Ph.D. Thesis

The final result of µ+ → e+ γ searchwith the MEG experiment（MEG実験によるµ+ → e+ γ 探索の最終結果）

byDaisuke Kaneko
Department of Physics, Graduate School of Science,
The University of Tokyo
July 2016

2

Abstract
The charged lepton flavor violating decay, which has never been observed, is an evidence ofphysics beyond the Standard Model, if it is discovered. The MEG experiment has been searchingfor one of the charged lepton flavor violating decays µ+ → e+ γ with sensitivity in branching ratioof order 10−13 . The MEG experiment is conducted at the πE5 beam line in the Paul Scherrer
Institute where the world’s most intense positive muon beam is available.
The data taking of the MEG experiment started in 2008 and finished in 2013. The analysis tosearch for µ+ → e+ γ with the full dataset of the MEG experiment is presented, which is doubled
compared to the previous result. The total number of muon stopped on the target is 7.5 × 1014 .
In this analysis, a deformation of the target was found, and countermeasures against the issue
are applied. In addition, several improvements in analysis algorithm are also introduced. The
sensitivity with all data in MEG experiment found to be 5.3 × 10−13 .
No significant excess of the signal events compared to the expected background events isfound. The most stringent branching ratio upper limit of 4.2 × 10−13 (90% C.L.) has been
established, which is tighter by factor of 30 than the previous experiment.

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4

Contents
1

Introduction
1.1 Physics motivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.1 µ → eγ by theories beyond the standard model . . . . . . . . . . . . .
1.2 µ → eγ search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.1 Past experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.2 Signal and background . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 Relation with other experimental searches . . . . . . . . . . . . . . . . . . . .
1.3.1 µ − e conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3.2 µ → eee decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3.3 Muon anomalous magnetic moment . . . . . . . . . . . . . . . . . . .
1.3.4 LFV search with τ decay . . . . . . . . . . . . . . . . . . . . . . . . .

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9
10
13
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15
16
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2

MEG experiment setup
2.1 Beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.1 PSI accelerator facility . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.2 Beam transport system . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Stopping target . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Gamma detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.1 Liquid xenon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.2 Scintillation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.3 PMT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.4 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.5 Xenon handling system . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 Positron Spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.1 COBRA magnet . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.2 Drift chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.3 Timing counter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5 Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5.1 DAQ scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5.2 Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5.3 Online computers . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5.4 Slow control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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25
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3

Event reconstruction
3.1 γ reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1 Waveform analysis for each PMT . . . . . . . . . . . . . . . . . . . .

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Contents
3.1.2 γ position reconstruction . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.3 γ timing reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.4 γ energy reconstruction . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.5 Pile-up identification . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.6 Cosmic ray rejection . . . . . . . . . . . . . . . . . . . . . . . . . . .
Positron track . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Hit reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.2 Clustering and track finding . . . . . . . . . . . . . . . . . . . . . . .
3.2.3 Track fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.4 Per-event error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.5 Missing turn recovery . . . . . . . . . . . . . . . . . . . . . . . . . .
Positron timing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 Timing calculation by TICP . . . . . . . . . . . . . . . . . . . . . . .
3.3.2 DCH-TIC interconnection . . . . . . . . . . . . . . . . . . . . . . . .
Combination of γ and positron . . . . . . . . . . . . . . . . . . . . . . . . . .
Reconstruction of AIF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5.1 Candidate finding . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5.2 Matching DCH and LXe . . . . . . . . . . . . . . . . . . . . . . . . .

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50
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4

Calibration
4.1 LXe detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.1 PMT calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.2 Gamma calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.3 Energy scale stability . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.4 LXe detector alignment . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Drift chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.1 z-coordinate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.2 Time calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.3 Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.4 Mott calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 Timing counter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.1 PMT gain adjustment . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.2 z calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.3 Relative calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4 Target alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4.1 Conventional alignment methods . . . . . . . . . . . . . . . . . . . . .
4.4.2 Target deformation and countermeasure . . . . . . . . . . . . . . . . .
4.5 DRS calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5.1 Voltage calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5.2 Timing calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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5

Performance
5.1 Timing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.1 γ timing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.2 Positron timing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.3 Combined timing . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Gamma energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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3.2

3.3
3.4
3.5

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Contents
5.3
5.4

Positron energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Relative angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.1 Gamma position . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.2 Positron angle and vertex position . . . . . . . . . . . . . . . . . . . .
5.4.3 Combined angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Detection efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5.1 Gamma efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5.2 Positron efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5.3 Efficiency of DAQ system . . . . . . . . . . . . . . . . . . . . . . . .

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6

Run
6.1 Engineering run 2007 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2 Run2008 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3 Run2009 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.4 Run2010 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.5 Run2011 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.6 Run2012 and 2013 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.7 Data summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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7

Physics analysis
91
7.1 Analysis scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
7.2 Data sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
7.2.1 Pre-selection and blinding . . . . . . . . . . . . . . . . . . . . . . . . 91
7.2.2 Analysis region and side bands . . . . . . . . . . . . . . . . . . . . . . 92
7.3 Likelihood analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
7.3.1 Likelihood function . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
7.3.2 Fitting and the confidence region . . . . . . . . . . . . . . . . . . . . . 95
7.4 PDF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
7.4.1 Signal PDF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
7.4.2 RMD PDF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
7.4.3 Accidental background PDF . . . . . . . . . . . . . . . . . . . . . . . 101
7.5 Target Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
7.6 AIF reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
7.6.1 Definition of the distance . . . . . . . . . . . . . . . . . . . . . . . . . 104
7.6.2 Fit parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
7.7 Normalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
7.7.1 Michel normalization . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
7.7.2 RMD normalization . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
7.7.3 Combination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

8

Results
113
8.1 Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
8.1.1 Results in the sidebands . . . . . . . . . . . . . . . . . . . . . . . . . 114
8.1.2 Systematic error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
8.2 Results in analysis window . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
8.2.1 Event distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
8.2.2 Highly ranked events . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

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Contents

8.3

9

8.2.3 Fit results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
8.2.4 Upper limit for branching ratio . . . . . . . . . . . . . . . . . . . . . . 119
Check for the analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
8.3.1 Comparison with previous analysis . . . . . . . . . . . . . . . . . . . 121
8.3.2 Fitting without constraints . . . . . . . . . . . . . . . . . . . . . . . . 123
8.3.3 Comparison with alternative analysis . . . . . . . . . . . . . . . . . . 123

Prospects
125
9.1 MEG II experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
9.1.1 Beam and target . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
9.1.2 LXe detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
9.1.3 Magnetic field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
9.1.4 Drift chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
9.1.5 Timing counter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
9.1.6 Radiative decay counter . . . . . . . . . . . . . . . . . . . . . . . . . 127
9.1.7 Projected sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
9.2 Future projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

10 Conclusion

131

A Performance of BGO detector
133
A.1 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
A.2 Position resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
A.3 Energy resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
B AIF cut efficiency in signal/RMD event
137
B.1 Accidental background and signal/RMD events . . . . . . . . . . . . . . . . . 137
B.2 Event scrambling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
B.3 Probability to find no AIF candidate . . . . . . . . . . . . . . . . . . . . . . . 138
B.4 Error of inefficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
C List of abbreviations

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Chapter 1
Introduction
The Standard Model (SM) of the particle physics have been surviving many experimental trials,
although it is thought not to be the "ultimate" theory but an effective theory at low energy. The
SM contains quarks and leptons and both have three generations. But it cannot answer why three
generations exist, and how flavors are mixed to each other. The question about the generationand flavor is one of the greatest themes of particle physics. Theories beyond SM which give theanswer for this question is longed for, and many experiments have been searching for the hints
for the new theories.
In year 2012, the last SM particle Higgs was found at 125 GeV by ATLAS [1] and CMS [2]collaborations at the CERN Large Hadron Collider, while no evidence beyond SM has been
discovered. The existence of the mass and the flavor mixing of neutrino is one of the few
discrepancies between experiments and the SM [3]. The mixing of the neutrino flavor canbe described by Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix [4]. Also in year 2012,
reactor and accelerator neutrino experiments revealed the last mixing angle: θ 13 to be relatively
large (9◦ ) [5] [6] [7].
However, the mixing in the charged lepton sector has never been observed since the discoveryof the muon in year 1937 [8].
The MEG experiment has searched for µ → eγ with unprecedentedly high sensitivity.

1.1

Physics motivations

When the neutrino mixing is considered, charged lepton flavor violating (CLFV) process (e.g.
µ → eγ) occurs as shown in a diagram in Fig. 1.1. The probability of this decay mode is given
by Eq. (1.1). This is too small to be measured experimentally, in other words, the discovery ofthe µ → eγ will be an unwavering evidence of new physics.

γ

W
µ

νµ

νe

e

Figure 1.1: µ → eγ decay via neutrino mixing, the probability amplitude is extremely small.
9Chapter 1. Introduction∆m2
3α X ∗Uµi Uei 2i1
B(µ → eγ) =32π i=2,3
MW2∼ 10−55,(1.1)

where Ui j is i- jth element of the PMNS matrix. The absolute value of this formula is extremely
suppressed by the fourth power of the mass difference between W boson and neutrinos.

1.1.1µ → eγ by theories beyond the standard model

A model-independent Lagrangian for the µ+ → e+ γ process can be written as Eq. (1.2) [9].
g
4G F f
L µ→eγ = − √m µ AR µ̄ R σ µν e L Fµν + m µ AL µ̄ L σ µν e R Fµν + (h.c.) ,
2

(1.2)

where G F is Fermi coupling constant, and AR and AL are coupling constants corresponds toµ+ → eR + γ and µ+ → eL + γ, respectively, and are expressed as,√
2e∗∗
AR = − 2 2 ( f E1(0) + f M1
(0)),
(1.3)
8G F m µ
√
2e
∗
AL =
( f ∗ (0) − f M1
(0)).
2
8G F m2µ E1
f E1 and f M1 are electro-magnetic form factors when the general transition amplitude of vertex
of muon (4-momentum p µ ), electron (pe ) and photon (q = p µ − pe ) is written as,
M = −eA∗µ (q)ūe( f E0 (q2 ) + γ5 f M0 (q2 ))γν (g µν −

q µqν
)
q2

iσ µν u µ (p µ ).
+( f M1 (q ) + γ5 f E1 (q ))
mµ
2

2

(1.4)

The differential angular distribution is given by Eq. (1.5).
dB(µ+ → e+ γ)= 192π 2 | AR | 2 (1 − Pµ cos θ e ) + | AL | 2 (1 + Pµ cos θ e ) ,d cos θ e

(1.5)

where θ e is the angle between the muon polarization and the positron momentum in the muon
rest frame, and Pµ is the magnitude of the muon polarization. AR and AL depend on the model,
so the measurement of positron emission angle with respect to polarized muon gives anotherinformation to restrict models.
The introduction of the supersymmetry (SUSY) [10] is one of the most prevailing extensionsof the standard model. It helps the SM from the ultraviolet divergence of Higgs boson mass dueto the higher order quantum effect. Even in the minimum SUSY extension of the standard model(MSSM), there are huge degrees of freedom in the parameter space. Hence, the MSSM is often
considered within the constraints to meet the phenomenological observations (pMSSM). In the
MSSM scheme, a muon can decay into a positron and a photon as in Fig. 1.2 [11].
In this example, the decay occurs via a loop of neutralino and slepton. The slepton isspin-0 SUSY partner of lepton, and neutralino is spin-1/2 particle which is made by mixing of
SUSY partners of electro-weak boson and Higgs boson. The decay of Fig. 1.2 is possible if the10Chapter 1. Introduction

f
µ

µ

ee
f0
χ

γ
e

Figure 1.2: An example of µ → eγ decay in the SUSY model.
theory has non-diagonal element (mixing) in slepton mass matrix. However some mechanism
which suppresses the matrix to be almost diagonal is thought to exist, otherwise the probabilityof the decay was much higher than experimental observation. Two kinds of sources of thenon-vanishing off-diagonal element are proposed in the pMSSM scheme.
seesaw mechanism with SUSY Heavy right-handed neutrino with seesaw model is a wellmotivated candidate of the new physics. Since it can naturally explain the small neutrino mass
by introducing a right handed neutrino with a heavy Majorana mass. As the Yukawa coupling
matrix for electron and neutrino are independent, off-diagonal elements appear in left-handed
slepton mass matrix as,(ml2˜L )i j ≈ −MP1∗(yν ) ki),(yν ) k j m02 (3 + | A0 | 2 ) ln(
2
MR
8π

(1.6)

where yν is the Yukawa coupling matrix for neutrino, m0 is the universal scalar mass, A0 is
the universal trilinear coupling, MP and MR are the Planck mass and mass of the right handed
neutrino. The effect from right-handed neutrino contributes only AR , in other words, onlyµ+ → e+R γ occurs and thus the angular dependence will be a form of (1 − Pµ cos θ e ). Figure 1.3
shows the prediction of branching ratio of µ → eγ and τ → µγ by MSSM with seesaw model[12]. Since θ 13 is already found to be ∼ 9◦ , purple region is remaining.
SUSY GUT A combination of the MSSM and Grand Unification Theory (GUT) is a candidate
for the origin of the slepton flavor mixing. The GUT is a theory to explain the electroweak
and the strong interactions using a larger gauge group which includes the gauge groups both
SU (2) L × U (1)Y and SU (3)C . The quarks and leptons are summed up into one multiplet andnewly introduced bosons causes a new kind of the interaction that transforms quarks to leptons
vice versa. The SUSY GUT is a favoured theory, because coupling constants of electromagnetic,
weak and strong interactions converge to one value as the energy scale goes up to ∼ 1015 GeV(GUT scale). The smallest group which satisfies the requirement is SU (5), while SO(10) or
larger groups are also the candidate of the extended theory of the SM.
The GUT as a source of LFV is suggested in [11]. This is an independent LFV source ofthe see-saw mechanism, since it originates from off-diagonal element in up-type quarks. In
the case of SU (5), LFV appears in the right-handed slepton sector (negligibly small in theleft-handed side). In this model, the higher branching ratio is expected with the larger tan β,
where β = hh2 i/hh1 i is the ratio of the expectation values of two Higgs fields. (h1 for down-type
quark and lepton, h2 for up-type quark.) Figure 1.4 shows the calculation with SU (5) model[16]. In the case of SO(10), both AR and AL have non-vanishing values [17].
11Chapter 1. Introduction

Figure 1.3: Branching ratio of µ → eγ and τ → µγ, expected by MSSM with seesaw mechanism[12] depending on neutrino mixing angle θ 13 and mass of right handed neutrino. The lines
showing the experimental bounds [13] [14] [15] are added to the original figure.

Figure 1.4: µ → eγ branching ratio calculated in SUSY SU (5) model [16]. The horizontal axis
is mass of the right-handed selectron. The top Yukawa coupling at the Planck scale ( f t (M)) is
fixed to be 2.4, and the bino mass (M1 ) is fixed to be 50 GeV. (a) and (b) show the cases withpositive and negative sign of the higgsino mass parameter (µ), respectively.
other models Not only theories mentioned above, many theories such as, SUSY with Rparity violation [18], SM with 4-th generation [19], littlest Higgs model with T-parity [20],Randall-Sundrum model [21], etc. predict sizable rates of the LFV process.
Therefore, the search for the µ → eγ is a good probe for the new physics beyond the SM,
12Chapter 1. Introduction
and the precise measurement of the branching ratio gives a information to restrict theories. The
branching ratio in O(10−13 ) is a region where many theories predict and it is meaningful tosearch for µ → eγ in the sensitivity.

1.2µ → eγ search

1.2.1

Past experiments

The search for µ → eγ has a long history since the first result in year 1947 using cosmic
ray [22]. From the result that a muon doesn’t directly change to an electron, it turned out thata muon is not a excited state of an electron. Then in 50s, the upper limit of the branchingratio was improved in the experiments using accelerators, such as 2 × 10−5 in year 1954 [23],
7 × 10−7 in 1959 [24]. These results are inconsistent with the theoretical calculation under anassumption of one "meson" [25]. The existence of the "lepton flavor" was established from thesemeasurements results, where it is considered that electron and muon are different particles, andthere are different types of neutrino to interact.
In the following decade, the search for µ → eγ was not so active, but in late 70s, intense
muon sources were becoming available, for example at Swiss Institute for Nuclear research(SIN1), TRIUMF in Canada, and Los Alamos National Laboratory Meson Physics Facility(LAMPF). In 1982, LAMPF group reached to the branching ratio sensitivity of 1.7 × 10−10 [26].
The world record of the branching ratio limit was overwritten with Crystal Box [27] and then
MEGA [28]. 1.2 × 10−11 set by MEGA experiment was the most stringent upper limit before
the MEG experiment was started. The history of the branching ratio improvement in the LFVsearch is summarized in Fig. 1.5 [29]. Table 1.1 shows the world records of the muon LFVsearch [30].
1
10-1
10-3

Table 1.1: Current limits of muon
decays from Particle Data Group [30].

10-5
10-7
10-9
-11

10

10-13
10-15
10-17
10-19
1940

1950

1960

1970

1980

1990

2000

2010

2020

2030

Figure 1.5: History of the result of CLFV searchexperiments [29].

1 former organization of Paul Scherrer Institute (PSI)

13

Mode
e− ν¯e ν µ
e− ν¯e ν µ γe− ν¯e ν µ e+ e−
e− νe ν¯µe+ γe− e+ e−e− 2γBranching ratio≈ 100%
1.4 ± 0.4%
3.4 ± 0.4 × 10−5
< 1.2%< 5.7 × 10−13< 1.0 × 10−12< 7.2 × 10−11

C.L.

90%
90%
90%
90%

Chapter 1. Introduction

1.2.2

Signal and background

The µ+ → e+ γ signal has a very simple kinematics. When the initial state is a stopped muon,
the directions of γ-ray and positron are back-to-back and simultaneously emitted from a point,
and the energies are well approximated to be the half of the rest mass of muon. Therefore, themeasurement of the emission angle, timing and energy of γ-ray and positron is important inorder to separate signal from background.
There are two kinds of backgrounds (BG): One is called "prompt" background or Radiative
Muon Decay (RMD), and the other is "accidental" background (ACC). As for RMD, the muon
decays as µ+ → e+ νe ν̄ µ γ and when the energy carried by the neutrinos is small, the event looks
like a signal. The "accidental" (the dominant in our case) is a coincidence of positron fromnormal muon decay and γ-ray from other sources. The probabilities of RMD and accidental
background are estimated below.
radiative muon decay An approximative decay width of the radiative muon decay is given in[31]. (Its exact calculation is demonstrated in [32] [33].)g
α f
J1 (1 − Pµ cos θ e ) + J2 (1 + Pµ cos θ e ) .
(1.7)
dB(µ+ → e+ νe ν̄ µ γ) =16π
When γ-ray energy, positron energy and angle resolutions of an experiment are taken into
account, the J1 and J2 in Eq. (1.7) are expressed by
δz
δz
1 1
δz
8
(δx) 3 (δy)( ) 2 − 2(δx) 2 ( ) 4 + ( ) 2 ( ) 8,
3
2
2
3 δy
2
δz
δz
8 δz
J2 = 8(δx) 2 (δy) 2 ( ) 2 − 8(δx)(δy)( ) 4 + ( ) 6,
2
2
3 2
J1 =

(1.8)
(1.9)

where δx = 2δE e /m µ , δy = 2δEγ /m µ and δz = δθ eγ . The δEe , δEγ and δθ eγ show the half
width of the analysis region of the γ-ray energy, positron energy and angle, respectively.
accidental background The accidental background makes majority of all background event.
The branching ratio by the accidental can be estimated with a formula of Eq. (1.10) [9].
Ωeγ
· 2δt,(1.10)
4π
where R µ is beam rate, f e 0 and f γ 0 are fraction of positron and gamma ray whose energy iswithin the signal region, respectively, Ωeγ is range of solid angle of angle resolution, if it issquare shape, Ωeγ /4π = (δz) 2 /4 and δt is half width of the time window.
Since Ee spectrum from Michel decay shows flat distribution near m µ/2, and a sharp edge at
higher energy side, f e 0 can be approximated as f e 0 ∼ 2δx. The gamma background from RMD
rapidly drops as the energy approach to the signal energy, after integration over energy aroundsignal and the polarization,


α
fγ0 ≈
(δy) 2 ln(δy) + 7.33
(1.11)
2π
B(ACC) = R µ · f e 0 · f γ 0 ·By summarizing all above, we get the approximation of the number of the background,!
α δθ 22
B(ACC) ≈ R µ · (2δx) ·(δy) (ln(δy) + 7.33) ·· (2δt) .
(1.12)
2π
414Chapter 1. Introduction

E γ ,min (MeV)In Eq. (1.12), only γ-ray from RMD is taken into account, and other sources of the BG γ-ray
depend on the apparatus of the experiment. For the situation of MEG experiment, anothermajor BG source is annihilation-in-flight (AIF) of positron. The AIF mainly occurs in the muon
stopping target and the drift chamber (positron tracker). The amount is comparable to that of
RMD, and has larger fraction near the signal energy.
Figure 1.6 shows the effective branching ratios for (a) accidental background and (b) RMD,
as functions of lower edge of the energy window, which is defined by Ee,min < Ee < 53.5 MeV,
Eγ,min < Eγ < 53.5 MeV, |t eγ | < 0.24 ns and |Θeγ | < 28 mrad. With the given window, thebackground of the accidental is about one order of magnitude more.
Therefore, the continuous muon beam is required, instead of the pulsed beam to minimise
the accidental background. There is an optimal beam rate to achieve best sensitivity, since
the branching ratio of accidental background increases in proportion to beam rate as shown in
Eq. (1.12), while that of the signal do not depends on beam rate. The timing resolution is also
important to reject accidental background.
53

53

(a)

(b)
10-13

52

52

10-12

51

48
50

50
10-11

51

10-14
10-13

51

50
49

10-15

10-12

49

52

53

48
50

51

52
53
E e,min (MeV)

Figure 1.6: Effective branching ratio of (a) accidental background and (b) RMD. The plot for
accidental background is made from observed number in the MEG experiment. The branchingratio of RMD is calculated from formula and the detector performance.

1.3

Relation with other experimental searches

1.3.1µ − e conversion

When negative muon stops inside of the matter, the muon can be captured by an atom to forma muonic atom. In the standard model, the muon decays as µ− → e− ν¯e ν µ (decay in orbit), or iscaptured by the nucleus of the atom in a process as µ− + N ( A, Z ) → ν µ + N ( A, Z − 1) where
N ( A, Z ) is a nucleus of the atom whose mass number is A and atomic number is Z.
The µ − e conversion is a phenomenon which is expressed as Eq. (1.13).
µ− + N ( A, Z ) → e− + N ( A, Z )The decay is forbidden within SM but predicted in the theories beyond the SM.
15(1.13)

Chapter 1. Introduction
The effective Lagrangian for this process can be written as [34],L=mµκµ̄ R σ µν e L F µν +µ̄ L γ µ e L ( f¯L γ µ f L )2(κ + 1)Λ
(κ + 1)Λ2(1.14)

where Λ is a parameter of mass 1-dimension which represents the effective mass scale of the
new physics, κ is a 0-dimension parameter which shows the relative size of first and second
term. f is the ferimionic fields: quarks in a nuclei in this case.
The first term in Eq. (1.14) corresponds to a interaction via electro-magnetic coupling(shown in Fig. 1.7(a)), and is dominant when κ  1. It has a common term in Eq. (1.2) of
the case of µ → eγ decay. However the diagram of a µ-e conversion includes one more vertex
comparing with that of µ → eγ, the probability of the conversion is more suppressed by several
hundred times than µ → eγ decay. The second term originates from four fermion coupling (treeinteraction), and is dominant when κ  1. There is no corresponding term in Eq. (1.2), hence
the µ − e conversion search is complimentary to µ → eγ search.
The signal is characterized by only one electron whose energy around 105 MeV, whichslightly depends on the different binding energy of muon in 1S orbit by different nuclide. A
major background against this reaction is called Decay in Orbit (DIO) where the muon decays innormal way. The energy of the decayed electron has edge at the half of the muon mass, however
the spectrum has a long tail and sharply drops at the signal energy due to the interaction with
nucleus [35]. Another background for the µ − e conversion experiment is contamination in themuon beam (especially π). Therefore pulsed beam is better, and beam system to remove thecontamination is important.
As of year 2016, the best experimental upper limit is achieved by SINDRUM-II experiment [36], and several experiments are being prepared, DeeMe experiment [37], COMET
experiment [38] at J-PARC in Japan and Mu2e experiment at Fermilab in USA [39].
e

N

e

µ

µ

e
(a)

e

(b)

Figure 1.7: A diagram of µ-e conversion (left) and µ → eee decay (right). Intermediate particle
is not limited for photon in these cases.

1.3.2µ → eee decay

A decay process: µ → eee is also a CLFV decay which is forbidden within the SM. Figure 1.7(b)shows an example of the diagram for µ → eee decay, the intermediate particle is not necessarily
photon as well as µ − e conversion. From the theoretical point of view, the search for this decay
is similar to µ − e conversion, because the model-independent Lagrangian for this decay can be
written as the same as that in Eq. (1.14), the coupling fermion is, however, not quarks but anelectron in this channel.
16Chapter 1. Introduction
Many well-motivated theories predict κ  1, but some theories such as supersymmetricmodels with trilinear R-parity violation or theories which include leptoquarks predict κ  1. In
the case of κ  1, the µ → eγ search have an advantage, and opposite in the case of κ  1. In
Fig. 1.8, the sensitivities of experiments are shown as functions of κ value.
a

b

4,000

B(µ → eee)>10–16
3,000❇

B(µ → eγ)>10–13(µ → econversion in 48Ti)>10–18

104

B(µ → eee)>10–15

B(µ → eee)>10–14

B(µ → econversion in 48Ti)>10–16

(TeV)

(TeV)

2,000

✁

✁

B(µ → eγ)>10–14

1,000
900
800
700
600

B(µ → eγ)>10–13

500
400
103

Excluded300

Excluded
10–2

10–1

100

101

10–2

102

κ

10–1

100

101

102

κ

Figure 1.8: Sensitivities of the experiments, as functions of the κ parameter. (left) experimental
sensitivity of µ → eγ and µ − e conversion (normalized to a case of 48 Ti), (right) and that ofµ → eγ and µ → eee. Λ is the scale of new physics as seen in Eq. (1.14) [34].
An experiment to search for µ → eee is planned in PSI (Mu3e) [40].

1.3.3

Muon anomalous magnetic moment

There is a well known relation M µ = g · es/2m µ , where M µ is magnetic moment by muon spinand s is spin angular momentum. g is a factor to connect magnitudes of magnetic momentum
and spin, and is exactly 2 when only tree-level process is considered, but deviates from 2 withhigher order processes. Recent both theoretical [41] and experimental [42] progresses found a
non-negligible discrepancy between the SM prediction and the experimental observation ∆a µ at
the order of O(10−9 ).
If it is true, the deviation comes from a contribution of loop diagrams with new particles.
One of the diagrams contains SUSY particles like in Fig. 1.9. This diagram is topologicallythe same as that in Fig. 1.2 except for the flavor violation. In a SUSY model discussed in [43](Fig. 1.10), the µ → eγ branching ratio and ∆a µ are related to each other as,
!2
∆am u
−4
2
B(µ → eγ) ≈ 10
|δ12
(1.15)
LL | .
−11
200 × 10−4
|δ12
LL | is a factor coming from CLFV coupling and assumed to be 10 .
Experiments of next generation ∆a µ measurements, E989 experiment at Fermilab in USA,and J-PARC g-2/EDM experiment in Japan, are in preparation.

17

Chapter 1. Introduction

γ

µ

f
µ

f
µ

µ

f0
χ

Figure 1.9: An example of contribution to vertex function of µ in the SUSY model.

E821(2006)

Figure 1.10: Expected relation between branching ratio of µ → eγ and muon anomalous
magnetic moment [43]. The lines to show the experimental bounds of µ → eγ [13] and δa µ [44]are added to the original figure. Large area is already excluded by measurements.

1.3.4

LFV search with τ decay

LFV searches via τ particle decay are undertaken by B-factory experiments such as Belle, BaBar
and LHCb. A lot of LFV decays are possible for τ, since τ has a mass of 1.777 GeV and islarger than that of µ and lightest baryons and mesons. Those collaborations are searching for
the LFV decay with a data of ∼ 1 ab−1 in each possible channel, however no evidence for the
LFV has been found. The results are summarized in Fig. 1.11.
A decay channel τ → µγ has the same topology as µ → eγ, and correlation is pointed out insome model of new physics. Figure 1.3 shows a prediction by MSSM with seesaw model [12].
According to the plot, µ → eγ search is more advantageous than τ → µγ, and being consideredthe θ 13 ≈ 9◦ , the experiment starts covering the predicted area.
In year 2016, LHCb is still taking data, and Belle is updating results of τ → lγ channels.
SuperKEKB/Belle II in Japan is in construction. A τ and charm factory is also being consideredin Russia.

18

Chapter 1. Introduction

Figure 1.11: Upper limits of LFV search in τ decay [45].

19Chapter 1. Introduction

20

Chapter 2
MEG experiment setup
The MEG experiment is performed at a national laboratory of Switzerland, Paul Scherrer Institute(PSI). An overview image of the experiment setup is shown in Fig. 2.1.

y
x
z

x
z
y

Figure 2.1: Overview of the MEG setup
The MEG experiment uses positive muon beam, because negative muons can be captured
by atomic nuclei and form muonic atom. The positive muons from the beamline are stopped on
the target at a center. The liquid xenon detector (Sec. 2.3) detects γ-ray, and the positrons aremeasured in a magnetic field by COBRA magnet (Sec. 2.4.1) via the drift chamber (Sec. 2.4.2)
as a tracking detector, then hit the timing counter (Sec. 2.4.3).
The coordinate system is defined as follows. The origin is set at the center of the COBRA
magnet. The z axis is parallel with muon beam, the y axis is set vertical upward, and the x isdefined as such (x, y, z) to be a right-handed-system, i.e. the liquid xenon
p detector locates negativeside of x coordinate. In addition, the cylindrical coordinates, r = x 2 + y 2 , θ = tan−1 (z/r) and
φ = tan−1 (y/x) are also used.
The details of the detector design are described in [46].
21Chapter 2. MEG experiment setup

2.1

Beam

In order to achieve a high sensitivity in the MEG, there are two important requirements on beam.
One is the intensity in order to gain data statistics. The other one is the property of Direct
Current (DC), to minimize the accidental pile-up. The MEG experiment is being conducted inthe πE5 beamline where the most intense DC µ+ beam up to 108 /s is available. The beam bunchinterval is ∼ 20 ns (repetition rate 50.6 MHz), and is well shorter than the mean life of muon atrest state: 2.2 µs. Therefore, the beam can be considered as DC beam. Requirements for beam
property are the small transverse size, small momentum spread and small beam contamination.

ŵĂŝŶƌŝŶŐĐǇĐůŽƚƌŽŶ

ƚĂƌŐĞƚʋϱĂƌĞĂ

Figure 2.2: Top view of beam facility in PSI main experimental hall. The beam path is shownin arrows.

2.1.1

PSI accelerator facility

In Figure 2.2, a map of PSI main experimental hall is shown. PSI provides µ+ beam withHigh Intensity Proton Accelerators (HIPA) [47]. HIPA consists of three accelerators, CockcroftWalton accelerator, Injector 2 cyclotron and main ring cyclotron (Fig. 2.3(a))1. The energy of
1 In operation since 1974.

22

Chapter 2. MEG experiment setup
proton is 590 MeV and the nominal beam current at the year 2013 was 2.2 mA.

(a) PSI proton main ring cyclotron(b) Target E. The outermost
part is graphite target.

Figure 2.3
The proton beam is lead to a production target made of carbon graphite with 4 cm length
along beam axis. The target is shown in Fig. 2.3(b), the wheel keeps on rotating during theoperation for cooling. The surface muon is produced from decay of positive pion (π + → µ+ ν µ )which stopped near surface of the target. The energy of µ+ s is uniform (since the pion is stopped)and spin is completely polarized. The surface muon beam is contaminated with positron, which
is needed to be removed before it reaches the MEG detector. The πE5 beam line is located at166◦ from the original beam, where surface muons [48] from the target are extracted with anarray of magnets. The main specification of the beam is summarized in Table 2.1.
Table 2.1: Specs of πE5 beam lineItemmomentum center
momentum spread (FWHM)
solid angle
spot size (FWHM)
angular divergence (FWHM)

2.1.2

Value
28 MeV/c
5-7%
150 msr
15 mm horizontal
20 mm vertical
450 mrad horizontal
120 mrad verticalBeam transport system

Figure 2.4 shows the layout in the πE5 area. The secondary beam runs through the control
magnets which consist of a chain of bending, quadrupole and sextupole magnets. An Wien filter
is equipped between two quadrupole triplets, in order to separate µ+ from the other particles(mainly positron). In the Wien filter, horizontal 133 Gauss magnetic field and vertical 195 kVelectric field in 19 cm gap of electrodes are applied to the beam. The separation power formuon from positron is as high as 8.1 σ. The muon beam is then injected into Beam Transport
23

Chapter 2. MEG experiment setup

Figure 2.4: Layout in πE5, MEG experiment area
Solenoid (BTS, picture in Fig. 2.5). The main component of the BTS is liquid helium cooled
superconducting2 solenoid with 380 mm bore diameter and 2.63 m length. The nominal current
is 199 A and the field strength is 0.36 T. The purposes of BTS are to conduct and focus muon attarget, and to make beam spot smaller with collimator. A degrader of thin Mylar film is placedat the center of BTS to maximize the stopping efficiency at the target. The thickness of the film
is 300 µm.

Figure 2.5: Beam Transport Solenoid
The BTS and the spectrometer magnet are connected with an end-cap with thin beam window.
While all the beam pipes are evacuated, the spectrometer volume is filled with helium3 gas fordrift chamber (Sec. 2.4.2.1).
2 Nb/Ti superconductor
3 Synthetic air is slightly mixed for measure against discharge.

24

Chapter 2. MEG experiment setup
At the stopping target, the beam has round Gaussian profile of σ x,y ≈ 10 mm, and the+0.05 (syst.) and is consistentpolarization of muon is measured to be Pµ = −0.86 ± 0.02(stat.)−0.06
with the expectation [49].

2.2

Stopping target

The purpose of the stopping target is to stop muon on it. Therefore, a certain thickness ofmaterial is required. On the other hand, the target material on the trajectory of the decayed
positron should be minimized for two reasons. The electromagnetic multiple scattering worsens
angular resolution, and positron can annihilate with electrons in target. γ-ray which is emitted
by annihilation is one of the sources of γ-ray background.
The muon stopping target is shown in Fig. 2.6. It is made of a layered films of polyethylene
and polyester with a total thickness of 205 µm and is assembled in a flame, which is made oflight but rigid material: Rohacell4. The target is laid with a slant angle of 20.5◦ with respect
to the beam direction. The angle was optimized considering muon stopping power (stopping
efficiency ∼ 80%) and multiple scattering. The target has elliptical shape of 20 cm and 8 cm
respectively in major and minor axes and has six holes (10 mm in diameter) and seven crossmarkers, which are used for the alignment of the target (Sec. 4.4).
The target can be moved remotely for when another target is inserted from the downstreamside for the LXe γ-detector calibration.

Figure 2.6: MEG stopping target, 6 holes and 7 cross markers are seen.

2.3

Gamma detector

The gamma detector plays a key role in a µ → eγ search, because background γ energy spectrum
rapidly falls around the endpoint, and the energy resolution is important to reject backgrounds.
Therefore, also the past experiments [27] [50] paid special attention on gamma detection. The
MEG experiment adopted liquid xenon (LXe) scintillation detector. The details will be discussed
in next sections.
The design of LXe gamma detector [51] is shown in Fig. 2.7. The concept of the detector
is viewing many fast scintillation photons from single active volume with high performance
sensors. Because we need to detect ∼ 175 nm wavelength photon in environment of liquid
xenon, we developed a special PMT for LXe detector. The development of the MEG LXedetector can be found in [52].
4 By EVONIC, foamed polymethacrylimide (PMI)25

Chapter 2. MEG experiment setup

Figure 2.7: Schematic view of gamma detector

2.3.1

Liquid xenon

Liquid xenon is nowadays widely used in experimental physics [53], dark-matter search experiment such as XENON [54] and XMASS [55], or neutrino-less double beta decay experiment
EXO [56] etc. Not only for experiment, but also applications are developed for medical use.
Excellent characteristics of LXe are as follows.
• High light yield• High density• Fast response• Uniformity as fluid• No self-absorption of scintillation photon
These properties enable high rate, high precision γ-ray measurement. The LXe also hasproperties of the ionization and phonon which are available for many applications for particle
detection such as timing projection chambers, but we utilize only scintillation light for thesimplicity of the detector.
On the other hand there are some difficulties to deal with liquid xenon. As shown in Fig. 2.8,
the pressure of triple point is near normal pressure. The range to be in liquid state is therefore
narrow at operation pressure. This means the stable temperature and pressure control is required.
The wavelength is also a difficulty with LXe scintillation detector. The wavelength of LXe is
measured to be 174.8 ± 0.1(stat.) ± 0.1(syst.) nm [57]. The wavelength is in a range which iscalled Vacuum Ultra-Violet (VUV) light, where special treatment for detection is needed (SeeSec. 2.3.3 and 2.3.5.3). Basic physical properties of xenon is listed in Table 2.2.

2.3.2

Scintillation

When a gamma-ray is injected into material, generally 3 types of reactions are possible, photoelectric absorption, Compton scattering and pair creation. Figure 2.9 shows the probabilityof the reactions in liquid xenon. Around the energy of the γ-ray from the µ → eγ, Compton
26

Chapter 2. MEG experiment setup

Table 2.2: Basic properties of xenon
Item
Atomic Number (Z)Atomic Weight
Density
Triple point temperature
Triple point pressure
Radiation length
Moliere radius
Scintillation Wavelength
Decay constant (fast)
Decay constant (slow)
Decay constant (recomb.)
W (for α)
W (for electron, γ)

Value
54
131.2932.978 g/cm3
161.405 K
0.0816 MPa
2.872 cm5.224 cm
175 nm
4.2 ns
22 ns
45 ns
17.9 eV21.6 eVFigure 2.8: Phase diagram of xenon
scattering and pair creation are dominant. Therefore the gamma-ray around the signal energy
makes electromagnetic shower starting from the first conversion by scattering or creation.

Figure 2.9: Photon interaction in LXe as a function of photon energy [58].
Some part of the deposited energy in the liquid xenon is used to emit scintillation photon.
The scintillation photons are generated from two reaction paths [53]. The first path is excitation
as follows,27

Chapter 2. MEG experiment setup

Xe∗ + Xe → Xe∗2
Xe∗2 → 2Xe + hν

(2.1)
(2.2)

where Xe∗2 is called excimer: excited state of diatomic molecule of xenon and hν corresponds
photon. The second path is called recombination,
Xe+ + Xe → Xe+2
Xe+2 + e− → Xe∗∗ + Xe
Xe∗∗ → Xe∗
Xe∗ + Xe → Xe∗2
Xe∗2 → 2Xe + hν

(2.3)
(2.4)
(2.5)
(2.6)
(2.7)

Since the excited state of Xe in Eq. (2.5) is the same state as that in Eq. (2.1), the rest part ofthe process is the same as the first. The fraction of excitation and recombination depends on thespecies of the incident particle. In the case of the gamma, the recombination part is more. The
recombination step of Eq. (2.4) has the time constant of 45 ns. The time constant of excitation
path consist of fast and slow components, which are determined by the step Eq. (2.2). Due totwo different spin state of the excimer 1 Σu+ and 3 Σu+ , there are two time constants 4.2 and 22
ns [59].

2.3.3

PMT

Scintillation photons are detected by photo-multiplier tube (PMT). For our application for MEG
LXe detector, the difficulties are (1) detection of VUV light whose central wavelength is 175
nm and (2) operation in liquid xenon at 165 K. We developed a VUV-sensitive PMT for the LXedetector in collaboration with Hamamatsu Photonics [60]. In order to detect VUV light, photocathode of VUV sensitive material5 and VUV-transparent quartz window is adopted. Aluminum
strips (seen in Fig. 2.10(a)) is introduced to stabilize performance in cold environment. For ourdesign, PMTs are located between target and LXe volume, hence a compact design is required.
The metal channel dynode is employed for the PMT for that reason.

2.3.4

DesignThe schematic view of the LXe gamma detector is illustrated in the Fig. 2.7. It has "C"-shaped
structure fitting the outer radius of COBRA. The detector is assembled inside of a vacuuminsulated cryostat. In order to reduce heat inflow, a multi-layered superinsulator installed in thevacuum-insulation. The total volume of liquid xenon is 900 l (2.7 t).
LXe volume covers 11% solid angle viewed from center of the target. The radial depth of
LXe of 38.5 cm was determined to completely absorb signal γ of 52.8 MeV. It corresponds to
14X0 . The LXe detector local coordinates (u, v and w) are used to indicate position inside of
detector. u shows the direction parallel to the beam axis, v is curved axis along inner face, andw is the depth from the inner face. The definition is also illustrated in Fig. 2.11(a).
5 K-Cs-Sb

28

Chapter 2. MEG experiment setup(a) Outer view of Hamamatsu
R9869(b) Drawing of PMT

Figure 2.10: PMT for the LXe detector

ǀ

(cm)

The PMTs are inserted in PMT holders, and the PMT holders are arrayed on the six faces.
As shown in Fig. 2.11(b), the six faces are named inner, outer, up-stream, down-stream, top andbottom. 216 PMTs are installed on inner face with an array of 9 columns along u direction and
24 rows along v. In w direction, there are 6 levels of PMTs from inner to outer. Outer face has
the same number of PMTs as inner face basically, but PMTs are arrayed denser in a small region
at the center. The total number of the PMTs is 846.

100

Top

0

Ƶ

Up-streamǁDown-stream

50

Inner

-50

Bottom-100-100(a) Definition of local coordinates.

Outer

-50

0

50

100

150

200

(cm)

(b) PMT arrangement in developed figure

Figure 2.11
The γ-ray from the target must traverse the inside and outside vessel walls. It is desirable
to have less material at inner wall to reduce the interaction of γ-ray before reaching the LXevolume. However the mechanical strength is also required to bear the pressure difference ofxenon–vacuum layer–air. This issue is solved by installing an aluminum honeycomb panel
covered with carbon fiber sheet for the entrance in the inner vessel (Fig. 2.12). The honeycomb
material is Aluminum 5052 with the cell thickness of 0.0254 mm, and the cell size is 4.76 mm.
The averaged material amount in the window region corresponds to 0.075X0 [61].
29Chapter 2. MEG experiment setup

Figure 2.12: Honeycomb panel is attached on the entrance window of inner vessel. The panel
has a dimension of 1315 × 611mm2 along curved inside face.

2.3.5

Xenon handling system

2.3.5.1

Pulse tube refrigerator(a) Pulse tube refrigerator for LXe
detector(b) Operation principle of pulse tube refrigerator

Figure 2.13: Pulse tube refrigerator
As explained in Sec. 2.3.1, liquid xenon has narrow liquid state range at the operationpressure. Powerful and stable refrigeration is required for LXe detector. A 200 W pulse tube
refrigerator (Fig. 2.13(a)) is mounted at the top of the cryostat. The refrigerator was developed
for the MEG LXe detector [62]. The pulse tube refrigerator does not cause mechanical vibration
nor electric noise thanks to the operation principle as shown in Fig. 2.13(b). It contributes stable
operation and low-noise measurement. During xenon liquefaction and a situation when coolingpower is insufficient, liquid nitrogen is used supplementarily. The piping for liquid nitrogen is30

Chapter 2. MEG experiment setup
attached on outside of the inner cryostat.
2.3.5.2

Storage system

Gas piping
Liquid piping

Cryostat

LiquidPurifier

1000 lTank

Handling
Panel

Storage
Tanks

Figure 2.14: Connection of xenon control system
Besides the xenon detector cryostat, auxiliary components are connected to control the xenon
flow for the purpose of storage and purification of the xenon. Figure 2.14 shows a diagram of
the xenon handling system.
Two types of xenon storage are prepared in the auxiliary system. One is the 1000 l tankwhich can hold all LXe. It has an independent liquid nitrogen cooling system. It is used tostore LXe during the short-term maintenance of the detector. The other one is high pressure gas
storage. The storage consists of 8 tanks of the same design. Each tank has 250 l capacity andis tolerable to 8 MPa pressure. Xenon is transferred to the high pressure tanks for long-term
detector maintenance.
2.3.5.3

Purification system

The scintillation light yield is very sensitive to impurities in LXe such as Oxygen, Nitrogen,water [63]. The impurities affect scintillation in two ways. (a) The electronegative molecules trap
ionized electron in recombination process. (b) The molecules such as water absorbs scintillation
photon. The contaminations must be suppressed in ppb order. Therefore the purification system
and monitoring of light yield are mandatory.
In order to remove contaminations from xenon, 2 types of purifiers are connected to thesystem. One is a gaseous state purifier which is installed in the handling panel in Fig. 2.14. The
purifier is based on a metal-heated getter which can absorb most of kinds of molecules except
rare gas. Xenon goes through the getter when it is sent from storage to detector. Purification bygas state circulation is also available. But the purification speed was limited by the evaporationof gas xenon (0.6 l/hour). The liquid phase purification is introduced to improve the speed of thepurification. The liquid purifier is connected to liquid circulation path. It has molecular sievesto adsorb water. A centrifugal pump is used and the circulation speed is ∼70 l/hour [64].
31Chapter 2. MEG experiment setup

2.4

Positron Spectrometer

The positron detector has to treat very high rate positrons. Firstly the all muons eventually decay
into positrons, secondly the ratio of positron with energy around signal region is high. (SeeFig. 2.15). The normal (positive) muon decay in SM is given by Eq. (2.8) [9].

mµ 4 2 q 2
d2Γ
= 3 Weµ G F x − x 20 F (x) + Pµ cos θ e G(x)dxd cos θ e 4π2
F (x) = x(1 − x) + ρ(4x 2 − 3x − x 20 ) + η x 0 (1 − x)
9(
)
q
q
1
2
2
2
2
G(x) = ξ x − x 0 1 − x + δ[4x − 3( 1 − x 0 − 1)] ,
3
3

(2.8)

Differential Branching Ratio

where Weµ = (m2µ + m2e )/(2/m µ ), x = Ee /Weµ , and x 0 = me /Weµ . The parameters ρ, η, ξ andδ are called Michel parameters, and given as 43 , 0, 1 and 34 in the SM. The energy distribution
as a function of x is shown in Fig. 2.15, the probability is at maximum around x = 1. It means
positron cannot be vastly reduced just by a precise energy measurement like in the case of
gamma-ray. However, it is important to reduce low energy positron to suppress the total hit ratein the detector.

1
0.8
0.6
0.4
0.2
0
0

0.2

0.4
0.6
0.8
1
Normalized Positron Energy (x)Figure 2.15: Spectrum of positron from rest muon. The spin of the final state positron isaveraged. The radiative correction is considered here.
The mass of the detector must be small, because the original information of positron caneasily be deteriorated by the effect of electro-magnetic multiple scattering in the detector, aroundthe signal momentum of 52.8 MeV/c. Low material detector also has an advantage for reducing
generation of gamma-ray background.
To meet all the requirements above, we designed a positron spectrometer system, in a special
gradient magnetic field with the spectrometer magnet COBRA. The tracking of positron is done
by ultra low mass drift chambers and a plastic scintillator hodoscope for timing measurement.
32

Chapter 2. MEG experiment setup

2.4.1

COBRA magnet

2.4.1.1

Gradient field

The name "COBRA" is an abbreviation of COnstant Bending RAdius. The COBRA magnet was
specially developed for the MEG experiment and is characterized by the gradient field [65]. The
magnetic field varies from 1.27 T (center) to 0.49 T (both ends) along the z-axis (See Fig. 2.16).
There are two advantages on the gradient field, as shown in Fig. 2.17. (1) Positron trajectoriesof the same momentum have the constant bending radius not depending on the emission angle.
This is the origin of the name "COBRA". This characteristics enables to easily separate positions
by their radius. (2) A positron which emit on perpendicular to the direction of solenoid axis is
rapidly swept out. With constant B-field, such a positron hits chambers many times, causing
pile-up.
Due to the advantage of (1), positrons whose energies are much lower than signal energy
can be isolated, by putting detectors in region of larger radius.

Figure 2.16: Magnetic field by COBRA magnet(a) The case of the uniform magnetic field. Positron of θ ∼ 90◦ turns many times before leaving drift
chamber (left). The radius of the trajectory depends on the θ angle (right).

(b) The case of the gradient magnetic field. The number of turns is suppressed (left). Radius is
independent of the emission angle (right).

Figure 2.17: Comparison of uniform and gradient field.

33

Chapter 2. MEG experiment setup
2.4.1.2

DesignThe COBRA magnet is needed to have low mass structure for gamma ray to minimize theinteraction of the γ-ray before reacting the gamma detector which is located outside of the
COBRA. The requirement was achieved by thin superconducting (NbTi/Cu) coil with highstrength aluminum stabilizer. The superconducting coil is cooled with two GM refrigerators.
The thickness of the magnet (including all support structure) is 3.83 g/cm2 (∼ 0.2X0 ). The
concept of the gradient field is realized by the array of 7 solenoids which have common axis andhave three different coil diameters (700, 810, 920 mm in inner diameters, Fig. 2.18(a)).
Two compensation magnets are installed in the COBRA. They are ring-shaped normal
conducting magnets in common axis with COBRA. The purpose of the compensation magnets
is to reduce the stray magnetic field at the PMTs in the xenon detector down to < 5 × 10−3 T.
The arrangement of magnet is seen in Fig. 2.18(b).
Compensation coil

Central coil
Gradient coil
Inner end coil
Outer end coil

GM Refrigerator
1m(a) Cross-sectional image of the COBRA magnet(b) Assembled COBRA magnet

Figure 2.18: COBRA magnet

2.4.1.3

Magnetic field

The magnetic field of COBRA is measured with a specially developed field measuring machinewith 3-axis Hall probes, scanning the range of |z| < 110 cm, 0 < r < 29 cm and 0◦ < φ < 360◦ .
The probes are orthogonal to each other to individually measure Bz , Br and Bφ . Because thestrength of the field along z axis is much larger than the other (Bφ = 0 in ideal case), Bz
contaminate the measurement of Br and Bφ if the probe is misaligned. In order to reduce
uncertainty, we use magnetic field based on measured Bz and measurement on reference planez = z0 [66]. z0 is considered to be the center in magnetic field where the measured Br is
minimized. Br and Bφ are calculated from following formulas,
Z z∂ Bz (z0, r, φ) 0
Br (z, r, φ) = Br (z0, r, φ) +
dz ,
(2.9)
∂r
z0
Z
1 z ∂ Bz (z0, r, φ) 0
Bφ (z, r, φ) = Bφ (z0, r, φ) +dz .
(2.10)r z0∂φ
The formulas are derived from the Maxwell’s equations. The magnetic field map to be usedin the track reconstruction is obtained by interpolating the measuring points with B-spline
34

Chapter 2. MEG experiment setup
prescription [67]. Figure 2.16 shows the magnetic field inside of the COBRA magnet. The
magnetic field around the LXe detector is illustrated in Fig. 2.19. Thanks to the compensation
magnets, the strength of the field is suppressed to be ∼ 5 × 10−3 T.

6WUD\ILHOGPHDVXUHGKHUH

P7/;H GHWHFWRUP7
P7&RPSHQVDWLRQFRLOP7
7(QGFRLO*UDGLHQWFRLO&HQWUDOFRLO

7
7

Figure 2.19: Magnetic field around the LXe detector. PMTs of LXe detector are placed along
the trapezoidal line.

2.4.2

Drift chamber

Drift CHamber (DCH) is adopted for the positron tracker [68]. It detects the ionization charge
by the positron, then the positron trajectory is reconstructed, and finally the emission angle andthe vertex position are reconstructed. The DCH is assembled inside of the COBRA magnet. As
the momentum of positron is roughly separated by track radius, positron of near signal energy
can be selected by simple detector geometry. In other words, if the detector is installed at a large
radius r, positrons with lower momentum go away without hitting drift chamber.
In order to reduce multiple scattering and background γ-ray generation, an ultra low mass
drift chamber has been developed for the MEG experiment. The DCH consists of identical 16
modules arrayed radially in φ direction with an interval of 10.5◦ . The DCH modules coverazimuthal (φ) region from 191.25◦ to 348.75◦ and radial (r) region from 19.3 cm to 27.9 cm.
The assembled DCH is seen in Figure 2.20. The detail of the R&D of the drift chamber can befound in [69].
2.4.2.1

Drift chamber module

DCH module has a frame structure of a trapezoidal shape whose base lengths of 40 cm and104 cm, as illustrated in Fig. 2.21. The frame is made of carbon fiber reinforced plastic. The
structure is characterized by the open frame geometry which is designed to reduce material on
positron trajectories. In other words, a module doesn’t have rigid frame on longer base sidewhich is assembled in inner side.
35

Chapter 2. MEG experiment setup

Figure 2.20: Assembled drift chamber. The DCH modules are radially arranged at the bottom
half of the COBRA volume. A red elliptical object at the center is stopping target whose
dimension is 8 × 20 cm2 .

Anode and field wires are stretched parallel to z-axis, with a 9.0 mm anode-anode interval.
The length of the longest (inner most) wire is 82.8 cm, and the shortest is 37.6 cm. The
configuration in r − φ plane is shown in Fig. 2.22(a). One DCH module has two independent
layers sharing gas, the gap between layers is 3.0 mm. Each layer has 9 drift cells and r positionsof cells are shifted by half of the width of the cell in 2 layers. The staggered structure is designed
to remove left-right ambiguity.
Cathode consists of thin aluminum-deposited polyimide6 film of 12.5 µm thickness. The
distance between films is 7.0 mm, and thus the distance anode and cathode is 3.5 mm. The
cathode pattern is separated into 9 cells, and each cell is further separated into two, by zig-zag
shaped gap as seen in Fig. 2.22(b). This is called vernier pattern, it will be explained in Sec. 3.2.1.
The inner end of the chamber is covered with a hood film.
The chamber is filled with counting gas of 50%:50% mixture of He and C2 H6 . It is adopted
to reduce the multiple scattering and the energy loss of the positrons. Another advantage is fast
drift velocity, which is important for the operation in the high-rate environment. At the nominal
voltage (1800 V), the velocity is ∼ 4 cm/µs. The field map and electron drift is simulated using
GARFIELD program. Figure 2.23 shows the result of the simulation.
The pressure is carefully controlled, because only a slight change of the pressure causes
deformation of the thin cathode film and thus results in the disturbance of electric field. The
fluctuation of the pressure difference to outside of chamber (He volume inside of COBRA) is
suppressed to be less than 0.005 Pa.
The design information is summarized in the Table 2.3. The average amount of the material
per a module is 2.6 × 10−4 X0 , and total amount in a positron track is 2.0 × 10−3 X0 on average.

6 UPILEX®

36

Chapter 2. MEG experiment setup
5

4

2

6

.

6

0

6

.

1

5

5

0

0

1

.

1

1

2

0

2

.

0

4

(a)

(b)

(c)

Figure 2.21: Drawing of a drift chamber module. (a) anode and field wire (b) cathode foilʔϵ͘ϬƐĞŶƐĞǁŝƌĞĨŝĞůĚǁŝƌĞϰ͘ϱϯ͘Ϭ ϯ͘ϱ ϯ͘ϱƌƉŽƐŝƚƌŽŶ

(a) Intersectional view of DCH module (unit inmm). Thanks to the staggered structure, leftright ambiguity (in which side of the wire a
positron passed) can be solved.

(b) The vernier pattern on cathode film. This is
introduced to improve position resolution alongz-axis.

Figure 2.22: Features of DCH module design
2.4.2.2

Readout of drift chamber

One drift chamber module has 2 planes × 9 cells. Each cell consists of an anode wire andtwo cathode pads. The anode and cathodes are read out by pre-amplifier at the both end of themodule. The anode signal is coupled with condenser to cut HV. The pre-amplifier is designed
to meet DCH requirement, the gain is ∼ 50, and band width is 190 and 140 MHz for anodeand cathode respectively. The outputs of all channels are sent to DCH patch panel via coaxial
cables. At the patch panel, anode signal is split into two by a fraction of 1:9. The larger part is37

y Axis [cm]y Axis [cm]Chapter 2. MEG experiment setupxAxis [cm]x Axis [cm](a) Contour plot of electric potential.

(b) Isochron (green) and drift line (red).

Figure 2.23: Result of GARFIELD simulation
Table 2.3: Details of drift chamber design
Part
Sense wire
Field wire
Cathode
Gas
HV

Item
material
diametertensionmaterial
diametertensionfoil
pad
mixturepressure
anode
cathodeDescription
Ni Cr (80:20)
25 µm
50 gf
Be Cu (2:98)
50 µm
120 gf12.5 µm polyimide
250 nm aluminum deposition
He C2 H6 (50:50)∼ 1 atm+1800 V (nominal)
groundsent to Domino Ring Sampler (DRS, a kind of waveform digitizer) and the smaller is used forthe trigger.

2.4.3

Timing counter

Timing counter (TIC) [70] [71] is placed at the both end side of the spectrometer to measure
the timing of the positron (Fig. 2.1 and 2.24(a)). It also has a role to generate the trigger
information for the positron. The TIC is composed of two independent detectors; however, zcounter (Sec. 2.4.3) was not used.

38

Chapter 2. MEG experiment setup
φ counter One is called φ-counter (TICP). One TICP is an array of 15 plastic scintillator barsof 4.0 × 4.0 × 79.6 cm3 . We adopted BC404 scintillator, for the fast rise time constant and large
light yield. The bars are set with the interval of 10.5◦ along φ-axis (the same pitch of the DCH
modules), they lie at r > 32 cm and from 29 cm to 109 cm in z-axis. The bars are read out by
PMT (Hamamatsu R5294) at the both ends. The PMT has a fine-mesh dynode structure andattached to bar with slanted angle (Fig. 2.24(b)), in order to reduce the effect of the magnetic
field. The TIC is covered with plastic bag (made of 0.5 mm thick EVAL) in order for PMT toprevent from being exposed to helium gas. The volume inside of the bag is continuously flushedwith nitrogen gas.
z counter The other part is z-counter (TICZ), which is an array of 128 arch-shaped scintillation
fibers. It is designed to detect z position of positron. The fiber material is 6 × 6 mm2 SAINTGOBAIN BCF-20. The fibers are separated at the center, and each side is read out by Hamamatsu
S8664 avalanche photo diodes (APD).
ƌŽƐƐͲ^ĞĐƚŝŽŶĂůǀŝĞǁϭϬ͘ϱ䜪WDdĂĐƚŝǀĞ
ĚŝĂŵĞƚĞƌ͗ϯϵŵŵƉŽƐŝƚƌŽŶ

WDdŽƵƚĞƌ
ĚŝĂŵĞƚĞƌ͗ϱϮŵŵ>ŽŶŐŝƚƵĚŝŶĂůǀŝĞǁ(a) The assembled TIC module ofone side.

ͮǌͮ ϭϬϵ ĐŵϮϵ Đŵ Ϭ͘ϳϱd͕ϭϬ䜪ϭ͘Ϭϱd͕ϯϬ䜪(b) The schematic image of the TICP counter.

Figure 2.24: MEG Timing counter

readout The signal from PMT is first sent to passive splitter and split into two in a ratio of
80%:20%. The larger part is then sent to Double Threshold Discriminator (DTD). DTD has two
thresholds one for trigger and the other is veto for small signal. The output of DTD is digital
NIM level signal, and is recorded with DRS. The smaller fraction is sent to an active splitterand then sent to the trigger and the DRS. The scheme is adopted for minimizing the time-walkeffect. The method to reconstruct hit timing is described in Sec. 3.3.

2.5

Electronics

The MEG experiment adopts MIDAS system [72] which was developed in PSI and TRIUMF
for general data acquisition and slow control framework. It gives a front-end readout in many
39

Chapter 2. MEG experiment setup
platforms such as CAMAC, VME, etc. The users can control start/stop DAQ and access slow
control via dedicated HTTP server.

2.5.1

DAQ scheme

A schematic image of MEG DAQ is shown in Fig. 2.25. The signals from all (except APD of
TICZ) detectors are recorded with waveform digitizer "DRS" (details in Sec. 2.5.2.1), and thesignal waveforms are sent to trigger system in parallel. In order to split the signals into two,
active splitters with high-bandwidth amplifier are used. These electronics are all implemented
on VME boards. For each triggered event, the digitized signal is processed by online computers.
Then, waveforms are recorded with MIDAS support data format (".mid") and are compressed.
The data size of raw data is 2.4 MB/event in typical runs, and compressed to be 0.9 MB/event
using bzip2 algorithm. The data can be monitored in display simultaneously. The data quality
can be checked after offline data processing. The result of the offline process is output in ".root"
format.

yĞŶŽŶĞƚĞĐƚŽƌ

ĐƚŝǀĞ
^ƉůŝƚƚĞƌ

dƌŝŐŐĞƌ

ŝŶŶĞƌWDdŽƚŚĞƌWDddŝŵŝŶŐŽƵŶƚĞƌ
d/WWDdd/WƌŝĨƚŚĂŵďĞƌ

ƐƉůŝƚƚĞƌ

d

ϴϬй
ϮϬй

ĨƌŽŶƚͲĞŶĚďŽĂƌĚĚŝŐŝƚĂůŽƵƚĂŶĂůŽŐŽƵƚƐƉůŝƚƚĞƌ
ƉƌĞĂŵƉ

ĂŶŽĚĞǁŝƌĞ

ƐƵŵ

Z^

ϭϬй
ϵϬй

ĐĂƚŚŽĚĞƉĂĚ

'KĞƚĞĐƚŽƌ

ĚŝƐĐƌŝŵ
ŝŶĂƚŽƌ

ƐƉůŝƚƚĞƌ

ĐĞŶƚĞƌWDd

ϱϬй
ϱϬй

ŽƵƚĞƌWDd

ϱϬй
ϱϬй

ƐƵŵ

Figure 2.25: Schematic diagram of signal from detectors.

40

Chapter 2. MEG experiment setup
Layer 1
Type1 boards
LXe inner
216 PMTs

Layer 2
Type2 boards

Layer 3
Type2 board

14
boards
2 boards

LXe lateral
630 PMTs 4 in 1

Timing counter
60 PMTs640 APDs 8 in 1
Drift chamber
32 groups

Auxiliary devices
16 channels

12boards
1 board

1 board9
boards
1 board2
boards1
board

Figure 2.26: Schematic diagram of trigger structure

2.5.2

Trigger

The trigger system [73] is based on flash analog to digital converters (FADC)7 for 10-bit, 100
MHz waveform sampling, and field programmable gate array (FPGA)8 for data processing.
There are two types of trigger board: (1) Type1 board, which is implemented on 6U VME board
with 16 input channels, (2) type2 board on 9U VME board, which integrates information fromtype1 boards.
The trigger system has three layers as shown in Fig. 2.26. The first layer is composed of
type1 boards. This layer receives the waveform from each sensor. The second layer combines
the outputs of the first layer for each sub-system. The third layer is composed of one type2
board, and makes final decision of the trigger.
The γ-ray and positron are reconstructed [74], independently of the data taken with DRS.
The energy is estimated by summing up the photons from all PMTs in LXe detector. The timing
is calculated from the sampled waveform. The position (angle) of γ-ray is given as the positionof the inner PMT which detected the largest number of photons. The positron reconstruction isdone for first-hit TIC bar. The timing is calculated from the sampled waveform with two PMTs
in the bar. The position in z direction is reconstructed from the ratio of the light yield of PMTs
in both ends.
The MEG trigger is determined according to (1) energy of γ-ray (2) timing between γ-ray andpositron, and (3) direction matching of γ-ray and positron. Not only the trigger for µ+ → e+ γ,
there are several kinds of triggers for calibration. The trigger types are listed in Table 2.4.
A pre-scaling factor is a factor to adjust the number of the taken data. For the trigger with a
7 Analog Devices, AD9218
8 Xilinx Virtex-IIpro XC2VP20

41

Chapter 2. MEG experiment setup
Table 2.4: List of trigger types, pre-scaling factor (Presc.) and conditions
Id
0
1
2
3
4
5
6
7
8
9
10
12
14
15
16
18
22
31

name
Presc.
MEG
1
MEG lowQ
200
MEG Wide Angle
550
MEG Wide Time250
RMD Narrow Time
1100
RMD Wide Time
Pi0
Pi0 w/o PrSh
BGO
LXe HighQ
20000
LXe LowQ
Alpha
22000
LED
6
Neutron Ni
Michel
1.5 × 107
DC TrackTC
1 × 107
Pedestal
20000

Condition(QLXe High) ∧ (∆TNarrow) ∧ (DMNarrow)(QLXe Low) ∧ (∆TNarrow) ∧ (DMNarrow)(QLXe Low) ∧ (∆TNarrow) ∧ (DMWide)(QLXe Low) ∧ (∆TWide) ∧ (DMNarrow)(QLXe Low) ∧ (∆TNarrow)(QLXe Low) ∧ (∆TWide)(QLXe High) ∧ preshower counter coincidence(QLXe High) ∧ BGO detector coincidence
BGO detector alone(QLXe High)(QLXe Low)
(QLXe Alpha) ∧ A/Qratio
LED pulser
Neutron generator
DCH ∧ TIC
DCH alone
TIC alone
Random trigger

pre-scaling factor of n, the data is taken once in every n time trigger requests.
2.5.2.1

Waveform digitizer

In the MEG experiment, all waveforms from the detectors are recorded in order to enable analysis
such as removing pile-up etc, which cannot be done with conventional DAQ with ADC/TDC.
Domino Ring Sampler (DRS) [75] is originally developed at PSI, and adopted for the MEG
waveform digitizer. The DRS is based on switched capacitor arrays (1024 cells) with a highspeed and a high accuracy. Figure 2.27(a) shows the schematic diagram of the DRS sampling.
The sampling speed of DRS is adjustable from 0.7 to 6 GSPS9. An actual sampling speed is 1.4
GSPS except DCH waveform (0.7 GSPS). DRS version 2 was used for all detectors at the firstrun of MEG in year 2007. All of them were replaced with DRS version 4 by the run in 2009.
One DRS chip can read 4 channels plus a synchronizing clock signal at the same time. FourDRS chips are mounted on a "mezzanine" board and the mezzanine is mounted on a VME
board. (16 channels per module, see Fig. 2.27(b)). All of the DRS boards are in operation with asynchronization signal, in order to adjust timing among the boards. 19.44 MHz common clock
signal from low-jitter clock generator is transferred to each mezzanine board.

2.5.3

Online computers

The MEG online computer consists of 9 front-end computers ("megon01"-"megon09") and 1
backend computer ("megon00"). The trigger (DAQ) boards are mounted in 4 (5) VME crates,and each crate is connected with one front-end computer with optical fibers. The nine online
9 giga samples per second

42Chapter 2. MEG experiment setup/ŶǀĞƌƚĞƌ͞ŽŵŝŶŽ͟ƌŝŶŐĐŚĂŝŶ

h
ƐƉĞĞĚ

/EϬ
KhdϬ
/Eϭ
Khdϭ

ϯϯD,

^ŚŝĨƚZĞŐŝƐƚĞƌ

(b) DRS mezzanine board. 4 square shaped
chips on left side are DRS4 chips.

(a) A simplified diagram of DRS.

Figure 2.27: Domino Ring Sampler
computers and the backend computer are connected via a Gigabit Ethernet switch. On the
back-end computer, a process to associate data from each frontend is running, and the processeddata is written in online storage in the computer, then the data is transferred to offline cluster(named "lcmeg").

2.5.4

Slow control

The slow control manages the control and monitoring of the experimental apparatus, such astemperature, pressure and etc., as their change is slow (> ms) comparing with the signal (∼ ns).
We adopt a system called Midas Slow Control Bus (MSCB) which is a part of the MIDAS. The
feature of the MSCB is the ability to handle via Ethernet. In order to connect the end-devices(sensor, voltage source, etc.) to the Ethernet, a device developed at PSI: "SCS" is commonly
utilized in the MEG experiment. In an SCS module, daughter cards can be mounted, and thecards work as ADC and etc.
ƚƌŝŐŐĞƌĐƌĂƚĞƐ;ϰͿ

Z^ĐƌĂƚĞƐ;ϱͿƐůŽǁĐŽŶƚƌŽů

dZ'ϭ dZ'Ϯ dZ'ϯ dZ'ϵ Z^ϰ Z^ϱ Z^ϲ Z^ϳ Z^ϴ

ŶŽĚĞ
ŶŽĚĞ

ŵĞŐŽŶ ŵĞŐŽŶ ŵĞŐŽŶ ŵĞŐŽŶ ŵĞŐŽŶ ŵĞŐŽŶ ŵĞŐŽŶ ŵĞŐŽŶ ŵĞŐŽŶ
Ϭϭ
ϬϮ
Ϭϯ
Ϭϵ
Ϭϰ
Ϭϱ
Ϭϲ
Ϭϳ
Ϭϴ

ƚŚĞƌŶĞƚ
^ǁŝƚĐŚ
ůĐŵĞŐ͙ƚŚĞƌŶĞƚ
^ǁŝƚĐŚ

ŵĞŐŽŶϬϬ

Figure 2.28: Schematic diagram of online computers

43

͙

^^

Chapter 2. MEG experiment setup

44Chapter 3
Event reconstruction
In this chapter, the way to reconstruct event is discussed. A simplified diagram of the data flow
is summarized in Fig. 3.1.

>yĞĚĞƚĞĐƚŽƌ

ƌŝĨƚĐŚĂŵďĞƌ
ŚŝƚƌĞĐŽŶƐƚƌƵĐƚ

WDdĐĂůŝď͘

dŝŵŝŶŐĐŽƵŶƚĞƌ
ĂŶĂůŽŐ
ƐŝŐŶĂů

E/DƐŝŐŶĂů

ĐůƵƐƚĞƌŝŶŐ
ɶƉŽƐŝƚŝŽŶ

ŚŝƚƌĞĐŽŶƐƚƌƵĐƚ

ƚƌĂĐŬĨŝŶĚŝŶŐ
ƚƌĂĐŬƌĞĐŽŶƐƚƌƵĐƚ

ɶĞŶĞƌŐǇ

ŚŝƚĐůƵƐƚĞƌŝŶŐ
,ͬd/ŵĂƚĐŚŝŶŐ

ɶƚŝŵŝŶŐ

ƌĞůĂƚŝǀĞ
ĂŶŐůĞƌĞůĂƚŝǀĞ
ƚŝŵŝŶŐ

Figure 3.1: Flowchart of the MEG event reconstruction

3.1

γ reconstruction

Reconstruction of the γ-ray is done from information of 846 PMTs in the liquid xenon detector.
First, hits are defined for each PMT, and then the γ-ray observables are reconstructed with theprocessed PMT hits.

3.1.1

Waveform analysis for each PMT

The waveform is integrated to obtain charge (Q) and thus the number of photo-electrons. Before
the integration, the waveform is processed with software filtering. A high-pass filter basedon moving-average method is adopted, since we found low frequency (∼ 1MHz) noise. The
45

Chapter 3. Event reconstruction
filtering is written as,M

y[i] = x[i] −1 X
x[i − M + j],
M j=1

(3.1)

Amplitude (mV)

Amplitude (mV)where x[i] and y[i] is original and filtered waveform, M is a number of averaged bins: 125. It
corresponds to a cut frequency of 11 MHz. The integration width is 67 ns. Figure 3.2 shows
raw and filtered waveform.
0
-5
20%

-10
-15
-20

10

67 ns

0
-10

-25
-20

-30
-35

-30

-40
-600

-500

-400

-300

-600

Time (nsec)(a) Raw waveform. The horizontal line
shows the threshold for timing reconstruction.

-500

-400

-300

Time (nsec)(b) Waveform after high-pass filtering.
The charge is obtained by integration of
the waveform.

Figure 3.2: Typical waveform of PMT
Sometimes the PMT waveform exceeds the dynamic range of the digitizer. If the photon
interacts within 1 cm from a PMT (This happens in 15% of all the triggered event.), mostly theclosest PMT saturates like Fig. 3.3. In the saturated cases, the charge integration is done withanother method: Time-over-Threshold (ToT). The ToT is defined as the duration time that thepulse is higher than a threshold (150 mV). The charge is calculated with a conversion function
from the ToT.
The number of photo-electron (Nphe ) and the number of photon (Npho ) are calculated fromthe charge for each PMT as formula Eq. (3.2) and (3.3). Gi and QEi are the gain and quantum
efficiency of i-th PMT respectively. The quantum efficiency used in this paper includes thecollection efficiency of photo-electron to dynodes unless otherwise remarked. The methods toobtain these values are discussed in Sec. 4.1.
Nphei = Qi /(e × Gi )Nphoi = Nphei /QEi

(3.2)
(3.3)

The timing is calculated with the technique of constant fraction: The time walk due to thedifference of absolute pulse size can be suppressed by this technique. In order not to lose thetiming information, non-filtered waveform is used for timing reconstruction. The time when
the waveform cross the line of 20% of height is defined as the timing of a PMT (t hit,i ). Here,"height" is not a direct height but estimation from the charge.
46

Chapter 3. Event reconstruction

Figure 3.3: Saturated waveform of PMT

3.1.2

γ position reconstruction

The position of the γ-ray conversion is computed from the photon distribution measured by 216
PMTs on the inner face. The first estimation of position is a weighted mean of the amplitudes,
on PMTs around the PMT of the maximum signal. Then, a fitting is performed to minimize thefunction χ2position which is defined as Eq. (3.4). The function is based on an assumption that the
scintillation photons are isotropically emitted from one point.
PMT
X!
Nphoi − c × Ωi (u, v, w) 2
σi (Nphoi )iqσi (Nphoi ) = σ(Nphei /QEi ) = Nphoi /QEi
χ2position (u, v, w) =

(3.4)
(3.5)

In the Eq. (3.5), error of the QE estimation is ignored for simplicity. Ωi (u, v, w) is the solid
angle of PMT active area seen from the point (u, v, w). The PMTs used for the fitting is within
3.5 times of PMT interval from maximum Npho PMT (about 45 PMTs). If w (depth from innerface) is fitted less than 12 cm, the second fit is performed with a reduced number of PMTs whose
2D (u, v) distance from fitted peak is less than 2 times of PMT interval (about 15 PMTs).
The fitted u and w include biases, because the electro-magnetic shower by γ-ray has a finite
size, and the shower spreads larger in the direction of momentum of gamma ray. It results |u|and w fitted larger than the first conversion point. The bias is corrected by a correction function
made from Monte Carlo simulation. The reason of the bias is the slant incident angle of γ-ray.
That is why v is not biased because γ-ray is always perpendicular to the inner face in x − y plane.

3.1.3

γ timing reconstruction

The time of gamma-ray conversion in liquid xenon (t LXe ) is calculated from the estimated hit
time by each PMT (t hit ).
t hit = t PMT − t delay − t offset,(3.6)
where t PMT is timing for each PMT calculated in Sec. 3.1.1. The second term is the timefrom the photon emission to the detection. The flight time of the photon is calculated with theposition of γ-ray conversion and effective speed of light in LXe (≈ 8 cm/ns), which is measured
in the calibration using two γ-rays in π 0 → γγ (Sec. 4.1.2.3). The shadowing effect of thecylindrical chamber shape, reflection and scattering effect and the time walk effect of PMT are
also considered in second term. The third term is constant for each readout channel due tohardware effects such as the cable length.
47

Chapter 3. Event reconstruction
The combined timing of γ-ray is calculated by the fitting, such that t LXe minimizes thefunction χ2time as defined in Eq. (3.7).
χ2time =

PMT
X
i

!
(t hit,i − t LXe ) 2
σt,i (Nphei )(3.7)

The sum is done over PMTs which detect > 50 photo-electrons, typically about 150 PMTs are
involved and typical number of used photo-electrons is ∼ 70000 in a signal event. σt,i , the time
resolutionof PMT, is a function of the number of photo-electron (approximately proportional top
1/ Nphe ). The fitting is iterated, rejecting PMTs which contribute to largely increase the χ2time
value. Those PMTs are affected by the γ-ray pile-up.

3.1.4

γ energy reconstruction

The γ-ray energy is reconstructed based on an assumption that the total number of the scintillation
photon is proportional to the γ-ray energy, since the γ-ray deposits its all energy in the liquid
xenon volume.
The γ-ray energy is determined by integrating the summed waveform with 67 ns window.
The summed waveform is made by superposing filtered waveforms from all PMT with the weightof Fi where the timing is shifted considering the time of flight of the scintillation photon. The
variable defined as Eq. (3.8) is calculated from the result of the PMT calibration, position andtiming reconstruction.
Fi =Ai · Wi (r γ )· Ω(r γ ) · U (r γ ) · H (t) · S,
eGi (t)·QEi (t)(3.8)

where Ai is a factor to correct for the position-dependent PMT coverage, Wi (r γ ) is a factor to
optimize energy resolution. It depends on the reconstructed position and is common for each
6 faces of the detector. The value is determined from the π 0 calibration. Ω(r γ ) shows a solidangle correction, which is a correction by the solid angle of PMT sensitive region seen from theconversion point, because when γ-ray conversion happens at very close point to the inner PMT,
the scintillation photon collection largely depends on the relative location of conversion point
and PMT array. This correction is applied for events of w < 3 cm. U (r γ ) is a correction by
non-uniformity factor in order to correct remaining position dependence. It will be explainedin Sec. 4.1. H (t) represents the time-dependent transition of light yield. Finally the factor isconverted to the absolute energy scale with the factor S that is determined from 55 MeV γ-ray
in a π 0 calibration.

3.1.5

Pile-up identification

More than one gamma ray hits xenon detector in 15% of the event at 3 × 107 µ/s beam rate.
In such an event, the γ-ray observables reconstruction can be failed due to the pile-up γ-ray.
There are two methods to identify pile-up, one by spacial distribution on the PMT outputs, andthe other utilizes the summed waveform [76]. The former method searches for peaks in innerand outer faces. If the second (the smaller) peak is found, the distribution is fitted except forthe pile-up region. Then the PMT output in pile-up region is replaced with the estimation fromfitting and calibration data. Finally the energy of main γ-ray is reconstructed. The later method48

Chapter 3. Event reconstruction

Amplitude

is based on the summed waveform which is made in Sec. 3.1.4, considering the reconstructed
position and timing and pile-up (if found in the former method). In case a pulse is found in
the sum waveform, and if the pulse is judged to be pile-up, the pulse is subtracted using atemplate waveform, and the energy is calculated again with the summed waveform. An exampleof unfolding of pulses is shown in Fig. 3.4.
10000

10000

(a)

0

0

-10000-10000-20000-20000-30000-30000-40000-40000(b)-50000-50000
-600

-550

-500
Time (nsec)

-600

-550

-500
Time (nsec)

Figure 3.4: (a) Black line shows the summed waveform after high-pass filtering; the fitted
waveform is also shown in red line (Two lines are almost overlapping). (b) Waveform after
pile-up unfolding is shown with black solid line. The start time of integration is changed fromgreen dashed line to solid line.

3.1.6

Cosmic ray rejection

Figure 3.5: The cut criteria are shown with blue lines in (charge ratio)-w plane. The green dotsshow signal by Monte Carlo. The black dots are the events collected in the dedicated CR runs.
The cosmic ray (CR) is a source of the background. The cosmic ray is efficiently rejectedusing topological cuts. The cosmic ray events are characterized by the position in the detector,
because most of the cosmic rays enter LXe volume from the outer side of the detector. We
49

Chapter 3. Event reconstruction
defined CR cut focusing on two parameters: the charge ratio collected by inner and outer PMT,
and reconstructed depth w. The cosmic ray rejection is demonstrated in Fig. 3.5. The cut criteria
are selected to optimise rejection power keeping signal efficiency in 99%. The removable CR
event is 56% of all CR, and combined signal efficiency of pile-up identification in Sec. 3.1.5 andCR rejections is 97%.

3.2

Positron track

The charge induced by positron is detected with the anode wires and the cathode pads in thedrift chamber. The positron momentum, the position at the target and the emission angle arereconstructed from those hits. The information about the trajectory by DCH and the reconstructed
hit position at TIC are sent to the DCH/TIC matching reconstruction described in Sec. 3.3.2.

3.2.1

Hit reconstruction

3.2.1.1

Waveform analysis

We record six waveforms per single drift cell, two sides of an anode wire and two sides of twoseries of cathode pads as shown in Fig. 3.6. In order to suppress known noise components, afiltering based on FFT1 is applied on the raw waveform [77]. The pulse larger than threshold(5 mV) from the baseline is considered as a hit. The threshold is set to be 3 times larger thanthe baseline noise σB . The charge of the hit is obtained by an charge integration from −24ns to
56ns around the peak excepting region where waveform exceeds −2σB .
3.2.1.2

Hit position

The rough position on z axis is given by the ratio ( a ) of the charge on two sides of the anode.
QU − QD
QU + QD
!
L Z
z=
+
· a
2 ρ

a =

(3.9)
(3.10)

where L is the length of the anode wire, Z is the input impedance and ρ is the resistivity of
the anode wire. The estimation will be improved by the vernier method. As explained inSec. 2.4.2.1, the cathode foil is divided into two series by zig-zag pattern, and the fraction of
detected charges on the cathode depends on the z position. The charge-fractions of two channels( 1 and  2 ) makes pattern as Fig. 3.7. The final z estimator with the vernier information isdefined as,
α

z=l·
+i ,
(3.11)
2π
where l is the period of the pattern (5 cm), α = tan−1 ( 2 / 1 ) is the azimuthal angle and i showsin which period the hit is belonging (count from DS side). There was a mistake in treatmentof the case with faulty pad readout, previously. Therefore, all data are processed again withcorrected algorithm.
1 Fast Fourier Transform

50

Amplitude [mV]

Amplitude [mV]

Chapter 3. Event reconstruction

200
150
100
50

80
70
60
50
40
30
20
10
0

0

-10
-500

0

Time [ns]Amplitude [mV]

Amplitude [mV]

-1000

25
20
15
10
5

-1000

-500

-1000

-500

-1000

-500

0

Time [ns]

70
60
50
40
30
20
10

0

0
-5

-10
-500

0

Time [ns]Amplitude [mV]

Amplitude [mV]

-1000

100
80
60
40

0

Time [ns]

20
15
10
5

20

0

0

-5
-10

-20
-1000

-500

0

Time [ns]0Time [ns]Figure 3.6: Example waveform of DCH. Top low from anode wire, and central and bottom lowsfrom cathode pads. Recognized hit timing is shown in red vertical line [77].
The drift distance, which gives the detailed information of the positron position in a drift
cell, is calculated from the time of the detected pulse and the estimated time of the track where
the information of the timing counter is also considered. Since the drift time from the initial
ionization to the detection by wire depends on the strength of the magnetic field and the incident
angle, the drift distance is calculated with a function which is generated from a simulation using
GARFIELD. The drift time is shown in a function of the incident angle and distance in Fig. 3.8.

3.2.2

Clustering and track finding

The hits in one DCH module are combined into a cluster, to remove many accidental hits which
are not related to the real positron track. If hits in a chamber lie in near cells and z position thehits are associated to one hit cluster, especially hits in the neighbouring period in the vernier
pattern are taken into account for the case of misreconstruction to the next period.
The next step is to find the seed of the positron track. Starting from the largest r cluster,neighboring clusters are connected to make a candidate of the positron track. In searching forclusters on the trajectory, an adiabatic invariant pT2 /Bz is used (pT is the positron transverse
momentum), because the axial component of magnetic field slowly varies The left/right ambiguity can be solved during track seed finding in most of cases. Then, the track seed (connectedclusters) is fitted by circle in the x − y plane. With the more precise x, y hit position by fitting,51

Chapter 3. Event reconstruction(a) The circle pattern, a turn correspondone period of the pattern.

(b) α angle vs  a . vernier gives better z resolution. A
period is the length of pattern, 5 cm.

drift time (µ s)Figure 3.7: z hit reconstruction by vernier pattern.

0.18+60 deg

B=1.1T

0.16+30 deg

0.14
0 deg

0.12
-30 deg

0.1
0.08-60 deg

0.06
0.04
0.02
0
-0.5 -0.4 -0.3 -0.2 -0.1

0

0.1

0.2

0.3

0.4

0.5

drift distance (cm)Figure 3.8: Drift time simulation with GARFIELD. The result with B = 1.1 T is shown as afunction of the distance and angle.
the track timing can be estimated by using track time-distance dependence in Fig. 3.8, a solution
for left/right ambiguity is also improved.

3.2.3

Track fitting

We adopted the technique of Kalman filter [78] [79] for the track reconstruction. The Kalmanfilter is an algorithm to estimate the status from the given information of state which is discretein time, and it has wide application in technological and engineering field. Since it can handle
the existence of an unexpected disturbance, and can include it as the error of the estimation,
the method of Kalman filter is suitable for tracking of positron that is affected by multiple
52

Chapter 3. Event reconstruction
scatterings. The GEANE software [80] is also used.
The state vector of the positron is successively estimated from hit to hit. Finally the track is
propagated to the muon stopping target to retain the initial state vector of the positron on target.
The hits used in the track fit are updated by the fitting result in the track reconstruction: hits notincluded in the candidate are added if appropriate and hits are removed if they are inconsistent.
The positron track fitting method was revised in our previous physics analysis. Details of
the revised method can be found in [81] and [77].

3.2.4

Per-event error

The method of Kalman algorithm enables us to calculate the error propagation in the trackfitting. It also provides information of the error matrix which includes the correlation between
variables. Since the calculation is done event-by-event, it is called "per-error". It will be used
to compose event-by-event PDF in the physics analysis.
The errors of following variables are represented with the per-error of Eq. (3.12),• Ee : initial energy of positron,• φe : φ emission angle on target,• θ e : θ emission angle on target,• ye : y position on target plane,• ze : z position on target plane,
σ 0 = (σ0Ee, σ0φe, σθ0 e, σ0ye, σ0ze )(3.12)

where σ0 is per-error, and σ0x represents the uncertainty of the parameter "x".

3.2.5

Missing turn recovery

Since the MEG drift chamber covers only bottom-half region in φ, a positron trajectory is
separated when the positron turns more than one time. The separated turns are connected toeach other in the normal case of the track fitting algorithm. If the connection fails, there isfear about reconstructing those tracks to be different positrons. It is dangerous especially when
the first turn is missed, because the decay vertex is reconstructed at a wrong position, and then
the timing is also wrongly reconstructed. In the current analysis, an algorithm to identify andrecover the missing turn is newly implemented.
The algorithm works as follows. For all found tracks, hits are searched for in the expectedz range and modules. When potential missing turn hits are found, the vertex state vector
is propagated toward each potential hit, and the hit is discarded if the position is far frompropagation. If the remaining number of the hits is more than threshold, the track fit algorithm
as in Sec. 3.2.3 is applied for the track candidate. The track fitting is further propagated tothe stopping target, and if the crossing point is found in the target, the recovered vertex andmomentum of the positron is calculated. In Fig. 3.9, a recovered missing track is illustrated.
profit of missing turn recovery The improvement in overall positron detection efficiency by
the missing turn recovery is defined as, the ratio of total number of the recovered Michel positron
to the total number of reconstructed Michel positrons. The improvement in the efficiency is
53

Chapter 3. Event reconstruction
Run 51847, Event 1325

Run 51847, Event 1325

X [cm]

Y [cm]

5
0
-5

30
20
10

-10
0
-15
-10

-20

-20

-25
-30
-30

-20

-10

0

10

20

-30
-40

30

-30

-20

-10

0

10

20

X [cm]

30

40
Z [cm](a)(b)

track reco. eff. improvement (%)

track reco. eff. improvement (%)

Figure 3.9: An example of the recovered missing first turn. Originally reconstructed track hits
are shown in magenta, the brown hits are identified to be a part of track. The original andrecovered vertex are shown with magenta and blue star.
7
6
5
4
3
2
1
0
50

51

52

53

54

35
30
25
20
15
10
5
0
70

55

Ee (MeV)

75

80

85

90

95 100 105 110
θe (deg)

Figure 3.10: Improvement in overall positron detection efficiency due to missing turn recovery,
as a function of Ee and θ e .
evaluated using data and shown in Fig. 3.10. The averaged improvement is ≈ 4%. The
improvement decreases as increasing the Ee , it is due to more efficient positron reconstruction athigh Ee . The efficiency improvement is maximal around θ e = 90◦ , because the positron whichemitted around the angle are likely to make multiple turns in the drift chamber.

3.3

Positron timing

The timing of the positron is measured by 15 × 2 TIC φ counters (Sec. 2.4.3). The timing
measured by TIC (t TIC ) is combined with the track information, then the timing of positronemission on target (t e ) will be obtained.

3.3.1

Timing calculation by TICPThe PMT signals are divided into two with a ratio of 8:2. The larger fraction is converted todigital pulse (NIM signal) by DTD and is recorded by DRS. The leading edge of the NIM pulse
54Chapter 3. Event reconstruction
is fitted with a template waveform to get the timing. The smaller fraction is directly used in
DRS and trigger. The time walk effect in the NIM pulse is corrected by using the direct DRS
waveform with a formula.
√(3.13)
w(x) = A + B x + C log(x),where x is the ratio of the DTD low level threshold to the pulse height. The parameters A, B
and C are determined for each PMT, by fitting a template waveform made from calibration data.
The optimal DTD threshold is determined to get the best timing resolution. Two PMTs (IN: neartarget side, OUT: far target side) read one scintillator bars, so the timing and z position can becalculated from the two timing,Lt IN + t OUT bIN + bOUT wIN + wOUT
−
−
− ,
2
2
2
2v
v
zTIC = {(t IN − t OUT ) − (bIN − bOUT ) − (wIN − wOUT )} ,2

t TIC =

(3.14)(3.15)

where L is the length of scintillator bar, v is the effective speed of light in the scintillator, andbIN,OUT are offsets peculiar to channel and wIN,OUT are time walks in Eq. (3.13). When there
are more than two bars hit by one positron, hits are combined to TIC cluster. The fastest hit
represents the cluster.

3.3.2

DCH-TIC interconnection

In order to get the time of the positron emission, the time-of-flight (t TOF ) is needed to beconsidered. We compute it from the length of track between the decay vertex and the hit point
at TIC. Due to the drift chamber support structure between the DCH sensitive region and TIC,
the positron can be scattered during flight. The effect of the scattering is evaluated by matchingquality of DCH and TIC. The fitted track from the drift chamber is propagated to the surface oftiming counter. The event is classified by the matching quality of estimation from track and TIC
hit.
• (MQ 0) The track is propagated to the hit bar, and ∆z < 12 cm.
• (MQ 1) The track is propagated to the extended region of the bar, and ∆z < 12 cm.
• (MQ 2) The track do not cross the extended region, but ∆r < 5 cm.
• Otherwise, matching is judged to be failed.
∆z is distance between zTIC and z of propagated point and ∆r is the distance in r coordinate
from the TIC surface to the closest point of track to TIC bar. Then, the Kalman filter algorithm
is applied to back-propagate to target, in order to get the best estimation of the emission timingof positron on target (t e ).

3.4

Combination of γ and positron

In this section, the variable of relative angle and timing between γ-ray and positron are defined.
The reconstructed position of γ-ray and positron vertex at the target are written as (r γ ) and (r e ),respectively. The normal vector of the γ-ray momentum (n γ ) and positron momentum on target(n γ ) are also used.
55

Chapter 3. Event reconstruction
The emission angle of γ-ray is defined as the vector from the reconstructed vertex to thereconstructed position of the γ-ray, because LXe detector cannot reconstruct the direction of
γ-ray.
rγ − re,(3.16)nγ =|r γ − r e |The relative angle of γ-ray and positron (Θeγ ) is given byΘeγ = cos−1 (n e · n γ ).

(3.17)The relative angle is separated to two directions, θ eγ and φeγ .
θ eγ = (π − θ e ) − θ γ
φeγ = (π + φe ) − φγ

(3.18)(3.19)The relative time of γ-ray and positron is given by the difference between the time of γ-ray
and positron. The timing of γ-ray is defined by the timing of γ-ray emission from the vertex.
The time is calculated by using time of flight of γ-ray from the target to where it is detected.
t eγ = t γ − t e = (t LXe − t tof ) − t e|r γ − r e |t tof =
c

3.5

(3.20)(3.21)

Reconstruction of AIF

Annihilation In Flight (AIF) of positron is one of the sources of γ-ray background in LXe
detector. The γ-ray background mainly consists of RMD and AIF, and in the signal energy
region the AIF is dominant. Figure 3.11 shows background spectrum where the horizontal
axis is shown in y = 2Eγ /m µ . If we can tag the γ-rays which come from AIF, the µ → eγ
search sensitivity can be improved by removing the tagged accidental background. The AIF
which occurred inside of the DCH can be tagged, because the positron leaves a track before theannihilation.
We newly developed a method to find AIF that happens in the drift chamber. The method
is done in two steps. The first step is to look for a positron track which disappears in the drift
chamber. It is called an AIF track. The second step is to compare the AIF track and the γ-ray
detected by the LXe detector.

3.5.1

Candidate finding

In order to find the AIF candidate track, we use the hit and cluster data independent of normal
positron reconstruction explained in Sec. 3.2.2. The method starts from connecting positronclusters. The series of the cluster is called AIF seed. The clusters which can be considered asa part of a track are added to the seed. Following criteria are required for the seed: (a) containno hit in the last plane of DCH and (b) the last hit must not be the inner most cell. Otherwise anormal track can be recognised as an AIF seed.
A circle fit is applied for all AIF seed. Along the fitted circle, the number of the empty DCH
plane is counted, and AIF candidate must have more than 2 empty planes after the last cluster.
The (x, y) position of the AIF is given by the intersection point of the fitted circle and the DCH
56

Photon Yield per Decay

Chapter 3. Event reconstruction
10-4
10-5
10-6
10-7
10-8
10-90.9

0.92

0.94

0.96

0.98
1
y Threshold

Figure 3.11: Integrated Eγ spectra of RMD (red) and AIF (green) by MC for the MEG detector,
γ-ray whose energy is more than y is integrated.
cathode plane, DCH support or COBRA wall which appears just after the last cluster. The z
coordinate is calculated by the extrapolation of xz-vector of last two clusters. The directionof AIF is also calculated from the tangent of the fit circle and the xz-vector. Time of AIF is
also reconstructed from the timing information of DCH hit. If the last cluster includes hit inplane-A (down-stream side), then the candidate is categorised into type-A, else the candidate iscategorised into type-B.
An example of the AIF candidate is shown in Fig. 3.12.
Run 51824, Event 806 (Eg = 52.7 MeV, Ee = 51.4 MeV,∆θ = 0.5 degs, ∆φ = 0.9 degs, ∆t = -0.9 ns)

X [cm]

Y [cm]Run 51824, Event 806 (Eg = 52.7 MeV, Ee = 51.4 MeV,∆θ = 0.5 degs, ∆φ = 0.9 degs, ∆t = -0.9 ns)

5
0
-5

30
20
10

-10
0
-15
-10

-20

-20

-25
-30
-30

-20

-10

0

10

20

30

-30
-40

-30

-20

-10

0

X [cm]

(a)

10

20

30

40
Z [cm](b)

Figure 3.12: An example of the AIF candidate in 2009 data. The AIF candidate is plotted inyellow circle, the result of circle fit is shown in green dashed line, the AIF position is blue starand the direction is drawn in green arrow. The vector to observed γ-ray is shown in dashedmagenta line.

3.5.2

Matching DCH and LXe

According to the AIF candidate information and the γ-ray, AIF observables are calculated.
57

Chapter 3. Event reconstruction

1800
2500
2500

1600
1400

2000

2000
1200
1500

1000

1500

800
1000

1000

600
400

500

500
200
0

−100

0

−50

0

50
100
∆θ AIF (deg)

−100

0

−50

0

50
100
∆φ AIF (deg)

−100

−50

0

50
100
∆t AIF (ns)Figure 3.13: AIF observables ∆θ AIF (left), ∆φAIF (center) and ∆t AIF (right) found in calibration
data, in year 2009.

∆θ AIF = θ AIF − θ γ−AIF,∆φAIF = φAIF − φγ−AIF,∆t AIF = t γ − t AIF,

(3.22)(3.23)(3.24)

where θ AIF and φAIF are θ and φ component of the AIF vector and t AIF is the reconstructedtiming of the AIF, and θ γ−AIF and φγ−AIF are θ and φ component of the vector from AIF point
to reconstructed point of γ-ray.
When there are multiple AIF candidates in an event, those candidates are selected byfollowing variable,
χ2AIF =

2
∆θ AIFwθ2

2(∆φAIF − φoffset ) 2 ∆t AIF
,
+
+
wφ2
wt2

(3.25)

where wθ = 4.5◦ (3.5◦ ), wφ = 10◦ (4.5◦ ), φoffset = −10◦ (0◦ ) and wt2 = 10 ns for type-A (B)candidate. The candidate of the least χ2AIF is selected, as it is most likely to be a true pair withobserved γ-ray.
Figure 3.13 shows the result of the AIF reconstruction in ∆θ AIF and ∆φAIF , the peak around
0 comes from events truly correlated in the track and γ-ray. The peak around −10◦ in ∆φAIF is
due to events where the positron annihilates at the first plane of the next module after leaving
the last hit in plane-A.

58

Chapter 4
Calibration
The calibration is an indispensable operation in physics experiments. The calibrations are
performed to measure the performance of the detector, to monitor the detector status or to check
our understanding about the detectors. In this chapter, the calibration methods will be describedfor each. The main calibration sources are summarized in Table 4.2.

4.1

LXe detector

4.1.1

PMT calibration

4.1.1.1

Gain calibration

The PMT gain calibration is mandatory in order to convert the charge into the number of photoelectron. For this calibration, blue-light LEDs are mounted on the up-stream and down-streamsides of the inside wall of the detector. The positions of the LEDs are shown in Fig. 4.1. The
data of all PMTs are taken with a trigger which is synchronized to a LED pulser.
gain calculation We calculate the gain under an assumption that the number of photo-electronsobserved with each PMT follows the Poisson distribution.
σ 2Nphe = µ Nphe + σ02(4.1)

σ Nphe and µ Nphe are the standard deviation and mean of the number of observed photo-electrons,
respectively, and σ0 is additional fluctuation such as noise from electronics. Using the PMT
gain G, we can transform Eq. (4.1) as follows,
σQ2 = G × µQ + Gσ02

(4.2)

where Q = G × Nphe is charge observed by the PMT, σQ and µQ are the standard deviation andmean of the charge, respectively.
In one set of gain calibration runs, the LEDs are driven with different 9 intensities. For eachintensity, σQ and µQ is calculated by fitting the Q distribution with a Gaussian function. The
gain is obtained from a linear fit on σQ2 − µQ plot. Figure 4.2 is an example of the result.
59

Chapter 4. Calibration(b) LED for the gain calibration. Three LEDs ofdifferent intensities are bundled.

(c) α-source rolled on a wire.

(a) Location of the calibration sources

Figure 4.1: Calibration sources inside of the LXe detector. (a) is view from outside of thedetector. A set of LEDs is shown with blue circle, and an 241 Am alpha source is shown with a
red rectangle.
gain shift by beam It is known that the PMT gain shifts by the light irradiation. It resultsin the dependence on the beam condition. When we take the calibration data, beam blocker isclosed, and it is opened before the physics data taking. The change of the gain is corrected by
the LED light events during the operation of the beam blocker. The gain shift is about 2-3% inaverage, but depends on individual PMT. Figure 4.3 shows gain shift of PMT which is the mostsensitive to the beam condition.
gain adjustment The gain is normally set to 1.8 × 106 for all the PMTs by adjusting HV tomatch the dynamic range of the electronics. The gain G is proportional to V nk , where V is
voltage bias, n is number of stages of the dynodes and k is a factor determined by the PMT
design. For LXe PMT, the gain voltage dependence is more complex due to Zener diodes toregulate voltage between the last dynodes, but is approximately proportional to V 10 around thenominal operation voltage.
The PMT gain tends to decrease during run, and the speed is individually different. So the
PMTs are needed to be adjusted periodically. We adjusted HV before the physics run in eachyear. Some PMTs need more frequent adjustment for the fast gain decrease. Averaged PMT
gain in year 2012 is shown as a function of date in Fig. 4.4. The leftmost marker shows the result
just after the gain adjustment. The gain decrease is an issue for the trigger, because the energy
60×10-3σ2Counts

Chapter 4. Calibration

4002

χ / ndf
51.59 / 46
Constant
165 ±3.3
Mean
0.452 ± 0.000
Sigma
0.01546 ± 0.00021

350
300

0.25
0.2

250

Gain = 1.55 x 106

0.15
200
150

χ2 / ndf

0.1

100

8.158 / 7

p0

2.108e-06 ± 8.819e-07

p1

0.0005179 ± 8.711e-06

0.05
50
0

0

0.2

0.4

0.6

0

0.8
1
-Charge (e+)

0

0.2

0.4

0.6

0.8

1
Q mean2 vs µ . The gain is calculated(b) 2D plot of σQ
Q
from fitted slope.

(a) Charge distributions with different LED intensities.

Figure 4.2: PMT gain calibration with LED.

Figure 4.3: PMT gain shift when the beam blocker is opened (top) and closed (bottom) [82].
threshold for the LXe detector in the trigger condition is changed if the PMT gain decreases. The
trigger parameter is adjusted by the PMT gain calibration, otherwise trigger efficiency would bedecreased.
4.1.1.2

QE calibration

The calibration of the quantum efficiency (QE) of a PMT is performed with α-sources which areattached on gold plated tungsten wires with 100 µm diameter [83]. Five sources are attached oneach of five wires, therefore 25 sources in total are mounted. The wires are stretched inside thexenon volume along z-axis. The locations of the α-sources are shown in Fig. 4.1. The nuclide of
the source is 241 Am. It emits α of 5.485 MeV (84.5%) and 5.443 MeV (13.0%), and its half-life
is 432.2 years. The strength of the source is ∼ 1 kBq each.
We calculate the PMT QE by comparing observation and MC simulation. The positionof the source, number of emitted photons, and photon propagation (scattering, absorption and61

Chapter 4. Calibration
2.2E+6
2.1E+6
2.0E+6
1.9E+6
1.8E+6
1.7E+6
1.6E+6
1.5E+6
1.4E+6
4/1

5/1

5/31

6/30

7/30

8/29

9/28

10/28

11/27

12/27

Figure 4.4: Average PMT gain obtained from LED calibration. An interval from August to
September is a period for π 0 calibration. A small gain recovery is seen after the interval whichis due to non operational period of the detector modification for the calibration.

(cm)

reflection) in the liquid xenon are simulated in the MC, under a constant known QE. The numberof photo-electrons in data and MC are compared for each α source. The QE of the PMT isdata /N MC . Figure 4.5 illustrates a result of QE calibration.
obtained by combining the ratio, Nphe
phe
0.22
100
0.2
50
0.18
0
0.16
−50

0.14

−100

0.12
−100

0

100

(cm)

200

Figure 4.5: QE of PMTs in LXe detector. The plot shows an averaged result of some calibration
runs.

4.1.2

Gamma calibration

4.1.2.1

CW accelerator calibration

We perform calibrations with Cockcroft-Walton (CW) proton accelerator1 to monitor the lightyield of the LXe, and the data is also used to estimate the position dependence of the γ-ray
response.
reaction A target made of lithium tetra-borate (Li2 B4 O7 ) is adopted in this calibration. This
allows us to utilize both Li and B reactions simultaneously. The nuclear reaction 73 Li(p, γ) 84 Be
1 High Voltage Engineering Europe

62Chapter 4. Calibration

Events / 700

12produces 14.8 MeV and 17.6 MeV γ-ray. The reaction 11
5 B(p, γ) 6 C produces some energies∗
of gamma, 4.4 MeV γ-ray from deexcitation of 12
6 C is used for calibration for the sharp peak.
Figure 4.6 is an observed spectrum with the Li reaction.

350
300
250
200
150
100
50
0

50

100

150

200
nsum2corr

×103

Figure 4.6: An example of the spectrum with 73 Li(p, γ)48 Be reaction. The right most peak is thepeak from 17.6 MeV γ-ray.

setup The CW is installed at the down-stream side of the MEG detectors as illustrated inFig. 4.7. Before the CW calibration, the normal target for muon is remotely removed by apneumatic drive system with compressed He gas, and a movable beam pipe is inserted to the
COBRA volume. The airtightness is kept by extendable bellows system with a stroke of ∼ 2 m.
It takes as short about 20 minutes to replace the targets.

Figure 4.7: Location of the CW accelerator in the experimental area. The accelerator and beam
pipe are settled at the opposite side of muon beam line.

63Chapter 4. Calibration
4.1.2.2

Neutron generator

59
γ-ray from the neutron capture reaction of nickel, 58
28 Ni(n, γ) 28 Ni is used for calibration. A
neutron generator2 and nickel plates are set as shown in Fig. 4.8, and the setup is put on the
opposite side of the LXe detector against the COBRA magnet. (γ-ray transits COBRA from theneutron generator to the LXe detector.) An advantage of this calibration is the availability inbeam time. By using a trigger which is synchronized with neutron generator, the data with theneutron generator can be taken even during the normal data taking with the beam. This enables
a direct comparison between beam on/off.

іƚŽ>yĞĚĞƚĞĐƚŽƌ

EŝƉůĂƚĞƐ

ƉŽůǇĞƚŚǇůĞŶĞ
ƐŚŝĞůĚ

ŶĞƵƚƌŽŶ
ŐĞŶĞƌĂƚŽƌ

Figure 4.8: Setup of the neutron generator. The generator and target are surrounded by polyethylene shield.

4.1.2.3

π 0 calibration

π 0 calibration is one of the most important calibrations of the LXe detector, because it provides
γ-ray near the signal energy. We determine the absolute scale, i.e. the factor to convert the
number of the detected photo-electrons to the energy of γ-ray according to this calibration. It
requires a special target and another γ-ray detector, so it was operated once or twice per year.
principle We use π − beam in this calibration, and the target is proton. The Charge EXchenge
reaction (CEX) occurs and then π 0 immediately decays to two γ-rays, namely
π − + p → π 0 + n → γ + γ + n.

(4.3)

The momentum of the π − beam is optimized to be 70.5 MeV/c . π 0 particle has a momentum∼ 28 MeV/c in the laboratory frame, and the γ-rays are emitted back-to-back in π 0 ’s rest frame.
In the laboratory frame, γ-rays are boosted by π 0 momentum.
Eγ =

mπ0
γ(1 ± β cos θ CM ),
2

(4.4)

where β is the velocity, γ is the Lorentz factor and θ CM is the angle between direction of π 0momentum and γ-ray in the rest frame.
2 ThermoFisher

64Chapter 4. Calibration
111111000000000000111111000000111111000000111111

He inletThreshold valve

He outlet
H2 inletFeed−back valve

He recovery

H2 bottle

H2 Buffer

Figure 4.9: Scheme to hold liquid hydrogen in LH2 target for π 0 calibration.
The energy spectrum of the γ-ray shows flat distribution between 54.9 and 82.9 MeV. Theenergies of two γ-rays have correlation with the opening angle between two directions of gamma.
If gammas with opening angle > 175◦ (> 170◦ ) are selected, their energies are sharply definedwith a width narrower than σ/Eγ < 0.2% (1.0%). Besides the CEX reaction, there are reactions
where the final particle is one γ-ray and neutron (radiative capture: Eq. (4.5)) and neutral pion
decay into γ-ray and electron-positron pair (Dalitz decay: Eq. (4.6)).
π− + p → γ + n(4.5)

π − + p → π 0 + n → γ + e+ + e− + n(4.6)

liquid hydrogen target In the π 0 calibration, the normal target is removed together with the
CW beam line. A liquid hydrogen target is installed instead. The target has a cylindrical shapeand the volume (where liquid hydrogen is liquefied) is ∼ 150 cm3 . It has a vacuum window(warm side) and LH2 window (cold side) as the beam entrance. Both windows are made of
135 µm thickness Mylar. The cooling is done by liquid helium from a Dewar tank. During theoperation, the temperature and pressure are controlled at 20 K and 0.12 MPa (Fig. 4.9).
tagging detector The LXe detector covers only ∼ 120◦ in φ axis, therefore another detector is
mandatory to detect γ-ray at 180◦ opposite side.
We use a smaller, but movable γ-ray detector and move it to scan the LXe detector. Fromyear 2008 to 2010, a detector of 3 × 3 arrayed NaI(Tl) crystals (62.5 × 62.5 × 305 mm3 ) read out
with APDs was used [84], and it was replaced with a one with 4 × 4 arrayed Bismuth Germanium
Oxide (BGO)3 crystals (46.0 × 46.0 × 200 mm3 ) read out with PMTs from year 2011 to 2013.
(See Fig. 4.10(a).) In order to avoid event where a large fraction of the shower escapes from thecrystals, the trigger is set to require a hit only at the central NaI crystal. It was widened to central
2 × 2 crystals of the BGO detector. The trigger efficiency is improved by this modification, andresulted in the more efficient calibration. The energy and position resolutions are also improved.
The detail about the BGO detector is described in Appendix. A.
The detector is mounted on a detector mover (Fig. 4.10(b)). It can be controlled remotely
without interrupting beam. The mover has motors to move the detector in φ (vertical), z
3 Bi4 Ge3 O12

65

Chapter 4. Calibration(a) Tagging detector with BGO crystal is installed in detector mover. A cover in front of
the crystals is not attached.

(b) Detector mover, NaI detector ismounted on it. The degree of freedom
is shown with arrows.

Figure 4.10: Apparatus for π 0 calibration(horizontal) direction, and to rotate detector in order to face the detector perpendicular to LH2target.
The energy reconstruction is done by summing light yield in each crystal, and γ-ray positionin NaI detector was reconstructed to the center of the detector, while position in BGO detector
was reconstructed by weighted mean of the light yield.
In addition to NaI (BGO), there is small counter to detect the timing of γ-ray. It consists of
two plastic scintillator plate and a 5 mm thick lead plate as a photon converter, the scintillators
are read out by fine mesh PMTs on top and bottom side via light-guides.
operation The acceptance of the LXe detector is divided into 3 × 8 patches as shown in
Fig. 4.11(a), and each has an area corresponding to 3 × 3 array of inner PMTs. We scan LXe
detector by moving the tagging detector at the opposite side of the patch with respect to LH2target. For the π 0 calibration, a dedicated trigger which requires a coincidence of (a) LXe
detector, (b) pre-shower counter hit and (c) energy deposit in tagging detector. Figure 4.11(b)shows measured energy with the LXe and BGO detectors in the calibration.
analysis The energy resolution is evaluated with the CEX γ-ray, and the face factor and nonuniformity of scale (Wi (r γ ) and U (r γ ) in Sec. 3.1.4) dependent on the position position in thedetector are evaluated at the same time.
The LXe Eγ is corrected in order to remove correlation of Eq. (4.4) with opening angle
between two γ-rays, then corrected γ-ray energy distribution is fitted with a dedicated function.
The function is composed starting from a normal response function which is a combinationof Gaussian at higher region and exponential at lower region. It is then convolved with γ-ray
66

ϭ

Ϯ

ϯ

ϰ

ϱ

ϲ

ϳ

ϴ

ϵ

LXe Energy (MeV)ǀї

Chapter 4. CalibrationϭϬ ϭϭ ϭϮϭϯ ϭϰ ϭϱ

100
80
60
40

ϭϲ ϭϳ ϭϴϭϵ ϮϬ Ϯϭ20

ϮϮ Ϯϯ Ϯϰ

0
0

20

Ƶї

(a) 24 patches for π 0 calibration. LXearea is divided into 3 × 8. Calibration
data is taken for each, the tagging detector
located at the opposite position.

40

60
80
100
BGO Energy (MeV)(b) The energies in LXe and BGO detectors in π 0calibration. The two bunches of events 54.9 MeV
in LXe and 84.9 MeV in BGO and the reversed
pattern are seen.

Figure 4.11: π 0 calibration.
energy spread and extra pedestal fluctuation due to different beam condition. Figure 4.12 shows
an example of fit in a region.

4.1.3

Energy scale stability

The long-term stability of the LXe detector is monitored with various calibrations (Sec. 4.1).
Figure 4.13 illustrates the relative light yield by measuring several types of calibrations as afunction of date. The absolute scale is adjusted with π 0 calibration for each year, and relative
scale is determined by interpolating different light yield calibrations.

4.1.4

LXe detector alignment

We performed 3D alignment of the LXe detector with laser scanner. According to the result of
the 3D measurement, we correct the position of the reconstructed γ-ray.
result of the measurement We measured the positions of the 24 × 2 holes on arch structure
which is used to fix PMT holders at both (US and DS) end of the detector, and the surface of theinner window where the PMT holders are installed. The measured misalignment of the vector
from DS hole to US hole from that in the drawing is displayed in Fig. 4.14. The surface points
array on the window are fitted with a cylinder, and error from cylinder is negligible, but slant
and displacement is also found (Table 4.1).
The following vectors are calculated from the measurement, hi : a direction vector whichshows the direction of PMT holder, and di : a normal vector which is perpendicular to the surface
67

Number of events

Chapter 4. Calibration

1200
sigma = 1.38 ± 0.08 %1000

FWHM = 3.97 ± 0.25 %

800
600
400
200
0

400000 500000 600000 700000
Total number of photons

Energy scale (arb. unit)

Figure 4.12: Fit on the π 0 calibration data (cross with error). Red line shows the fit result, andblue dashed line shows the detector response function before convolution.
1.04

1.02

1

0.98

0.96

31/12

Energy scale (arb. unit)

2009

01/09

01/11

01/07

2010

31/08

31/10

31/08

2011

31/10

31/12

2012

02/07

2013

1.04

1.02

1

0.98

0.96

31/12

2009

01/09

2010

01/11

01/07

31/08

2011

31/10

31/08

31/10

2012

31/12

02/07

2013

Figure 4.13: History of light yield by calibration before (top) and after (bottom) scale adjustment.
Black marker is by CW calibration, red marker is from background spectrum.
of the inner window at the center of the holder. An index i shows the value of i-th PMT holder
from top. These are used in correction of the γ-ray position.
method to correct position Since the position of the γ-ray is reconstructed in internal coordinate (u, v, w), we previously used dimensions of drawing which is expressed by a simple
coordinate transformation,
68

Chapter 4. Calibration
25

25

25

20

20

20

15

15

15

10

10

10

5

5

5

0
620.5

621

0
621.5
622 -4
Distance [mm]

0
-2

(a)

0

2
4
6
x rotation [mrad]

0

(b)

1

2
3
4
y rotation [mrad](c)

Figure 4.14: Measured distance and tilt angle of DS→US vector. The designed distance is
622 mm and angle 0. y-axis just shows the id number of the holes which is enumerated fromtop (1) to bottom (24).
Table 4.1: Fitted parameters of inner window
Item
RadiusX shift
Y shift
X slant
Y slant

Unit
mm
mm
mm
mrad
mrad

Measured
681.0
3.24
-0.14
-3.4
5.5

Design
678.5
0
0
0
0

v
) + x 0,RINv
y = (w + RIN ) + sin(
) + y0,RIN
z = u + z0,

x = −(w + RIN ) + cos(

(4.7)
(4.8)
(4.9)

where RIN is radius of the inner face of the LXe detector, and (x 0, y0, z0 ) is parallel shift of LXe
detector from drawing. They were determined from cosmic ray data, where the cosmic rays
penetrate the LXe detector and the drift chamber. x 0 and y0 are found to be consistent with zero,
while z0 is shifted by 6.2 mm in 2009, 2010 data, and 4.2 mm in 2011-2013 data.
According to the distortion which was measured with 3D scanner, we introduced a position
correction which is based on how the PMTs are settled in the LXe detector.
• For 24 PMT holders, unit vectors of the longitudinal direction of the holder hi , and normal
vectors of the holder di are calculated.
• The LXe acceptance is divided into 25 sections by v coordinate. A section-i ranges
between centers of i-th and i + 1-th PMT holders, the section 0 and 24 are top-end andbottom-end part.
69

Chapter 4. Calibration• The index of a section (i) and a coordinate in the section (s) are calculated according to
the v position where γ-ray is reconstructed.
• The vectors h γ and d γ are calculated by interpolating i-th and i + 1-th h and d according
to s for the case where γ-ray is in section 1-23. In section 0 or 24, 0-th or 24-th vectors
are used.
• The point P is calculated by interpolating points of i-th and i + 1-th hole on the US-side
arch. The ratio of the interpolation is calculated from s.
• The point Q is calculated by adding a vector to the point P, the vector is parallel to h γ andthe length of the vector is calculated from the u position of the γ-ray.
• The point Q is projected onto the surface of the inner window with respect to the axis of
the fitted cylinder face; the point is named point R.
• The vector w · d γ is added to the point R. The point is the corrected reconstructed positionof the γ-ray.
In the procedure of position correction, thermal expansions of the detector parts are considered. The main structure of the detector cryostat is made of stainless steel, SUS316L(α ∼ 16 × 10−6 /K), and PMT holders are made of PEEK4 resin (α ∼ 50 × 10−6 /K).
effect of the correction Average shift of γ-ray position over acceptance is (-0.6, -1.9, 2.1)(mm) in (x, y, z). The shift is LXe detector shift with respect to the COBRA frame. Additionalz shift to connect the COBRA frame to drift chamber frame is determined from measurements
which use both LXe detector and drift chamber, alignment run by cosmic ray and AIF, result is+2.0 ± 0.4 mm for shift in z coordinate.
Figure 4.15 shows the effect by the correction. Shift toward negative y is consistent withthermal shrink, but also consistent with the zero shift with other measurement within uncertainty.
The effect of thermal shrink of PMT holder was not considered in previous analysis but is includedin the correction, although the thermal effect cannot be confirmed in any calibration. Average
difference in stereo angle is ∼ 4 mrad, it is not negligible compared with the angular resolutionof γ-ray.

4.2

Drift chamber

4.2.1

z-coordinate

Since the reconstruction of z (longitudinal direction of wire) is based on the charges measured
at both ends Eq. (3.10), the calibration is done via the calibration of relative gain of thepreamplifiers.
Figure 4.16 is an example of the calibration for the anode wire for the Michel positron data.
The gains of the amplifiers at the both ends are calibrated so the fitted curve to pass the originof the plane. For the cathode the relative charge in both end of two series were compared likein the anode, but more precise ztrack which is obtained from the track fitting is used instead of
zanode . The uncertainty in z is estimated to be 70 µm from the comparison of zanode and ztrack .
4 polyetheretherketone70

v [cm]Chapter 4. Calibration

80

60

180

40

160

20
140

0

120

100

−20

80

−40
60

−60

40

20

−80
0

−20

−10

0

10

0

20
u [cm](a) Shift in u and v coordinate, w is fixed at 1 cm. The
arrow shows the direction and distance of correction at
the position. The length is magnified by factor 10.

1

2

3

4 5 6 7 8 9 10
stereo angle shift [mrad](b) Difference of reconstructed points
with previous and current methods instereo angle.

Figure 4.15: Result of the LXe detector alignment

4.2.2Time calibration

The timing offset between channels is caused by the difference of the amplifier characteristics,
cable length and electronics at down-stream. The time offset information is extracted from theMichael and cosmic ray data. The leading edge timings after z coordinate correction and thetrack timing fitting are plotted, and the timing for the channel is found by fitting the leading edge
timing distribution.

4.2.3

Alignment

The relative position of each DCH module is quite important as a high precision tracker. We
have two methods to measure the alignment of the drift chamber modules, an optical survey
with laser-tracker, and a method by reconstruction of the tracks.
4.2.3.1

Optical method

For the optical survey, a drift chamber module is equipped with cross-hair markers and cornercubes at both ends of the module, as shown in Fig. 4.17. The position of the wire and cathodeagainst the DCH module is measured when it was produced. The position is related to a71

AhoodChapter 4. Calibration
1

Cell #57

0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
-40

-30

-20

-10

0

10

20

30
40
zanode [cm]Figure 4.16: zanode versus asymmetry found in cathode. The wave length of the sinusoidal curveis 5 cm of the cathode pattern.

alignment pin, which is also measured in survey. In each year before data taking, measurementwith theodolite5 is performed for cross-hairs and pins, target markers are also surveyed (Sec. 4.4).
The accuracy is expected to be 0.2-0.3 mm in x and y and 1.5/2.5 mm in z for DS/US side of
the modules. The difference in US and DS is because the theodolite is located in DS side of thedetectors. From year 2011, the optical survey is updated with corner cube and laser tracker6.
The accuracy of the method is determined from the uncertainty of the alignment of the cornercube and expected to be 0.15-0.25 mm in x, y and z, although the spacial resolution of the
tracker is 0.015 mm for each axis.

ĐŽƌŶĞƌĐƵďĞĐƌŽƐƐŵĂƌŬĞƌ

Figure 4.17: View from down-stream side of drift chambers. Corner cubes and cross-hairmarkers are seen.

5 Leica Geosystems Total Station TC2002
6 Leica Absolute Tracker AT901

72

Chapter 4. Calibration
4.2.3.2

Software method

The relative positions of the modules were also measured with two independent methods ofcosmic ray and Michel positrons.
The cosmic ray counter (CRC) was installed for this calibration, to trigger events in which
the cosmic rays pass through the DCH modules. The CRC consists of 10 plastic scintillator bars
with PMT read out, and are mounted on the outer surface of COBRA magnet as illustrated inFig. 4.18. The magnet is turned off during the cosmic ray dedicated runs. We processed thecosmic ray data by the algorithm called "Millipede" [85]. It is a kind of linear fitting with a lotof free parameters in a matrix of a large number of laws and columns. The optimal displacement
vector for each module is calculated with the algorithm, by minimizing the residuals with respect
to straight track of cosmic rays. The parameters are determined within 150 µm accuracy by themethod.

ZĐŽƐŵŝĐƌĂǇ,ŵŽĚƵůĞƐ

Ǉ
ǆ

Z

ǌ

Figure 4.18: CRC mounted on the COBRA magnet. The figure is shown in cross-sectional viewof a plane perpendicular to the beam axis.
The other method is an iterative algorithm to optimize radial and longitudinal displacement ofeach module using Michel positron tracks. This method is conducted by minimizing the residualof radial and longitudinal directions between the reconstructed track and hits in each module.
The process repeated iteratively, updating positron tracks with corrected modules position. Thismethod is confirmed by checking consistency with Mott calibration data (Sec. 4.2.4).

4.2.4

Mott calibration

Mott scattering Mott calibration [86] takes a use of Mott scattering, which is elastic scatteringof a relativistic Dirac particle by point like nucleus. We make a use of Mott data to evaluate thepositron track resolution, and alignment of chamber.
When the nucleus satisfy Z  137, the scattering cross section is approximated as [87],
dσ
Ze2
=
dΩ
2E

!2

73

cos2 (θ/2)
sin4 (θ/2)(4.10)

Chapter 4. Calibration
where E is the initial energy of the particle (positron). The energy of the positron after scattering
is given as,!
1 − cos θE0.
(4.11)
E = E 1−Mc2 1 + (E/Mc2 )(1 − cos θ)operation In operation, we select positron beam of momentum 53 MeV/c (rejecting pulsecorrelated particles with RF signal from accelerator). The positrons with uniform energy hitstarget and undergo Mott scatting, a noticeable point is that in our setting, energy of scatteredpositron can be regarded approximately monochromatic (Fig. 4.19). The energy spread of
measured positrons are 620 keV in σ.

Counts/200keV

Mott events - RF selection
600

500

400

300

200

100

0
40

42

44

46

48

50

52

54

56

58
60
E(MeV)

Figure 4.19: Spectrum of Mott scattered positron

4.3

Timing counter

4.3.1

PMT gain adjustment

As the TICP is placed at off-centered in z, the PMTs at both ends are subject to the magnetic
field of different strength and direction. The gains of the PMTs are needed to be equalized, anda rough equalization is done with cosmic-ray events. When the cosmic-ray passes through the
TICP bar, the hit rate and energy deposit is uniform throughout the bar. The PMT bias voltages
are adjusted to equalize the fitted peak of the charge distribution by cosmic ray events. The finetuning is done in software, by finding a weight to get uniform trigger rate.

4.3.2

z calibration

Since we reconstruct z-coordination from the time difference of two PMTs at the end of bar, thez calibration is equivalent to the timing offset calibration. The extended track from DCH is used
for reference in each bar calibration. The time offset is determined so zDCH−TIC to be zero. In
Fig. 4.20, the z coordinate calibration is demonstrated.
74φ( °)

Chapter 4. Calibration
0

0

-20

-20

-40

-40

-60

-60

100
80
60

-80

-80

-100

-100

-120

-120

-140
-150

-140
-150

40
20

-100

-50

0
z (cm)

50

100

150

-100

-50

0
z (cm)

50

100

150

0

Figure 4.20: TICP cosmic ray hit map before (left) and after (right) z calibration.

4.3.3

Relative calibration

12
Timing offset between bars is calibrated with CW-B reaction 11
5 B(p, γ, γ) 6 C. In this reaction,
gammas of energy 4.4 MeV and 11.6 MeV are always simultaneous. We calibrate TIC timingwith 11.6 MeV, while monitoring 4.4 MeV γ in LXe detector.
This method can be also used for the crosscheck of LXe-TIC relative timing adjustment.
For the same purpose, we use timing information of RMD, where gamma ray and positron arealways coincident.

4.4

Target alignment

Information about the target position is an important issue for the high precision measurement.
Since we reconstruct the initial position and direction by the propagation of the measured track
to the target plane, the position of the target along zt (direction that perpendicular to target plane)
is especially important. For example, ∼ 1 mm of zt error causes 10 mrad error in φe : positronemission angle in φ direction (Fig. 4.21(a)). The shift of φe by target displacement ∆z can be
expressed as,∆φe (∆z) = −∆z sin θ e,
R cos φe sin(θ e + θ tar )(4.12)

where R is the radius of curvature at the decay point, and θ tar = 20.5◦ is the slant angle of thetarget.

4.4.1

Conventional alignment methods

The position of the target is confirmed by an optical survey with theodolite in every year. The
estimated accuracy of this survey is ±(0.5, 0.5, 1.5) mm in the (x, y, z) directions. A plane
fit of the measured point of 7 cross-marks are adopted for target–drift chamber alignment in
the previous analysis. For crosschecking with optical alignment, we observe the reconstructed
position of hole on the target. Target holes can be seen in mapping of reconstructed vertex
positron on target like Fig. 4.22. If assumed position of the target is wrong by ∆p, the positionof hole depends on the incident angle of positrons, and ideally yhole is proportional to ∆p andtan φe (Fig. 4.21(b)). By checking all six holes, position and inclination of the target can beobserved.
75

Chapter 4. CalibrationdĂƌŐĞƚ
ȴʔĞ

Ǉ

Ğн

ȴǌƚ
ƚƌƵĞ
ŚŽůĞ

ȴǇ
ǌƚ

ȴǌƚ

Ğн
ƌŝĨƚŚĂŵďĞƌ

ƚƌƵĞƚĂƌŐĞƚ

ĂƐƐƵŵĞĚ
ƚĂƌŐĞƚ

(b) Relation of φe and yhole , when target is assumed at wrong position. The horizontal axis
is zt : an axis perpendicular to target face, andvertical axis is y.

(a) Schematic image of the target and positron
track shown in projection to x − y plane. Errorof the assumed target position causes error in φe .

Figure 4.21: Relation between target shift and error in φe .
Y (cm)# of vertices
3
1200
2
1000
1
800
0
600
−1
400
−2
200
−3
−8

−6

−4

−2

0

2

4

6

0

8
Z (cm)

Figure 4.22: Vertex distribution on target in y − z projection. Beam spot is around the center oftarget. The holes are seen as the deficit of vertexes.

4.4.2

Target deformation and countermeasure

The both results of the hole position and the optical survey indicate that the target was gradually
getting deformed. The target deformation is obvious in year 2012 and 2013. On the other handin 2009 and 2010, the target was consistent with a plane shape.
Further investigation into the shape was performed with the 3D laser scanner7 at the endof year 2013. The result of 3D scan is displayed in Fig. 4.23(b) and also supports the bendingof the target. The reference target plane for reconstruction of positron track is changed fromconventional plane to paraboloid which is parametrized as
zt = cx (x t − x 0 ) 2 + cy (yt − y0 ) 2 + z0,(4.13)

where (x t, yt, zt ) are target local coordinate which x t and yt are semi-major and -minor axis oftarget and (x 0, y0, z0 ) are vertex of paraboloid (in target frame). The parameters are determined by
7 FARO portable coordinate measuring machines

76Chapter 4. Calibration
fitting on the result of theodolite measurement. The result of year 2013 is shown in Fig. 4.23(a).
The two results largely differ especially in outer region, but considering the vertex distribution
in Fig. 4.22, the agreement around the beam spot is good.
Yt (cm)Zt (cm)
3

0.1

2

0.05

1

0

0

−0.05

−1

−0.1

−2

−0.15
−0.2

−3
−8

−6

−4

−2

0

2

4

6

8
X t (cm)(a) Paraboloid fit on year 2013 optical survey data.
Yt (cm)Zt (cm)
3

0.1

2

0.05

1

0

0

−0.05

−1

−0.1

−2

−0.15
−0.2

−3
−8

−6

−4

−2

0

2

4

6

8
X t (cm)(b) Target deformation found with 3D laser scanner.

Figure 4.23: Results of the target measurements.
The track fitting is improved by the reconstructed paraboloid, not a plane as the previous
analysis. The uncertainty of the target z0 is determined by comparing the zt with central fourholes. Systematic uncertainties are estimated as σ z0 = 0.3 mm for year 2009-2012 data, andσ z0 = 0.5 mm for year 2013. The uncertainty due to the deformation from paraboloid shape oftarget is taken into account, using the difference between paraboloid and 3D scan.

4.5

DRS calibration

4.5.1

Voltage calibration

Each cell in the DRS chip has different characteristics. Since the DRS boards have calibration
voltage source, the voltage calibration can be performed online. The response curve for each cellis stored, and recorded waveform is already corrected. Measured RMS after voltage calibration
is 0.3 mV.

4.5.2

Timing calibration

Since the sampling speed is controlled by switching pulse inside the chip, it can be varied byeach cell. The difference between DRS boards must be adjusted.
We used sinusoidal test wave to calibrate cell-by-cell speed. By taking events with random
trigger, the time period of zero-crossing are compared. The adjustment is repeated until the
all zero-crossing period to become that of input wave. In order to synchronize the boards, a
dedicated clock signal of 19.44 MHz is distributed to all the boards. The accuracy to synchronize
different boards improved in 2010, after DRSs were upgraded to version 4.
77

78

γ > 40 MeV
e+ > 45 MeV
52.83 MeV end-point e+≈ 50 MeVe+
14.8, 17.6 MeV γ
4.4, 11.6, 16.1 MeV γ
9 MeV γ5.5 MeV α
4.4 MeV γµ+ → e+ νe ν̄ µ γµ+ → e+ νe ν̄ µe+ N → e+ N

7 Li(p, γ) 8 Be
34
11 B(p, γ) 12 C
5
6
58 Ni(n, γ) 59 Ni

241 Am(α, γ) 237 Np

9 Be(αCEXRMDMichel decay

Mott

CW accelerator

Neutron generator

Am source

LED

AmBe source

55, 83, 129 MeVγ

π−p → π0n12 ?
241 Am, n) C
12 C∗ (γ) 12 C

π 0 → γγ

SourceWide spectrum µ± O(GeV)

Process
atmospheric showers

Category
Cosmic ray

LXe PMT calibration

LXe energy scale

LXe PMT QE/purity

LXe energy scale

LXe uniformity/purity
TC inter bar/ LXe–TC timing

LXe-TC relative timing
Normalisation
DCH energy scale/resolution
DCH and target alignment
Normalisation
DCH energy scale/resolution
DCH alignment

LXe energy scale/resolution

Main Purpose
LXe-DCH relative position
DCH alignment
TC energy and time offset calibration
LXe purity

Table 4.2: Summary of calibration tools in MEG experimentcontinuously

on demand

weeklyweeklyweeklyweeklyannually

continuously

continuously

annually

on demand

Frequency
annually

Chapter 4. Calibration

Chapter 5
Performance
The methods to estimate detector performance and the typical results are shown in this chapter.

5.1

Timing

The timing resolution which is finally used in the physics analysis is given by the RMD calibration
which contains all the same elements: γ-ray, positron and the trigger as for the signal events.
We also calculate breakdown of each to crosscheck of our understanding for the detectors.

5.1.1

γ timing

The timing resolution of LXe detector is evaluated with two ways. The data with 54.9 MeV
γ-ray in π 0 calibration is used.
One is called intrinsic resolution, all PMT are divided into two groups alternatively inarrangement. Timing is reconstructed independently with two groups (call them t even and t odd )The intrinsic resolution is defined from the distribution of a half of the difference, (t even −t odd )/2.
It is found to be σγint ≈ 36 ps. The resolution with other energies revealed that the resolutionpfollows 1/ Eγ curve, and it implies the intrinsic resolution is dominated by statistic uncertainty.
The other way is more practical so it is normally called as the resolution of LXe detector.
That is evaluated with time difference of two γ-rays from π 0 decay, the 54.9 MeV onw seenby the LXe detector and the 82.9 MeV onw seen by pre-shower counter (Sec. 4.1.2.3). The
resolution σLXe is calculated the from distribution of t LXe − t psc . The example in year 2013 isshown in Fig. 5.1. A Gaussian fit is applied on the distribution. As the resolution still includes
the TOF uncertainty of γ-ray and the resolution of pre-shower counter, the contributions arequadratically subtracted to obtain σLXe . In year 2012 and 2013, resolutions are 64 ps and 66 ps,
respectively.

5.1.2

Positron timing

The timing resolution of the timing counter is determined from positrons which hit neighbouring
TIC bars. The hit timing is compared considering the difference of pass length. The timing
resolution of the single timing counter bar is 65 ps. The timing resolution of the total positron
spectrometer is composed of the resolution of the timing counter and the uncertainty of the track
length from vertex to the TIC hit. The positron timing resolution is estimated to be ∼ 100 ps
79

Chapter 5. Performance

54.9
82.9 in 2013 CEX calibration. A fitted σ is calculated to be
Figure 5.1: Distribution of t LXe− t psc
113.5 ps.

5.1.3

Combined timing

Number of events /(0.080 ns)

The resolution of the time difference of γ-ray and positron is evaluated using the RMD data,
which was taken by MEG trigger. For energy sideband (definition will appear in Sec. 7.2.2) data,
the RMD event makes a peak on the top of the flat distribution by the accidental background.
We fit the distribution with a double Gaussian plus constant function, and the result is shown in
Fig. 5.2.

60000

40000
N

20000
45<E e <55 MeV
40<E γ <48 MeV|θ e γ | < 0.3 rad|φ e γ | < 0.3 rad

0
−2

−1

eννγ

= 74889 ± 704

f core= 0.78 ± 0.01

σcore

= 130 ± 2 ps

σtail

= 280 ± 5 ps

0

1

2
t eγ (ns)Figure 5.2: Fitting for t eγ distribution with RMD data, year 2009-2013 are combined.

80

Chapter 5. Performance

5.2

Gamma energy

Number of events /(0.50 MeV)

The energy resolution of γ-ray is evaluated with the method explained in Sec. 4.1.2.3. Theenergy resolution is worse in smaller w due to the fluctuation of photon collection efficiency
which comes from the relative position of PMT and γ-ray. In other words, photon collection
gets maximum when γ-ray converts just in front of PMT and minimum in an interval of PMTs.
The difference in the width can be seen is the energy spectrum in Fig. 5.3. Figure 5.4 shows theenergy resolution as a function of the position (u, v).

(a)
100

wγ < 2 cm

50

0

(b)
200

wγ > 2 cm

100

0
30

40

50

60

70
E γ (MeV)

Figure 5.3: Response for 54.9 MeV γ in π 0 run. Top (bottom) figure is w < 2 (w > 2) area, theevent fraction is 42% (58%).
The absolute scale factor S is determined from π 0 calibration run with the way explainedin Sec. 4.1.2.3. Uncertainties in Eγ scale are estimated by combining various calibration data.
The total uncertainty of γ-ray energy scale is 0.3%. The sources of the uncertainties are (1)the accuracy in estimation of peak energy in π 0 calibration (0.1%), (2) uncertainty between
difference in conditions of π 0 calibration and normal muon beam (0.1%), (3) the accuracy oflong term scale stability (0.2%), and (4) accuracy of the non-uniformity correction (0.2%).

5.3

Positron energy

The positron energy is evaluated in different two methods.
81

3.5

40
20

4
60

3.5

40
20

3

0

σup (%)

60

V (cm)

4

σup (%)V (cm)

Chapter 5. Performance

3

0
2.5

-20
-40

2.5

-20
-40

2

-60

2

-60
-20

-10

0

10

20
U (cm)

1.5

-20

-10

0

10

20
U (cm)

1.5

Figure 5.4: Energy resolutions measured in π 0 calibration of year 2012. Left and right figures
show shallow (0 < w < 2 cm) and deep (w > 2 cm) event, respectively.
The first method uses the Michel spectrum. Since the Michel spectrum has a sharp edge atthe energy m µ/2, the energy scale and resolution can be extracted by fitting. The fit function iscomposed of the theoretical Michel spectrum, the acceptance function, and the detector response.
A result of the fit is shown in Fig. 5.5.


f (Ee ) = (Michel) × (Acceptance) ∗ (Resolution)!!
Ee − µAcc
1(Acceptance) =1 + erf √
2
2σAcc

(5.1)
(5.2)

where µAcc and σAcc are parameters that model the acceptance of detector. They are extracted
from the sideband data for each year and are µAcc ∼ 49 MeV and σAcc ∼ 2.5 MeV through theperiod. The resolution factor in Eq. (5.1) is composed by double Gaussian functions,
Second method is called "double turn" and is described in Sec. 5.4.2. The positron energy
resolutions measured in 2012 and 2013 are listed in Table 5.1.

5.4

Relative angle

5.4.1

Gamma position

The resolution of γ-ray position is evaluated with MC simulation and is confirmed by dedicated
π 0 [84] and CW calibration [82] with lead collimators on the entrance window of the LXedetector. Figure 5.6 shows the result of the π 0 run with a collimator made of lead plate with a
10 mm width slit.
The evaluated resolution is 5 mm in u and v direction and 6 mm in w direction.
82

Number of events /(0.25 MeV)

Chapter 5. Performance

15000

Relative efficiency

10000

Table 5.1: Energy resolution of
positron. σcore/tail means sigma of thecore/tail part of the double Gaussian,and f core shows fraction of the core
part.

5000

0
1

Value
2012
σcore
340 keVσtail 1.84 MeV
f core
0.872

0.5
0
40

45

50

55
Ee (MeV)2013
325 keV
1.91 MeV
0.852

Entries / 0.12cm

Figure 5.5: Fit on the Michel spectrum for all years
averaged data. Dot-dashed line is the theoretical
spectrum, blue dotted line is resolution function of
the detector, and the acceptance function is drawn
in bottom box.
220
200
180
160
140
120

χ2 / ndf

117.6 / 121

Scale 0mean0

119.9 ± 4.9-5.706 ± 0.027

σ00.6592 ± 0.0271

Scale 1130.1 ± 5.0

mean1

0.05354 ± 0.02542

σ1
Floor

0.6748 ± 0.0274
60.4 ± 0.9

100
80
60
40
20
0

-15

-10

-5

0

5

v (cm)

Figure 5.6: v projection of γ-ray reconstructed position. The slit lies along u direction [84].

5.4.2

Positron angle and vertex position

The positron energy, angle, vertex position are correlated to each other, so they are treatedwith per-error as introduced in Sec. 3.2.4. The parameters for resolutions and correlations are
obtained from the double turn technique. It uses positrons which turn in drift chamber twice.
83

Chapter 5. Performance

events / 2.5 [mrad]

events / 0.6 [mm]The first and second turns are not connected for this study and are propagated to imaginary
target plane which locate between first and second turn. The intersection (imaginary vertex) andmomentum on the plane should agree to each other if the turns come from the same positron
track.
Figure 5.7 shows the result of double turn analysis which implies the averaged resolution.
After dissolving the correlations, the averaged resolutions are found to be σθe = 9.4 mrad,
σφe = 8.4 mrad, σ ye = 1.1 mm and σ ze = 2.5 mm. In the physics analysis, resolution are treatedas in Sec. 7.4.
60000

40000

30000

20000

20000
10000

0

−2

0

2

0

δ Y [cm]

−0.1

20000

10000

0

0.1

0

0.1

δθ [rad](b)
events / 2.5 [mrad]

events / 0.6 [mm]

(a)

0

20000

10000

−2

0

2

0

δ Z [cm]

(c)

−0.1

δφ [rad](d)Figure 5.7: Differences in reconstructed observables from first and second turn. ye , ze , θ e andφe , averaged data in year 2012.

5.4.3

Combined angle

The angle between γ-ray and positron, θ eγ and φeγ are reconstructed by Eq. (3.18) and (3.19).
The resolutions are evaluated from γ-ray postilion resolution, decay vertex resolution andpositron angular resolution. The combined θ eγ resolution after removing the correlations is14.4 − 14.9 mrad depending on the year. The resolution of φeγ is 9.4 − 9.9 mrad after thecorrelations are resolved.
84

Chapter 5. Performance

5.5

Detection efficiency

5.5.1

Gamma efficiency

We define a fiducial volume of the LXe detector as |u| < 25 cm∧ |v| < 71 cm∧0 < w < 38.5 cm.
The signal γ-ray detection efficiency is evaluated with the MC simulation, taking into accountthe other observables distribution in signal. The loss is mainly coming from the material between
the vertex and the LXe detector, the COBRA magnet (14%), the cryostat (7%), the PMT andthe other materials (6%). Another kind of the inefficiency is the escape of shower from theentrance face (6%). The inefficiency, coming from pile-up rejection and cosmic ray rejection
are taken into account. The estimated detection efficiency is  γ = 0.625 ± 0.023. The value isalso confirmed by the π 0 calibration.

5.5.2

Positron efficiency

The absolute positron detection efficiency is difficult to measure; hence we do not use theabsolute value in physics analysis but as in Sec. 7.7. We evaluated the efficiency for the signal
positron with MC simulation, and the result is  e ∼ 0.48. (for Michal positron, the efficiency is0.37.)

5.5.3

Efficiency of DAQ system

The trigger efficiency consists of the efficiencies of (a) γ-ray trigger, (b) positron trigger and (c)direction matching of γ-ray and positron. The largest inefficiency is from the direction matchingpart.
At the beginning of the physics data taking, the bottleneck was the data transfer from VME
board to the online disk, which took t ro ≈ 24 ms while the dead time of DRS4 chip is 625 µs.
It was overcome by upgrading to "multi buffer scheme", and our application has 3 buffers. The
trigger is still active even when data is read out unless all three buffers are filled with unread
data. With 3 buffers, the fraction of the livetime to total time is written as following formula,f LT = exp(−Rdaq ·t ro )[1 + Rdaq ·t ro + (Rdaq ·t ro ) 2 /2!].

(5.3)

The livetime efficiency is ≥ 99% for the event rate up to ∼ 13 Hz, which is normal trigger
rate after the improvement in year 2011, while it was ∼ 7 Hz until year 2010. With the improved
deadtime, an optimization in trigger rate and trigger efficiency (direction matching) was done
as Fig. 5.8.

85

Live time

Chapter 5. Performance

1

1

0.95

0.9

0.9

0.8
0.85

0.7
0.8

0.75

0.7

0.65
0.65

0.6

First part
0.5

Second part
0.7

0.75

0.8

0.85

0.9

0.95

1

Online efficiency

Figure 5.8: Trigger (online) efficiency and livetime ratio in previous scheme (black star) andcurrent scheme (blue cross).

86Chapter 6
Run
The status of the experiment is summarized in this chapter.
The PSI proton facility has a long maintenance period from the end of the year to latespring. The MEG physics data taking was also stopped and maintenances of the detector were
performed during the period. There is scheduled shutdown in every two weeks, so the special
calibrations which do not require beam, the repairment or modification works are performed in
the shutdown.
The calibrations of the LXe detector were done twice per week basically. In the calibration,
the PMT gain, QE light yield monitoring with γ-ray sources were performed. It also includes
calibration with the CW accelerator which need the CW beam pipe operation is required. It
took 3-4 hours to this calibration after we were trained to operate it.

6.1

Engineering run 2007

The assembly of instrument was finished in year 2007. We took data with muon beam in order
to examine the normal operation of all instruments from October to December.
Some major problems were found in the engineering run. (1) Sparks happened at the
HV feedthrough for the Xe PMT, hence we replaced connectors. The sparks damaged circuit
elements at the input stage of readout electronics, also we must replace them. (2) Discharge
happened at the DCH board. The He gas inside COBRA volume changed to contain small ratioof synthetic air. (3) The target misaligned due to the interference between DC support structure.
The structure redesigned therefore.
These problems were fixed before the run 2008 were started.

6.2

Run2008

The data acquisition for the physics study started in this year. After the CEX calibration fromthe end of July to the end of August, the physics DAQ restarted in September. We published our
first physics result with the data from September to December [88]. While the sensitivity of thesearch was 1.2 × 10−11 , the upper limit for the branching ratio was 2.8 × 10−11 (90% C.L.).
During the data taking, the drift chamber suffered from high-voltage discharge. It resulted
in decrease in the number of operational modules and thus loss of positron detection efficiency
87

Chapter 6. Run(finally the efficiency decreased about a third of that in beginning.), and poor angular resolution.
The data of this year is not used for later analysis for this reason.

6.3

Run2009

In this year, the waveform digitizer, DRS was upgraded from ver.2 to ver.4, the final version.
About the LXe detector, the light yield was improved by purifying the xenon. To take into
account the condition of 6% air mixture inside of the COBRA volume, the degrader for muon
beam was replaced from the one of 300 µm thick to 200 µm thick at the middle of DAQ period.
The problem of the drift chamber discharge was solved by improving the design.

6.4

Run2010

Before physics data taking, we improved the timing accuracy by modifying the readout board.
The effect for the timing resolution can be seen in Table 6.1. We started taking physics data in
August and finished at beginning of November. The CEX calibration was performed between
August and September. The finished date was earlier than the original plan due to a problemof helium leakage with the BTS magnet. However, the amount of taken data is about a doubleof that in run 2009. We published results by analysing data in year 2009 and 2010 to find thesensitivity of 1.6 × 10−12 and the upper limit of 2.4 × 10−12 in 90% C.L. [89].

6.5

Run2011

The noise condition of DCH was found to be bad. The problem was fixed by changing HVunit for DCH, and the software filtering process (Sec. 3.2.1) was also effective. As described inSec. 5.5.3, the DAQ efficiency was improved by the modification of the data readout scheme in
DAQ boards.
Many calibration techniques were developed in this year. (a) The BGO detector for CEX(Sec. 4.1.2.3). (b) A new γ source, neutron generator for LXe detector calibration (Sec. 4.1.2.2).
(c) A spectrometer calibration with monochromatic energy which make use of Mott scattering(Sec. 4.2.4). (d) A drift chamber alignment with a laser tracker and corner cube.
We started data taking in July and ended in beginning of December due to a power failure in
the experimental hall. The taken data amount in this year slightly exceeded the sum of those in2009 and 2010. Our previous publication [13] based on the data up to this year.

6.6

Run2012 and 2013

A beam development was performed before the physics run in 2012, and thus the beam intensity
was increased by ∼20% without deterioration of the beam profile. As we experienced run andcalibration for more than 5 years, we did not have severe troubles in the operation of run 2012
and 2013. Data taken in these years are analyzed for the first time in this study. The statisticalamount is about the same as that of accumulation of the previous years.
As mentioned in Sec. 4.4, it was found that the muon target in neither plane nor simple
paraboloid. It seems to be deformed during long term operation. In order to treat this problem
88Chapter 6. Run
as a systematic uncertainty, we introduced a new way of fitting in physics analysis. It will be
discussed in Sec. 7.5.

6.7

Data summary

Accumulated N µstop(1014)The statistical information of total data taken in MEG experiment is summarized in the Table 6.2
and Fig. 6.1. The total number of µ+ s which were stopped on target is 7.5 × 1014 . The lengthof a run is optimized to be ∼ 2000 MEG trigger event, considering a loss by accidents in DAQ
and an overhead time for the start and stop of the run. The taken data amount is 94 TB in total.
The performance of the detector after final calibration is also summarized in Table 6.1.
8
7
6
5
4
3
2
1
0

31/Dec/09

31/Dec/10

01/Jan/12

31/Dec/12

31/Dec/13
Date

Figure 6.1: Accumulation of number of muons which stopped in the target. Flat regions between
slopes correspond to the long maintenance periods.

89

Chapter 6. Run

Table 6.1: Summary of detector performanceYear2009 2010 2011 2012
γ-ray resolutions
Eγ (w>2 cm) (%) 1.8
1.9
1.6
1.6
Eγ (w<2 cm) (%) 2.4
2.5
2.3
2.3
t γ (ps)
96
67
67
64
u, v (cm)5555w (cm)
6
6
6
6
Positron resolutions (core component)
Ee (MeV)
0.31 0.31 0.30 0.34
θ e (mrad)
9.2 10.3 10.4 10.9
φe (mrad)
8.5
9.5
9.4 10.1
ye (mm)
1.2
1.2
1.3
1.3
ze (mm)
2.3
2.9
3.0
3.2
Combined resolutions (core component)t eγ (ps)143 126 117 119
θ eγ (mrad)14.5 14.4 14.5 14.8
φeγ (mrad)
9.5
9.8
9.5
9.5

2013
1.6
2.3
66
5
6
0.33
11.2
10.4
1.4
3.3
111
14.9
9.9

Table 6.2: Summary of taken data amountYear
DAQ time
Number of runsµ+ on target (×1014 )(2008)
48d 21h
10634
0.9

2009
37d 17h
10343
0.6

90

2010
56d 10h
12167
1.1

2011
81d 1h
30852
1.8

2012
90d 20h
43809
2.3

2013
63d 0h26985
1.6

Chapter 7
Physics analysis
In this chapter, the analysis methods of the search for µ → eγ is discussed.

7.1

Analysis scheme

We adopt the maximum likelihood analysis to estimate the number of signal event (Nsig ). A
likelihood function is composed of probability density functions (PDFs) of signal, radiative
muon decay (RMD) and accidental background (ACC). The best fit value of Nsig is defined tomaximize the likelihood function.
The normalization factor, which is used to convert Nsig to the branching ratio: B, is calculated
from the number of Michel decay and RMD. The confidence interval of B is obtained with the
Feldman-Cousins approach, by processing many pseudo experiments considering systematic
uncertainties.

7.2

Data sets

We analyzed data taken from year 2009 to year 2013. The data can be separated into two groups,(a) taken in year 2009-2011 or "Old" and (b) taken in year 2012-2013, or "New". We havealready analysed the old data, however the analysis is revised in this study. The latter is first timeto analyse for µ+ → e+ γ search. The data statistics of two groups are comparable (Sec. 6.7).

7.2.1

Pre-selection and blinding

In order to reduce the data size, "pre-selection" is applied before detailed calibrations. The
definition of the pre-selection is as follows.
• −6.875 ns < t γ − t TIC < 4.375 ns• |t track − t TIC | < 50 ns
The window is determined so wide that we do not lose good event. The events which satisfy
both criteria for at least one positron track remain in later analysis. As for the first condition, t γ isa rough online estimation by trigger assuming the vertex at center of the target. The asymmetricrange is set because t TIC is not subtracted by the time of flight and the number of turns of positron
before hit at the TIC cannot be known without track reconstruction.
91

Chapter 7. Physics analysis
When the event includes more than one positron, the likelihood analysis will be biased bycorrelations, i.e. not all the pairs of γ-ray and positron are independent in such a case. We apply
a selection with a variable which indicates goodness of the track reconstruction.
P = −51 rad−1 × σ0φe −185 rad−1 × σθ0 e −4.19 MeV−1 × σ0Ee −0.033×χ2+0.224× Nhit, (7.1)
d.o.f.

where χ2 is fitting chi-square, and Nhit is the number of hits associated to the track.
The positrons are ranked with P, and the positron of highest P is selected. The selection
eliminates ghosts which are additional track candidates reconstructed near a real positron track.
The real signal positron is sometimes rejected by the accidental pile-up with higher P, but theprobability of such a case is negligible.
We set a blind box in order to avoid human bias. Before the calibration and the analysis
methods are finalized, we cannot access the data inside of the blind box. The 2009-2011 data
which were already unblinded in the previous analysis. However, the data were blinded again
after process with the renewed reconstruction algorithm. The blind box is defined by• 48 MeV < Eγ < 58 MeV,
• |t eγ | < 1 ns,
and is also shown in Fig. 7.1.

7.2.2

Analysis region and side bands

We define the analysis region, where the likelihood fitting is applied, as follows.
• 48 MeV < Eγ < 58 MeV• 50 MeV < Ee < 56 MeV• |t eγ | < 0.7 ns• |θ eγ | < 50 mrad
• |φeγ | < 75 mrad
Figure 7.1 shows the projection of the analysis window to (t eγ − Eγ ) plane. The analysis
region is not so called a signal region but is wide enough to include the background events,
which is also estimated in the likelihood analysis. The size of the analysis window is determinedby the resolution for each observable. The width of the region is set from 5 to 20 times of theresolutions, in order not to lose signal events, and not to contain so many background events.
The width for φeγ is widened in this analysis (previously 50 mrad [13]), for the reason of thetarget issue written in Sec. 7.5.
The region out of the blind box is called sideband. The sideband data is used to determine
the parameters that are necessary for the physics analysis. The events with t eγ < −1 ns ort eγ > 1 ns are included in the negative or positive timing sideband. The timing sideband
data with Eγ > 40 MeV is used for extract the accidental background. The selection of|t eγ ± 2 ns| < 0.7 ns and the same criteria as the analysis window for the other observable areused to test the likelihood fit. The angle sideband is defined as the signal window except for theangle criteria 50 < |θ eγ | < 150 mrad or 75 < |φeγ | < 225 mrad, which is used for consistency
check.
The energy sideband of92

Chapter 7. Physics analysis• 40 MeV < Eγ < 53 MeV• 48 MeV < Ee < 53 MeV• |θ eγ |, |φeγ | < 300 mrad

60
1200

58

1000

56

events / bin

E γ (MeV)

events (a.u.)

is examined for the RMD dedicated study [90]. In the energy sideband, events from the RMD
are clearly seen which is suppressed in the analysis region. The number of the RMD is used todetermine the normalization. (Sec. 7.7)

Blinding Box

54
52

Negative
TimingSideband

Positive
TimingSideband

Analysis
Window

50

600

400

48
46
−3

800

200

EnergySideband

−2

−1

0

1

2

3
t eγ (ns)0Figure 7.1: The analysis region and sideband in (t eγ − Eγ )-plane. Top part is an 1D projection
to t eγ axis.

7.3

Likelihood analysis

7.3.1

Likelihood function

The µ+ → e+ γ search analysis in the MEG experiment is performed using a likelihood fit. The
basic likelihood function (L) is defined when the total number of event N is fixed as
L(X |θ) =NYp(x i |θ),

i

where
• x i : a set of observables found in i-th event x = (t eγ, Ee, Eγ, θ eγ, φeγ ),• X : an array of all of N sets of the observables (x 1, x 2, · · · , x N ),
93

(7.2)

Chapter 7. Physics analysis• θ : a set of unknown parametersand p(x i |θ) is a probability density function (PDF) which shows the probability to find x i undera condition of θ. p is normalized as the integration over all possible region of x to be 1. The
maximum-likelihood estimator, θ̂ is defined such that maximizes the likelihood function with agiven set of observations.
Although Eq. (7.2) is a basic definition of the likelihood function, we adopted the "extended
likelihood function" [91] written as Eq. (7.3) for our µ+ → e+ γ search analysis. That is because
in the MEG experiment, the number of signal events itself is one parameters to be estimated.
N

L(X |θ) =obs
N Nobs e−N Yp(x i |θ),Nobs !
i(7.3)

where Nobs is the number of events found in the analysis region. The statistical fluctuation of
number of the signal in Poisson distribution is considered.
We set θ for the number of events of the signal (Nsig ), the radiative muon decay (NRMD ) andthe accidental background (NACC ). In addition, we introduce nuisance parameters according to
the study about the target deformation (t), namelyθ = Nsig, NRMD, NACC, t .
(7.4)
The N in Eq. (7.3) and parameters in Eq. (7.4) have a relation of N = Nsig + NRMD + NACC .
The PDF p(x i |θ) can be written as,
Nsig
NRMD
NACC
· S(x i, t) +· R(x i ) +· A(x i ),
(7.5)
N
N
N
where S(x i, t), R(x i ) and A(x i ) are the PDF for signal, RMD and accidental background,respectively and are normalized for each. Then the likelihood function is described considering
constraints for NRMD , NACC and t as,p(x i |θ) =L(X |Nsig, NRMD, NACC, t)

(7.6)

Nobs
Y
Nsig
NRMD
NACC
N Nobs e−N
C(NRMD, NACC, t)
S(x i, t) +R(x i ) +A(x i )=
Nobs !
N
N
N
i

!

N

obs 
Y

e−N
=
Nsig S(x i, t) + NRMD R(x i ) + NACC A(x i )C(NRMD, NACC, t)
Nobs !
i

The constrain function C has a form of Gaussian distribution
C(NRMD, NACC, t) = exp *−,2(NRMD − µRMD ) 2 +*− (NACC − µACC ) + c(t),
exp
2
2
2σRMD
2σACC
,
-

(7.7)

where µx and σx (x = NRD or ACC) are respectively the average and error of the NRMD or NACC
estimated in the sidebands. The last term c is the constraint for the target parameter, whose
detail is explained in Sec. 7.5.
94

Chapter 7. Physics analysis

7.3.2

Fitting and the confidence region

The best fit value for θ is obtained by searching for θ̂ which maximizes the likelihood function.
The confidence interval is computed with the unified approach by Feldman and Cousins [92]with the profile-likelihood ordering [30]. The following test statistic is calculated on the data,
as a function of Nsig .
qdata (Nsig ) = −2 ln λ(Nsig )L(Nsig, N̂ˆRMD (Nsig ), N̂ˆACC (Nsig ), ˆt̂ (Nsig ))λ(Nsig ) =L( N̂sig, N̂RMD, N̂ACC, t̂)

(7.8)
(7.9)

ˆ sig ) are the best estimate
where x̂ is the best estimate when all parameters are free, while x̂(Nunder the condition of fixed Nsig .
Then, an ensemble of toy-MC is generated. It is not normal a Monte Carlo but is just to
simulate observables considering the spectra, the detector response and the uncertainty, and thecorrelations between them are also considered. The number of events can fluctuate following
Poisson distribution around the fixed Nsig , and expected number of NRMD and NACC . For every
event, one set of observables is randomly selected from the PDF of corresponding type of event.
In order to consider the systematic uncertainty, a set of uncertainty is randomly selectedaccording to the list at the beginning of toy-MC (one set of value is common in one toy), and theuncertainties are included to observables. The considered uncertainties in the generation are,the target alignment parameter (position and shape), Eγ scale, Ee bias, the center of signal t eγ
PDF, the shape of PDF and the correlation between errors of positron observables. The impactof the systematic error on the result will be shown in Sec. 8.1.2.
For each toy-MC, qMC (Nsig ) are calculated in the same way as in Eq. (7.9), and qdata (Nsig )and the distribution qMC (Nsig ) are compared. If the Nsig where
qdata (Nsig ) < qMC (Nsig )(7.10)

is satisfied in more than (1 − X )% of toy-MC were found, the upper or lower limit of X%
confidence level can be set.

7.4

PDF

The formalism of the probability density function is explained in this section. As introducedin Sec. 7.3.1, there are three types of PDF: S, R and A which represents signal, radiative muon
decay and accidental background, respectively.

7.4.1

Signal PDF

The signal PDF can be factorized into five factors, (1) Energy of γ-ray, (2) Energy of e+ (3)Time difference of the e+ and γ, (4) and (5) Angular difference between e+ and γ in θ and φ.
i.e.
95

Chapter 7. Physics analysis

S(Eγ, Ee, t eγ, θ eγ, φeγ |r γ, r e, σ0Ee, σθ0 e, σ0φe, σ0r e, φe, q e, t) =(7.11)

S1 (Eγ |r γ )×S2 (t eγ |Eγ, Ee, σ0Ee, q e )×
S3 (Ee |σ0Ee, φe )×
S4 (θ eγ |r γ, r e, Ee, σ0Ee, σθ0 e, σ0r e )×
S5 (φeγ |r γ, r e, θ eγ, Ee, σ0Ee, σθ0 e, σ0φe, σ0r e, φe, t),where r γ is the first conversion point of the gamma-ray, r e is the decay point of muon, and q e
is a set of the variable to indicate the quality of the positron tracking.
7.4.1.1

Signal Eγ PDF

The signal Eγ is defined by the detector response to signal γ-ray, where the dependence on the γ
incident position is considered. The 54.9 MeV γ-ray in CEX calibration is used to evaluate thedetector response. The extraction of PDF is as shown in Sec. 5.2. The position dependence isintroduced by subdividing the acceptance as shown in Fig. 7.2, and each section has four regions
for w (depth) direction. (w < 0.8 cm), (0.8 < w < 3 cm), (3 < w < 8 cm) and (8 < w cm).
The division is so determined that area of different response to be different region, keeping therequired statistic per region. In the areas of the same color in Fig. 7.2, the data are combined
because the response of the detector is similar.
7.4.1.2

Signal t eγ PDF

The PDF for the relative timing of γ-ray and positron is evaluated with the radiative decay
peak by fitting the distribution of the relative timing in Eγ sideband data with two Gaussianfunctions and a constant. The constant term is added to fit the accidental pile-up and is notincluded in the signal PDF. The PDF is categorized into 6 types by "Positron Category" (HQ,
LQ) which represents the goodness of the positron trajectory estimation [77], and DCH-TIC
matching quality which was explained in Sec. 3.3.2. The result of t eγ fitting is shown in Fig. 7.3.
Ee correlation There is a correlation between t eγ and Ee . As shown in Fig. 7.4, we extracted
the correction parameter from signal Monte Carlo. The slope is 52.81 ± 1.6 ps/MeV.
Eγ correlation Since the LXe timing resolution depends on the number of the scintillation
photons, the error of estimation of Eγ scale affects the t eγ PDF. The effect is considered when
including the systematic error.
7.4.1.3

Signal Ee PDF

The positron energy response is evaluated as described in Sec. 5.3. The signal Ee PDF is defined
as resolution function corrected with window function. As we adopt the event-by-event PDF,
96

ǀ

Chapter 7. Physics analysis

ƵFigure 7.2: A map which shows the division of γ-ray acceptance in u−v plane. Thin dashed lines
show the border of the area corresponding to each PMT. The response for signal is calculated
for each area in this map, the areas of the same color are combined.
the resolution is written by a product of sigma of pull (s, fixed value which is determined fromcalibration) and per-event error σ0 (introduced in Eq. (3.12)).

(Resolution)i = f core · G(µcore, score σ0Eei ) + (1 − f core ) · G(µtail, stail σ0Eei ),(7.12)

where G(a, b) means a Gaussian distribution whose mean is a and standard deviation is b.
Then the correlations of Ee with θ e and φe are corrected. Finally, the corrected function ismultiplied with the "window" function that simulates the effect due to the analytical region cutof t eγ , θ eγ and φeγ . The window function is obtained by fitting Ee distribution of toy-MC withand without region cut for t eγ , θ eγ and φeγ . An typical example of the window function is shownin Fig. 7.5.
The errors in the fitting are introduced as a covariance matrix. For the signal PDF, thecorrelation among f core , µtail and σtail are taken into account.
97

Probability density

Chapter 7. Physics analysis

3.5
3

MQ0, LQ

MQ0, HQ

MQ1, LQ

MQ1, HQ

MQ2, LQ

MQ2, HQ

2.5
2
1.5
1
0.5
0

−1

−0.8 −0.6 −0.4 −0.2

0

0.2

0.4

0.6

0.8
1
t eγ (ns)Figure 7.3: t eγ PDF of individual 6 categories for 2012 data. HQ and LQ show high and low
quality of positron track fitting. MQ means matching quality between DCH and TIC, and (MQ0,
MQ1, MQ2) means (good, middle, bad) matching.

Figure 7.4: The correlation in Ee and t eγ for MC signal events. The correlation parameter is
extracted by a linear fit on this distribution.
7.4.1.4

Signal θ eγ PDF

The θ eγ PDF is formed by per-event scheme. The detailed method to include the correlation in
the per-event PDF can be found in [77]. The correlation between y coordinate of vertex and
Ee is corrected with the following formula. We extract the correlation parameter pye Ee from the
double-turn positrons.
µδye = pye Ee δEe98(7.13)

(with cut) / (without cut)

Chapter 7. Physics analysis

1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0

50

51

52

53

54

55
56
Ee (MeV)Figure 7.5: Event ratio of toy-MC with and without region cut is shown with line and statistic
error. The window correction function for Ee PDF is shown with the red line (year 2009).
The correlation between z and θ e is also introduced. However the correlation is not directly
used to shift the center of peak, but to correct the positron resolution. The θ resolution for
positron: σθe is then calculated as,q2σθe = σcore+ σθ2e + 2σθe Czθ .
(7.14)The resolution of θ eγ is finally calculated by adding σθγ quadratically to the positron resolution.
The σθγ is composed of core and tail part each u and w direction.
7.4.1.5Signal φeγ PDF

The φeγ PDF depends on the parameters which are shown in Eq. (7.11).
σφe dependence on φe The resolution of φe depends on φe itself, the dependence is incorporated in the pull of σφe as,vuut 1 − (c2 ) − 2c k tan(φ )/σφ φe
φe (0)
φ,(7.15)s φe inner = s φe min2
1 + k φ tan(φe )/σφe (0)where s φe min is the pull sigma where s φe is minimum. σφe (0) and k φ are extracted from the data,
while cφ is from MC.
φe and Ee correlation The φe center is shifted by the next formula.
p0Ee φe = qcφ − k φ tan(φe )σφe (0) + (k φ tan(φe )) 2

(7.16)

φeγ and θ e γ correlation The correlation between φeγ and θ eγ are corrected with p0φeγ θeγ which
is defined by a polynomial function as Eq. (7.17).
p0φeγ θeγ = a + bφe + cφ2e + dφ3e99

(7.17)

Chapter 7. Physics analysis
In summary, the center of the mean of φeγ is shifted by the formulaδ µφeγ = p0Ee φeσ0φeγ0δEe + pp0
θ eγ + E φ (pEe ye δEe ).
φeγ θeγ σ 0
σ0Ee
θ eγ
σ0φe

(7.18)E φ is a function to translate δye to δφeγ .
The resolution of φeγ is finally composed by combining the resolutions of φe , contribution
from the vertex position resolution and the φ resolution of LXe detector.
σφeγ =

q






02
2 s
0 , s σ0 + σ 202
s2φe inner σ02
1
−
ρ
1
−
ρ
+
F
σ
y
,inner
z
y
z
e
e
e
e
φe
z e φeφ
θ e φeφXEC ,(7.19)

where F is a function which convert the resolution of ye and ze to the resolution of φeγ , andσφXEC is the φ resolution of the LXe detector.

7.4.2

RMD PDFThe PDF for the RMD event is written as,
R(Eγ, Ee, t eγ, θ eγ, φeγ |r γ, r e, σ0Ee, σθ0 e, σ0φe, σ0r e, φe, q e ) =(7.20)R1 (t eγ |Eγ, Ee, q e )×
R2 (Eγ, Ee, φeγ, θ eγ |Eγ, Ee ).
7.4.2.1

RMD t eγ PDF

The t eγ PDF is the same as the signal PDF except for the t eγ − Ee correlation. The correlation
coefficient is measured from data and MC, but is found to be much smaller than that in signal.
It is understood by the fact that Ee is not fixed in the RMD event.
7.4.2.2

Physically correlated part

In RMD events, all of the energy of the γ-ray, energy of positron, relative angle between them
are correlated each other. The relation can be calculated using the standard model as,
dB(µ+ → e+ νe ν̄ µ γ) =(7.21)αdy
βdx dΩe dΩγ F (x, y, d) − β p µ · p̂ e G(x, y, d) − p µ · p̂ γ H (x, y, d) ,3y64π
where p µ is polarization of initial muon, p̂ is the unit vector of the vector p, d = 1 − β p̂ e · p̂ γ ,and the functions F, G, H are given in [9].
The theoretical spectrum is convoluted with the detector response function for each observable.
100Chapter 7. Physics analysis

7.4.3

Accidental background PDF

The PDF for the accidental background is defined as,A(Eγ, Ee, t eγ, θ eγ, φeγ |r γ, σ0Ee, φe ) =(7.22)A1 (θ eγ |uγ )×
A2 (φeγ |vγ )×
A3 (Ee |σ0Ee, φe )×
A4 (Eγ |r γ ).

The t eγ distribution in accidental background events should be flat and it is confirmed by
sideband analysis. Therefore, the t eγ factor for the accidental background is constant.
7.4.3.1

Accidental θ eγ and φeγ PDF

The PDF of the relative angle (θ eγ and φeγ ) is made from the timing sideband. The angularselection is loosened to gain data amount, and to fit the angular distribution in wider range. The
dependence on the position on the LXe detector is included by slicing data into 5(8) sections invγ (uγ ) for φeγ (θ eγ ) and fit them with a polynomial function of degree 5.
7.4.3.2

Accidental Ee PDF

The Ee PDF is extracted from the timing sideband, by fitting the spectrum with a fit function
which is a convolution of theoretical function, the acceptance function and the resolution functionof double Gaussian. The correlation in the event-by-event error is considered in systematic error.
The correlation matrix of each parameter is shown in Fig. 7.6.

0.5
σACC

1

0.0035-0.002854

0.0271-0.0147

0.03820.00351

0.0025-0.0237

0.0124-0.0312

0.4
0.3

µ

core

0.2
f core-0.002854

0.00251

0.2442-0.1180.2958s core0.0271-0.02370.24431

0.0632-0.16

s tail-0.0147

0.0124-0.1180.06321

0.4259

0.1
0
−0.1
−0.2
−0.3

µ

ACC

0.0382-0.03120.2958-0.16

0.4259

σACC

µcore

f cores cores tail

1

µ

−0.4
−0.5

ACC

Figure 7.6: Correlation among Ee PDF parameters, which is included in the systematic error.

101

Chapter 7. Physics analysis
7.4.3.3

Accidental Eγ PDF

There are two dominant source of the accidental γ-ray, RMD and AIF. In addition, a part of thecosmic ray remains after CR cut as discussed in Sec. 3.1.6. Figure 3.11 shows the Eγ spectrum
from RMD and AIF. A fraction of the RMD is 55% and the AIF is 45% when threshold is at
y = Eγ /Esignal = 0.9. In order to include the difference of the fraction of the source γ-ray andto include the position dependence of energy resolution, the accidental Eγ PDF is composed foreach section which is shown in Fig. 7.7.
The accidental background Eγ PDF is based on the observed energy spectrum. The spectrum
is fitted by Eγ template function which is composed by, (a) adding the RMD and AIF spectra, (b)smearing the spectrum to simulate pedestal, (c) convoluting a response function of Gaussian, (d)adding the CR spectrum, and (e) multiplying a function which simulates the trigger efficiency.
One of the fit results is shown in Fig. 7.8.

Ϭф ǁфϭ͕ ϭфǁфϮ Đŵ

ϰϯ

ϰϰ͕ϰϱ

ǀ

ǁхϮĐŵϱ ϳ ϵ ϭϭ ϭϯ ϭϱ ϭϳϭϵ Ϯϭ ϮϯϮϱ Ϯϳ Ϯϵϯϴ͕ϯϵϰ ϲ ϴ ϭϬ ϭϮ ϭϰ ϭϲϭϴ ϮϬ ϮϮϮϰ Ϯϲ ϮϴϯϬ

ϰϰ͕ϰϱ

ϰϮ

Ƶ

Figure 7.7: Division of the γ-ray acceptance in LXe detector for accidental background PDF.

102

Number of events/(0.4MeV)

Chapter 7. Physics analysis

104
103
102
10
1
10−1

45
0.045

50
0.05

55
60
0.055
0.06
Energy (MeV)

Figure 7.8: Example of Eγ fit on year 2012 data. The green line shows sum of RMD and AIF.
The blue shows green convolved with pedestal pile-up. The black line is contribution fromcosmic ray. The red line is total fitted function which is sum of blue and black.

7.5

Target Alignment

As concluded in Sec. 4.4, the target bowing is confirmed with the consistent results from three
independent measurements. The positron momentum and vertex position are corrected by themethod shown in the section.
The shift of the observable φeγ mainly comes from the shift of φe in Eq. (4.12). The shift ofthe decay point (∆x e, ∆ye, ∆ze ) does not affect reconstruction of φeγ significantly, because we
select almost back-to-back positron and γ-ray, hence the contribution from the shift of vertex
cancels out. The effect by the shifts of the any observables on θ eγ is not significant.
The target position uncertainty in zt axis and local deformation which is seen with FARO
scanner still remains as the source of the systematic uncertainty. The uncertainties are taken
into account by profiling. We introduce two nuisance parameters for each year. The parameters
are pi and si to indicate the uncertainty of global shift and local shape respectively. (i indicatesthe year.) These parameters are used to shift the center of φeγ PDF. This shift is done after all
corrections shown in Sec. 7.4.1.5.
µφ = ∆ p φeγ (p, φe ) + [∆FARO φeγ (x e, ye ) − ∆para φeγ (x e, ye )] · s(7.23)∆FARO is scaled for each year according to the fitted curvature of paraboloid. When s = 1, thePDF follows the shape observed by FARO scanner. On contrary, the PDF follows paraboloid
when s = 0.
Finally, the PDF for θ eγ and φeγ including the nuisance parameters can be written as,
P(θ eγ, φeγ ) = G(θ eγ ; µθ (p, s), σθ ) · G(φeγ ; µφ (p, s), σφ ) · P(p) · P(s),(7.24)

where G(x; µ, σ) shows a Gaussian distribution, P(p) and P(s) are PDF for the nuisanceparameters p and s to determine the region to be fitted and uncertainty. We assigned a Gaussian
PDF for p with mean of 0 and year-dependent σ according to the accuracy of the reliability
103

Chapter 7. Physics analysisof the target hole analysis. For the shape parameter s, constant distributions are assigned, andthe range of the distribution is 0 to 1 for year 2013 data, while a narrower range is assigned for2009-2012 data, as the deformation is not visible for 2009 and 2010 data, and the deformation isthought to gradually progressed. The parameters for the P(p) and P(s) are shown in Table 7.1.
Table 7.1: PDF parameters for p global shift and s the parameter for shape
Year
2009
2010
2011
2012
2013

7.6

p σ (mm)
0.3
0.3
0.3
0.3
0.5

Range of s[0, 0.1][0, 0.1][0, 0.4][0, 0.5][0, 1.0]

AIF reduction

The AIF which was described in Sec. 3.5 is newly introduced in physics analysis. For the events
where AIF candidates are found, the "distance" is calculated. If the distance is smaller than thecertain threshold, the event is discarded from the likelihood analysis.

7.6.1

Definition of the distance

There is structure with two peaks in ∆θ AIF − ∆φAIF distribution, and the size and shape of
the peak differ from year to year. In order to treat the nearness in common scale, we defined
the distance in the AIF analysis, based on Mahalabinos distance (a distance considering thecorrelation in multi-dimensional space).
D = Min(D1, D2 )f
g1
Di = (x − c i )T Si−1 (x − c i ) 2 ,(7.25)(7.26)

where i = 1, 2 indicate peaks of type-A and B events, x = (∆θ AIF, ∆φAIF ), and c shows the
positron of the peak, and S is a matrix which shows spread of the distribution. The Mahalabinos
distance is normalized with the width of the distribution. If the distribution has no correlation
and Gaussian shape for each axis, D = 1 means the distance of σ from the peak. The parametersc i and S are determined by fitting the data in the timing sideband. The fitting is performed forthe data with• 48 MeV < Eγ < 58 MeV,
• 50 MeV < Ee < 56 MeV,
• |θ eγ |, |φeγ | < 200 mrad,• |∆t AIF | < 50 ns.
The angular cut is loosened in order to collect more data. It is known that, when the φeγ cut
is loosened, the shape of ∆φAIF distribution changes.
104Chapter 7. Physics analysis
However, this fit is used just to parameterize the shape of the distribution and define the cut
threshold, so an excellent agreement between the fitting function and the data distribution is notnecessary. It is found that in the range of 200 mrad, the distribution still shows the similar shape
to that for the final analysis range of 75 mrad. The fitting function is defined as,F (∆θ AIF, ∆φAIF ) =3X

ai Gi(2)

i=1
3
X

!
1
T −1
exp − (x − c i ) Si (x − c i ) ,
=
ai
2
2π
|S
|
i
i=1
1
√

(7.27)

where i = 1, 2, 3 show components of type-A, B peaks and base and G (2) is Gaussian distribution
with correlation in 2D space (is defined in the second line). There are 3 components times 6
parameters, i.e.
!
α γ
0 0 T
a, c = (θ , φ ) , S =.
(7.28)
γ β
√ −1
√ −1
α and β corresponds σ in ∆θ AIF and ∆φAIF axis.

7.6.2

Fit parameters

Figure 7.9 and 7.10 shows the result of the fit for each year. The fraction of the type-A, B, baseand the fraction not to find any AIF candidate is summarized in Table 7.2.

Figure 7.9: Fit result on sideband data of each year. The fitted function is shown with contour.
105

Chapter 7. Physics analysis

5000

year 2009

4000

year 2010

6000

5000

10000

4000

8000

3000

6000

2000

4000

1000

2000

3000

year 2011

12000

2000

1000

0

−40

−20

0

0

20
40
∆θAIF (deg)

−40

−20

0

20
40
∆θAIF (deg)

0

−40

−20

0

20
40
∆θAIF (deg)

−40

−20

0

20
∆φ

4500
3000

10000
4000

2500

3500

8000

3000
2000
6000

2500
1500

2000
4000

1500

1000

1000

2000

500
500
0

−40

−20

0

20
∆φ

AIF

0

40
(deg)

−40

−20

0

AIF

year 2012

18000
16000

20
∆φ

40
(deg)

0

AIF

40
(deg)

year 2013
12000

14000

10000

12000
8000

10000
8000

6000

6000

4000

4000
2000

2000
0

−40

−20

0

20
40
∆θAIF (deg)

0

−40

−20

0

20
40
∆θAIF (deg)

−40

−20

0

20
∆φ

14000
10000
12000
8000
10000
8000

6000

6000
4000
4000
2000
2000
0

−40

−20

0

20
∆φ

AIF

40
(deg)

0

AIF

40
(deg)

Figure 7.10: Projection of 2D fit to ∆θ AIF and ∆φAIF for each year. The data and fitted function
are shown with black and blue lines, respectively.

106

Chapter 7. Physics analysis
Table 7.2: Fraction of the fitted peak and events out of the selection. f 1 , f 2 , f base , f out and f noAIF
means the fraction of type-A, type-B, base, out of the boundary and no AIF events, respectively.
The numbers are shown in percentage.
Year
2009
2010
2011
2012
2013

f1
4.1 ± 0.1
1.5 ± 0.03
1.2 ± 0.02
1.4 ± 0.02
1.7 ± 0.03

f2
f base3.1 ± 0.1 32.0 ± 0.3
1.5 ± 0.03 33.6 ± 0.2
1.3 ± 0.02 36.2 ± 0.1
1.5 ± 0.03 35.3 ± 0.1
1.8 ± 0.03 38.3 ± 0.2

f out
44.5 ± 0.4
46.4 ± 0.3
43.3 ± 0.2
46.3 ± 0.2
45.6 ± 0.2

f noAIF
16.3 ± 2.4
17.0 ± 1.9
18.0 ± 2.1
15.4 ± 2.1
12.6 ± 2.0

Ϭ͘Ϭϲ

ϯ

Ϭ͘Ϭϱ

Ϯ͘ϱ

Ϭ͘Ϭϰ

Ϯ

Ϭ͘Ϭϯ

ϭ͘ϱ

Ϭ͘ϬϮ

ϭ

Ϭ͘Ϭϭ

Ϭ͘ϱ

Ϭ
Ϭ͘ϵϲ

Ϭ͘ϵϳ

Ϭ͘ϵϴ

'ͬƐŝŐŶĂů

'ƌĞũĞĐƚŝŽŶ

Since the timing sideband only includes accidental background, the fitted result is what
actually expected for the accidental background in the analysis window. The information of
the timing is different, but it is not used in calculation of the distance. Figure 7.11 shows theefficiency to reject accidental background and acceptance of the signal. The efficiencies ofeach year are shown in Table 7.3. The way to estimate efficiency for signal is described inAppendix B. As the signal inefficiency of more than 1%, which is the same as that for CR cut
in LXe, is not acceptable, and the BG/signal ratio is relatively flat there, the cut threshold is set
to be 0.7σ (blue circle in Fig. 7.11).
The sensitivity was examined with and without the AIF cut, and it is shown that the cut does
not significantly improve the sensitivity. However, the AIF event possibly lie in the signal region
accidentally. The cut is applied for just to avoid such an outlier event.

Ϭ
Ϭ͘ϵϵ
ϭ
^ŝŐŶĂůĐĐĞƉƚĂŶĐĞ

Figure 7.11: Black marker shows relation of the signal acceptance and BG rejection with various
cut thresholds. The cut at the blue circle is adopted. Red marker shows the ratio of BG against
signal as a function of signal efficiency. Data of the all years are summed.

7.7

Normalization

Since the result of the likelihood fitting provides the number of the signal event, we need toconvert it to the branching ratio of the µ+ → e+ γ decay. We defined the normalization factor k107

Chapter 7. Physics analysis
Table 7.3: Selection inefficiency by the AIF cut. The numbers show fraction in percentage.
Year
2009
2010
2011
2012
2013
Old
New
Full

ACC
signal/RMD
1.00 ± 0.03 3.00 ± 0.20
0.64 ± 0.02 1.33 ± 0.09
0.61 ± 0.01 1.34 ± 0.10
1.46 ± 0.02 2.23 ± 0.11
1.30 ± 0.02 2.22 ± 0.11
0.68 ± 0.01 1.57 ± 0.06
1.39 ± 0.02 2.23 ± 0.08
1.05 ± 0.01 1.94 ± 0.05

as follows,Γ(µ+ → e+ γ) Nsig
(7.29)=
Γtotalk
The normalization factor is regarded to be the number of the muon multiplied by detector
acceptance and efficiency, k = N µ × Ω × ε. (N µ is the number of all muons which stopped on
MEG target.) The inverse of factor, k −1 is equivalent to a single event sensitivity in the box
counting scheme (though we do not adopt that analysis scheme). We calculate the normalization
factor from two independent samples and combine them to reduce the uncertainty.
B(µ+ → e+ γ) =7.7.1

Michel normalization

One method is to calculate the normalization from the number of Michel decay events withfollowing formula.
eγεe
N Michel PMichel
eγ
eγ
eγ
eγ
× Aγ × ε γ × ε trg × ε sel,k Michel = Michel × Michel × Michel
f Ee
ε trg
εe

(7.30)• NMichel : The number of observed event in analysis window, for data taken with Michel
trigger, which requires only hits in TIC. NMichel = 245860 is the number which areobserved in the full data set.
• f EMichel: The fraction that the energy spectrum of the Michel positron within the analysisewindow.
• PMichel : (= 107 ) The pre-scaling value of the Michel trigger. See Sec. 2.5.2.
•  Michel: The correction factor to recover trigger live time, where paralyzable behavior ofetrigger is assumed.
ee• ε signal/ε Michel: The ratio of efficiencies of the positron spectrometer for signal and Michel
events. It is obtained to be 1.149 ± 0.017, by fitting response function which is thetheoretical Michel spectrum convoluted with the detector resolution and the acceptancefunctions.
eγ• Aγ : (= 0.985 ± 0.005) The geometrical acceptance for γ-ray when a signal positron isdetected.
eγ• ε γ : γ-ray detection efficiency which is described in Sec. 5.5.1.
eγ• ε trg : The efficiency to trigger positron–γ-ray pair for signal events. It is calculated to be
0.91 ± 0.01 from 2009 to 2010 and 0.96 ± 0.01 after 2011. (Also see Sec. 5.5.3)
108Chapter 7. Physics analysis• ε sel : This term includes the selection efficiency calculated from (a) efficiency that signal
event comes within the analysis window. It is evaluated with signal PDF. (b) missreconstructed positron track, missing turn. (Sec. 3.2.2) (c) signal inefficiency due to AIF
rejection (Sec. 7.6 and Appendix. B). The efficiency is 0.943 ± 0.010 in total of (a)-(c).
In total, the uncertainty on kMichel is 4.5%.

7.7.2

RMD normalization

The normalization factor from RMD is calculated as,
signalsignalsignalsignal
ε trg
ε sel
εγ
NRMD ε ekRMD = RMD × RMD × RMD × RMD × RMD .
BEe
εe
εγ
ε trg
ε sel

(7.31)

Since RMD contains also γ-ray, more terms can be written as the ratio between signal and
RMD and it helps to reduce systematic uncertainty from normalization factor. The definition of
the parameters are,
• N RMD : The number of observed RMD events, the trigger is the same for MEG signal,
but analysis window is different (Sec. 7.2.2). The number is obtained by fitting on the t eγ
distribution.
• B RMD : (∼ 4.9 × 10−9 ). The branching ratio of muon decays into RMD with the range ofkinematics. It is calculated from the theoretical formula by standard model.
• positron efficiency : Ee dependent detection efficiency is extracted from the Michel
spectrum, Ee dependence of the missing turn probability is considered in this factor.
• γ efficiency : Energy dependent γ detection efficiency is calculated from the data withdifferent Eγ threshold. The effect by muon polarization, which makes asymmetric angular
distribution, is taken into account here.
• other differences in efficiency : Inefficiency by direction matching for RMD is evaluatedfrom accidental background. The window efficiency for the timing of RMD is the sameas signal, so the difference in efficiency on angular window is taken into account. The
inefficiency by the AIF rejection is thought to be equivalent to signal and to RMD, therefore
no correction term is needed for that.
The number of muons is evaluated in 12 independent bins (3 bins for Ee and 4 bins for Eγ ),and the best value was obtained with χ2 fitting to be 29950 ± 527 in the full data set. Figure 7.12
shows the distribution of observed events in the energy sideband, projected on Eγ and Ee , theexpectation from the standard model is superposed. The measured number is consistent to the
expectation within 5% error. The details are described in our another publication [90]. Total
uncertainty for k RMD is 5.5%.

7.7.3

Combination

The two methods of the normalization uses different data, hence the uncertainties of normalization can be reduced by combining them. The combination is done by averaging the values
with weighting by errors. The result is shown in Fig. 7.13. The results from Michel and RMD
are in good agreement, the breakdown for each year is summarized in Table 7.4, and the final
normalization factor for 2009-2013 combined data is k = (1.71 ± 0.06) × 1013 .
109

Number of events

Number of events

Chapter 7. Physics analysis(a)
43 <E γ< 53 MeV|θ eγ| < 0.3 rad|φeγ| < 0.3 rad

4000

(b)

4000

48 <E e< 53 MeV|θ eγ| < 0.3 rad|φeγ| < 0.3 rad

3000
2000

2000

blinded

1000
0
48

49

50

51

0

52
53
E e (MeV)

44

46

48

50
52
E γ (MeV)N µ / 1012

Figure 7.12: Number of observed RMD events in sideband year 2009-2013 projected on (a) Eeand (b) Eγ . The data is plotted with marker and error. Expectation with theoretical calculationof the lowest order SM with the detector response is shown in yellow band.

5
4
3
2

Michel
RMD

1Combined

0

2009

2010

2011

2012 2013
Dataset (Year)

Figure 7.13: Calculated normalization factors from Michel (Red), RMD (Blue) and combined
result (Black).

110

Chapter 7. Physics analysis

Table 7.4: Summary of normalization constant.
Year
2009
2010
2011
2012
2013
Old
New
Full

k Michel (×1012 )1.18 ± 0.05
2.73 ± 0.12
4.19 ± 0.19
5.32 ± 0.24
3.70 ± 0.17
8.10 ± 0.36
9.02 ± 0.41
17.12 ± 0.77

k RMD (×1012 )1.20 ± 0.11
2.53 ± 0.24
4.52 ± 0.39
5.33 ± 0.46
3.55 ± 0.28
8.27 ± 0.55
8.85 ± 0.53
17.10 ± 0.94

111

k Combined (×1012 )1.18 ± 0.05
2.69 ± 0.11
4.26 ± 0.17
5.32 ± 0.21
3.66 ± 0.14
8.16 ± 0.30
8.96 ± 0.33
17.11 ± 0.60

Chapter 7. Physics analysis

112

Chapter 8
Results
8.1

Sensitivity

The search sensitivity is given by the median of the 90% C.L. upper limits observed in the
many pseudo experiments with a background-only hypothesis: in generation, Nsig is fixed to
be zero, NACC and NRMD are randomly fluctuated around the expectation value by Poisson
distribution. The procedure to calculate the upper limit is as explained in Sec. 7.3.2. The
systematic uncertainties (It will be discussed in Sec. 8.1.2) are included in the calculation of theupper limit.

140
120
100
80
60
40
20
0
0

5

10

×10−1315
20
Upper limit

Figure 8.1: The distribution of the ULs of pseudo experiments. UL in Nsig is converted to that inbranching ratio, with the normalization factor which was explained in Sec. 7.7. Vertical dashedline shows median which represents the sensitivity. Two arrows show the upper limits obtained
from the timing sidebands.
Figure 8.1 shows the distribution of the upper limit (UL) for pseudo experiments for 20092013 combined, full dataset. The horizontal axis is shown in branching ratio. The sensitivity
for the full, old and new data are 5.3 × 10−13 , 8.0 × 10−13 and 8.2 × 10−13 , respectively.
The sensitivity with new statistics has worse sensitivity despite more data amount. It isdue to worse positron angle resolution, and the larger uncertainty of the target parameter. We
already analysed 2009-2011 dataset in our last publication [13] with the sensitivity 7.7 × 10−13 .
The sensitivity for 2009-2011 data presented here is slightly worse than that presented in the113

Chapter 8. Results
previous publication even though the analysis method was improved. The main reason for thisdegradation is that more conservative uncertainty is assigned for the target alignment also for
2009-2011 data where an obvious target deformation was not observed.

8.1.1

Results in the sidebands

For the purpose of the sanity check of our likelihood analysis, a likelihood analysis on the timing
sideband is performed. The timing sideband is defined as the same selection for analysis window
except for the timing (Sec. 7.2.2). In the timing sideband, the data can essentially be regarded
as pure accidental background. The likelihood function is modified for the timing sideband in
two points. (a) The constraint term for the NRMD is removed. (b) The definition of t eγ in PDF is
shifted.
The fit results are shown in Fig. 8.2 and Table 8.1. The projected PDF spectra agree to data
spectra. The best fit Nsig and NRMD , which are expected to be null, are zero consistent within
the statistical error.
The confidence interval for the branching ratio is calculated. The upper limits for thenegative (−2ns) and positive (+2ns) sidebands in the full combined datasets are 8.4 × 10−13 and8.3 × 10−13 . They are consistent with the sensitivity as shown in Fig. 8.1.
Table 8.1: Best fit value and fit error in the timing sidebands.
negativetiming(−2ns)
positivetiming(+2ns)

8.1.2

Data set
Full
Nsig
2.8 ± 5.8
39 ± 45
NRMD
NACC
7756 ± 38
Nsig
3.9 ± 4.6
17 ± 45
NRMD
NACC
7736 ± 38

OldNew
7.3 ± 5.2 −3.7 ± 2.1
46 ± 32−3.7 ± 32
3475 ± 26 4281 ± 28
1.0 ± 3.1
2.8 ± 3.6
21 ± 31−3 ± 32
3468 ± 26 4268 ± 28

Systematic error

The systematic uncertainties considered in the analysis are the alignment of γ-ray and positrondetectors, the alignment of the muon stopping target, the γ-ray energy scale, the positron energybias, the center of the t eγ PDF, the shapes of signal and background PDFs, the correlations
between the errors of the positron observables and the normalization factor.
The largest systematic uncertainty comes from the alignment of muon stopping target; itdegrades the average sensitivity by 13%, while the effect from all the other systematics is lessthan 1%. The breakdown of the systematic errors is listed in Table 8.2.

8.2

Results in analysis window

8.2.1

Event distributions

Figure 8.3 shows the event distributions in the analysis window. In order to avoid the window
is too much crowded, selections of cos Θeγ < −0.99963 and |t eγ | < 0.24 ns are applied for
114

102

10

1

−2.6

−2.4

−2.2

−2

−1.8

−1.6

−1.4

(b)

103

102

1

1

51

52

53

54

102

55

56

48

103

(e)
102

1

1

1

20

30

40

52

53

54

55

−60

50

56

57

58

(f)

102

10

10

51

103

10

0

50

E γ (MeV)

10−50 −40 −30 −20 −1049E e (MeV)

events / 3.0 (mrad)

events / 2.0 (mrad)

(d)

102

10

50

(c)

103

10

t e γ (ns)103

events / 0.4 (MeV)(a)

events / 0.6

103events / 0.24 (MeV)

events / 56 (ps)

Chapter 8. Results

−40

−20

0

20

40

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60

−8

−6

−4

−2

0

2

φ e γ (mrad)θ e γ (mrad)

4

R sig

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10

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2.6

(b)

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(e)
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(d)

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t e γ (ns)103

events / 0.4 (MeV)(a)

events / 0.6

103events / 0.24 (MeV)

events / 56 (ps)(a) Negative Timing Sideband (−2.7 < t eγ < −1.3ns)

−60

−40

−20

0

20

40

60

−10

φ e γ (mrad)θ e γ (mrad)

−8

−6

−4

−2

0

2

4

R sig

(b) Positive Timing Sideband (1.3 < t eγ < 2.7ns)

Figure 8.2: Result of the fitting on the timing sidebands for the full dataset. The projection on
the main observables and Rsig (Sec. 8.2.2). The parameters f R and f A are set to be 0 and 1, in
calculation of the Rsig .
115

Chapter 8. Results
Table 8.2: The list of the considered systematic uncertainties. The impact of the target isdominant. The fractions of impacts of the other uncertainties are written in parentheses.
Element
Impact on sensitivity
Alignment of muon stopping target 13%
All the other<1%
Alignment of LXe detector - tracker (37%)
Eγ scale(23%)
bias of center of t eγ PDF(19%)
Ee bias(11%)
Normalization(7%)
errors in event-by-event PDF(3%)
left figures both with 90% efficiency for signal, and 51.0 < Eγ < 55.5 MeV and 52.4 < Ee <55.0 MeV are applied for right figures with 74% and 90% efficiency, respectively. The contoursof the averaged signal PDFs are also shown. An obvious correlated excess of signal is not foundin any datasets.

8.2.2

Highly ranked events

We rank the events in the order of the signal likelihood Rsig which is defined as
Rsig = log10!
S(x i ),
f R R(x i ) + f A A(x i )(8.1)

where f R and f A are ratio of RMD and accidental background which are taken from the best fit
values 0.07 and 0.93, respectively. The events with the highest Rsig are listed in Table 8.3.
Table 8.3: Highly ranked (signal like) events
Rank

Year

Run

Event

Rsig

1
2
3
4
5
6
7
8
9
10

2010
2012
2012
2012
2009
2012
2013
2011
2012
2010

77431
19518718915016073756081
167931228740123579185612
87743

1715
1856
1089
785
35
1076
1892
1318
1612
1484

3.01
2.70
2.41
2.31
2.26
2.25
2.23
2.23
2.18
2.15

t eγ
(ps)
142
-75
-6
48
-22
415
397
-21
13
-81

Ee
(MeV)
52.93
53.34
52.19
52.82
52.52
53.18
52.95
52.81
52.82
52.91

Eγ
(MeV)
53.98
51.74
52.95
51.92
52.81
53.78
50.55
55.13
55.41
52.28

θ eγ
(mrad)
-25.2
-0.1
10.6
8.3
-20.7
-7.7
-0.8
-33.6
12.9
-18.1

φeγ
(mrad)
-2.4
-9.2
16.6
6.1
15.8
-23.6
-5.7
13.0
-29.8
24.0

cos Θeγ-0.99968-0.99996-0.99981-0.99995-0.99967-0.99969-0.99998-0.99936-0.99948-0.99955

Figure. 8.4 shows the (Ee − Eγ ) and (cos Θeγ − t eγ ) plots for 10 events of highest signal-like.
Some events which are not drawn in Fig. 8.3 appear, as the selection defined in Sec. 8.2.1 is notapplied here. The contours show averaged signal PDF of 1σ, 1.64σ and 2σ, respectively.
116

58

t eγ (ns)E γ (MeV)

Chapter 8. Results

2
1.5

56
1
0.5

54

0
52

−0.5
−1

50

−1.5
48
50

51

52

53

54

−2
−1

55
56
E e (MeV)−0.9995−0.999−0.9985cosΘeγ58

t eγ (ns)E γ (MeV)(a) 2009-2013 dataset
2
1.5

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54

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52

−0.5
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50

−1.5
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56
E e (MeV)−0.9995−0.999−0.9985cosΘeγ58

t eγ (ns)E γ (MeV)(b) 2009-2011 dataset
2
1.5

56
1
0.5

54

0
52

−0.5
−1

50

−1.5
48
50

51

52

53

54

−2
−1

55
56
E e (MeV)−0.9995−0.999−0.9985cosΘeγ(c) 2012-2013 dataset

Figure 8.3: Event distributions observed in the analysis window. The signal PDFs are shownwith contour (1σ, 1.64σ and 2σ).

117

56

t eγ (ns)E e (MeV)

Chapter 8. Results

ϵ
ϴ

55

53

0.1

ϭ

ϱ

−0.1

52

ϰ

ϵ

ϰ
ϯ

0

ϭϬ

ϴ

ϱ

Ϯ

ϭϬ

−0.2

Ϯ

−0.3

51

−0.4

ϳ
50
51.5

ϲ

ϳ

0.2

ϲ
ϯ

0.4
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ϭ

54

0.5

52

52.5

53

53.5

54

−0.5
−1

54.5

−0.9998−0.9996−0.9994−0.9992−0.999cosΘeγE γ (MeV)

Figure 8.4: Top 10 highest signal-like events in (Ee − Eγ )- and (cos Θeγ − t eγ )-planes. Contours
show averaged signal PDF of 1σ, 1.64σ and 2σ.

8.2.3

Fit results

The maximum likelihood fitting was performed on the data in the analysis window. The best fit
value, ( N̂sig, N̂RM D, N̂ ACC ) for the all combined dataset is (−3.8±3.6, 624.6±28.4, 7739.1±37.7).
The errors are the fit error with MINUIT. With this best fit Nsig , the best fit branching ratio is(−2.2 ± 2.1) × 10−13 . The projections onto the 5 main observables are shown in (a)-(e) ofFig. 8.5.
The data and the fitted PDF shows good agreement. The agreement of fit is checked withthe variable Rsig . The comparison of data and the PDF on Rsig axis is shown in (f) of Fig. 8.5.
Table 8.4: Best fit value and fit error
Data set
Full
Nsig
7739.1 ± 37.7
NRMD
624.6 ± 28.4
NACC
−3.8 ± 3.6
p09
10 ± 297−83 ± 321p10
p11
−1 ± 297p12
8 ± 289p13−2 ± 499s09
0 ± 0.7s100 ± 0.5s11
1 ± 0.5s12
1 ± 1.0s13
0 ± 0.5

Old
3470.7 ± 25.2
284.6 ± 16.6
−1.0 ± 2.0
6 ± 300−32 ± 300
−1 ± 3000 ± 0.1
0 ± 0.1
1 ± 0.1

New
4269.0 ± 27.6
337.1 ± 17.8
−4.9 ± 4.4

11 ± 300−4 ± 500

1 ± 0.1
0 ± 0.1

The results for the other datasets are shown in Fig. 8.6 and summarized in Table 8.4. The
best fit value for target observables p and s are found by the fitting, but it does not imply thereal shape of the target, because only the signal PDF has a peak in φeγ and the best fit Nsig is
consistent with 0. No information for the true center of φeγ can be extracted from the observed
118

(a)

450
400
350
300

800

events / 0.4 (MeV)

events / 0.24 (MeV)

events / 56 (ps)

Chapter 8. Results

(b)

700
600

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E e (MeV)

events / 3.0 (mrad)

events / 2.0 (mrad)t e γ (ns)events / 0.6

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60

φ e γ (mrad)θ e γ (mrad)

−10

−8

−6

−4

−2

0

2

4

R sig

Figure 8.5: The 1D projections of the 2009-2013 combined data. The marker is data withstatistic error. The solid blue lines are sum of the best fit PDFs. The dashed magenta anddot-dashed red lines are accidental background and RMD PDF which are normalized to best fit
value of each component. The hatched green histograms show signal PDF scaled to 500 events.
data.

8.2.4

Upper limit for branching ratio

The confidence interval for the data is calculated with the procedure described in Sec. 7.3.2.
Figure 8.7(a) shows the negative log likelihood Eq. (7.9) as a function of the branching ratio.
The best fit value of the target parameter s shifts from one to another, when the branching ratio
moves over zero. This is the reason for the bending of the curve around zero. The results for the
all datasets are consistent with null-signal hypothesis, therefore only upper limits are defined.
In Fig. 8.7(b), the fraction of the toy-MCs which satisfies Eq. (7.10) are shown as the functionof the branching ratio. The 90% C.L. upper limits are obtained to be• 4.2 × 10−13 with 2009-2013 (full) data set,
• 6.1 × 10−13 with 2009-2011 (old) data set and• 7.9 × 10−13 with 2012-2013 (new) data set, respectively.
Our previous result with 2009-2011 data is 5.7 × 10−13 [13]. The previous limit is slightly
more stringent but is consistent when differences of the analysis are considered. Firstly since
the reconstructed observables were slightly changed because of the updates of the analysis,
the observed upper limit can be changed due to the statistical effect. Secondly the sensitivity
becomes worse as described in Sec. 8.1 due to the larger systematics.
119

(a)

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180
160
140

events / 0.4 (MeV)

events / 0.24 (MeV)

events / 56 (ps)

Chapter 8. Results

(b)

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250

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(c)

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events / 3.0 (mrad)

events / 2.0 (mrad)t e γ (ns)events / 0.6

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φ e γ (mrad)θ e γ (mrad)

4

R sig

(a)

250

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events / 0.4 (MeV)

events / 0.24 (MeV)

events / 56 (ps)(a) 2009-2011 dataset
(b)

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300

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events / 3.0 (mrad)

events / 2.0 (mrad)t e γ (ns)events / 0.6

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φ e γ (mrad)θ e γ (mrad)

−10

−8

−6

−4

−2

0

2

4

R sig

(b) 2012-2013 dataset

Figure 8.6: The 1D projections of (a) old and (b) new data. Notation follows Fig. 8.5. Normalization of the signal PDFs are 250 events for both (a) and (b).
120

5Confidence Level-2 lnλp

Chapter 8. Results

4

3
2

1
0.8
0.6
0.4

2009-20111

0.2

2012-20132009-20130

×10-13

−10

−5

0

0
0

5
10
Branching Ratio(a) The negative log likelihood as a function of the branching ratio. The point
where −2 ln(λ) = 0 shows the best fit
value.

2

4

6

×10−138
10
Branching Ratio(b) The confidence level as a function of the
branching ratio. 90% C.L. limit is defined by
the crossing point of curve and 0.9 horizontal
line.

Figure 8.7: Result of the limit calculation by maximum likelihood analysis.
The effect of the systematic uncertainty is studied with the observed data. The largest
contribution is the effect from the target uncertainty. The deterioration in upper limit is calculated
to be ∼ 5% for the full dataset. The other systematics are also considered, however, the impactof all the other systematics is less than 1%.

8.3

Check for the analysis

8.3.1

Comparison with previous analysis

The difference of the result between this and the previous analysis was studied. We havechanged the analysis method from the reconstruction level, so the main observables can moveevent-by-event. The changed item and affected observables are the followings.
• Drift chamber pad issue : There was a mistake in the treatment of the case of defective
cathode pad (Sec. 3.2.1). The hit position in z axis is fixed in track reconstruction, for hits
at defective channels. All of the positron observables are affected. For newer data, thesize of the effect is larger.
• Target alignment : The affected observable is mostly φeγ . The impact for the observable
is almost negligible for 2009 and 2010 data.
• LXe detector alignment : γ-ray position is affected. θ eγ and φeγ moves in all events.
• Missing turn : The fraction of the affected event is small. However if a missing turn isrecovered, the event moves out or in the analysis window.
• AIF reduction : If the AIF distance is less than the threshold, the event disappears.
We compared the current 2009-2011 combined dataset with the previous one. Out of theevents included in previous dataset, 14% go out from the analysis window, and 62% (of thenumber in the previous dataset) newly appeared in the analysis region. The reason of more
121

Chapter 8. Resultsappearance than disappearance is the current analysis window is widened. Figure 8.8 and 8.9
shows the comparison of the observables for the events commonly selected in previous andcurrent analysis.
102

102

10

10

1

1
-40

-20

0

20

-0.3 -0.2 -0.1

40ǻteȖ (ps)0

0.1 0.2 0.3
ǻEe (MeV)

01020ǻĳeȖ (mrad)

102
102

10

10

1

1
-20

-10

0

10
20
ǻșeȖ (mrad)

-20

-10

Figure 8.8: Change of the observables. (previous) - (current)

Current
Previous

Figure 8.9: Move of the observables in (Ee − Eγ )- and (cos Θeγ − t eγ )-planes. Only events of
the higher signal-likelihood are plotted.
The bias and the RMS of ∆t eγ , ∆Ee , ∆θ eγ and ∆φeγ are −4 ± 14 ps, −15 ± 79 keV,
−2.1 ± 3.8 mrad and −1.6 ± 5.8 mrad. Eγ is unchanged.
We performed a simulation of the change in the upper limit by the change of the reconstruction
with pseudo experiments which include both previous and current information. The difference122Chapter 8. Resultsin the average branching ratio upper limit simulated for 2009-2011 dataset has a spread of
4.2 × 10−13 in RMS. The observed shift in the data 0.4 × 10−13 lies within the spread.

8.3.2

Fitting without constraints

The constraint function C(NRMD, NACC, t) is dropped from Eq. (7.6) of likelihood function. The
other conditions are the same as the main likelihood analysis. This is another way to check theconsistency of the analysis. The fit result is shown in Table 8.5. The fitted number agrees withthe expected number within the statistical error.
Table 8.5: The expected and observed numbers of events in the analysis region.
Data set
Full
Nobs
8344
exp
NACC
7744 ± 41
fit
NACC
7684 ± 103
exp
NRMD
614 ± 34
fit
NRMD
663 ± 59

8.3.3

Old
New
3761
4583
3469 ± 28 4274 ± 31
3477 ± 70 4210 ± 75
284 ± 19 330 ± 20
285 ± 40 378 ± 43

Comparison with alternative analysis

We have prepared an alternative simplified analysis for cross check with the main event-by-event
PDF. It is called constant PDF, and the PDF parameters do not change for every event but there
are only several categories of the PDF parameters. The category is classified by the quality ofthe positron reconstruction and the first conversion point of the γ-ray. The angular observableΘeγ : stereo angle between momenta vector of positron and γ-ray (in degree) is used insteadof θ eγ and φeγ . A angular selection criteria for the analysis window is defined differently as
Θeγ > 176◦ . Figure 8.10 shows the data and the best fit PDF projected on observables Eγ , Ee ,Θeγ and t eγ .
The consistency between the main and alternative PDF is tested with common pseudo
experiments. The upper limits with the ensemble of the toy MCs under null signal hypothesis
are plotted in red dots in Fig. 8.11. The upper limits by two analyses show clear correlation, andthe sensitivity is found to be better in event-by-event PDF by ∼ 20%.
The best fit branching ratio by the maximum likelihood fitting with the constant PDF is−2.5 × 10−13 , and 90% C.L. upper limit is 4.3 × 10−13 . They show good agreement and it
is consistent with the correlation observed with the common pseudo experiments as seen in
Fig. 8.11. The best fit values of NACC and NRMD are 630 ± 66 and 7927 ± 148, while expectationfrom sidebands are 683 ± 115 and 7915 ± 96. Considering the difference in selection criteria,
the result is consistent with that with event-by-event PDF.

123

Chapter 8. Results

350

700
600

300

500

250

400

200

300

150

200

100

100

50

0
0.048

0.05

0.052

0.054

0
0.05

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0.058
Eγ (MeV)

0.051

0.052

0.053

0.054

0.055
0.056
Ee+ (MeV)

180
160

300

140

250

120
200

100

150

80
60

100

40
50

20
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0
176

177

178

179

0

180

Θstereo
(deg)
e+ γ

−0.5

0

0.5
∆Te+ γ (ns)×10Upper limt (constant PDFs)

Figure 8.10: Likelihood fit result with the constant PDF. The notations are the same as with
Fig. 8.5 as well as the scaling of the signal PDF.

20

×10−13

15

10

5

0
0

×10−135101520Upper limit (event-by-event PDFs)

Figure 8.11: Red dots show 90% upper limits of common toy MCs with event-by-event PDF(horizontal axis) and with constant PDF (vertical axis). The data is plotted with black starmarker, and it lays around center of the distribution.
124

Chapter 9
Prospects
We took data for 5 years, but the speed of the sensitivity improvement is slowing down. It isbecause the expected number of background is becoming non-negligible. When the experimentis background-free, the sensitivity improves in proportional to the data amount, while when the
average number of background is large, the sensitivity is proportional to the square root of thedata amount.
In order to achieve higher sensitivity efficiently, the increase of data statistics per unit timeor the improvement of rejection power of background are mandatory.

9.1

MEG II experiment

The MEG II experiment is an upgrade of the MEG experiment, aiming at one order of magnitude
higher sensitivity. The upgrade takes over the basic concept of MEG experiment, while almost
all major detectors are upgraded. Our upgrade proposal was approved in year 2013, and we arein a construction stage. The sensitivity improvement will be achieved by 10 times larger statistic
amount of data, and the detector resolutions improved by a factor of two.
The schematic view of the upgraded experiment is illustrated in Fig. 9.1. Here the items in
upgrades are explained for each component.

9.1.1

Beam and target

MEG II continues to be conducted in the πE5 area in PSI, which is capable of providing muon
intensity up to 1 × 108 /s. The expected muon stopping rate in MEG II is 7 × 107 /s. The target
will be replaced with thinner one for less disturbance to positron, and the slant angle is alsochanged to keep the effective thickness. As we learned in MEG experiment, the stability of thetarget is crucial. Therefore, the study of the target material is underway. We are also studying
the possibility of the active target which is composed of scintillating fiber and SiPM sensor.

9.1.2

LXe detector

As seen in Sec. 5.2, the performance of LXe detector is limited by the size of the PMT. We
overcome it by replacing PMTs in the inner face with smaller sensor, MPPC1. The size of the
1 Multi-Pixel Photon Counter, by Hamamatsu Photonics.

125

Chapter 9. Prospects

Figure 9.1: CG image of the MEG II detectors.
sensor is 12 × 12 mm2 , considering the performance and the number of readout channels, andthey will be arranged in 44 × 93 array.
The θ angle acceptance will not be extended, but the entrance width is widened, by meansof improvement of energy, position resolutions near lateral edge. The PMTs on lateral face areshifted outward as well, and their attached direction is modified to parallel to the lateral wall.
MPPCs operational in the LXe was not commercially available when MEG II was planned.
There were mainly two issues to adopt MPPC in our LXe detector, (a) sensitivity to 175 nm
wavelength (VUV) light and (b) large sensor capacitance with size of 12 × 12 mm2 . We
successfully developed a new type of MPPC in collaboration with Hamamatsu Photonics. The
design of the new MPPC is shown in Fig. 9.2.

9.1.3

Magnetic field

The COBRA magnet remains in the MEG II experiment. However, the magnetic field map will
be upgraded according to the measurement with a new measurement with an improved precision.

9.1.4

Drift chamber

The drift chamber in MEG I is totally replaced with a new one. The new drift chamber has
cylindrical shape and stereo-wire geometry. In MEG I drift chamber, some of the positrons hit
the support structure and readout electronics at the end of module, and it caused an efficiency
decrease. The drawback is solved by making drift chamber longer. Schematic images with126

Chapter 9. Prospects
ŶŽƌŵĂůϯǆϯŵŵshsDWWϱϭ ϮϭYƵĂƌƚǌǁŝŶĚŽǁ

ϰǆDWWĐŚŝƉĞƌĂŵŝĐ
ďĂƐĞD'>yĞWDd(b) Drawing of VUV MPPC. Four 6 ×
6 mm2 chips are mounted on ceramicbase, not to block VUV light; the cover ismade of artificial quartz.

(a) VUV MPPC is put on 2-inch PMT
together normal 3 × 3 mm2 MPPC.

Figure 9.2: VUV MPPC for MEG II
MEG I and MEG II are compared in Fig. 9.3. The tracking performance will be improved withmore hit points due to finer segmented drift cell.

(a) Case of MEG I(b) Case of MEG II

Figure 9.3: Drift chamber is replaced with longer one. The ratio of positrons which is scatteredby the support structure will be reduced.

9.1.5

Timing counter

The timing counter system is also replaced with a new one. The concept of the new timing
counter is to use multiple hits. The new system is composed of many (256 pcs both in US andDS side) small counters, and the timing is reconstructed using multiple-hits.
The single counter is based on a fast plastic scintillator (120 × 40(50) × 5 mm3 ). Two circuitboards with 6 series connected SiPMs are attached on both ends. The counters are mounted on
backplane readout PCBs as shown in Fig. 9.4.

9.1.6

Radiative decay counter

The radiative decay counter (RDC) is a brand new component in MEG II. It is designed toreduce accidental background whose γ-ray is originated from radiative muon decay. When
127

Chapter 9. Prospects

Figure 9.4: Assembled prototype of the new timing counter.
γ-ray energy is near signal energy, the momentum of the associated positron is likely to be low,
and results in a small radius of the positron trajectory. The RDC is placed on the beam axis near
beam axis of up-stream and down-stream side of target.
The DS side detector is composed of LYSO crystal and plastic scintillator which are both
read by MPPC. The US side detector is a thin layer of scintillating fibers. A careful study about
the effect on the beam property is needed as for US side detector.

9.1.7

Projected sensitivity

The expected performance of the upgraded detector is summarized in Table 9.1 [93]. With 3
years of data tracking, the expected branching ratio sensitivity is 4 × 10−14 .
Table 9.1: performance of MEG II and MEG I detector
Item
Beam intensity
Resolution
γ energy (%) (w<2/w>2)
γ position (mm) (u/v/w)
e+ energy (keV)
γ − e+ angle (mrad) (θ/φ)γ − e+ timing (ps)
Efficiency (%)
triggerγe+128

MEG II
7 × 107

MEG I
3 × 107

1.1 / 1.0
2.4 / 1.7
2.6/2.2/5
5/5/6
130306 (core)
5.3/3.7
9.4/8.7
84
122
>99
69
88

>99
63
40

Chapter 9. Prospects

9.2

Future projects

In order to search µ → eγ with further improved sensitivity, a significantly improved detector
technologies and muon sources with a much higher intensity will be needed. There are several
projects which can provide more intense muon beam near future.
PSI is planning an new muon source "High-intensity Muon Beam" (HiMB) [94] with a novel
concept. MEG I and MEG II use beam line πE5 where the secondary beam is produced with
4 cm thick graphite target and only about 10% of the beam interact at the target. The most of
beam is sent to SINQ (neutron study facility) target (Fig. 2.2). The idea of HiMB is to produce
surface muon beam at the SINQ target. According to a MC simulation, available muon intensity
will be O(1010 ) µ+ /s.
At Fermilab, a project "Proton Improvement Plan-II" (PIP-II)2 is proposed. It is a plan for
the accelerator complex for intensity-frontier. It is designed to be used for various experiments
such as long-base line neutrino oscillation experiment or µ − e conversion search experiment.
A new muon beam facility in RCNP3, Osaka univ. started operation with a characteristicpion capture solenoid. It has very efficient muon collection for primary beam power, 108 µ+ /s
by 400W beam. If the injector accelerator in RCNP is upgraded by one order of the magnitude(for example 1 → 10 µA), it can produce more intense DC muon beam of 109 µ+ /s.
Although the new beam facilities are projected in the following decades, new concepts forthe µ → eγ search have not been established. There are two difficulties to utilize those beams.
One is the accidental pile-up. As seen in Eq. (1.10), the rate of accidental background increases
in proportional to beam intensity. The other one is beam quality. Above mentioned muon
beams are expected to have larger emittance, comparing with beam in PSI πE5, the detector
arrangement as MEG experiment may not work well. It is impossible to efficiently reach theO(10−15 ) sensitivity, unless the issues about the detector are solved.

2 previously called project-X
3 Research Center for Nuclear Physics

129Chapter 9. Prospects

130Chapter 10
Conclusion
The µ+ → e+ γ search is an excellent probe to look for the physics beyond the standard model.
The MEG experiment has been searching for µ+ → e+ γ with unprecedentedly high sensitivity.
The final result of the MEG experiment was obtained with all the data which were taken fromyear 2009 to year 2013. We analysed the full dataset with improved analysis algorithms, andthereby accomplished a sensitivity of 5.3 × 10−13 . No excess of the signal was found, and themost stringent upper limit is set as
B(µ+ → e+ γ) < 4.2 × 10−13 (90% confidence level).

(10.1)

It is 30 times more stringent result than the bound set by the previous experiment. The historyof the µ+ → e+ γ search with the MEG experiment is summarized in Fig. 10.1. The preparationof the MEG II experiment is underway and will start physics data taking in year 2017. The
expected sensitivity is one order of the magnitude higher, 4 × 10−14 .

131Branching ratio

Chapter 10. Conclusion

MEG 2009
Obtained 90% UL

MEGA
90% UL sensitivity

10−11

±1 σ
±2 σ

MEG 2011

10−12

MEG 2013
MEG Final

10−13
0

50

100

150

200
250
300
Accumulated DAQ days

Figure 10.1: Improvement of search sensitivity of MEG experiment.

132

Appendix A
Performance of BGO detector
As mentioned in Sec. 4.1.2.3, we replaced the NaI detector for the π 0 calibration for the LXedetector with the BGO detector in 2011. The fundamental specifications of these detectors are
summarized in Table A.1.
Table A.1: Specifications of tagging detectors
Item
Material
Density
Radiation length
Molière radius
Relative light
Wavelength
DesignSize(x, y)Size(z)Arrangement
Readout
Catalog No.

unit

NaI

BGO

g/cm3
mm
mm
%
nm

3.67
25.9
41.3
100
415

7.13
11.2
22.3
21
480

mm
mm

62.5
46.0
305
200
3×3
4×4
APD
PMT
Hamamatsu Hamamatsu
H8664-1010 H8409-70

Due to the higher density, BGO has a shorter radiation length and a smaller Molière radiusthan NaI. The shorter radiation length allows us to shorten the detector length and hence toswitch the photo-sensor from APD to PMT with a larger coverage and a higher QE. The highQE of PMT can compensate the lower light yield of BGO. The fine-mesh-type PMT is chosen,
since the BGO detector is operated in the magnetic field by COBRA. (∼ 50 Gauss) The smaller
Molière radius reduces shower escape from the side of the detector. The previous detector was
based on 3x3 array of NaI crystals of 62.5 × 62.5 × 305 mm3 each, and only events where thecentral crystal detect maximum light was triggered. The new detector is more segmented with
4x4 array of BGO crystals (46 × 46 × 200 mm3 each), while the total size is kept. The new
trigger condition is any hit in the central four crystals. The detector acceptance was, therefore,
increased by the factor of 9/4.
Figure A.1(a) is a picture to compare the size of the crystals of NaI and BGO. Each BGO
crystal is wrapped by a film of aluminized Mylar. Figure A.1(b) shows a CAD drawing for the133Chapter A. Performance of BGO detector
housing of the BGO detector. The housing is designed to be interchangeable with that for the
NaI detector, hence the replacement of the detector is completed just by replacing the housings.

(a) (bottom) BGO crystal attached with H840970 PMT, (top) NaI crystal.

(b) Design of the housing to store BGO crystals.

Figure A.1: BGO detector.

A.1

Calibration

Each-crystal is calibrated with cosmic ray events. The high voltages for PMTs are determined so
as events when a 129 MeV γ-ray (Eq. (4.5)) deposits all energy in one crystal, the pulse height
to be the full dynamic-range of DRS.
The detector is mounted on a moving stage to scan all the acceptance of the LXe detector.
Since the COBRA stray field around the detector is suppressed by the compensation coils as
for the LXe detector, the operation of the PMT is not affected at any position. We tested thedependence of the output on the detector position by checking the spectrum of the 17.6 MeV γ in
CW run of Li target (See Sec. 4.1.2.1). It turned out that the position dependence is very small,
0.4% toward the φ direction and 0.3% toward the z direction. The temperature dependenceof the BGO light yield is known, we measured the temperature dependence by monitoring the54.9 MeV γ-ray peak and the temperature. The coefficient is -0.97 %/K, while the temperature
coefficient shown in the catalogue1 is -1.2 %/K.
In order to minimize the effect of the position and temperature dependence, we decided tocalibrate the absolute energy scale for each patch data. By using the 54.9 MeV γ-ray peak, theenergy scale is calibrated. The formula to reconstruct energy is,
X
X
EBGO = C1
qi gi ai + C2
qi gi,
(A.1)
outer

inner

where qi is the observed charge and gi is the gain measured by the cosmic ray calibration. ai is
an additional correction for the gain of inner 4 crystals, which is fixed by fitting the spectrumof each crystal. The value is determined for each patch. It is possible because the peak is clear
for central crystals. C1 and C2 are the parameters to adjust the balance of the inner and outer
contribution from the correction by ai .
1 SAINT-GOBAIN

134

Chapter A. Performance of BGO detector

A.2

Position resolution

The position resolution can affect the performance of the π 0 calibration, because in the energy
resolution evaluation of LXe detector, the correlation between the opening angle and energy iscorrected using the reconstructed positions of two γ-rays. We introduced a position reconstruction by the weighted sum of the detected number of the photo-electrons. The position resolution
is estimated with the MC simulation (Fig. A.2) to be 1.0 cm (RMS).

Figure A.2: Error distribution between the reconstructed position and MC truth.

A.3

Energy resolution

The energy resolution of the BGO detector is estimated by fitting 54.9 MeV peak with a function
where a Gaussian function and a exponential functions are smoothly connected. Figure A.3
shows the observed spectrum in a π 0 run in year 2011. In the events, a cut is applied where theenergy deposit in the central 4 crystal is more than the half of total deposit. The fitted σ for 54.9
MeV peak is 2.4%, while that of the NaI detector was 3.9%.

135Chapter A. Performance of BGO detector

Figure A.3: Energy distribution by the BGO detector in year 2011 π 0 run.

136

Appendix B
AIF cut efficiency in signal/RMD event
The selection efficiency for the signal (item (c) of ε sel in Sec. 7.7) is estimated with simulated
distribution of AIF observables for the signal event. The way to estimate the efficiency is
described herein.

B.1

Accidental background and signal/RMD events

The simulation used the timing sideband data with the same trigger as physics data, since wewant to use the same position and timing distribution and the correlation of γ-ray and positron
as data. In the timing sideband, only the accidental backgrounds are included. The accidental
background can be categorized by the source of the γ-ray. In cases an AIF occurs in the detector,
and the γ-ray is detected by the LXe detector (we call it "real AIF"), the AIF observables makea peak. In cases the γ-ray is not due to AIF or is due to AIF but the original positron is notfound, the AIF observables do not make a peak (base events in Fig. 3.13). On the other hand in
signal and RMD event, γ-ray and positron must be correlated (from one µ+ ). Figure B.1 shows
possible types of the events. What we want to know is the observable distribution of the (s-2)
category and the fraction of (s-1) and (s-2).

B.2

Event scrambling

The distribution of (s-2) is thought to be equivalent to that of (a-2), however, it is impossible
to extract only (a-2) from all mixed events. We simulate the distribution where the γ andpositron are uncorrelated, by scrambling information of γ-ray and positron. However, if thetrigger condition of the direction match (about φ direction) is not maintained, the output AIF
observable is biased. Therefore, we developed a method of trigger simulation to scramble thedata with keeping the trigger condition. The scrambling is done before Sec. 3.5.2, and theprocedure in Sec. 3.5.2 is processed with the scrambled data. It is proceeded with following
algorithm.
• The trigger table is prepared. The table is a 2D map of V position of γ-ray and id number
of TIC bar. It shows the probability to find TIC hit at j-th bar, when the γ is found in i-thPsegment. The table is normalized as j Pi ( j) = 1 for each i.
• The events are listed, according to which TIC bar has a hit. The lists are 15-fold (number
of TICP bar) array of event numbers.
137

Chapter B. AIF cut efficiency in signal/RMD eventƐŝŐŶĂů
ZDɶĞнϬ Ğнϭ͙ŶŽ/&ĞнĐĐ' ŶŽƚďǇ/&͍ɶĞнϬ Ğнϭ͙ŶŽ/&Ğн

;ƐͲϭͿ

ĐĐ'
ďǇ/&ɶĞнϬ Ğнϭ͙Ğн/&Ă
;ĂͲϯ͘ϭͿ

;ĂͲϭͿ

͍
ɶ

ĞнϬ Ğнϭ͙Ğн/&Ă ͙ɶĞнϬ Ğнϭ͙Ğн/&Ă ͙ɶĞнϬ Ğнϭ͙Ğн/&Ă Ğн/&ď ͙

͍

͍
;ƐͲϮͿ

;ĂͲϮͿ

;ĂͲϯ͘ϮͿ

͍

Figure B.1: Types of the events, categorized by the AIF positron. The red line shows the γ-ray
and its source, the blue line shows the found AIF and the γ-ray, and the green box shows thetriggered gamma positron pair.
• For every event, the V position of γ (in region a, for instance) is checked, and the a-th
row in trigger table is picked up.
• An id of TIC bar is randomly selected, the probability to select b-th column is Pa (b)• A positron data in the b-th list is randomly selected. If the selected number of event is thesame as that of γ, select again.
Figure B.2(a) shows the trigger table and vγ -TIC bar distribution of simulated data. The
effect of the scrambling is demonstrated in Fig. B.2(b), the shape of the base agrees better withthe trigger simulation. The effect of the direction matching is obvious in φ-direction, but theeffect cannot be seen in θ-direction. So the trigger simulation only considers φ. Figure B.3
shows the result of the estimation of AIF observables in signal/RMD events. The distance fromthe peak is calculated with the same parameter c and S the same as for accidental backgroundwhich were introduced in Sec. 7.6.1.

B.3

Probability to find no AIF candidate

The purpose of this section is to estimate not to find AIF candidate in the Signal/RMD events.
The relation of γ and e+ in category (a-1) and (a-2) are thought to be equivalent with that in
Signal and RD events. Therefore an estimation can be written as,
SNOAIF,1 =P(a-1).
P(a-1) + P(a-2)(B.1)

On the other hand, the category (a-3) should not be found in the Signal/RMD events. The(a-3) can be further separated into (a-3.1): True AIF and no other AIF candidates and (a-3.2):
True AIF with other AIF candidate(s). The Signal or RD events do not contain true AIF events.
However, if the most probable AIF candidate track is removed, relation of (a-3.1) and (a-3.2)
138

Chapter B. AIF cut efficiency in signal/RMD event

1200
1000
800
600
400
200
0
-150 -100

-50

0

50
✁

100

150

ΔφAIF (deg)(b) The ∆φAIF distributions with (black)data, (red) scramble with trigger simulation, (blue) random scramble.

(a) A trigger table made from the sideband data in year
2013.

Figure B.2: Trigger simulation
800
500
700

700

600

400

600

500

500
300

400

400

300

200

300

200

200
100

100

100
0
− 100 −80 −60 −40 −20

0

20

40

60

80

100

0
− 100 −80 −60 −40 −20

0

20

40

60

80

100

− 100 −80 −60 −40 −20∆φ AIF (deg)∆θ AIF (deg)

0

20

40

60

80

100

∆t AIF (ns)Figure B.3: The AIF observables of, (red) estimation for signal/RMD events, and (blue) data of
the accidental background. φeγ selection is applied.
corresponds to that of (s-1) and (s-2). In this assumption, no-AIF probability of signal/RMD
can be written as,
SNOAIF,2 =P(a-1) + P(a-3.1).
P(a-1) + P(a-2) + P(a-3.1) + P(a-3.2)(B.2)

The no-AIF probability for each year is listed in Table B.1.

B.4

Error of inefficiency

The error in not finding AIF depends on the method, but the difference in the SNOAIF,1 andSNOAIF,2 are negligibly small (< 0.2%). The method to estimate the observable distribution iscomplex, and contains assumptions. As one example of the mistake in the calculation, is wrong
positron data. When we use positron data not from MEG trigger data, but positron triggered139

Chapter B. AIF cut efficiency in signal/RMD event
Table B.1: Probability to find no AIF candidate in an event. ANOAIF is the probability for
accidental background.
Year
2009
2010
2011
2012
2013

ANOAIF
0.163
0.170
0.180
0.154
0.126

SNOAIF,1
0.185
0.187
0.198
0.172
0.143

SNOAIF,2
0.183
0.186
0.199
0.171
0.141

without LXe coincidence, or pedestal trigger data, the number of the AIF candidate around peakvaries in several tens of percents. Although the error at this level can remain in the estimation,
the uncertainty in the normalization factor is only 1.1%, even if the 100% error is assumed
for AIF cut inefficiency. It is enough less than 3.5%: estimated systematic uncertainty fornormalization factor. The additional systematic error in the normalization by the AIF reduction
can be neglected.

140

Appendix C
List of abbreviations
ACC ACCidental (background)
AIF Annihilation In Flight (of positron)
APD Avalanche PhotoDiodeBGO Bismuth Germanium Oxide, Bi4 Ge3 O12BTS Beam Transport Solenoid
CEX Charge EXchange (reaction), π − + p → π 0 + n
COBRA COnstant Bending RAdius (magnet)
CW Cockcroft-Walton (accelerator)
DCH Drift CHamber
DRS Domino Ring Sampler
LFV Lepton Flavor Violation
LXe Liquid Xenon
PDF Probability Density Function
PMT PhotoMultiplier Tube
PSI Paul Scherrer Institute
RMD Radiative Muon Decay
TIC TIming Counter

141

Chapter C. List of abbreviations

142

Acknowledgment
I would like to express my thanks to everyone in the MEG collaboration, primarily to myacademic adviser, Prof. Toshinori Mori who serves the spokesperson of the MEG experimentwith Prof. Alessandro Baldini. He supervised all my study in the doctoral course and gave mean opportunity to participate in the concluding work of the MEG experiment.
I also offer my gratitude to Assoc. Prof. Wataru Ootani, who managed analysis project andlead us in the MEG upgrade studies. He gave me advises for this thesis in detail. I am obligatedto Dr. Toshiyuki Iwamoto for supports not only in experiment but also in whole sojourn in PSI.
To Dr. Ryu Sawada and Dr. Yusuke Uchiyama, I feel appreciation about giving me a lot ofadvices always when I met difficulties in our research.
In order to accomplish our tasks in final analysis studies, the discussion with Dr. Fabrizio
Cei, Dr. Francesco Renga and Dr. Gordon Lim was meaningful and was enjoyable at the sametime. The collaborators from KEK, Prof. Satoshi Mihara, Dr. Hajime Nishiguchi, the period towork together was not so long but gave me valuable suggestions in meetings and in PSI.
I learned much technical knowledge and skills to live in Switzerland from Dr. Hiroaki Natori,
Dr. Yasuhiro Nishimura, Dr. Xue Bai, Dr. Kei Ieki and Dr. Yuki Fujii. Ms. Miki Nishimura,
Mr. Shinji Ogawa, Mr. Naoya Shibata, Mr. Shota Nakaura, Mr. Kohei Yoshida, Mr. Ryoto Iwai,
Mr. Mitsutaka Nakao and all students come to PSI from Kyushu univ. supported me about works
in the university and gave me pleasant life as a student.
I want to present my thanks to all the staffs in international center for elementary particle
physics, especially secretaries who helped me from clerical sides. I am deeply grateful to thestaffs in PSI too, for accepting us in PSI and for supporting about accommodation, exports, andso on.
I would like to show special thanks to the members of Hamamatsu Photonics, it was an
exciting experience to collaborating with a leading company and develop advancing products.
I owe gratitude to my former colleagues in Hitachi Ltd. to send me off the academia. I
learned precious things not only as an engineer but also a member in the society.
Finally, I gratefully acknowledge my family to supporting my unproductive days.
May 2016, Tokyo
Daisuke Kaneko

143

144

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