ndf

15.7 / 44

CutoffEnergy 0.06105 ± 0.00044

1

Sigma

0.08634 ± 0.00777

Efficiency

The lower threshold eﬃciency in Figure 7.32 is estimated from an event ratio of datawith diﬀerent lower thresholds, that is data triggered with id 0 over that with id 1 (Idis deﬁned in Table 9). This eﬃciency does not aﬀect the physics analysis because it issuﬃciently low, but can be used for the studies in Eγ sideband data.

1
0.9
0.8

0.8

0.7

Entries7010
Mean
0.04865
RMS
0.003847
Underflow
0.3242χ2 / ndf
64.83 / 17
p0
0.04235 ± 0.00002
p1
0.001884 ± 0.000016
p2
0.973 ± 0.004

0.6

0.6

0.5

0.4

0.4

0.2

0.2

0.3

0.04

0

0.05

0.06

0.07
Eγ (GeV)Figure 7.31: Veto eﬃciency curve.

0.045

0.05

0.055
Eγ (GeV)Figure 7.32: Lower trigger threshold efﬁciency.

Finally the background spectrum is ﬁtted with the gamma-ray spectrum of RD and
AIF, the cosmic ray and the trigger eﬃciencies. The spectrum is sum of two RD and
AIF histograms weighted with each rate, convolves a pedestal with taking the pileup
elimination into account and is smeared by the detector resolution. Energy scale, thedetector resolution, the trigger threshold and the fraction of cosmic ray are extracted
as free parameters. Figure 7.33 shows a background histogram in 300 µm degrader run
and a ﬁt result superimposed with each component. The energy scale and sigma as aresult of the ﬁtting is used to check the uniformity, the stability and the scale of energy
independently from other calibrations.

7.5

3

RD + AIF in MC+ Resolution + Pedestal

Efficiency

117

Entries
10387
Mean
0.04502
RMS
0.003303
χ2/ ndf
82.24 / 69
AIF RD Con
245.9 ± 15.2
CR
0.025 ± 0.011
Sigma
0.02779 ± 0.00576
EScale0.9926 ± 0.0051
TRGAcc0.04254 ± 0.00010
TRGRes
0.03954 ± 0.00164

10

102

Total background10

Cosmic ray+ Veto efficiency
1

0.03

0.035

0.04

0.045

0.05
0.055
Eγ (GeV)

0.06

0.065

0.07

Figure 7.33: Background spectrum (300 µm degrader) from teγ -sideband data. Fitting
results from RD decay, AIF, cosmic ray and trigger eﬃciency of lower threshold are shownwith each component. RD and AIF are estimated in the MC and smeared by a resolution
as free parameters. Cosmic ray is taken from beam-oﬀ data with including veto eﬃciency
and the lower-threshold eﬃciency is ﬁtted as free parameters.

7.5

Eﬃciency

7.5.1

Detection eﬃciency

The LXe detector has a suﬃcient stopping power for a gamma ray with ∼14 X0 radiation
length. However, in order to reach liquid xenon from the target, gamma rays ought topenetrate the 0.075 X0 window of the LXe cryostat and COBRA magnet of 0.197 X0 .
Therefore gamma rays may not be detected or sometimes lose the energy before reachingliquid xenon. In the signal MC at 52.8 MeV, Figure 7.34 shows event distribution of theﬁrst conversion point of a gamma ray in radius on x-y plane, and 58% of events is withthe liquid xenon. Lower tail of a gamma energy peak mainly due to the energy depositin materials before reaching liquid xenon and the energy leak near the face. The fact
is indicated by the MC simulation as shown in Figure 7.35, where a diﬀerence between
energy deposit in xenon and reconstructed energy is symmetric.
The gamma detection eﬃciency is used for normalization in physics analysis as described later in Section 9.3. The eﬃciency in the whole acceptance was estimated withthe signal MC, and the consistency with data was checked. Counting two gamma raysfrom π 0 decay with tagging one in the NaI detector is a useful way to conﬁrm the absolutedetection eﬃciency. Then the diﬀerence between the data and the π 0 MC is regarded asa systematic uncertainty.

7. Performance of the Liquid Xenon Detector

0.035
0.03

(a.u.)

Events118

COBRA Magnet

Reconstructed energy
Reconstructed energy - Energy deposit
Pedestal

Liquid Xenon
Cryostats

0.025
0.02
0.015
0.01
0.005
0

48

0
20
40
60
80
100
Distance from target to first conversion on x-y plane (cm)Figure 7.34: First conversion point of
gamma rays in the MC simulation. Radius
on x-y plane shows that a conversion sometimes occurs before reaching liquid xenon.

7.5.2

49

50
51
52
53
54
55
Signal energy in the MC simulation (MeV)

Figure 7.35: Signal gamma-ray energy in
the MC simulation. Reconstructed energy
has a lower tail originated from energy loss.
A diﬀerence between reconstructed energy
and true energy deposit in xenon shows asymmetric distribution. Pedestal distribution is superimposed with shifted.

Measurement of two-gamma decay

We had dedicated run to take two gamma-ray decays triggered by the NaI detector. One
concern is a contamination of neutron backgrounds from π − p → γn, which is coincident
with a gamma ray in the tail from 129 MeV energy peak in the NaI detector.
By selecting gamma rays around 82.9 MeV in the NaI detector without any position
selections in the LXe detector, one can obtain energy spectrum in the LXe detector as
shown in a red dashed line in Figure 7.36. The procedure to obtain the detection eﬃciency
is following,
1. Gamma rays appear in the energy range of 54.9-82.9 MeV and 129 MeV at the NaI
detector. Fit 129 MeV energy in the NaI detector with an exponential-Gaussianfunction.
2. By using the ﬁtting result in the previous step, estimate the tail contribution from
129 MeV in 82.9 MeV region where is the same selected region in the ﬁfth step.
3. Make a template of 9 MeV neutron energy spectrum in the LXe detector by selecting
129 MeV peak at the NaI detector.
4. Scale the 9 MeV template of the LXe by the ratio obtained in the second step (bluehistogram).
5. Make a template of 54.9 MeV gamma-ray energy spectrum in the LXe detector by
selecting 82.9 MeV region at the NaI detector (red histogram).
6. Subtract neutron template (blue dashed histogram, in the fourth step) from raw
54.9 MeV distribution (red histogram, in the ﬁfth step), then obtain a 54.9 MeV

7.5

Efficiency

119energy spectrum (green distribution) only from π 0 decay without neutrons.
7. Set a lower energy threshold according to a window of physics analysis. The diﬀerence between µ → eγ signal and lower edge of two gamma rays from π 0 decays is
considered in the threshold, scaled by its peak ratio of 54.9(MeV)/52.8(MeV).

Subtract 129MeV tail at NaI with fit function
Subtract 129MeV tail at NaI with raw spectrum
2γ decay in the MC without neutrons

0γ from π and neutron

0.05

Efficiency at 55MeV peak

Entries [a.u.]

8. The number of events higher than the lower threshold normalized by total integration is regarded as detection eﬃciency

Neutron0

γ from π

0.04

0.03

0.02

0.01

0

0

20

40

60

80

100

120

Eγ [MeV]

0.75

0.7

0.65

0.6

0.55

44

46

48
50
52
Lower energy threshold (MeV)

Figure 7.36: Energy spectrum in the LXe Figure 7.37: Detection eﬃciency curve as adetector triggered by the NaI detector in function of lower energy threshold. A conπ 0 run.
tinuous line is the estimation from the MC,and dotted lines are actual measurementwith diﬀerent estimations of neutron background. 50 MeV energy corresponds to thelower edge of physics analysis region.

The detection eﬃciency is shown as a function of lower energy threshold in dotted lines
in Figure 7.37. The measured eﬃciency in π 0 run is diﬀerent from the signal eﬃciency
because the energy and position distributions are diﬀerent; therefore we use the data
only for validating MC. The signal eﬃciency used in physics analysis is calculated from
MC. In the π 0 setup, measured eﬃciency from the real data is 64-67 %, and the absolute
diﬀerence from that in MC with the same setup is 2%. We use the diﬀerence as asystematic uncertainty in the physics analysis.
7.5.3

Eﬃciency for analysis

Finally, the gamma-ray detection eﬃciency is calculated from the signal MC with the
2% error estimated from diﬀerence between real data and MC in π 0 run. The detection
eﬃciency is deﬁned by a probability that the reconstructed energy of a signal gamma ray
is within analysis region, that is larger than 48 MeV in 2009.
The detection eﬃciency depends on the position on the inner face, thus we estimated itby eight divisions. For example, at corners or edges, the eﬃciency is 55-56% and at center,
it is 68%. In order to calculate the normalization factor, we need to know a conditional

120

7. Performance of the Liquid Xenon Detector

probability to detect and reconstruct a gamma ray once a positron is triggered. Thus
we take a weighted average of eﬃciencies with taking the angle distribution of positrondetection into account, and it is estimated to be 64.7%. Taking analysis eﬃciency of a
LXe
gamma ray, 89.3%, into account, the conditional probability, ϵLXe=eγ , is resulted in ϵeγ
0.647 × 0.893 = 0.578.

121Part IV

Combined Analysis and Performance
8

Performance of Positron Detector

8.1

Time resolution of timing counter bars

2400

χ2 / ndf = 70.73 / 17

2200
2000
1800
1600
1400
1200
1000
800
600
400
200
0

Constant

2177 ± 18.4

Mean

0.2162 ± 0.0007

Sigma

0.09552 ± 0.00067

σ(tA - tB) / 2 (nsec)

High-energy positron from µ+ → e+ νe ν µ sometimes penetrates a few bars and it canbe used for the calibration. Time oﬀset of each scintillation bar is calibrated in µ+ →e+ νe ν µ by collecting positron hits in two adjacent scintillator bars. Time oﬀsets of bars
are calibrated relatively between bars. Although the averaged time of ﬂight between bars
is estimated to be 200 ps in MC simulation, the diﬀerence of time between bars can bealso calculated event by event by using a positron track. When calibrating the time oﬀset
in µ+ → e+ νe ν µ we considered the time of ﬂight between bars based on the reconstructed
track.
The width of the time diﬀerence distribution of the two hits gives the time resolution.
For a single bar resolution, the width is divided by squared root of two assuming thatthe two have the same resolution. Figure 8.1 shows the time diﬀerence between bar 1
and 0, and Figure 8.2 shows the time resolution of each bar in 2008 and in 2009. The
periodical worse resolutions come from the accuracy of the clock synchronization overdiﬀerent DRS chips because internal synchronization for four channels in a chip is better
than that between chips with a use of diﬀerent clocks. One worst point of bar 15 in 2008is because the DTD channel had a defect. The averaged resolution is 76 ps in 2008 and75 ps in 2009. We also checked a quality of calibration by using the CW-Boron run. Once
the LXe detector detects a 4.4 MeV low energy gamma of coincident two gamma raysfrom boron as a reference time, then the other 12.0 MeV gamma allows a measurementof timing at a timing counter bar.

Sep. 2008

0.12

Nov. 2008
2009

0.1
0.08
0.06
0.04

downstream

upstream

0.02
-1

0

1
2
t bar1 - tbar0 (nsec)

0

0

5

10

15

20

25
Bar #

Figure 8.1: Time diﬀerenceof two bars in double-hit Figure 8.2: Time resolution of single bar for each two bar
set.
events.

122

8. Performance of Positron Detector

8.2

Quality of positron reconstruction

The quality of positron tracking is categorized into two in order to treat the diﬀerent
performance with two sets of PDFs for the µ+ → e+ γ physics analysis. Mainly a diﬀerencealong z and r between drift-chamber and timing-counter hit, ∆z and ∆r, separates thequality. That is the diﬀerence between the extrapolated track by only the drift chamber
and the hit reconstruction only by the timing counter. Low quality is selected within|∆z| < 12 (cm), |∆r − 1.8| < 5 (cm) and the number of hits larger than seven, while thehigh quality is more strict within |∆z| < 6 (cm) and |∆r − 1.8| < 3 (cm), the numberof hits larger than ten and less uncertainties of the momentum, the angle and the chisquared of ﬁt. In Figure 8.3 the ﬁlled area shows a high-quality region of ∆z and ∆r.
3500

600

3000

500

2500

400

2000

300
1500

200
1000

100

500
0

-30

-20

-10
0
10
20
30
∆ z (Tracking - Timing counter) (cm)

0

-6

-4
-2
0
2
4
6
∆ R (Tracking - Timing counter) (cm)(a) ∆z(b) ∆rFigure 8.3: z or r diﬀerence between tracking andtiming-counter hit. The ﬁlled area is high-quality region.

8.3

Positron energy

In actual data we have two ways to obtain the resolution of positron momentum. The
ﬁrst method is to ﬁt the energy distribution of normal muon decay, µ+ → e+ νe ν µ , witha convolved function of a theoretical prediction in the SM and a double Gaussian distribution as the resolution contribution of a core and a tail. Figure 8.4 illustrates theGaussian in a dotted line and convolved function in a solid line. These estimations of low
and high quality are separately shown in Figures 8.5 (a) and (b). We ﬁt only high energy
region (> 50 MeV) to exclude possible momentum dependence of the resolution. The energy scale of the positron is determined by the Michel spectrum. There is a discrepancy
between upstream and downstream side, thus it is corrected by a shift about 64 keV.
The other way is to estimate the energy resolution by the diﬀerence between two
independent energy reconstructions of only one-turn track in the events observed as twoturn track. In the MC a true resolution deﬁned as a diﬀerence between reconstructed
and generated energies can be checked. The systematic uncertainties associated to the
double turn method have been evaluated by comparing true and measured resolutions in
MC samples with diﬀerent single hit resolutions and by comparing resolutions from two
diﬀerent methods. Statistical uncertainties are negligible compared to them.
The resolution is described by triple or double Gaussian. In 2009 the two-turn method
is used and the resolution is described with double Gaussian, estimated to be 0.39 MeV

Number of events /(0.10 MeV)

8.3

Positron energy

5000

4000

3000

2000

1000

50

51

52

53

54

55
56
Ee (MeV)

Number of events /(0.18 MeV)

Number of events /(0.18 MeV)

Figure 8.4: Energy distribution of positrons from muon decays, µ+ → e+ νe ν µ .
2500
2000
1500
1000

4000
3500
3000
2500
2000
1500
1000

500

500
0
50

51

52

53

54

55
56
Ee (MeV)

0
50

51

52

53

54

55
56
Ee (MeV)(a) Low-quality tracking(b) High-quality tracking
Figure 8.5: Energy distribution of tracking positrons from muon decays, µ+ →e+ νe ν µ , by two categories of the tracking quality.

123

124

8. Performance of Positron Detector

as the core resolution (σcore ) in 79% fraction (fcore ) with 1.71 MeV sigma as a tail (σtail )in 21%. The typical energy performance is summarized in Table 13 with the two qualitiesof positron tracking.
Table 13: Resolution of signal positron energy Ee with double-turns methodEeσcore (MeV)
fcore
σtail (MeV)

8.4

GlobalHigh Quality Low Quality
0.390±0.003 0.340±0.004 0.414±0.004
0.788±0.003 0.907±0.008 0.740±0.005
1.71±0.02
0.907±0.008
1.76±0.02

Positron angles

The resolution of emission angle ϕe is taken from actual data in the two turn method.
Typical ϕe resolution is given in Table 14 and expressed in double Gaussian with zeromeans.
Table 14: Positron ϕe of signal
ϕe
σcore (mrad)
fcore
σtail (mrad)

GlobalHigh Quality Low Quality
7.08±0.05
6.03±0.137.42±0.07
0.852±0.004 0.878±0.017 0.831±0.005
26.6±0.4
16.2±0.8
27.6±0.4

The resolution of θe is also estimated from double turns and expressed in Gaussianwith correcting the diﬀerence of a measured value from true one in the signal MC. Table
15 summarizes θe resolution with tracking qualities.
Table 15: Positron θe of signal
θe
σ (mrad)

8.5

GlobalHigh Quality Low Quality
11.15±0.03
9.72±0.05
11.63±0.04

Decay vertex resolution

The position of the decay vertex is determined by the extrapolated positron tracking
because there is no vertex detector and the LXe detector has a poor determination of a
gamma-ray direction. There are two ways to estimate the position resolution of positron
tracking in data. One is to see holes on the target and the other is to estimate thediﬀerence of each separated turn of the track, which is recognized with over two turns.
The vertex resolution in 2009 is obtained from the hole method along minor verticalaxis (Y ) and major axis on the plane (Z) as listed in Table 16. In the case of the two-turn9. Combined analysis of a Gamma ray and a Positron125

method, the resolution is calculated as 2.3 mm and 2.8 mm along minor and major axis
respectively.
Table 16: Vertex position resolutions from views of the holes on the muon target
Vertex (Z,Y)σZ (cm)σY (cm)GlobalHigh Quality Low Quality
0.344±0.007 0.330±0.009 0.360±0.015
0.328±0.007 0.302±0.009
0.42±0.04

9Combined analysis of a Gamma ray and a Positron

9.1

Relative angle, θeγ and ϕeγ

The direction of a positron emission on the stopping target is determined by extrapolating
positron tracks to the crossing points on the target. The emission angle of a gamma ray
is calculated from the position in the LXe detector and the vertex position expected bya positron. The opening angle Θeγ between these two directions is obtained from twodimensional angle of gamma ray and positron,cos Θeγ = sin θγ cos ϕγ sin θe cos ϕe + sin θγ sin ϕγ sin θe sin ϕe + cos θγ cos θe .

(71)

We use a two dimensional angles of the polar θ and the azimuthal ϕ directions from beamaxis. The diﬀerence of these angles is deﬁned as
θeγ = θγ − (π − θe ), ϕeγ = ϕγ − (π − ϕe ),(72)

so that these make peaks at zero for the signal events.
The µ+ → e+ γ decay is physically identiﬁed with opening angle of Θeγ between apositron and a gamma ray. In the PDF point of view it is desirable to adopt θeγ and ϕeγ
as observables with a better expression of the position dependent resolution, instead of
Θeγ . This is because the resolutions in the MEG detector with a cylindrical symmetry
depends strongly on θ and a dependence of resolutions on θ is diﬀerent from that on ϕ.
Practically the resolutions of relative angles are calculated from those of z and ϕ for boththe LXe and the DCH detectors and those of vertex position with measured positions.

9.2

Relative timing teγ

The coincident radiative decay, µ+ → e+ νe ν µ γ, has a peak of the relative timing on theﬂat accidental ﬂoor. The time resolution from RD includes all contributions of timingfrom the LXe detector, positron tracking and electronics. Even before opening the blind
region, the coincident timing peak appears in the lower Eγ sideband and it is useful toknow a combined timing performance.
Figure 9.1 shows the peak in Eγ sideband in a range of 40 MeV ≤ Eγ ≤ 47 MeV, 45
MeV ≤ Ee ≤ 55 MeV and within 300 mrad opening angle. The peak is ﬁtted with double
Gaussian function and timing resolution resulted in 149±10 ps in 70% fraction as core
sigma and 250 ps sigma. To evaluate the performance at the signal region, we correct

126

9. Combined analysis of a Gamma ray and a Positron

Number of events /(0.080 nsec)

small gamma-energy dependence of the timing resolution, and it is estimated to be 142
ps in sigma. We carefully checked the stability of teγ and conﬁrmed the constant peakwithin 15 ps.

2000

1500

1000
mean = 0 ± 8 ps
sigma = 149 ± 10 ps

500

0

-1

0

1
teγ (nsec)

Figure 9.1: Time diﬀerence between positron and gamma ray in 2009.

9.3

Normalization factor for µ+ → e+ γ

9.3.1

Principle

A diﬃculty to determine the normalization factor is the treatment of the detection eﬃciencies. It is not independent of time, especially in 2008 due to HV discharge problems
in the drift chamber, and also of emission angles.
We have three methods to count muons by counting primary protons, gamma raysfrom radiative decays or positrons from Michel decays. In the ﬁrst method to count the
protons, monitored the intensity of the beam oﬀered from PSI and a measured ratio of
stopping muons in the target to primary protons allows to estimate the total number ofmuons. In order to calculate the normalization factor from protons, we have to know thedetection eﬃciencies in all the detectors.
Secondly, by counting radiative muon decays both in the LXe detector and in positron
spectrometer, both the detection eﬃciency of these detector and the direction match
eﬃciency in the trigger can be taken into account, however, the statistics is very low.
By the following reasons the best way to count muons is to use positrons from normal
Michel decays, µ+ → e+ νe ν µ , in the positron spectrometer.
• µ+ → e+ γ candidate is counted relatively from another channel of the Michel decay
and it is suitable to estimate branching fraction.
• The change of detection eﬃciency such as HV problem or missing channels is compensated by taking only positrons from Michel decays simultaneously with physics
data.

9.3

Normalization factor for µ+ → e+ γ

127

• The change of beam intensity is also included in counted positrons thanks to continuous data taking of Michel positrons during physics run.
• The detection eﬃciency of positron tracker can be almost compensated betweenµ+ → e+ γ and µ+ → e+ νe ν µ .
• Share the analysis cut for the positron with the signal event.
• Stopping eﬃciency in muon target does not need to be known.
For the gamma-ray detector we could acquire the detection eﬃciency in MC and checka consistency between measurement and MC with using two gamma-ray decay in π 0 run(Section 7.5.1). The method allows to obtain a branching fraction of µ → eγ normalizedby µ+ → e+ νe ν µ and µ+ → e+ νe ν µ γ, that is Γ(µ+ → e+ γ)/Γ(µ+ → e+ νe ν µ (γ)). Because
we do not use low energy positrons, the obtained total fractions are almost the same asthat of µ+ → e+ νe ν µ , Γtotal ≃ Γ(µ+ → e+ νe ν µ ).
9.3.2Counting the Michel decay, µ+ → e+ νe ν µ

The total number of the Michel decay (MD), NM D , is estimated from the event triggeredwith only timing ϕ counter (Trigger id #22 as described in Table 9) mixed in the MEG
physics data taking simultaneously. It consists of some eﬃciencies and acceptances,
Ee ∈Eselection
NM D = Nµ × Teνν × Beνν × feνν
×

1
Peνν

T IC
DCH
DCH
× ϵtrigeνν × Aeνν × ϵeνν × Aeνν ,(73)

where each factor is denoted as the following:• Nµ × Teνν : The number of stopped muons during a livetime, Teνν
• Beνν : The branching ratio of Michel decayE• feνν
: The fraction of Michel spectrum above 50 MeV• Peνν : The pre-scale factor of the TIC-self trigger• ϵtrigeνν : The conditional trigger eﬃciency
IC: The conditional acceptance of timing counter including the probability of• ATeνν
DCH-TIC matching: The conditional tracking eﬃciency including the selection criteria• ϵDCHeνν• ADCH: The geometrical acceptance of the drift chamber.
eννOn the other hand the total number of µ+ → e+ γ signal, Nsig , is described as,
DCH
T IC
× ALXe× ϵLXe× ADCH
Nsig = Nµ × Teγ × Beγ × ϵtrig
eγ ,
eγ
eγ
eγ × Aeγ × ϵeγ(74)

where the similar terms are deﬁned as the same way in previous expressions, while othercontributions for the gamma-ray detector and trigger eﬃciency of gamma rays and amatching are introduced as below,

128

9. Combined analysis of a Gamma ray and a Positron• ϵLXe: The gamma-ray detection and the reconstruction eﬃciency including selectioneγ
criteria• ALXe: The conditional acceptance of the gamma ray from µ+ → e+ γ decayeγ
The pre-scale factor of signal, Peγ , is equal to 1 and the monochromatic signal energyEmake a fraction of signal spectrum, feγeγ , is to be 1, thus these are omitted. The fractionof each term is
Ee ∈Eselection
IC
Nsig
ϵtrig
Beγ
feνν
ATeνν
ϵDCH
1
1
eνν
=
× trig × T IC × eνν×× LXe × LXe .
DCH
Beνν
NM D
Peνν
Aeγ
ϵeγ
ϵeγ
Aeγ
ϵeγ

(75)

What we have to estimate is k factor deﬁned as
1/k =

1
Beγ
·
Nsig Beνν

Ee ∈Eselection
IC
ATeνν
feνν
ϵtrig
ϵDCH
1
1
eνν
×
=
×
× eνν
×
× LXe × LXe .
trig
T
IC
DCH
NM D
Peνν
Aeγ
ϵeγ
ϵeγ
Aeγ
ϵeγ

1

(76)
(77)

The ineﬃciency of the Michel decay trigger originated from a high rate compared witha live time of trigger scaler. The intrinsic trigger rate by the Michel decay is about 107
Hz, while the trigger signal to be used is 80 ns width window to make a coincidence with
the LXe detector. Therefore the ineﬃciency from accidental pileup as a ratio of actual tomeasured rate, (Rtrue /Rmeasure − 1), is easily estimated to be 20% in 200 µm thickness
degrader and 15% in 300 µm. This diﬀerence is because the triggered rate in 200 µm
degrader is higher than in 300 µm at the timing counter, although actual Michel trigger
is lower.
The direction match eﬃciency between a positron and a gamma ray, ϵDM , is a domtrig
inant diﬀerence of ϵtrig
eγ from ϵeνν , which was estimated with signal and radiative eventsin MC. The eﬃciency to Θ = 180◦ region is estimated by extrapolating the eﬃciencies at
each opening angle, to be ϵDM = (83.5 ± 2(stat.) ± 0.5(syst.))%.
The each factor in 2009 was evaluated to be below:• NM D : The number of observed Michel decays, 18,096 events, 5% error,
Ee ∈Eselection• feνν
: Fraction of Michel spectrum, 0.114±0.002,• Peνν : Pre-scale factor, 107 (ineﬃciency correction : 1.17),
trig• ϵDM ≡ ϵtrig
eγ /ϵeνν : Reconstruction eﬃciency for positron, 0.84±0.02,
DCH DCHIC• ATeνν/ATeγIC × ϵeνν/ϵeγ : Timing counter eﬃciency given momentum distribution
and reconstruction eﬃciency for positron, 1.12±0.06,: The eﬃciency for the gamma inside the acceptance, 0.58±0.02,• ϵLXeeγ: 0.99±0.01,• ALXeeγthen the normalization factor is resulted in
1/k = (1.01 ± 0.08) × 10−12 .

(78)

9.4

9.4

Systematic uncertainty

129

Systematic uncertainty

The uncertainties in 2009 are listed in Table 17. The systematic uncertainty of Eγ isestimated in Section 7.3.6. As the relative angle, a large uncertainty is set because thez alignment of the LXe detector may have a shift of a few mm suggested by position
measurements with a radio active source or cosmic rays, while the uncertainty of positron
angles is about ±1.5 mrad. The systematic uncertainty from correlation of δEe − δϕe isroughly estimated from the MC, where δ means the true resolution between the reconstruction and the generation. The systematic uncertainty for the relative time is takenfrom the uncertainty in ﬁtting and the stability. The resolution of it is also taken fromthe ﬁt uncertainty and the correction uncertainty by the gamma-ray energy. The eﬀect of
the systematic uncertainty for the physics analysis is small as discussed later in Section
10.7.4.
Table 17: Systematic uncertainty in 2009.
Eγ

Ee

σEe

0.43%

50 keV

15%

θeγ ,
ϕeγ
7.5 mradσθeγ ,σϕeγ
10%δEe − δϕecorrelation
50%

Teγ

σTeγ

15 ps

10%

Normalization
8%

130

10. Analysis for the µ+ → e+ γ SearchPart V

Physics Analysis on 2009 Data
10

Analysis for the µ+ → e+γ SearchThis part shows the analysis to calculate the branching ratio of µ+ → e+ γ from 2009
data. What we exactly calculate is the branching fraction, but its ratio is approximately
equal to the branching ratio of µ+ → e+ γ,Br(µ+ → e+ γ) ≃Γ(µ+ → e+ γ),
Γ(µ+ → e+ νe ν µ )(79)

because the 8% error of normalization factor counted by Michel decay in Equation 78 ismuch larger than diﬀerence between Γ(µ+ → e+ νe ν µ ) and a total Γtotal .
A maximum likelihood analysis is performed to extract the number of signal from thedata. Thus, we deﬁne a likelihood function with probability density functions (PDFs) ofobservables.
A conﬁdence interval of the best ﬁt number and a sensitivity of the branching ratio are
estimated in a frequentist approach. To construct conﬁdence interval, a frequency probability of the 2009 data is estimated in many simulated experiments with each assumptionof the number of events. The sensitivity with null-signal assumption is calculated withtaking average of branching-ratio upper limits by many generated experiments.
In order to avoid some human biases, we blinded the region around µ+ → e+ γ until
calibration and analysis had been ﬁxed [61]. However, the above analysis can be done in
sidebands beside the blind region with the same procedure as that for the blind region
even before opening the blind region. The result of the maximum likelihood ﬁt in the
null-signal sideband region gives useful information such as backgrounds and a sensitivity.
The blind procedure is not necessarily for a likelihood analysis rather than a cut analysis,but it would make the analysis reliable.

10.1

Strategy

Our analysis proceeds with blinding a signal. The blind region is a little wider than theanalysis region because a precision of reconstructions is worse at the early stage of thecalibration. The analysis procedure is below:
1. Event pre-selection and process with blinding as soon as data taken.
2. Repeat calibration and reprocessing with improving quality before opening blind
region.
3. Estimate resolution, PDF and determine selection.
4. Study in the Teγ sidebands such as a maximum likelihood ﬁt and a sensitivity
calculation. Some predictions of backgrounds in the blind region are available.
5. Optimize and ﬁx the analysis procedures.

10.1

Strategy131

6. Open blinded region.
7. Maximum likelihood ﬁt for analysis region.
8. Calculate conﬁdence interval of branching ratio.
From the second to the fourth process, there are developments of the event reconstruction
and an iteration in order to improve calibrations and analysis before the ﬁnal physics
analysis.
10.1.1

Event selection and blinding

Pre-selection As soon as physics data is taken, a ﬁrst analysis is performed. During
the ﬁrst process a event pre-selection is performed and the original raw data is blinded
only in physics run. The purpose of pre-selection is to reduce data size and accordingly
to make the following physics analysis fast. Mixed calibration or monitoring sources areout of selection for the physics analysis and these become accessible as well as normal
dedicated calibration runs. At the ﬁrst analysis the quality of calibrations is low or not
done, thus the pre-selection is enough loose to avoid a loss of good events and uses only
timing information of PMTs in the LXe detector and timing counter.
The pre-selection is deﬁned as,• −6.875 ns < tγ − tT ICHIT < 4.375 ns,• |ttrack − tT IC | < 50 ns,
where tγ is the gamma-ray emission time at the center of target and tT ICHIT is a hit timingfrom the timing-counter bar. There is no use of tracking information at this stage. In theﬁrst window there is a wider region for a late tT ICHIT not to lose hits after multi-turn.
The second condition requires at least one track, associated with the trigger, is found.
The events are decreased by 0.3-0.4 factor with a pre-selection. Data out of pre-selection
is never used and analyzed except for calibrations, while the selected events has some
reprocessing and provides regions of a signal, blinded, an analysis and a sideband besidea blind box.
Blind region The blinding process for the pre-selected events uses two information ofa gamma-ray energy and a time diﬀerence,• |Eγ − mµ /2| < 4.8 MeV,
• |teγ | < 1 ns,
and the blind box is opened after all analysis and calibration are ﬁxed. The blind regionis shown in Figure 10.1, as well as sidebands. The sideband of teγ gives a useful information about accidental backgrounds because it is independent from teγ . Another usefulknowledge is obtained at lower Eγ sideband, where we can see the teγ peak from radiative
muon decays. Those two allow to estimate backgrounds level in blind box before openingit.

10. Analysis for the µ+ → e+ γ SearchEγ (MeV)

132

62
60

Blind box

58
56
54

Teγ
left
sideband

Analysisregion

52

Teγ
right
sideband50
48

Eγ sideband

46
44
-2

0

2
t e γ (nsec)

Figure 10.1: Event distribution on Eγ - teγ plane. Blind region is shown in a blank box.

10.1.2Analysis region and acceptance cut

The analysis window is considered separately from a signal window of cut analysis. In
general, the signal window is deﬁned as a narrow window according to the resolution of
the detector for observed kinematics in order to discriminate signals from background
events well. While the our analysis window uses a ﬁtting region for the likelihood analysis
and it can be deﬁned in wider range. Because all events both from signal and backgroundin the region are ﬁtted simultaneously, ideally the result is independent on the selectionof the window.
We deﬁned the analysis region in 2009 run as follows:• |teγ | < 0.7 ns,• 50 MeV < Ee < 56 MeV,
• 48 MeV < Eγ < 58 MeV,• |ϕeγ | < 50 mrad and |θeγ | < 50 mrad.
Lower energy limit of gamma-ray energy is high enough to avoid the bias from the trigger
threshold and upper energy limit is also set. The window is narrower than the analysis
in 2008 except for the same region of positron energy.
Additional cuts for the acceptance and the quality of the reconstruction are applied.
As the LXe detector, a gamma-ray position is reconstructed using only PMTs on innerface and energy leaks are larger around the edge of the detector. Therefore the acceptanceselection is applied as |u| < 25 cm, |v| < 71 cm and all depths, where the acceptanceregion excludes a half size of PMT around edges of u and v. The quality of positron
tracking is separated into two groups to apply diﬀerent PDFs as described in Section 8.2.
Additionally at least four hits in the drift chamber and a vertex position within 8.24 cm
along longitudinal axis and 2.8 cm along vertical axis are required.

10.1
10.1.3Strategy133

Experiments simulation

Our goal is to obtain a conﬁdence interval of the number of signal by a distribution ofa frequency probability. A frequency probability of the experiment is evaluated in many
simulated experiments with each assumption of the number of signal and backgrounds.
We can estimate a conﬁdence region by scanning the numbers to be generated.
The eﬀect of the statistical ﬂuctuation by experiments can be taken into accountwith a generation of many experiments under the same setup and the performance but
a diﬀerent event set. It is important to simulate a large number of experiments for arare-event observation such as the MEG experiment.
The simulated experiments are so called ‘toy Monte Carlo (toy-MC) experiments’generated by toy-MC simulation to be distinguished from a usual full MC simulation of
detectors started with particle generations. The toy MC uses only acquired performanceof the detectors and measured data set without using any information of materials orinteractions in the detectors’ geometry. That means there is only statistical treatment
in toy MC but no kinematics because PDFs and data set have all information of those.
For a precise way, the PDFs are prepared event by event to express the exact detector
performance. It is possible to use the same PDF set, associated with actual data set, forall toy-MC experiments because the performance of detectors are inherent in the detectors
setup and the the experiment. Actual data set are used for the event generation, whichcontains a realistic information about a correlation of observables and a distribution ofobserved events with a trigger and detection eﬃciency and particle emissions. A random
event pickup from data set provides associated PDF set in the event and the PDFs canbe a seed of new event generation with a random selection of observables from that PDF.
Events in a certain experiment are generated by PDFs with a speciﬁed set of thenumber, (Nsig , NRD , NBG ). Here we note that the number of µ+ → e+ γ events as Nsig ,that of µ+ → e+ νe ν µ γ events as NRD and that of accidental background events, which ismost dominant in the events, as NBG . The number to be generated is usually ﬂuctuatedwith Poisson distribution around speciﬁed number. One of advantages in toy MC isthat we can arbitrary determine the true number of each event type, signal and two
backgrounds in generation. It allows to evaluate the performance of the likelihood analysis
by comparing the best ﬁt result of the number with true generated number.
The strategy to simulate one experiment is below.
1. Prepare a data set from data in 2009.
2. Determine a set of number of events, (Nsig , NRD , NBG ), to be generated and is
randomly ﬂuctuated with Poisson distribution except for the number to be ﬁxed.
3. Select events from the data set randomly.
4. Form PDFs associated with the selected event for a speciﬁed event type.
5. Generate observed variables randomly from PDF distributions.
We prepare a data set based on actual data and it includes a detection bias by emission
angle or trigger eﬃciency and a correlation between observables. It is diﬃcult more orless to separate the data set by event type (Nsig , NRD , NBG ) and accidental backgroundis most dominant while others is less than that, so we determine to use a common list for134

10. Analysis for the µ+ → e+ γ Search

all event type. For a polarized muon we have to choose a diﬀerent list between event typeand a event distribution of signal depends on physics model.
10.1.4Conﬁdence region

There are some methods to extract conﬁdence region of branching ratio. We adopted
Feldman-Cousins approach to estimate the conﬁdence level of Br(µ → eγ) , which is thesame as 2008 analysis [62]. Other methods are also tried for a consistency check.
From now on, the best ﬁt values of N is represented with hat, N̂ , and type of event(data or j-th toy MC) on superscript and i-th sampling points on subscript. We introduce
data
data
data
the Feldman-Cousins procedure. The conﬁdence level around the point, (N̂sig, N̂RD, N̂BG),is estimated for each i-th sampling point, (Nsig,i , NRD,i , NBG,i ). The scan of interesting region by collecting sampling points gives a contour of the conﬁdence level on (Nsig , NRD , NBG ).
In order to estimate the conﬁdence level at each i-th sampling point, we simulate many
experiments by each sampling point that is used for the generation as the number of
events. The j-th toy experiment at the i-th sampling point gives the best ﬁt value of thejjjmaximum likelihood ﬁt, (N̂sig,i, N̂RD,i, N̂BG,i). To order the results, a probability of dataat sampling point, (Nsig,i , NRD,i , NBG,i ), is compared to those of toy-MCs at the same
point. Feldman-Cousins method uses a ratio of likelihood,
Rdata,i =
j
RM
C,i =

L(Nsig,i , NRD,i , NBG,i )
data
data
data
L(N̂sig, N̂RD, N̂BG)
L(Nsig,i , NRD,i , NBG,i )jjj
L(N̂sig,i, N̂RD,i, N̂BG,i
)

,

(80)

,

(81)

and the conﬁdence level is determined by the probability,j
P (RMC,i > Rdata,i ) =

N
MC
∑
j

{
j
H(RM
C,i − Rdata,i ) =j
H(RMC,i − Rdata,i )
,
NM C

j
1 (RM
C,i ≥ Rdata,i ),j
0 (RMC,i < Rdata,i ).

(82)

(83)

The scan by sampling points i gives the conﬁdence distribution. Our ﬁnal purpose is to
extract the 90% conﬁdence interval of Nsig from the conﬁdence region on (Nsig , NRD , NBG ).
We checked no obvious correlation between the numbers of (Nsig , NRD ). Hence we assume
that the number of signal and radiative decay are independent each other. The numberof radiative background and accidental background, NRD , NBG , can be ﬁxed to the best
data
data
ﬁt value respectively N̂RD
, N̂BGand we estimate the conﬁdence level along Nsig .
10.1.5Eﬀect of systematic uncertainty

The systematic uncertainty can be taken into account at the calculation of conﬁdence levelby randomly ﬂuctuating the PDFs according to the systematic uncertainties. Technicallyafter experiments’ simulation the PDFs are shifted when ﬁtting in the range of systematic
uncertainties such that the degree of shift is randomly determined by each experiment.

10.2

10.2

Maximum likelihood analysis

135

Maximum likelihood analysis

The goal of the maximum likelihood analysis is to obtain the best ﬁt value of the numberof µ+ → e+ γ signal, as well as prompt and accidental backgrounds. The reason why
we separate backgrounds to two types is that we can estimate each PDF and mixing of
two is diﬀerent by an selection window and a beam condition such as a rate or a muonpolarization. The likelihood function is also used to compare the probabilities at the given
number of events.
10.2.1Deﬁnition⃗ X)⃗ is deﬁned as
A likelihood function L(θ|
⃗ X)
⃗ =
L(θ|

No
∏

⃗
p(⃗
xi |θ),(84)

i=1⃗ is a set ofwhere x⃗i is a set of observables in i-th event within the selected region, X
x⃗i |i=0∼No in an experiment with an observed total number of events No , θ⃗ is a set of⃗ is a joint PDF for all obserunknown parameters of the likelihood. The function p(⃗
xi |θ)
vations of i-th event in a θ⃗ set. The parameters θ⃗ can be determined so that the likelihood⃗ which is θ⃗best (X).
⃗ These are the maximum likelihood ﬁt
is maximized with a given X,
best⃗ In the MEG experiment we deﬁne θ⃗ by the number of event:method to obtain θ⃗ (X).
θ⃗ = (Nsig , NRD , NBG ),No = Nsig + NRD + NBG .

(85)
(86)

However, it could be better to regard that parameters of (Nsig , NRD , NBG ) have anexperiment-by-experiment ﬂuctuation. We redeﬁne No with an unknown true value setof θ⃗true = (No,sig , No,RD , No,BG ) in the performed experiment and introduce N instead of
No as a mean in experiments,
N = Nsig + NRD + NBG
No = No,sig + No,RD + No,BG .

(87)
(88)

We assume that the ﬂuctuation of each number, f (No,j |Nj ) (j = (sig, RD, BG)), obeys
the Poisson distribution fpoisson (No,j |Nj ) (j = (sig, RD, BG)) respectively, then the ﬂuctuation of summed number No , f (No |N ), also shows a Poisson distribution fP oisson (No |N ).
f (No |N ) = fP oisson (No,sig |Nsig ) ∧ fP oisson (No,RD |NRD ) ∧ fP oisson (No,BG |NBG ) (89)∏=fP oisson (No,j |Nj )(90)
j=(sig,RD,BG)= fP oisson (No,sig + No,RD + No,BG |Nsig + NRD + NBG )= fP oisson (No |N )

(91)
(92)

Here we regard the θ⃗ as an independent parameter set and use a reproductive propertyof Poisson distribution from Equation 90 to Equation 91.

136

10. Analysis for the µ+ → e+ γ Search⃗ X),⃗
Then we can deﬁne the extended likelihood function Lext (θ|
⃗ X)
⃗ X)
⃗ = f (No |N )L(θ|⃗Lext (θ|No
N No exp (−N ) ∏⃗=p(⃗xi |θ),
No !
i=1

(93)
(94)

where N means the positive expected number of occurrences in the Poisson distributionof observed total events in experiments.
10.2.2

Observables

From a kinematic point of view, four parameters of energies, opening angle and time
diﬀerence, (Ee , Eγ , Θeγ , teγ ), can discriminate µ+ → e+ γ signal from backgrounds. Withconsidering the detector responses of the drift chamber and timing counter, they havea diﬀerent position performance between a z direction and a ϕ direction. Therefore weseparate the opening angle Θeγ to θeγ and ϕeγ .
Accordingly resolutions of the parameters, δ⃗x = (δEe , δEγ , δθeγ , δϕeγ , δteγ ), are introduced to construct event-by-event PDFs. These resolution parameters are determined by
the position on the LXe detector and emission angles of positrons. Other parameters of
two thicknesses of the degrader and two categories of tracking quality also specify the
PDFs, but we omit to express these in ⃗x. We deﬁne this parameter set to specify theshape of PDF as δ⃗x and the set can be used to generate events in the toy MC. Thenobservables are selected,⃗x = (Ee , Eγ , θeγ , ϕeγ , teγ , δEe , δEγ , δθeγ , δϕeγ , δteγ ).
The probability is expressed by each probability of event types,∑⃗ =⃗ j) Nj .
p(⃗xi |θ)
p(⃗xi |θ,
N

(95)

(96)

j=(sig,RD,BG)

Here we use PDFs of signal, radiative decay and accidental background deﬁned below,p(⃗xi |Nsig , NRD , NBG , sig) ≡ S(⃗xi ) = S(⃗
xi |δ x⃗i )p(δ x⃗i ),p(⃗
xi |Nsig , NRD , NBG , RD) ≡ R(⃗
xi ) = R(⃗
xi |δ x⃗i )p(δ x⃗i ),p(⃗
xi |Nsig , NRD , NBG , BG) ≡ B(⃗xi ) = B(⃗
xi |δ x⃗i )p(δ x⃗i ),

(97)
(98)
(99)

It is assumed that the function of p(δ x⃗i ) is common because the performance of all thedetectors is almost symmetric and is able to cancel out another asymmetry such as theevent distribution, for example, it may be asymmetric depending on a muon polarization.
Then we can deﬁne a likelihood function of (Nsig , NRD , NBG ) as
Lext (Nsig , NRD , NBG ))No (N No exp (−N ) ∏
NRD
NBG
Nsig
=
· S(⃗
xi ) +· R(⃗
xi ) +
· B(⃗
xi )
No !
N
N
N
i=1
o
N No exp (−N ) ∏=p(δ x⃗i )
No !
i=1
)
(
NRD
NBG
Nsig
· S(⃗
xi |δ x⃗i ) +· R(⃗
xi |δ x⃗i ) +· B(⃗
xi |δ x⃗i )
N
N
N

(100)
(101)

N

(102)

10.3

Probability density function

137

We use a negative log-likelihood (NLL) function to be minimized and it is suitable fora ﬁt,− ln Lext (Nsig , NRD , NBG ) +No∑p(δ x⃗i ) + const.

i=1

=N−

No
∑

ln (Nsig · S(⃗xi |δ x⃗i ) + NRD · R(⃗
xi |δ x⃗i ) + NBG · B(⃗
xi |δ x⃗i )) .

(103)

i=1

In our case MINUIT package is used [63]. From now on, we redeﬁne S(⃗xi ), R(⃗xi ), B(⃗xi )by S(⃗
xi |δ x⃗i ), R(⃗
xi |δ x⃗i ), B(⃗
xi |δ x⃗i ), or simply express these by S, R, B, respectively.

10.3

Probability density function

The Probability density functions (PDFs) are based on measured data and some set are
prepared separately by a certain period for a diﬀerent condition of degraders. We estimate
three types of PDFs, which is S, R and B for a signal, a prompt background from radiative
muon decays and accidental background respectively.
Diﬀerent conditions of experiment setup such as diﬀerent years or a normal MC events
can be considered in the same framework with regarding these condition as also observables and preparing a corresponding PDF set. Thus we prepared two separated PDF
set for diﬀerent degrader thickness of 200 or 300 µm, which is recognized by taken time.
Some parts of PDFs can be separated for independent variables, and three types of PDF
are deﬁned as
S(Ee , Eγ , θeγ , ϕeγ , teγ ) = S1 (Ee )S2 (Eγ )S3 (θeγ )S4 (ϕeγ |Ee )S5 (teγ ),R(Ee , Eγ , θeγ , ϕeγ , teγ ) = R1 (Ee , Eγ , θeγ , ϕeγ )R2 (teγ ),B(Ee , Eγ , θeγ , ϕeγ , teγ ) = B1 (Ee )B2 (Eγ )B3 (θeγ )B4 (ϕeγ )B5 (teγ ).

(104)
(105)
(106)

Figure 10.2 shows PDFs with simply averaged in observed events, as a functions of observable.
10.3.1SignalThe PDF is almost based on measured distribution. The signal PDF, S, is estimated as
below.
S1 (Ee ) The positron momentum is expressed with double Gaussian. Not only emission
angles but also the selection of the tracking quality determines S1 . In 2008 we extract S1with ﬁtting theoretical Michel spectrum by convoluting its response. Currently in 2009
we estimate the momentum resolution with the two-turn method as described in Section
8.3.
S2 (Eγ ) The S2 is position dependent and derived from 54.9 MeV gamma ray in π 0 decay.
In 2009 the energy dependence of the energy resolution is considered.

Probability / (0.1 MeV)

1

S:Signal
R:Radiative BG
B:Accidental BG

10-1

Probability / (0.06 MeV)

10. Analysis for the µ+ → e+ γ Search

138

10-2

1

10-1

10-2

10-3
48

50

52

54

10-3

56
58
Eγ (MeV)

0.16

S:Signal
R:Radiative BG
B:Accidental BG

0.14
0.12
0.1
0.08

0.02
0.04
φeγ (rad)

Relative angle ϕProbability / (0.014 nsec)

55
Ee (MeV)

S:Signal
R:Radiative BG
B:Accidental BG

0.08

0.02

0.16

54

0.1

0.04

0.02

53

0.12

0.04

0

52

0.14

0.06

-0.02

51

0.16

0.06

-0.04

50

Positron energy
Probability / (0.001 rad)

Probability / (0.001 rad)Gamma-ray energy0

S:Signal
R:Radiative BG
B:Accidental BG

0

-0.04

-0.02

0

0.02

0.04
θeγ (rad)

Relative angle θ

S:Signal
R:Radiative BG
B:Accidental BG

0.14
0.12
0.1
0.08
0.06
0.04
0.02
0

-0.5

0

0.5
teγ (nsec)

Time diﬀerence
Figure 10.2: Averaged probability density functions (PDFs) by observables. In the ﬁgure
the solid lines, the chain lines and the dashed lines show the PDFs of signal, of radiative
background and accidental background (S, R, B), respectively.

10.3

Probability density function

139

S3 (θeγ ), S4 (ϕeγ |Ee ) The angular resolution is constructed from resolutions of emission
angles and a vertex position by a positron and (u, v)-resolution in the LXe detector.
The diﬀerence between independent reconstructions of one turn, which is recognized asa two-turn track, gives the positron resolution of emission angles. Bias of this method
is eliminated by the signal MC. The holes on the muon target are estimated as a vertex
resolution. The position resolution of gamma-ray detection is evaluated in π 0 decay run
by putting a lead-slit collimator in front of the LXe detector at a certain position, thena position dependence of resolution is extracted with the signal MC. The signal MC
indicates that a reconstruction of ϕeγ has a bias depending on the positron energy, Ee .
The dependence is treated in the conditional probability, S4 (ϕeγ |Ee ).
S5 (teγ ) The time diﬀerence between positron and gamma ray is derived from a radiative
muon decay. We conﬁrm a peak of teγ from that decay and obtain S5 with subtracting
ﬂoor from accidental background. It contains a dependence of gamma-ray energy.
10.3.2

Radiative decay

The radiative decay has a kinematic correlation between observable parameters, which
forbids a separate treatment of PDF.
R1 (Ee , Eγ , θeγ , ϕeγ ) The R1 is formed with the theoretical correlation of radiative muon
decay folding with detector response of each signal PDF.
R2 (teγ ) This PDF is the same as signal PDF S5 from a peak of radiative decay.
10.3.3

Accidental backgroundTo avoid a contamination of coincident radiative decays, those PDF elements are estimated from teγ sideband data outside the analysis window.
B1 (Ee ) The positron energy spectrum in Michel decay is ﬁtted by a theoretical Michel
decay smeared by the resolution.
B2 (Eγ ) The PDF B2 is position dependent and estimated by ﬁtting teγ sideband datawith an expectation of a radiative muon decay and a positron annihilation ﬂight in theMC with folding a detector response.
B3 (θeγ ), B4 (ϕeγ ) The background PDFs of opening angle θeγ and ϕeγ are estimated byﬁtting third-order polynomial function to the distribution observed in the sidebands.
B5 (teγ ) The B5 is a ﬂat distribution because it is only accidental. The eﬀect of trigger
bias is not remained in the analysis region.

140

10. Analysis for the µ+ → e+ γ Search

10.4

Result of the maximum likelihood ﬁt

When we ﬁnished the optimization of the analysis and the background studies in the
sidebands, we opened the blinding box and performed a likelihood analysis. Then the ﬁrst
result in 2009 data of the MEG experiment is revealed. After unblinding events in theanalysis region, the numbers of signal, radiative muon decay and accidental backgroundare estimated to be,+38(N̂sig , N̂RD , N̂BG ) = (3.0+6.9 , 35+24−22 , 332−36 ), Nobs = 370,

(107)

where asymmetric errors are taken from MINUIT of ﬁtting, that is 1.645 sigma MINOS
errors. The negative error of N̂sig is outside of the deﬁned ﬁt region and is not described.
Figure 10.3 shows the distribution projected onto each observable with averaged PDFs
scaled with the best ﬁt number of each type. The highest blue line of four lines is a totalsum of all PDFs. Because we select the wide analysis window there is also radiative peakon the relative time window, while no obvious peak is seen in relative angle distributions.
Figure 10.3 (f) shows contour plots on Nsig -NRD plane and the black dot mark shows thebest-ﬁt value. The dashed-, solid-, dotted-lines show contours of the likelihood function
at 1, 1.645, 2 sigma (0.5, 1.353, 2 ∆NLL), respectively.

10.5

Sensitivity of Run 2009

A higher tail of the likelihood from N̂sig indicates a region to exclude the LFV events.
In case of the previous experiment by the MEGA collaboration, the shape of likelihood
distribution determined the upper limit on the branching ratio such that the area along
Nsig takes 90% area [2]. While in our case the conﬁdence interval is determined by many
toy experiments with assuming various Nsig in toy MC, according to Feldman Cousin
method described in Section 10.1.4. The upper limit of the branching ratio obtained ina single experiment suﬀers a statistical ﬂuctuation. We consider the ﬂuctuation by many
simulated experiments with null signal and can obtain the sensitivity by the average ofupper limits in the experiments.
The sensitivity of the experiment with the data statistics for the run 2009 is calculated
as an upper limit averaged over an ensemble of the simulated 1500 experiments, where thesame expected numbers of the RD and the accidental BG as the likelihood ﬁt result on
2009 data and the null signal are assumed. The upper-limit calculation does not include
the systematic uncertainties. Taking average of 90% branching-ratio upper limit as shownin Figure 10.4, it is calculated to be
S2009 = 6.1 × 10−12 .

(108)

The result is improved from 2008 result, S2008 = 1.3 × 10−11 , while it is from early dataand not a ﬁnal goal of the sensitivity in the MEG experiment.

10.6

Upper limit of µ+ → e+ γ branching ratio

In 2009 data the 90% C.L. upper limit for Nsig is estimated to be 14.5, while Nsig = 0 is
inside the conﬁdence interval of 90%. The systematic uncertainties are included in thiscalculation. The detailed eﬀect of each uncertainty is discussed later. With normalization
factor, the upper limit for the branching ratio is ﬁnally obtained as
Br(µ+ → e+ γ) < 1.5 × 10−11 at 90% C.L.

(109)

Events / ( 0.0004 GeV )Events / ( 0.00024 GeV )

10

1

10.7

Discussion

0.05

0.052

141

10

1

10-1
10-1
0.05

0.051

0.052

0.053

0.054
0.055
Positron energy (GeV)

0.048

25
20

25
20

15

15

10

10

5

5

0

0

-0.04
-0.02
0
0.02
0.04
Relative phi angle of flipped positron direction wrt gamma direction

-0.04
-0.02
0
0.02
0.04
Relative theta angle of flipped positron direction wrt gamma direction(d) Relative angle θ
Number of RD events(c) Relative angle ϕEvents / ( 5.6e-11 sec )

0.056
0.058
Gamma energy (GeV)(b) Positron energy
Events / ( 0.004 )Events / ( 0.004 )(a) Gamma-ray energy

0.054

30
25
20
15

100
80
60
40
20

10

0
5
0

-0.5

0
0.5
Time difference between positron and gamma (sec)(e) Relative time

×10-9

-20
0

5

10

15
20
Number of signal events(f) Contour plots on Nsig and NRD

Figure 10.3: Result of the maximum likelihood ﬁt. Summed PDFs weighted with best ﬁtvalues of each types are superimposed on (a)-(e). The notation of each PDF is the sameas in Figure 10.2.

10.7

Discussion

10.7.1

Event distribution

The event distributions after the unblinding are shown in Figure 10.5 where the eventsnear the signal are labeled with the order of the likelihood ratio deﬁned as S/(S + R + B).
In the ﬁgure, (a) and (b) show Eγ and Ee , while relative time and cos Θeγ are shown in (c)and (d). Separately, the events with a high-quality positron tracking are plotted in theﬁgures (b) and (d). The most signal-like events in the analysis region remain even after
high quality cut is applied in (b) and (d) out of all events without the quality selectionin (a) and (c).

10. Analysis for the µ+ → e+ γ Search

142

180
160
140
120
100
80
60
40
20
0
0

5

10
15
Nsignal upper limit (90% U.L.)

Figure 10.4: Distribution of Nsig upper limit at 90% conﬁdence level in a toy MC.

10.7.2Highly-ranked events

Table 18 shows properties such as Eγ , Ee , teγ , angles, positions and a proton currentof highly ranked events by means of the relative signal likelihood. The ZT C shows thereconstructed position of hit on z in the timing counter. The rank in the table is given by
the likelihood ratio of signal to backgrounds and corresponding to the numbers in Figure
10.5.
Table 18: List of the highly ranked events by S/(S + R + B).
Rank
1
2
3
5
8

Eγ , Ee(MeV)
52.3, 52.6
52.1, 52.7
51.8, 53.0
52.2, 52.6
52.3, 52.5

teγ
(ps)
27
-72
-136
287
-259

ϕeγ , θeγ
(mrad)
5, -2016, -14-12, 22
14, -1125, 11cos Θeγ-0.99978-0.99978-0.99968-0.99986-0.99964(u, v, w)LXe(cm)
1.6, -46.0, 3.1
14.9, -8.3, 0.5
3.4, -62.9, 3.5
24.3, -42.5, 0.99.5, -10.7, 4.7

ZT C
(cm)
-31.3
-61.5
-35.3
-89.2
-38.8

Proton
(µA)
2178
2185
1698
2191
2186

We thoroughly checked ten signal-like events with a high rank by the signal likelihood.
The high ranked events are almost categorized in high quality of positron tracking andthere is no pile ups of gamma rays. For example, observables and PDFs of the highestrank event are shown in Figure 10.6 to check which observable is dominant in a PDFs.
Figure 10.7 shows the event display of the highest ranked event. On the left hand side
two-dimensional display with positron tracks and light distribution in the LXe detector
are shown, while the distribution are drawn in development view on the right hand side.
Figure 10.8 (a) shows the proton current and the time of highly ranked events. The
third ranked event was taken when the proton current was low. We checked the qualityof the gamma-ray energy. The peaks of LED events mixed during the physics run (Figure 10.8 (b)) shows the third event in several sudden jumps about 1.5 % due to gains
misapplied between diﬀerent intensities of proton beam that is not large compared to the
1-sigma region in Figure 10.5 (a). Except for that, through the check neither strange nor
wrong reconstruction are found.

58

Eγ (MeV)Eγ (MeV)

10.7

57
56

56

54

54
53

81
5
23

51

52
51

50

50

49

49

48
50

51

52

53

54

48
50

55
56
Ee (MeV)(a) Eγ and Ee
2

1.5

54

55
56
Ee (MeV)

2

0.5

7
5

1
10
3
2
8 9

0
-0.5

-1

-1

-1.5

-1.5

-2
-1

53

1

0.5 6

-0.5

52

1.5

1

0

51

(b) Eγ and Eeof only high-quality positron trackingteγ (nsec)teγ (nsec)

57

55

52

143

58

55

53

Discussion-0.9995-0.999-0.9985cosΘeγ(c) Relative time and cos Θeγ-2-1-0.9995-0.999-0.9985cosΘeγ(d) Relative time and cos Θeγof only high-quality positron tracking

Figure 10.5: Distribution in analysis region. The signal 2D PDFs are superimposed as
contours at 1, 1.64, 2 sigma as blue solid, dot-dashed, and dashed lines respectively. The
number shows the rank by S/(S + R + B).

10.7.3Result in sideband data

The same analysis was performed with diﬀerent event sets such as in sidebands. The
likelihood ﬁt with null signal is possible with sideband of teγ , which is very convenient
way because the estimation of the upper limit sensitivity is also possible with the same
PDF set.
Before opening blind box we estimated upper-limit sensitivities to be 3 − 5 × 10−12
with shifting the analysis window along teγ . Figure 19 shows the best ﬁt values in both

10. Analysis for the µ+ → e+ γ Search

144

0.35

0.3

0.3

0.25

0.25

0.3
0.25
0.2

0.2

0.15

0.15

0.2
0.15

0.1

0.1

0.1

0.05

0.05

0.05

0

-0.5

0

0.5

×10

-9

0

0.05

0.051 0.052 0.053

Teγ (sec)

0
0.048

0.05

0.22

0.2
0.18

0.2
0.18
0.16

0.16
0.14
0.12

0.052

0.054

0.056

0.058

Eγ (GeV)

Ee (GeV)

0.22

0.14
0.12
0.1

0.1
0.08
0.06
0.04
0.02
0

0.054 0.055

0.08
0.06

-0.04

-0.02

0

0.02

0.04

θ eγ (rad)

0.04
0.02
0

-0.04

-0.02

0

0.02

0.04

φ eγ (rad)Figure 10.6: The observables in the highest-ranked event with PDFs (teγ (sec), Ee (GeV),
Eγ (GeV), relative angles(rad)). Three-type of S, R, B and summed PDF in the eventare drawn as green, red, magenta and blue lines. Mark superimposed on PDFs shows themeasurement value and the probability in the event.

(a) 2D x-y display(b) Map of the number of photons by PMTs

Figure 10.7: Event display of the highest rank.

sidebands of teγ . The result in the analysis window diﬀers from the ﬁnal result because
the systematic uncertainties are not considered.
10.7.4Eﬀect of the systematic uncertainty

The systematic uncertainty can be included in calculation of the conﬁdence interval by
ﬂuctuating the likelihood function when performing the likelihood ﬁt in each simulated
experiment. All the uncertainties are ﬂuctuated simultaneously in the C.L. calculation.

Proton current (µA)

10.7

2300

5

2

3

Discussion

1

145

8

2200
2100
2000
1900
1800
1700
1600
05/11

12/11

19/11

26/11

03/12

10/12

17/12

Date 2009

LED Peak during physics run (a.u.)(a) Proton current.
1.01

5

2

3

8

1

1.005
1

0.995
0.99

0.985
0.98

05/11

12/11

19/11

26/11

03/12

10/12

17/12

Date 2009(b) LED peaks in the LXe detector, which is the same as Figure 6.14.

Figure 10.8: Muon beam (a) and LED peaks in the LXe detector (b) during physics run.
The attached numbers are the rank listed in Table 18. The red lines beside the number
show the time of the events taken.
Table 19: The best ﬁt values and 90% C.L. upper limits (UL) on teγ side bands with ±2.5
ns oﬀset shift. The systematic uncertainties are not included.

Analysis window
Negative teγ sideband
Positive teγ sideband

events
370
290
300

N̂sig
3.0
0
0

N̂RD
35
0
4.4

N̂BG
332
290
296

Nsig UL
11.8
4.5
6.0

Br UL (10−12 )
14.3
4.5
6.1

We estimated the contribution of each systematic uncertainty by individually shifting
the parameter in PDF according to its uncertainty and see how the best ﬁt value of Nsig is
shifted. Figure 10.9 shows the best ﬁt values of the number of the signal by shifting eachparameter within uncertainties. The most dominant factor is a relative angle, and second
ones are both energies secondary. However, the eﬀect of the systematic uncertainty issmall compared to the statistical uncertainty of the likelihood ﬁt.

χ2 / ndf 2.289e-005 / 13
p0
3.017 ± 2.434
p1-0.9794 ± 5.63

12

Nsig

10. Analysis for the µ+ → e+ γ Search
Nsig

146

12
10

10

8

8
6

6

4

4

2

2

0-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0

-60

0.6
0.8
Eγ scale %χ2 / ndf
5.172e-006 / 3
p0
2.999 ± 4.213
p1
0.01641 ± 0.5953

3.4
3.3

-40

-20

0

20

40
60
E e scale (keV)(b) Ee : 0.40Nsig (50 keV)Nsig(a) Eγ : 0.42Nsig (0.43%)
Nsig

χ2 / ndf
1.85e-005 / 1
p0
2.978 ± 5.442
p1-0.008042 ± 0.1333

3.4
3.2

3.2
3.1

3

3
2.9

2.8

2.8
2.6

2.7
2.6

2.4
-10

-5

0

5

-20

10
σ(Eγ ) scale (%)

Nsig

10

8

8

6

6

4

4

2

2
-10

-8

-6

-4

-2

0

2

4

Nsig

S(teγ ), R(teγ )12

S(teγ )

10

0

5

10

15

20

σ (E e) scale (%)

-20

-15

-10

-5

0

5

10

15
20
φeγ (mrad)(f) ϕeγ : 0.99Nsig (7.5 mrad)
12

S(teγ ), R(teγ )10

S(teγ )

8

8
6

6

4

4

2

2

0 -60

-40

-20

0

20

40

60
teγ (ps)(g) teγ : 0.23Nsig (15 ps)
Nsig

0

6
θeγ (mrad)(e) θeγ : 0.90Nsig (7.5 mrad)

-5

12

10

0

-10

(d) σ(Ee ) : 0.14Nsig (15%)

Nsig

Nsig

(c) σ(Eγ ) : 0.3Nsig /0.1σEγ
12

-15

0

-30

-20

-10

0

10

20

30
σ (teγ ) (ps)(h) σ(teγ ) : 0.35Nsig (10%)

10
8
6
4
2
0

-60

-40

-20

0

20
40
60
δ Ee - δ φe correlation (%)(i) δEe − δϕe : 0.83Nsig (50%)
Figure 10.9: Eﬀect to the best ﬁt Nsig by each systematic uncertainty. Each notationshows a value, shift of the best ﬁt of Nsig in the uncertainty and systematic uncertainty
listed in Table 17.

10.7
10.7.5

Discussion

147

Future prospects

The sensitivity of the Br upper limit

The current statistics of muon decays is still low and we continue to take physics data
for several years. Future prospects of the sensitivity for the µ+ → e+ γ are estimated byyear as shown in Figure 10.10. The shown sensitivity in the ﬁgure is based on Bayesianinference for a fast calculation of 90% upper limit of the branching ratio, which diﬀers alittle from the previous result in Section 10.5. However, we have conﬁrmed a consistency
that these have similar results each other. In this method, the toy MC simulation by thedata set in 2009 was performed for the sensitivity calculation with the expected numberof events by year. Two types of PDFs are prepared for the event generation. One is thesame performance in 2009 and the other is taken from an expected performance achievedby upgrades of the detectors and the analysis. The assumption of the performance insigma is σEe = 32 keV, σEγ = 1.5% (2 cm ≤ w < 38 cm), 2.46% (1 cm ≤ w < 2 cm),
2.65% (0 cm ≤ w <1 cm), σteγ = 100 ps, vertex resolutions σZ = 2.5 mm, σY = 1.4 mm
and 8 mrad for both ϕ and θ angles. The sensitivity will reach a region lower than 10−12
within a few years.
10-11
2009 performance

2009
Prospective performance

2010

2011
2012

10-12

0

5

2013

10
15
20
µ + normalization factor k

Figure 10.10: Future prospects of the sensitivity for a next few years as a function of kfactor.

148

Part VI

Conclusion
The MEG experiment successfully took the physics data in the second year 2009 for twomonths. The enough puriﬁcation for the liquid xenon brought the large increase of thelight yield and it was quite stable during the run within 0.3%. The accumulated numberof stopped muons in 2009 is about 6.5 × 1013 , while 9.5 × 1013 in 2008 because of thelonger three-month run in 2008. Thanks to the investigation and the improvement for thedischarge problem of the drift chamber before the 2009 run, the positron spectrometer
was stably operated over whole period of the data taking and the muon decays observedin the detector increased largely compared to the 2008 run.
The obtained performance in 2009 is summarized in Table 20. We got large improvements for the performance of positron tracking especially.
Table 20: Resolution in 2009
Year
2009
1
2

σEγ
(%)
2.11

σ(u,v,w)
(mm)
5, 6

ϵγ
0.58

σEe
(%)
0.742

σϕe
(mrad)
7.12σθe(mrad)
11.2

Vertex σZ,Y
(mm)
3.4, 3.3

ϵe
0.4

σteγ
(ps)
1422

ϵtrig
0.84

w > 2cm
Core component

The branching-ratio sensitivity in 2009 is estimated to be
S2009 = 6.1 × 10−12 .
This result is better than the previous 2008 result of the sensitivity, 1.3 × 10−11 .
The analysis in 2009 data concludes that the upper limit of branching ratio isBr(µ+ → e+ γ) < 1.5 × 10−11 at 90% C.L.,and showed the improvement compared to the 2008 result, 2.8 × 10−11 (90% C.L.). The
90%-conﬁdence interval still includes the region of Nsig = 0.
The presented analysis uses only 2009 data while the MEG experiment just started
data taking and will run for a next few years. The result is still limited by the statistics
of muons and a ﬁner tuning and an improvement of the analysis is going on.

150

A. Radiative decay

AppendixA

Radiative decay

A.1

Radiative-decay diﬀerential branching ratio

Equation 5 shows the diﬀerential branching ratio of RD [19]. The functions of F (x, y, d),G(x, y, d), and H(x, y, d) are given in the SM as follows:
(
r =

me
mµ

)2
,

F (x, y, d) = F (0) + rF (1) + r2 F (2) ,G(x, y, d) = G(0) + rG(1) + r2 G(2) ,H(x, y, d) = H (0) + rH (1) + r2 H (2) ,8 2
F (0) (x, y, d) ={y (3 − 2y) + 6xy(1 − y) + 2x2 (3 − 4y) − 4x3 }d+8{−xy(3 − y − y 2 ) − x2 (3 − y − 4y 2 ) + 2x3 (1 + 2y)}+2d{x2 y(6 − 5y − 2y 2 ) − 2x3 y(4 + 3y)} + 2d2 x3 y 2 (2 + y),{}
32y(3 − 2y)(1)
F (x, y, d) = 2 −− (3 − 4y) + 2xdx8
+ {y(6 − 5y) − 2x(4 + y) + 6x2 }d+8{x(4 − 3y + y 2 ) − 3x2 (1 + y)} + 6dx2 y(2 + y),{}
32 (4 − 3y)48y(2)
F (x, y, d) = 2
−3 +
,
d
x
d
8
G(0) (x, y, d) ={xy(1 − 2y) + 2x2 (1 − 3y) − 4x3 }d+4{−x2 (2 − 3y − 4y 2 ) + 2x3 (2 + 3y)} − 4dx3 y(2 + y),
32
8G(1) (x, y, d) = 2 (−1 + 2y + 2x) + (−xy + 6x2 ) − 12x2 (2 + y),
d
d
96
(2)
G (x, y, d) = − 2 ,
d
8 2
(0)
H (x, y, d) ={y (1 − 2y) + xy(1 − 4y) − 2x2 y}d+4{2xy 2 (1 + y) − x2 y(1 − 4y) + 2x3 y}+2d{x2 y 2 (1 − 2y) − 4x3 y 2 } + 2d2 x3 y 3 ,{}32
y(1 − 2y)(1)
H (x, y, d) = 2 −
+ 2y
d
x
8
+ {y(2 − 5y) − xy} + 4xy(2y − 3x) + 6dx2 y 2 ,d
96y 48y
H (2) (x, y, d) = − 2 +
.
dx
d

(110)

(111)

(112)
(113)

(114)
(115)
(116)

(117)

(118)
(119)

B. Engineering run in 2007

B

Engineering run in 2007

B.1

Overview of 2007 run

151

Detector and trigger setups and various calibrations （engineering run 2007） started
in September in 2007. In December a trigger for µ+ → e+ γ was tested for a day andcorrectly worked with both gamma-ray and positron detectors. Data set taken for thedrift chamber are cosmic rays and positrons from Michel decays in positive muon beam,and for the liquid xenon detector LEDs, alpha sources in both liquid and gas phase, cosmic
rays, gamma rays with Cockcroft-Walton accelerator, gamma rays from radiative muon
decays and two gamma rays in π 0 decay. Coincident events were able to be acquired
between the timing counter and the drift chamber and also between the timing counterand the liquid xenon detector. The charge exchange reaction (CEX) run in π − beam, inother words π 0 run, gives the ﬁrst performance evaluation of the liquid xenon detector
about timing, position and energy near the signal at a certain position of the detector.
A successful trigger for the π 0 decay between the anti-tagging NaI detector and the LXedetector enabled it. The engineering run 2007 ﬁnished at the end of December whichenable us to conﬁrm all setup working, then some upgrades were performed for a next
2008 run.

B.2

The LXe detector status

The gains of PMTs were set to 1.5 × 106 and typical HV was 810 V. There were 17 deadchannels out of 846 PMTs, some of that are ﬁxed by changing cables and circuits after
2007 run ﬁnished. The liquid phase puriﬁer worked for 205 hours, and the light yield
increased by 1.6 times and saturated after 180-hours puriﬁcation. That brought a longer
absorption length from 60 cm to over three meters.

B.3

MEG engineering run in 2007

For two days on 16 and 17 in December the trigger for the µ → eγ was tested with 4 Hz
and 40 MeV lower threshold in the LXe detector.

B.4

π 0 run in 2007

For the ﬁrst performance evaluation of the LXe detector, the π 0 decay data was taken forthree days. The timing and energy resolutions was estimated with a region corresponding
to 3 × 2 PMTs region at the three part of center, central lower and central upstream side
on inner face, respectively 765k, 260k and 156k events were taken. Trigger rate was 12
Hz in the energy measurement and 2.5 Hz in the timing measurement. We also measured
the position performance by the lead collimator with holes of 5 mm and 10 mm diameterand 18 mm thickness, which was mounted on the LXe detector’s vessel at the lower part
. During the run the APDs attached on the NaI had no thermal control but the changeof the temperature was within a Celsius degree.

152

C. Calibration of the NaI detector

C

Calibration of the NaI detector

C.1

Gain adjustment of APDs

Entries / MeV

The gain of the NaI detector is adjusted to detect gamma rays from a π − beam in anenergy region under the 150 MeV. The scintillation light of the NaI(Tl) is detected by an
APD and signal charges from it are integrated by a charge ampliﬁer, thus a gamma-ray
energy is proportional to an amplitude of the output. All HVs of APDs are determinedat 2.6 mV/MeV gain in 2008 and 3.2 mV/MeV in 2009 to be able to measure gamma
rays without saturation in a DRS digitizer.
At the same time we can acquire all gains by cosmic rays, which is also used to adjust
HV. The peak of cosmic ray is ﬁtted with Landau distribution with an exponential tailas shown in Figure C.1. It is diﬃcult to determine HVs of all APDs with using tens-MeV
gamma rays from a target by each crystal because of energy leaks. To use a radio active
source is inconvenient to calibrate all at the same time and the measurement of a MeV
gamma ray is diﬃcult with the same HV set for tens-MeV because of a noise from APD.
Cosmic rays make peaks around 30 MeV and allow the same energy deposit in each crystal
without any cut. The energy deposit in the NaI crystal is estimated by MC simulationand no selection for zenith angle is applied to treat all crystals in the same way. However,it should be taken into account that the gain of APD depends on a temperature. To know
the gain dependence for HV and temperature, LEDs equipped in the NaIs are useful fora quick calibration. A linearity and a saturation region are measured with changing thewidth of LED pulse.
500

Central NaI crystal

450

With upper&lower NaI cut (>10MeV)

χ2 / ndf
203.7 / 84
Constant
801.9 ± 26.0
MPV
33.57 ± 0.13
Sigma
2.702 ± 0.069

400
350
300
250
200
150
100
50
0
0

10

20

30

40

50

60

70

80
90 100
Energy (MeV)

Figure C.1: Energy deposit of cosmic-ray muons in the central NaI crystal. The selection
with upper and lower crystal gives a clear Landau peak, although HV is determined byplots distribution to treat all crystals as the same way.

Figure C.2 shows the thermal dependence of APD gains by changing a APD temperature with Peltier devices. The relation in Figure C.2 (a) is measured with LED peaks ina certain APD, which is under a room temperature because only around APD is cooling.
Figure C.2 (b) describes relative change of gains in the all nine APDs. The shift of eachcurve is probably due to a variation of break down voltage that is ﬂuctuated from 400 to

C.2

153

Performance of the NaI detector

χ2 / ndf

114

19.16 / 3

p0

140.3 ± 0.203

p1-1.566 ± 0.009859

112

Gain / Temperature (%/ °C)

Amplitude (mV)

430 V. The temperature of APDs is typically kept at 18 degrees Celsius, while the gain
has a 1-2 %/◦ C dependence. With considering the stability of the thermal system within
0.1% as shown in Figure 3.58, the gain has a good stability under 0.2%.
-1

-1.5
-2

-2.5

110

108

-3

-3.5

106

-4
-4.5

104
17

18

19

20

21

22
23
24
Temperature (°C)

-5
370

380

390

400

410

420

430
440
Bias HV (V)(a) LED peaks and APD tempera- (b) Gain shift by a Celsius and biased hightures.
voltage of nine APDs.
Figure C.2: Thermal dependence of APD gain measured by LED peaks.

For the HV determination, a constant LED peak is measured with diﬀerent HVs toknow gain-HV dependence quickly. The gain dependence by HV can be given by Equation
120,
gainAPD ∝

1−

(

1
V
Vbd

)−k ,

(120)

where V is a bias voltage, Vbd is a break down voltage of APD, and k is determinedwith a ﬁt. This relative change of LED peaks, as shown in Figure C.3, is scaled by
the gain obtained from cosmic rays. The blue horizontal line shows a target gain and acorresponding HV is applied.

C.2

Performance of the NaI detector

The NaI detector measures MeV-scale gamma rays by the total energy deposited in NaI.
To make a clear peak, the trigger requires the largest deposit in the central NaI and thereconstruction needs a cut such that a ratio of central NaI to sum of all is larger than 0.6.
In 2009 analysis, the position on the NaI was ﬁxed at the center of the detector.
Figure C.4 shows a peak from 17.7, 54.9, 82.9 and 129 MeV gamma rays. The linearity
between reconstructed energy and true energy is shown in Figure C.5. There is a deviationof 129 MeV peak from a linear correlation of others, because the energy leak becomesdominant around over hundred-MeV scale which is much higher than critical energy of
NaI. However, the response is linear in the interesting range of two gamma-ray region to
be tagged in π 0 run.
Figures C.6 and C.7 show the energy resolutions of sigma and FWHM, respectively.
The resolution of higher energy region obeys logarithmic function of energy, though leaks
are somehow suppressed by the selection of central crystal deposit. An interesting energy

C. Calibration of the NaI detector
Amplitude [V]154χ2 / ndf
factoroffsetbreakdownV
power

0.25

χ2 / ndf

0.2

0.1845 / 9-0.1027 ± 0.01871
0± 0452.1 ± 1.792-5.169 ± 0.5202
0.2352 / 10
-0.09189 ± 0.02237

factor0±

offsetbreakdownV
power

0.15

0

452.9 ± 1.913-5.557 ± 0.7798

0.1
0.05
370

380

390

400

410

420
430
Bias voltage [V]Figure C.3: HV-Gain curve of the central NaI crystal measured by LED peaks. Plotsfrom DRS are ﬁt with a red continuous line, while those from waveform taken in a trigger
board with a blue dashed line.

π0 → γ γπ- p → γ n

Energy in NaI (MeV)

Li(p,γ )Be120100

χ2 / ndf
13.2 / 1
p0
0.385 ± 0.04567
p1
0.9661 ± 0.001197

80
60
40
20
20

20

40

60

80

100
120
Energy in NaI (MeV)

40

60

80

100 120 140
Energy (MeV)

Figure C.5: Energy linearity.
Figure C.4: Energy distribution of the NaI in CW andπ 0 run.

region of two gamma rays from π 0 decay is ﬁt as a continuous line and shows energy
resolution as a function of energy in Equation 121,()
24.3
σupper√ ⊕ 0.5 % (E < a hundred MeV),
=
(121)
E
E
while other dotted lines are obtained by functions with additional logarithmic term forhigh energy. A MC simulation indicates that the resolution at ten-MeV scale is limited byenergy leaks. To achieve more eﬃcient trigger and higher resolution, there is an updateplan to replace 4 × 4 BGO crystals and PMTs instead of 3 × 3 NaIs and APDs. Thanks
to higher stopping power of BGO than NaI, the total size of acceptance is almost thesame with better resolution and much shorter length allows a use of PMTs geometrically.

χ2 / ndf
σ at 1MeV
σ∞

6.5
6

Gain adjustment of pre-shower counter

1.578 / 1
24.33 ± 2.267
0.5485 ± 0.2864

5.5

FWHM (%)

σ (%)

C.3

30

a

2177 ± 26.62bc104.9 ± 0.6572-688.8 ± 3.785

Eshift25

155-31.9 ± 1.804

5

20

4.5
4

15
3.5
3
20

40

60

80

100 120 140
Energy (MeV)

Figure C.6: Energy resolution in σ.

C.3

10
20

40

60

80

100 120 140
Energy (MeV)

Figure C.7: Energy resolution in FWHM.

Gain adjustment of pre-shower counter

The magnetic ﬁeld of the COBRA is symmetric on z axis, though the gain might change at
diﬀerent positions with a rotation of the NaI detector. The gains of four PMTs, attachedwith two plastic scintillators, are adjusted to have the similar gain. The adjustment is
not so severe because a signal should be clear if gamma rays are converted in lead in frontof those. Charges in PMTs are used to correct time-walk eﬀect. The triggered events by
PMTs for the timing measurement have a worse energy resolution in the NaI due to alarge energy deposit in the lead converter, thus the events were not used for the evaluationof energy performance. The gain is adjusted with radio active source such as Sr-90 or
cosmic ray.

157

Acknowledgment
Over the years I have experienced a research in the MEG experiment by a collaborationof the University of Tokyo, KEK, Waseda University, Paul Sherrer Institut, INFN and
Pisa, University of Genova, University of Pavia, University Roma Sapienza, University of
Lecce, and BINP, Novosibirsk, JINR, Dubna and University of California, Irvine.
I would like to express my great appreciation to my supervisor and also one of
spokespersons in the MEG experiment, Prof. Toshinori Mori. He guided me to theworld of the particle physics and supported the whole of my study.
I have greatly beneﬁted from Japan Society for the Promotion of Science (JSPS), Japan
Student Services Organization and the University of Tokyo. Them ﬁnancial support madeit possible to complete my study.
My ﬁrst life in Switzerland started in 2005 with a kind help from Dr. Shuei Yamada,Dr. Kenji Ozone and Dr. Yasuko Hisamatsu. They gave me a useful knowledge and apowerful support in my life. I would like to express my special gratitude to Dr. Satoshi
Mihara, Dr. Wataru Ootani, Dr. Toshiyuki Iwamoto, Dr. Hajime Nishiguchi and Dr.
Ryu Sawada. Through our works I have learnt a lot of skills and close acquaintancefrom them. Meaningful discussions with Mr. Hiroaki Natori, Dr. Yusuke Uchiyama, Ms.
Kinuyo Matsuda, Mr. Daisuke Kaneko, Ms. Xue Bai, Mr. Yuki Fujii and Mr. Teppei
Chiba supported my research and they gave me a pleasant time. I want to thank them alot.
I am deeply grateful to the members of the International Center for Elementary Particle Physics (ICEPP), the MEG collaborator and my friends. Although I could not
mention all acknowledgment, my thesis would not be accomplished without any support.
Finally, my deepest appreciation goes to my family.

December 2010,
Tokyo

Yasuhiro NISHIMURABIBLIOGRAPHY

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