A Liquid Xenon Scintillation Detector to Search
for the Lepton Flavor Violating Muon Decay witha Sensitivity of 10−13
Ryu Sawada
Department of Physics, School of Science
University of Tokyo
November 28, 2008

Abstract
The MEG experiment searches for a rare muon decay µ+ → e+ γ , which
is forbidden in the standard model. Several new theories beyond the standard
model predict branching ratio of the decay just below the current experimental
limit. The MEG experiment aims sensitivity of 10−13 where most of predictions
are covered. The discovery of the muon decay is a probe for new physics beyond
the standard model.
To realize such a high sensitivity, a new liquid xenon detector was developed
for measuring energy, position and time of gamma rays. The detector is thelargest xenon detector ever made. Characteristics of liquid xenon, Large atomic
number, high density, large scintillation output and fast decay time allow tobuild a detector with excellent resolutions and high efficiency. It consists ofmore than 800 litters of liquid xenon and 846 photo-multiplier tubes. We performed beam tests and evaluated resolutions by using a prototype. During theprototype test, fundamental techniques to operate the detector and to analyze
data were developed. The construction of the final detector was completed in2007. An engineering run was conducted in the year to preparing triggers, toevaluate detector performance and to collect a small amount of physics data.
The resolutions of the detector during the engineering run were estimated byusing gamma rays from pion decays. The estimated best values of resolutionsfor 54.9 MeV gamma rays are 2.1 ± 0.2 %, 5.9 ± 1.4 mm and 121 ± 8 psec
for energy, position and time respectively. Based on the measured resolutions
and counting rate in 2007, it was confirmed that the gamma ray detector has asufficient performance to improve the current experimental limit and realize asensitivity better than 10−12 in 2008.

Contents
1 Introduction
1.1 Physics motivation . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 cLFV search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

33
72 MEG experiment10
2.1 Beam and magnet . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2 Target . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3 Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3.1 Positron spectrometer . . . . . . . . . . . . . . . . . . . . 15
2.4 Electronics and DAQ . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.4.1 Data reduction . . . . . . . . . . . . . . . . . . . . . . . . 25
2.5 Proton accelerator . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.6 Signal and backgrounds . . . . . . . . . . . . . . . . . . . . . . . 30
3 Liquid xenon scintillation detector
31
3.1 Liquid xenon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.1.1 Scintillation efficiency . . . . . . . . . . . . . . . . . . . . 36
3.1.2 Attenuation of scintillation light and impurities . . . . . . 37
3.2 Liquid xenon gamma ray detector of MEG . . . . . . . . . . . . . 39
3.2.1 PMT for the gamma ray detector . . . . . . . . . . . . . . 41
3.2.2 Cryostat . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.2.3 Handling of xenon . . . . . . . . . . . . . . . . . . . . . . 46
3.2.4 PMT test . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.2.5 Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.2.6 Installation of PMT . . . . . . . . . . . . . . . . . . . . . 52
3.2.7 Slow control of the system . . . . . . . . . . . . . . . . . . 56
3.2.8 Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4 Simulation
61
4.1 Scintillation photon tracking in the gamma ray detector . . . . . 61
4.2 Gamma Ray Detector waveform simulation . . . . . . . . . . . . 61
4.3 Response of the gamma ray detector . . . . . . . . . . . . . . . . 62
5 Prototypes
64
5.1 Small prototype . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.2 Large prototype . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.2.1 Optical properties of xenon . . . . . . . . . . . . . . . . . 68
5.2.2 Purification . . . . . . . . . . . . . . . . . . . . . . . . . . 72

5.3

5.2.3 CEX beam test . . . . . . . . . . . . . . . . . . . . . . . .
Summary of prototypes . . . . . . . . . . . . . . . . . . . . . . .

75
90

6 MEG run 2007
92
6.1 Preparation of gamma ray detector . . . . . . . . . . . . . . . . . 92
6.2 Cockcroft-Walton . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
6.3 Pion charge exchange . . . . . . . . . . . . . . . . . . . . . . . . 93
6.4 Michel decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
6.5 Radiative muon decay . . . . . . . . . . . . . . . . . . . . . . . . 94
6.6 MEG trigger data . . . . . . . . . . . . . . . . . . . . . . . . . . 94
7 Analysis
96
7.1 Calibration of PMT . . . . . . . . . . . . . . . . . . . . . . . . . 96
7.1.1 PMT Gain . . . . . . . . . . . . . . . . . . . . . . . . . . 96
7.1.2 Photo-cathode quantum efficiency(Q.E.) . . . . . . . . . . 97
7.1.3 Time offset . . . . . . . . . . . . . . . . . . . . . . . . . . 104
7.2 Structure of event reconstruction . . . . . . . . . . . . . . . . . . 106
7.3 Waveform analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 106
7.3.1 Calibration and noise reduction . . . . . . . . . . . . . . . 106
7.3.2 Charge integration . . . . . . . . . . . . . . . . . . . . . . 108
7.4 Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
7.4.1 Position reconstruction . . . . . . . . . . . . . . . . . . . 109
7.4.2 Energy reconstruction . . . . . . . . . . . . . . . . . . . . 116
7.4.3 Time reconstruction . . . . . . . . . . . . . . . . . . . . . 119
7.5 Event type identification . . . . . . . . . . . . . . . . . . . . . . . 122
7.5.1 Higher tail identification . . . . . . . . . . . . . . . . . . . 122
7.5.2 Pile-up identification . . . . . . . . . . . . . . . . . . . . . 123
7.5.3 Cosmic ray event rejection . . . . . . . . . . . . . . . . . . 126
7.6 Summary and discussion on the gamma ray detector . . . . . . . 128
8 The MEG Sensitivity
131
8.1 Likelihood analysis with MEG 2007 data . . . . . . . . . . . . . . 131
8.1.1 Building likelihood function . . . . . . . . . . . . . . . . . 133
8.1.2 Probability density functions . . . . . . . . . . . . . . . . 134
8.1.3 Upper limit from 2007 physics run . . . . . . . . . . . . . 135
8.2 Sensitivity estimation for run 2008 . . . . . . . . . . . . . . . . . 138
8.2.1 Prompt background . . . . . . . . . . . . . . . . . . . . . 138
8.2.2 Accidental background . . . . . . . . . . . . . . . . . . . . 138
9 Summary and prospects
140
9.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
9.2 Prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

Chapter 1

Introduction
1.1

Physics motivation

The standard model of particle physics successfully explains most of particle
phenomena tested by experiments precisely. A missing piece is a direct observation of the Higgs particles, which LHC experiment is expected to find.
One phenomenon that is not explained by the standard model is the neutrino
oscillation. The original standard model assumes massless neutrinos and does
not allow flavor violating processes in the lepton sector, thus a modification of
the theory is needed to explain the phenomenon.
Neutrinos can obtain masses by introducing heavy right-handed neutrinos
close to GUT scale into the theory. Addition of such neutrinos requires tointroduce new mass scales in addition to that of the standard model. It implies
the existence of new physics beyond the standard model.
It is widely believed that the standard model would be a low energy approximation of more fundamental theories such as Super Symmetric Model (SUSY),Grand Unified Theory(GUT), Extra Dimensions and String Theories because
the standard model does not answer some questions known as “Gauge problem”, “Fermion problem”, “Higgs/hierarchy problem”, “Strong CP problem”
and “Graviton problem”. With a minimum modification of the standard model
to introduce non-zero neutrino mass, µ+ → e+ γ can occur through flavor mixing of neutrinos. However the branching ratio is far below from observable rate.

Br(µ → eγ) =3α X ∗∆m2
Uµi Uei 2 1i < 10−54
32π i=2,3
mW

(1.1)

where U is Pontecorvo-Maki-Nakagawa-Sakata matrix and ∆2ij = m2νi − mµj 2.
In SU(5) SUSY-GUT, LFV occurs in the right handed slepton sector as shown+in fig.1.1. So, in the model, µ+ → e+→ e+
L γ occurs, while µR γ does notoccur. These two processes could be distinguished from angular distribution by
an experiment with polarized muon decays. Predicted branching ratio is shownin fig1.2 with various values of input parameters of M2 (the SU(2) gaugino mass)and tan β (the ratio of the two Higgs vacuum expectation values) as a function

1.1 Physics motivation4of the mass of right-handed selectron. The minimal SU(5) SUSY-GUT is ruledout by the experimental limit on the lifetime of protons.
~

~
µ
R

τR

e~ R
µR
~

χ0
~

µ

e~R
~

χ0

µ

e

e

Figure 1.1: Diagrams of µ+ → e+ γ in SU(5) SUSY GUT.

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

���

��

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

���

�������

�������

���

��

��

���

���

��

��

���

���

��

��

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

�

���

����

���

� ��

��

�

���

����

� ��

���

Figure 1.2: Predicted Br(µ+ → e+ γ ) in SU(5) SUSY GUT.[1]In SO(10) SUSY-GUT, Br(µ+ → e+ γ ) is enhanced by contribution of thethird generation sleptons as shown in fig.1.3. In the model, LFV occurs in theboth right and left handed slepton sectors. Figure 1.4 shows predictions by themodel. They are close to the current experimental bound, which is 1.2 × 10−11 .
22(mτ~) LR(mτ~) RL
~

τR

~

τL
~

µL
µ

~

χ0

~

τL

~

τR
~

e~R

µR

e

µ

e~L
~

χ0

e

Figure 1.3: Diagrams of µ+ → e+ γ in SO(10) SUSY GUT.

From a study of muon anomalous magnetic moment by E821 experiment at
Brookhaven National Lab, it was found that there is a significant difference1.1 Physics motivation

5�������������� ������� ��

���

���

���

��
�������

�������

��

���

���

��

��

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

���

��

�������������� ������� ��

���

��

��

�

���

����

� ��

���

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

���

��

�

���

����

� ��

���

Figure 1.4: Predicted Br(µ+ → e+ γ ) in SO(10) SUSY GUT.[1]between measurement and SM prediction[2][3][4][5].
SM−11∆aµ = aexp
µ − aµ = 292(63)(58) × 10

(1.2)

where aexp
is experimental value, aSMµµ [6] includes contributions of QED, electroweek and NLO hadronic.
To explain the difference, new theories beyond the SM are necessary. Diagrams to explain the difference in SUSY are shown in fig.1.5, where the process
is mediated by super partners of leptons and Gauge bosons.
aSUSY' ±130 × 10−11 ·µ100GeV
mSUSY

2
tan β

(1.3)

γ

~
χ
µ

γ

~
χ
~
ν

~
µ
µ

µ

~
µ
~
χ0

µ

Figure 1.5: Typical SUSY contributions to g-2µ+ → e+ γ can occur with a similar diagram with adding flavor mixing ofsuper particles, therefore aSUSY
and Br(µ+ → e+ γ ) are correlated.
µFigure 1.6 shows relation between Br(µ+ → e+ γ ) and aSUSY
in SUSY seeµsaw model. Br(µ+ → e+ γ ) is predicted just bellow the current experimental
bound. An experiment with 10−13 sensitivity can explore most of the region of
the prediction.

1.1 Physics motivation

6

Figure 1.6: Br(µ+ → e+ γ ) and aSUSY. This figure is taken from ref.[7]. Hereµ√following parameters are assumed. V13 = 0.01, V23 = 1/ 2, tan β = 10, M2 =250 GeV. The solid and dashed lines are for cases where the scale for the generation of the SUSY-breaking terms in the SUSY SM(MX ) are the GUT scale
and the reduced Planck scale, respectively.

In this section, predictions of Br(µ+ → e+ γ ) were shown in the case ofSU(5) and SO(10) SUSY-GUT. Relation between the muon anomalous magnetic
moment and Br(µ+ → e+ γ ) was shown based on SUSY see-saw model. In
general, in the SUSY model, lepton flavor violation is predicted with a large
branching ratio. In the SUSY-GUT, the flavor mixing in the slepton sector isnaturally induced. A discovery of µ+ → e+ γ decay will be a clear evidenceof a new physics beyond the standard model. Predictions by new theories are
one or two orders of magnitude lower than the current experiment limit forvarious models and parameters. MEG would have a sensitivity of 10−13 whenrequirements summarized in table 1.3 is realized.

1.2 cLFV search

1.2

7

cLFV search

Since the first experiment to search for µ → eγ was done in the 1940’s, several
charged lepton flavor violation (cLFV) search experiments for µ, τ and K havebeen performed. Upper limits of rare decays are improving, while there is nota clear evidence of cLFV yet.
Muons can be used for study of cLFV by several decay processes such asµ → eγ, µ → 3e and µ − e conversion in nucleus and so on. The ratio of
branching ratio of these decay processes strongly depends on models of theory,
so studies of different decay process are complementary. Current upper limitsof rare muon decays are summarized in table 1.1.
Experiment
1999
1988
1988
1993
1996
2006

Year
MEGA
Crystal Box
SINDRUM
SINDRUM IISINDRUM IISINDRUM II

Decay modeµ+ → e+ γµ+ → e+ 2γµ+ → e+ e− e+µTi → e− TiµPb → e− PbµAu → e− Au

Upper limit
1.2 × 10−11 [8]7.2 × 10−11 [9]1.0 × 10−12 [10]4.3 × 10−12 [11]4.6 × 10−11 [12]7 × 10−13 [13]Table 1.1: 90 % C.L. upper limits of rare muon decays.

The history of µ+ → e+ γ search experiments in this 30 years is shown intable 1.2. Improvements of the limits have been made by improvements ofmuon beam, i.e. number of muons, and detector resolutions to discriminate
signals from backgrounds. The current upper limit of Br(µ → eγ ) was given
by MEGA experiment[8] in 1999. Improvements of MEG experiment with compared to MEGA is discussed in this section. The experiment was done by using
high intensity surface muon beam at LAMPF. The apparatus of the experimentis shown in fig.1.7. Positrons from muon decays were measured by inner multiwire proportional chambers(MWPCs) and scintillators for timing. The photon
detector consists of two 250 µm Pb conversion foils, scintillators, an MWPCand drift chambers. Energy and vertex of both particles were obtained fromreconstructed tracks of charged particles in a magnetic field in the apparatus.
Year
1977
1980
1982
1988
1999

Experiment
Crystal Box
MEGAUpper limit< 3.6 × 10−9[14]< 1.0 × 10−9[15]< 1.7 × 10−10[16]< 4.9 × 10−11[9]< 1.2 × 10−11[8]Table 1.2: History of the upper limit of µ+ → e+ γ decay search experimentsin this 30 years.
The single event sensitivity was 2.3 ± 0.2 × 10−12 . A likelihood analysis wasdone for 3971 events in an analysis window, and the best fit was 0 signal and
30 ± 8 ± 15 radiative decay events. The rests were accidental pileups.

1.2 cLFV search

8

The 90 % confidence limit was Neγ < 5.1 which gives the upper limit on the
branching ratio of 1.2 × 10−11
Major improvements of MEG from MEGA are time resolution and detection
efficiency of gamma ray detector, and muon stopping rate. Time resolution isbetter because MEG gamma ray detector contains full energy of a gamma ray,while in case of MEGA, a small fraction of energy deposits in thin scintillators
were available. The detection efficiency of gamma ray in MEGA was limitedby conversion probability of gamma rays in thin Pb foils. Thanks to DC muon
beam, MEG will be able to accumulate more events with lower muon stopping
rate which will reduce accidental pileup backgrounds.

Figure 1.7: MEGA detector.

∆Eγ [%]∆Ee+ [%]∆θγe+ [mrad]∆Tγe+ [nsec]
Acceptance × Efficiency [%]Muon stopping rate (108 )Running time [weeks]Single event sensitivity(10−13 )90 % C.L. limit(10−13 )MEGA(1999)
4.5
1.2
15
1.6
0.3
2.5(Pulse, 6∼7 % duty)
20
23
120

MEG goal
4.5∼5.0
0.8
12.4∼16.9
0.18>1.6
0.3(DC)
100
0.5
1.7

Table 1.3: Comparison of MEGA and MEG goal. Resolutions are written in
FWHM. One week is 4 × 105 seconds in this table.
In chapter 2, the MEG experiment and each component is described. In
chapter 3, general properties of liquid xenon to use for scintillation detectors
and the liquid xenon detector for MEG are explained. After discussing about
simulation of the liquid xenon detector in chapter4, performance tests by using1.2 cLFV search

9

prototype detector are described in chapter 5. In 2007, the final gamma ray
detector was constructed and the first beam test was carried out. In chapter
6, the setup of 2007 beam test is described and the analysis of the gamma ray
detector for the data is discussed in chapter 7. In chapter 8, 90 % confidence
level upper limit of the branching ratio is estimated from 2007 physics data. Expected sensitivity with more statistics is discussed in the chapter with assumed
performance in 2008.

Chapter 2

MEG experiment
The MEG experiment takes place at Paul Scherrer Institut (PSI) in Switzerland.
The signature of µ+ → e+ γ is back-to-back positron and gamma ray, in time,with respective energy of 52.8 MeV. In order to reduce background events,
precise measurements of energy, emission angle and time of two particles areimportant. The apparatus of MEG is shown in fig.2.1. Each components aredescribed in this chapter. In this thesis, a global coordinate system shown in
the figure is used, where z is direction along the muon beam, y is the verticalaxis, the gamma ray detector is located at the negative side of x. The origin(0, 0, 0) is the center of the target. θ is zero for positive direction of z-axis andφ is zero for positive direction of x-axis.
A muon stopping target is located at the center of a super conduction magnet
called COBRA. Positrons from muon decays travel through drift chambers andreach timing counters. Momentum and timings of positrons are measured bythese sub-detectors. Gamma rays are measured by the liquid xenon detector
located outside of COBRA.

2.1

Beam and magnet

To improve the sensitivity, a large amount of muon decays are necessary. The
most intense DC muon beam at PSI is used for the MEG experiment. DC beam
is better than pulsed beam to correct muon data without increasing accidental
pileup backgrounds so much.
PSI operates a 590 MeV proton cyclotron with the maximum current of
2 mA. The power of the beam is 1.2 MW. A production target is put on the
primary proton beam line, and produced pions and muons are extracted tothe πE5 area where the MEG experiment takes place. A surface muon beam,
which is used for the experiment, is produced from pion decays on the surfaceof the production target. The surface muon beam has high intensity and low
range straggling which allow to use a thin muon stopping target, hence multiple
scattering of positrons can be reduced. Figure 2.3 shows a schematic viewof the MEG beam line layout. Muons are transported from the production
target to the stopping target through Triplet I(quadrupole triplet), a Wien filter,
Triplet II(quadrupole triplet) and a beam transport solenoid(BTS). A Wien
filter separates electrons from muons by 8.1 σ with using crossing magnetic field2.1 Beam and magnet

COBRA Magnet

11

Liquid Xenon
Scintillation Detector�Thin Superconducting Coil

Stopping Target+eMuon Beam

Timing Counter�

Drift Chamber

�
1m

�

+

e

Drift Chamber

Figure 2.1: MEG apparatus.

��

2.1 Beam and magnet

12

Figure 2.2: An event display during MEG physics run. Reconstructed hits andtracks are shown. Color of PMTs in the display represent its output. In thisevent, two positrons are observed in time window.

2.2 Target

13(133 G) and electric field (195 kV). The BTS is used to adjust the oscillationof the beam profile to minimize the beam spot size on the stopping target.
A momentum degrader is installed in the BTS to adjust the momentum ofmuons so that they stop on the thin target. Muon momentum is degraded byMylar degrader(300 µm), Mylar vacuum window(190 µm) and helium gas in
the COBRA magnet (1475 mm). In run 2007, a few percents of air was added
artificially for stable operation of the drift chambers to suppress discharges.
Effect of the air admixture of 5 % is about 5 % loss of transmission. Different
settings of magnets for “high”, “normal” and “ultra low” modes for different
muon intensities were prepared. In the case of 2007 run, expected muon stopping
rates in 100 % helium were 8.6 × 107 , 3.2 × 107 and 6.1 × 106 when the proton
current is 2 mA. Nominal beam intensity to start physics data accumulationin 2008 is the “normal”. The ultra low intensity beam is used for studies andcalibrations of the detector and collection of radiative decay events in a cleaner
environment where there are less pileups. Measured beam spot sizes(σx , σy ) at
the center of the COBRA were (11.0, 12.7) mm and (9.5, 10.2) mm for high andnormal intensity beam respectively.

Figure 2.3: Schematic of the MEG beam line layout. A muon beam is injectedfrom the left of this figure.

2.2

TargetPictures of the muon target are shown in fig.2.4. The target is a polyethylene/polyester sandwich foil supported by a Rohacell frame. The density is
0.895 g/cm3 The design was optimized for balancing muon leakage and probability of scattering or annihilation in flight of positrons. The shape of the target
is ellipse with diameters along minor and major axises of 79.8 and 200.5 mm
respectively. The thickness of the target is 205 µm. Since the acceptance of the
MEG detector is around θ = 90◦ , the smaller slant angle is favored to decrease
multiple scattering, while the larger slant angle is favored to decrease muonleakage. A simulation work was done to optimize the slant angle by using measured beam profile and straggling. In 2007, slant angle was 12.5◦ which caused
12.6 % of leakage. In 2008, the angle was modified to be 20.5◦ . Several holesof 10 mm diameter are made on the target to study the vertex reconstruction
resolution.

2.2 Target

14

(a)

(b)

Figure 2.4: (a) A muon target installed in the spectrometer (b) A picture of thetarget.

2.3 Detector

2.3

15

Detector

Sub-detectors to measure positrons are installed in a super conducting solenoid
magnet called COBRA (Constant projected Bending Radius). 16 drift chamber
modules are put at the center of z in the COBRA. Positrons emitted on thetarget travel through the chambers, and they reach to timing counters locatedat upstream and downstream of the drift chambers.
A liquid xenon detector is used to measure kinematics (energy, time andposition) of gamma rays at the first conversion point in the detector. Since, thedetector does not have good capability to determine direction of gamma rays,
opening angle of a gamma ray and a positron is calculated with assuming the
gamma ray was emitted at the decay vertex determined by the spectrometer.
Details of the liquid xenon detector are discussed at section 3.2. The gamma
ray detector is located in one side viewed from the target, and the geometricalacceptance is about 10 %. Positron detectors are located at corresponding
position to measure back-to-back positrons. Sub-detectors are located to observe
particles in an acceptance defined to be |φ| < 60◦ and 0.08 < cos θ < 0.35.

2.3.1

Positron spectrometer

COBRA
As shown in fig.2.5, the COBRA magnet system consists of a main superconducting magnet and two normal-conducting compensation coils. The compensation coils were prepared to decrease magnetic field around the gamma
detector so that PMTs work. Super-conductor material is NbTi multi-filament
embedded in copper matrix and aluminum-stabilizer. Nominal current of thesuper-conducting magnet is 360 A, and the peak value of the magnetic field is
1.7 T in the central coil. The super-conducting magnet was designed to havesmaller radius in the central part and larger radius in large z part to form a
gradient magnetic field along z direction. As shown in fig.2.6, radius of positron
trajectory in cylindrical coordinates is almost independent of emission angle,
and it is approximately determined by energy of the positron. Therefore, itis easier to choose energy range to measure by designing the position of drift
chambers so that they cover proper range of radius. This allows to avoid measuring low energy positrons which come with very high intensity (thus it cansaturate the drift chamber system). If we use constant magnetic field, positrons
emitted almost perpendicular to the beam axis can hit drift chambers manytimes as shown in fig.2.6-a. On the other hand, in case of the COBRA field,
such positrons are swept out quickly.
COBRA was designed to be very thin to minimize interactions of gamma
rays in it before reaching the gamma ray detector. The thickness of components
used in the coil and the cryostat of the magnet within the acceptance of the
gamma ray detector corresponds to 0.197 radiation length.
Relative output of the PMT used in the gamma ray detector as a function ofmagnetic field is shown in fig.2.7. The tolerance to the magnetic field depends onthe direction due to the structure of the PMT. For the most sensitive direction,
the maximum allowed field strength is 50 G where output of PMT becomes half
compared with zero-field. Figure 2.8 shows the profile of the magnetic field along
the boundary of the gamma ray detector. PMT response was measured in the2.3 Detector

16

COBRA field, at 31 points in a region corresponding to the active volume of the
gamma ray detector and 1 point where magnetic field is higher. The maximum
reduction of the PMT output was 40 % in the active volume. However, output
reduction was negligible at almost all PMTs located in the inner face where large
fraction of scintillation photons will be observed. Figure 2.9 shows the result of
the measurement for PMTs placed along the magnetic field, 4.23 meters awayfrom the axis. The magnetic field at the position is 61.7 G, and this value ishigher than that in the gamma ray detector.
�����������������

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

���������������
��

Figure 2.5: The COBRA magnet.

(a)

(b)

(c)

(d)

Figure 2.6: Conceptual picture of positron tracks in the COBRA magnetic field.

Relative output [%]2.3 Detector

17x−axisy−axisz−axis

y

140

z

120

x

100
80
60
40
20
0
−300

−200

−100

0

100

200

300

Magnetic flux density [Gauss]
Figure 2.7: PMT response(R6041Q) and magnetic field. Measurement was done
by Hamamatsu photonics

���

���

���

�����

����

�����

�����
����

���

�����
�
������
�����������

���

�

���

���

���

���

�

���

���
���

���

���

���

���

�

���

���
���

�����
����

��

�����
�
������
�����������
�

Figure 2.8: The COBRA magnetic field.

2.3 Detector

18

(a)

(b)

Figure 2.9: PMT response(R9288) and magnetic field. (a) Gain curves underthe magnetic field of 61.7 G (triangle) and in zero magnetic field (circle). (b)Ratio of the effective quantum efficiency to that in zero magnetic field as afunction of applied voltage.

2.3 Detector

19

Drift chambers
Tracks of positrons are measured mainly by drift chambers located inside the
COBRA. Requirements of drift chambers are follows.
• It must be light to reduce probability of scattering of positrons for better
detection efficiency and resolutions. It is also needed to reduce the probability of positron annihilation in flight (AIF) which can make accidental
backgrounds.
• It must work under a condition with very high rate muon decays on thetarget.
• It must have good hit position measurement capability and detection efficiency to reconstruct tracks with high precision, without increasing number of readout channels.
Figure 2.10 shows a picture of a chamber module before the final assembly.
The main structure of a drift chamber is supported by a thin carbon-fiber frame.
One edge of the frame in the direction to the target is open, in order to reducematerials in a region where many positrons transverse. The shape of the frame
is designed by taking into account a deformation due to the tension of wires.
Cathodes of the chambers are made of 12.5 µm thick polyimide with aluminum
deposition. The shape of the chamber walls is maintained by pressure control
of chamber gas and helium outside of the chambers. The pressure difference iscontrolled with a precision better than 0.005 Pa by a feed back control system.
Figure 2.11 shows the distribution of radius of positron tracks. Since the drift
chamber is designed to find µ+ → e+ γ signal, positrons with a small radius is
not interesting, while such positrons can saturate the drift chamber system witha high rate. The fiducial region of the drift chambers fully covers positrons withlarger momentum than 40 MeV.
The drift chamber is filled with a gas mixture of 50 % helium and 50 % ofethane.
z coordinate of a hit is roughly estimated from the charge ratio of two ends
of a wire with resolutions from 6.58 mm to 11.50 mm depending on wire length.
A precise estimation is done by using a so-called vernier pattern on the cathodefoil[17][18][19][20] as shown in fig.2.12. The cathode of a drift cell consists offour strips with a special pattern. The pattern has an interval of 5 cm which islarge enough than the z measurement precision from the charge ratio. Phases ofthe pattern are shifted by 1/4 interval for each strip so that a precise z position
can be measured from the ratio of charges of four strips. Averaged resolutionof z reconstruction is 612 µm.
r position of a hit can be roughly determined from a hit time, and it isestimated with a better precision by connecting several hits and finding a track
where angle dependence of drift time to distance relation can be taken into
account. The resolution is from 170 µm to 351 µm depending on drift distance.
A momentum resolution of 0.9 % and angular resolution of 6 mrad in σ for52.8 MeV/c positron have been achieved in the MEG engineering run in 2007.
Construction and performance in 2007 are described in a thesis[21].

2.3 Detector

20

rate(Hz/cm2 )Figure 2.10: A picture of a chamber module before the final assembly.

105
104
103
102
10
1
0

DC region
5

10

15

20

25

30

radius(cm)Figure 2.11: Positron rate as a function of radius with assuming muon rate of
3 × 107 / sec.

2.3 Detector

21zr
Figure 2.12: Vernier pattern on cathode foils.

2.3 Detector

22

Timing counters
The timing counter system consists of 30 φ-measuring counters and 512 zmeasuring counters.
φ counters are straight plastic scintillator bars made of BC404 lying alongz direction as shown fig.2.13. Two inch fine-mesh PMTs(R5924) are attachedboth ends. 15 bars are located in upstream and downstream from the target.
Signal positrons in the angular range of 0.08 < |cos θ| < 0.35 hit the counters.
In MEG 2007 run, the time resolution was measured to be 52.0 psec from
distribution of time difference between adjacent bars. The resolution of muon
decay time was estimated from MC simulation with taking into account the measured time resolution of single bars. Obtained time resolution is 58.7 psec. The
difference between the muon decay time resolution and the single bar resolution
is uncertainty of track-length reconstruction[21].
A z counter is a curved scintillation fiber put perpendicular to φ counters
as shown in fig.2.14. The purpose of z counters is to determine the z positionof hits with a good resolution, and the counters do not measure hit time. The
measured position is used to estimate the time of muon decay with subtracting
estimated time of flight from the hit times in φ counters.

Figure 2.13: A picture of timing counters (φ-measuring counters).

2.3 Detector

23

Figure 2.14: A picture of timing counters (z-measuring counters). 256 curved
scintillators are put on φ-measuring counters in this picture. Readout cards
attached to z counters can be seen in the picture.

2.4 Electronics and DAQ

2.4

24

Electronics and DAQ

Waveforms of the gamma ray detector and the positron timing counters aresent to active splitters through coaxial cables. Each splitter board has 16 input
channels and three types of outputs. For the first type of outputs, high bandwidth(1900 MHz) amplifiers (THS4509) are equipped. These outputs are sent
to the primary readout boards named DRS(Domino Ring Sampler). The second and third type of outputs are used for trigger. For the second output, lowdistortion amplifiers(AD8138) with lower bandwidth(320 MHz) are equipped.
The third output is an analog sum waveform of each four input channel. Anodesignals of the drift chamber are split by resistive splitter into two groups in the
proportion of one to nine. The larger one is sent to DRS, and the smaller one
is sent to trigger system after amplified to recover pulse height and summed up
according to trigger logic.
Trigger system is equipped with 100 MHz FADC to digitize waveforms and
FPGA implemented on VME boards. The system has a tree structure shownin fig.2.15. Analog waveforms are digitized by type 1 boards and serialized data
is sent to type 2 boards to determine triggers of sub-systems. Finally datafrom sub-systems is sent to a type 2 board in the third layer to make trigger
decision. When a trigger condition occurs, a stop signal is sent to DRS system.
In addition to type 1 and 2, type 3 which is a modified version of type 1 to record
waveforms of all individual channels of the gamma ray detector. Data taken bytype 3 boards is not used for trigger decision, but it is used in offline analysis.
Triggering algorithms were prepared for various kinds of event types such asµ+ → e+ γ (MEG), radiative muon decay(RD), self trigger of each subsystem,
random trigger and so on. Several algorithms can be used simultaneously witheach pre-scaling factor. The system has scalers of each trigger type. Live timeof the system is measured by the system itself.

Figure 2.15: MEG trigger tree structure2.4 Electronics and DAQ

25

All the waveforms from PMTs of the gamma ray detector, PMTs of timing
counters, wires and cathodes of drift chambers are digitized by DRS[22]. All
the waveforms are recorded as raw data. Charge and time of waveforms are
extracted in offline analysis, so no ADC or TDC modules are used in the DAQ.
The main purpose of recording waveforms is to allow to do pileup identification
in offline analysis, because it is a major source of background events in physics
analysis. It also allows to use better waveform analysis after improving it.
For example, we can try different noise reduction algorithms, time extraction
methods by using template fitting or constant fraction.
DRS is a switched capacitor array developed in MEG experiment to digitize
fast signal. A simplified schematic is shown in fig.2.16. The second version(DRS2) was used in MEG run 2007. Two DRS2 chips are mounted on a board,and two boards are mounted in a VME module. Each chip has 10 channels, with
1024 capacitive sampling cells. Two channels out of 10 are used for calibration
purpose. So actual number of channels per chip is 8. In total, 32 channels per
VME module can be read. In MEG experiment, 94 VME modules of DRS in
5 crates are used. Sampling rate of DRS2 is adjustable from 0.5 to 4.5 GHz.
The cells are read by an external 12 bit FADC. In 2007, 0.5 GHz was used forthe drift chambers and 1.6 GHz was used for the gamma ray detector and thetiming counters. The ninth channel is used to record trigger stop signal to allow
to know cell number corresponding to the trigger. The last channel is used toread a common clock signal which is distributed to all the DRS boards to alignphase of measurement. Analysis of time calibration by using this information is
described in section 7.3.1. Measured waveforms of the gamma ray detector by
DRS with 1.6 GHz sampling rate are shown in fig.4.2-a,b,c.
0.2−1 nInvertor ("Domino") chain

Rotating
signalInput 1

O utput 1
Input 2O utput 2
Channels
3 to 10

Shift Register

40 M Hz

Figure 2.16: Simplified schematic of the DRS2 chip

2.4.1

Data reduction

Because waveforms of each channels of sub-detectors are recorded, raw data
event size of the MEG experiment is large. If no data reduction or compression isused, the maximum data size is more than 5 MB/event. Event rate of µ+ → e+ γ
trigger with the highest beam intensity is expected to be around 20 Hz. Such

2.5 Proton accelerator

26

a large event size could cause many problems, for example I/O of disk, datatransfer over network, process speed of data compression in offline system andthe amount of storage. The bottle neck of the data flow can be I/O speed oftape system, which is 20 to 30 MB/sec.
Data reduction in 2007 run was done in two steps. The one was done during
data acquisition, and the other was ZIP compression of data files in offline
system. In the second step, data is compressed by about 50 %. For the first stepof data reduction, several kinds of algorithms were implemented for each subdetector. For the drift chambers and timing counters, region of interest(ROI)
and so called zero-suppression work. In case of these sub-detectors, pulse widthis relatively short compared to full time window of readout, hence it is possible
to choose narrower time window for recording without degrading resolutions orefficiency. Number of channels which have hits is small in each event. So, only
channels which have a large enough pulse and related ones (i.e. channels in thesame cell of a drift chamber and those in adjacent cells) were recorded.
In the case of the gamma ray detector, about 40 % of channels have hits ineach event, and time window of readout is not very large compared to scintillation decay time. Therefore ROI or zero-suppression does not decrease data size
so much. Instead of that, rebinning of waveforms was used. To measure timeof gamma rays precisely, waveforms of the gamma ray detector are sampled in
1.6∼2.0 GHz. However, such a frequent sampling is required only around thepeak of waveforms. To reduce the data size, waveforms of gamma rays were rebinned with wider bin width except around the peak. When changing binning,
the new entry is redefined to be an average of original adjacent bins to conserve
integrated charge. In run 2007, rebinning size was eight. Namely, data size was
reduced to about 1/8.
By all of these compressions, single event size was 1.15 MB/event in 2007.

2.5

Proton accelerator

For calibration of the sub-detectors by using gamma rays from nuclear reactions,a 1 MeV Cockcroft-Walton(C.W.) proton accelerator was prepared. Figure 2.17
shows a photograph of the accelerator. The main purpose of the accelerator isto generate 17.6 MeV line from Li(p,γ)Be which is resonant at Ep = 440 keVwith a resonance width of about 15 keV. This energy is 1/3 of µ+ → e+ γ
signal, however high rate monochromatic gamma rays allow to calibrate andmonitor the performance of the gamma ray detector. In addition to that, twocoincident gamma rays with lower energies(4.4 and 11.7 MeV) can be generated
with B(p,γ)C reaction. Properties of the accelerator are summarized in table
2.1.
A C.W. accelerator area was prepared at the downstream side of the muon
beam line. Protons are transferred through a beam line prepared on the sameaxis with the muon beam line, from the accelerator to a target. A part of thebeam line is made of bellows to allow inserting it into the COBRA volume
toward the target. It is possible to switch from the normal muon measurementmode to the calibration mode by moving the muon target to a parking position
and inserting another target and beam line for calibration quickly in around 20
minutes. Therefore, daily calibration by using the C.W. accelerator is possible.
For actual operation, a LiF crystal is used for lithium reaction. Fluorine has2.5 Proton accelerator

27

Figure 2.17: C.W. accelerator seen from the front. RF coil is on the left.

Terminal energy range
Energy ripple
Angular divergence
Spot size at 3 m
Energy setting reproducibility
Energy stability FWHM
Range of current
Current stability
Current reproducibility
Start-up time

Nominal300∼900 keV< 500 Vrms
< (5×5) mrad2< (3×3) cm2
0.1 %
0.1 %
1∼100 µA3%
10 %< 20 minMeasured at PSI
200∼1100 keV< 50 Vrms∼(4×4) mrad2< 1 cm2
OK
OK
0.1∼135 µA
OK
OK< 15 minTable 2.1: Properties of MEG C.W. accelerator

2.5 Proton accelerator

28

another gamma line of 6.13 MeV. The 17.6 MeV gamma ray generation rate is
1.8 kHz/µA. For boron reaction, a metallic boron piece is used as the target.
Figure 2.18 and 2.19 shows spectrum of gamma rays from these reactions.

(a)

(b)
Figure 2.18: Gamma ray spectrum from lithium measured with (a)Ge(Li) detector and (b)NaI(Tl) detector.[23]2.5 Proton accelerator

Figure 2.19:
detector.[24]29Gamma ray spectrum from boron measured with NaI(Tl)2.6 Signal and backgrounds

2.6

30

Signal and backgrounds

Backgrounds of µ+ → e+ γ measurement are a radiative muon decay with ahigh energy gamma ray and a positron (prompt background), and an accidental
coincidence of a Michel positron and a particle hit the gamma ray detector(accidental background). Sources of gamma ray detector hits are those fromradiative muon decays, those from positron annihilation in flight, low energy
cosmic rays or secondaries of them and pile up of these hits. Kinematics ofsignal, prompt background and accidental background are shown in fig.2.20.

γ
νe

µ+

µ

γ

νµ

+

νe

νµ
e

e+
(a)

+

µ+
e+

(b)

(c)

Figure 2.20: Signal and backgrounds of µ+ → e+ γ .

γ

Chapter 3

Liquid xenon scintillation
detector
Xenon is used for various applications such as dark matter search, neutrinolessdouble beta decay search, medical applications(PET) and gamma ray astronomy
because of its excellent characteristics as ionization or scintillation medium, suchas a high light yield, fast decay time. It is also popular to use combination ofionization and scintillation. Details of the scintillation mechanism are describedin ref.[25]. In this chapter, general aspects about liquid xenon as a scintillation
medium are shown, then structure and construction of the gamma ray detector
for MEG experiment are described.

3.1

Liquid xenon

Figure 3.2 shows a comparison of properties of crystal scintillators and thoseof liquid xenon. As shown in the table, light output of liquid xenon is large
and decay time constant is fast. These properties make it possible to make adetector with good energy and time resolutions. Fast decay is suitable for highrate experiment like MEG to identify pileup events by waveform analysis. Large
atomic number and high density comparable with crystal scintillators allow tomake a rather compact detector, hence a detector can have a good reconstruction
capability of interaction positions. Because it is liquid, it is possible to makea large detector with a uniform response. Liquid xenon is not damaged byradioactivity.
Interaction of particles with xenon atoms can form both Xe+ (ion) and Xe∗(excited) state. Excited atoms lead to the formation of excited dimers(Xe∗2 )which emit scintillation photons in de-excitation process. Two excited states,
single and triplet, have different decay time constants of 4 and 22 nano seconds respectively. Ionized atoms emit scintillation photons through a processdescribed from equation.3.2 to equation.3.7. Decay time of recombination differs depending on ionizing particles. In the case of alpha particles or fission
fragments, it is less than 1 nano seconds, on the other hand for electrons andgamma rays, it is 45 nano seconds. Fractions of three processes depends onionizing particle and electric fields. Decay time constants of three processes3.1 Liquid xenon

32

Table 3.1: Properties of xenon
Atomic Number
Mass Number
Density at 161.4 K
Boiling point
Melting point
Emission peakSpectrum width
Refractive index
Wph for 1 MeV electrons
Decay time(recombination)
Decay time(fast components)
Decay time(slow components)
Absorption length
Scattering length54131.2932.978 g/cm [26]165.05 K
161.25 K
178 nm [27] [28]14 nm [27] [28]1.57 to 1.72 [29] [30] [31]21.6 eV [32]45 nsec [25]4.2 nsec [25]
22 nsec [25]> 100 cm
29 cm to 50 cm [31][33][34][35]Table 3.2: Comparison of physical properties of crystal scintillators with thoseof liquid xenon

Effective atomic number
Density (g/cm3 )Relative light output (%)
Decay time (nsec)

NaI
50
3.7
100
230

BGO
73
7.1
15
300

GSO
58
6.7
20-40
60

LSO
65
7.4
45-70
40

Liq. Xe
54
3.0
80
2.2,27,45

3.1 Liquid xenon

33

without electric fields are shown in table 3.3. Figure 3.1 shows scintillation
signals of liquid xenon by various particles. Two decay time components areclearly seen in signals by alpha particles and fission fragments, while it seems
that the signals by electrons have one slow component by recombination. The
recombination component must disappear when an electric field is applied. Scintillation signals with and without electric fields are shown in fig.3.2. When an
electric field is applied, the usual two components can be seen. Actual ratioof ionization and recombination can be estimated from the ratio of scintillationand ionization signals with various electric fields. According to ref.[32], it isconsidered from 0.06 to 0.20.
Xe + Xe∗ → Xe∗2 → 2Xe + hν

(3.1)

→

Xe+ + e→Xe+
2 + Xe
∗∗

(3.2)
(3.3)

Xe
+

Xe + Xe + Xe

Xe+
2 +e →∗∗

Xe
Xe + Xe + Xe
Xe∗2

∗

Xe

+ Xe

(3.4)

→
→

Xe + heatXe∗2 + Xe

(3.5)
(3.6)

→

2Xe + hν(3.7)∗

Radiation
Electrons
Alpha particles

τs
4.3 ± 0.6τt
22 ± 1.5

τr
∼ 45
-

Table 3.3: Decay time of liquid xenon
Figure 3.3 shows attenuation coefficients of gamma rays in xenon. It is
minimum around 4 MeV. Around 50 MeV, pair production dominates. Mean
free path in liquid xenon is 3.46, 9.37 and 5.48 cm for 0.5, 4.0 and 50 MeV
respectively.

3.1 Liquid xenon

Figure 3.1: Signal of liquid xenon scintillation.[36]343.1 Liquid xenon

35

Attenuation Coefficients [cm 2 / g]Figure 3.2: Signal of liquid xenon scintillation and electric field.[36]Total Attenuation

Photoelectric Absorption

Scattering

Pair
Production

Photon Energy [MeV]

Figure 3.3: Interaction of gamma ray in liquid xenon

3.1 Liquid xenon

3.1.1

36

Scintillation efficiency

The average value to produce one photon in liquid xenon (Wph ) has been measured by several groups, and it is known that there is a linear energy transfer(LET) region so called “flat top response” where scintillation light is fully emitted without any reduction processes. In this region, Wph is 13.8±0.9 eV. Figure
3.4 shows the dependence of relative scintillation yield on LET. Lines in the figure is calculations with using different η0 parameter. η0 is the scintillation yieldat zero electric field in the limit of zero LET. Low LET region and high LET
region have less yields than “flat top response” by different reasons. In thecase of electrons and gamma rays in the low LET region, the decrease is due toescaping electrons. Because the mean interval of electron-ion pairs produced bya minimum ionizing particle is comparable with the Onsager radius (49 nm), a
large number of electrons will not recombine with the parent ion. At the Onsager radius, Coulomb energy is equal to the thermal energy. By this reason,
scintillation yield depends on the density of ions, therefore it depends on LET.
Reduction factor of yield of 1 MeV electron was measured to be 0.64 ± 0.03[32].
In the case of the very high excitation density, it is considered that quenching
can happen by following process before forming excited molecules. Reduction
factor of yield of 5.3 MeV alpha particle was measured to be 0.77 ± 0.04[32].
Xe∗ + Xe∗ → Xe + Xe+ + e−

(3.8)

���

�� ��
���

�

�������

�������������������������������Y

���

���
�������

���

���

���

�

�� �

���
���

���

���
���

���

���

���

���

�������������������������� �

���

���

���

Figure 3.4: Dependence of scintillation yield on LET in liquid xenon. Solidcircles represent yields for relativistic heavy particles whereas open circles represent those for electrons, alpha particles and fission fragments. Open squares
represent gamma ray.[32]3.1 Liquid xenon

3.1.2

37

Attenuation of scintillation light and impurities

Attenuation consists of scattering and absorption. Scattering length depends
on wavelength of photons, density and the refractive index of the liquid. Attenuation length of liquid xenon has been measured and reported by several
groups[31][33][34][35] to be 30 to 50 cm. Scattering length for a single component
system can be calculated using the formula given in Landau and Lifshitz[37].
"
 2

2 #
∂
ω4
kT 2 ∂2kT ρ κT
h=
+
6πc4
∂ρ T
ρcV ∂T ρ(3.9)

where ω is the angular frequency of the radiation, c is the velocity of light, k
is Boltzmann constant, T is the temperature, ρ is the liquid density, cT is theisothermal compressibility, cV is the heat capacity at constant volume, and  isthe dielectric constant. These thermal properties of rare-gases can be found inref.[38]. By using measured dielectric constants( 2.85), scattering length of pureliquid xenon for 174 nm light was calculated to be 30 cm[31].
Since scintillation photons of xenon are emitted from exited dimers, there
is no self-absorption. Hence, if the liquid is completely pure, the liquid would
be transparent to its radiation. However, ultra-violet light is very sensitive toimpurities. Major impurities for liquid xenon scintillation are water and oxygen.
Figure 3.5 shows relative light intensity in liquid xenon as a function of distancefrom a light source for various amount of impurities. As seen in these figures,contribution of water is much higher than oxygen.
WArP collaboration recently measured effects of nitrogen and oxygen contamination in liquid argon[43][44]. In these articles, effect of quenching byfollowing reaction is discussed.
Ar2∗ + N2 → 2Ar + N2

(3.10)

Quenching factor for 1 ppm contamination is about 80 % and 60 % fornitrogen and oxygen respectively. It was reported in these articles that whenquenching happens, longer time component is reduced and pulse width becomesnarrower than pure argon.
For large liquid xenon detector for MEG, impurities need to be reduced
at least down to 10 ppb, 100 ppb, 100 ppb for water, oxygen and nitrogen
respectively.

Absorption Coefficient [m −1]

3.1 Liquid xenon

38

OxygenXe Scintillation Spectrum

1

0.1
Water Vapor

0.01
130
(a)

140

150

160
170
180
Wave length [nm]Absorption in H 2O−doped Xe

200 ppb

200 ppb
1 ppm

I0 / I

I0 / I

100 ppb

15 ppm
10 ppm

−1

−1

10

1 ppm

200

Absorption in O 2−doped Xe

1
100 ppb

190

10

5 ppm
10 ppm
−2

−2

10

10
0

(b)

10 20 30 40 50 60
Distance [cm]

0
(c)

10

20 30 40 50
Distance [cm]Figure 3.5: (a) Absorption coefficients for 1 ppm water vapor and 1 ppm oxygen[39][40][41][42]. Superimposed is the xenon scintillation spectrum. (b) Scintillation light intensity as a function of the distance from the light source for various
concentrations of water in liquid xenon. (c) Same as (b) but for oxygen.

3.2 Liquid xenon gamma ray detector of MEG

3.2

39

Liquid xenon gamma ray detector of MEG

Figure 3.6 is a schematic view of the MEG gamma ray detector. A C-shaped
gamma ray detector is located beside the positron spectrometer. Definition of
six faces of the PMT holders (inner, outer, upstream, downstream, top andbottom) are shown in the figure. It covers 10 % of the solid angle viewed fromthe muon stopping target. The cryostat of the gamma ray detector is filledwith over 800 litters of liquid xenon surrounded by 846 photo-multiplier tubes(PMT). The PMTs are immersed in the liquid xenon to observe scintillation
photons directly. Gamma rays from the target enter the active volume of thedetector through an entrance window consisting of an aluminum honeycomband carbon fiber plates. Then a gamma ray interacts with the liquid xenon anddeposit energy to excite xenon molecules, resulting in emission of a large amountof scintillation light. The scintillation light yield is as large as 80 % of NaI. The
decay time of scintillation is five times faster than that of NaI. Because of theseproperties, the liquid xenon scintillation detector is expected to have excellent
performance to measure energy, position, and time of gamma rays.

Liquid xenon
Top face

Level meter

Lateral (Upstream) face

PMTγ
Muon target

Outer face

Inner faceγ

Muon target

1m

Outer face

1m
Inner face

Bottom face

Lateral (Downstream) face

(a)

(b)

Figure 3.6: Schematic view of the MEG gamma ray detector. (a) Side view (b)Top view

The acceptance of the experiment corresponds to an area shown in fig.3.7.

3.2 Liquid xenon gamma ray detector of MEG

40

58 cm
51.4 cm

150.6 cm

144.0 cm

Figure 3.7: Projection of the acceptance of the experiment to the inner faceof the gamma ray detector. Red boxes correspond to the acceptance of theexperiment. The center part shown in light pink is a part of the acceptanceof the gamma ray detector, but corresponding back-to-back direction is not in
the acceptance of the positron detector because signal positrons in the angularrange do not hit the timing counter.

3.2 Liquid xenon gamma ray detector of MEG

3.2.1

41

PMT for the gamma ray detector

A new model of metal channel PMT was developed by MEG collaboration andHamamatsu photonics. The photo-cathode material is K-ScSb. This is designed
such that it can be immersed in liquid xenon and it can observe scintillation
light of liquid xenon directly. For this purpose there are several points to takecare of. Scintillation light of liquid xenon is vacuum ultraviolet(VUV) which
has a peak at 178 nm. Normal PMT windows made of glass is not transparent
to the light. Therefore in many experiments, scintillation photons are measured
after shifting wavelength longer. The PMT for MEG is equipped with a quartz
window which is 80 % transparent to the scintillation light. Pressure of the liquid
xenon in the detector is usually controlled to be around 0.12 MPa. However,it can be about 0.2 MPa during transfer. The cryostat is evacuated before
filling it with xenon. So, the PMTs must be tolerant to pressure from 0 to
0.2 MPa. Heat generation by PMTs is one of major sources of heat load of thedetector. In order to minimize the heat generation, current of the HV line isrelatively low. Usually, it is around 60 µA during measurement in MEG. During
the measurement of muon decays, there are high rate background scintillations
by gamma rays and neutrons. To stabilize PMT gain under high backgroundconditions, Zener diodes are put at the last two steps as shown in fig.3.9. Thanks
to these diodes, gain variation due to background is in a few % during themeasurement depending on individual PMTs. Resistance of cathode become
higher in low temperature than in room temperature. To avoid Q.E to be
decreased in a low temperature, aluminum strips are attached on the surface of
cathode as shown in fig.3.8-b.

3.2 Liquid xenon gamma ray detector of MEG

(a)

(b)
Figure 3.8: Hamamatsu R9288.

Figure 3.9: Base circuit of R9288.

423.2 Liquid xenon gamma ray detector of MEG

3.2.2

43

CryostatBecause the cryostat is located in a strong magnetic field, it is made of nonmagnetic materials. Materials with low permeability were carefully chosen tobuild the cryostat in order to reduce magnetic field around PMTs. Deformationand stress of the cryostat was studied by using simulation during designing withtaking into account weight of liquid xenon.
The cryostat consists of inner and outer vessels. The volume between the twovessels is evacuated for thermal insulation. Super insulation layers are installed
between the two vessels to suppress heat income due to radiation.
Xenon is liquefied by a pulse-tube refrigerator and a liquid nitrogen coolingpipe equipped at the top of the cryostat. After the liquefaction, the liquid
xenon is kept in a stable condition by the refrigerator. The effective coolingpower is controlled by a feed back system. Another line of LN2 is attached on
the outside of the inner vessel to directly cool the vessel. This is used mainly forpre-cooling of the vessel before starting liquefaction. The system can be usedalso when there is a problem to use the LN2 at the top of the cryostat. Picturesof the second LN2 line is shown in fig.3.10.

Figure 3.10: Liquid nitrogen pipe attached on inner vessel.

For measuring the level of the LXe, a capacitance level-meter is installed.
The temperature of the xenon is measured by 27 pt-100 sensors located atvarious positions. Additional temperature sensors are attached on the outsideof the inner vessel to monitor temperature of the cryostat. All the cables from
PMTs and sensors installed in the inner vessel go to feedthroughs attached on
chimneys at the top of the detector. A turbo molecular pump and a cryo-pumps
are directly attached at the chimney to evacuate with a high conductance. Since
water vapor is the largest component of the residual gas in the case of MEG
gamma ray detector, a cryo-pump works very well.
The inner vessel is designed to minimize heat coming from room temperature
part. For example, bellows plates are used to connect inner vessel with the top
chimney. Total heat load is shown in table 3.4. The largest sources are heatgeneration by PMTs and conduction of PMT cables.

3.2 Liquid xenon gamma ray detector of MEG

Radiation
Conduction
Conduction
Conduction
Heat generation
Conduction
Total

Outer Vessel → Inner Vessel (30 Mylar layers)
Nozzle via xenon gas
Nozzle via bellows
Support (brace and supporting pipe)
PMT (65 mW/PMT)PMT HV and Signal Cables

Table 3.4: Heat load of the gamma ray detector

44

3.1 W
0.2 W
4.6 W
6.3 W
52 W
50 W
116.2 W

3.2 Liquid xenon gamma ray detector of MEG

45Gamma ray entrance window is designed to be as thin as possible in orderto minimize the probability of gamma rays converting in it. As well as that,mechanical strength is required in wide range of temperature from 165 K toroom temperature. To satisfy these constraints, aluminum honeycomb panel
covered with carbon fiber plates was chosen. The panel was produced by an
Italian company Plyform. Three types of honeycomb panels was produced withdifferent materials and designs. First two panels failed during pressure tests. In
both tests, cracks appeared at the edge of carbon fiber plates. After optimizationof the design, the third panel successfully passed all the tests. Pressure test was
performed up to 0.5 MPa and no damage was found. For the third panel,
low modular and good elongation carbon fiber(T300) was used. The platesconsists of eight piles, and the total thickness is 1.5 mm, glued with epoxyresin (Hysol EA9361). The window consists of the central honeycomb of 24 mm
thickness, reinforcement, internal and external skins. The central honeycomb
made of aluminum and skins are made of carbon fibers. All these parts are
glued. Pictures of these parts and the complete panel are shown in fig.3.11.
The gamma ray entrance window on the inner vessel consists of the honeycomb
panel and a stainless steel plate of 0.4 mm thickness welded from the inside.
That on the outer vessel is a 0.7 mm thickness stainless steel plate welded fromthe outside
In total, thickness of the window corresponds to 0.075 radiation length.

(a)

(b)

(c)

(d)

Figure 3.11: Pictures of honeycomb panel. (a) Inner skin. (b) Outer skin. (c)Reinforcement. (d) After gluing all the parts.

3.2 Liquid xenon gamma ray detector of MEG

3.2.3

46

Handling of xenon

The gamma ray detector for MEG is the largest xenon detector ever made,which utilizes around 1000 litters of liquid xenon. This is the first time tohandle such a large amount of xenon. Since xenon is expensive and production
is not very fast, the xenon system was designed not to throw away xenon duringexperiment. Figure 3.12 shows a schematic view of xenon system of MEG.
There are two types of storage. The one (GXe storage) consists of eight tankswith each 250 litters of volumes. And the other (LXe storage) can store about1000 litters of xenon in liquid phase. A purification system is installed between
two storage systems to purify GXe when it is transferred from the GXe storage
tanks to the LXe storage tank or to the detector.

Vacuum Pump

Reducer

Purifier

Liquid phase purifier

Detector

LXe storage tankPurification system

GXe storage tanks

Figure 3.12: Xenon line. Thicker lines in the figure between detector, liquid
phase purifier and liquid storage are vacuum insulated pipes for liquid xenon
transfer.
Figure 3.13 is a photograph of the GXe storage tanks produced by Taiyo
Material Inc. Pressure of xenon is not increased linearly as a function of density
as shown in fig.3.14. GXe tanks are tolerant to 8 MPa, thus can contain up to
1.44 g/cm3 , 360kg of GXe (it is equivalent to 120 liters of LXe).
Figure 3.15 shows a schematic view and a photograph of the LXe storagetank produced by Taiyo Nippon Sanso Co. The purification system is shownin the right part of the photograph. The specification of LXe storage tank issummarized in table 3.5. The LXe storage tank consists of inner and outer
vessels. Xenon is stored in the inner vessel in liquid phase. The volume of theinner vessel is 1110 liters, and the maximum storage quantity is 1000 liters.
From cryogenics point of view, the structure is similar to that of the gamma
ray detector. A test of the LXe storage tank was done and it was checked thatthe heat income is same as expected(20 W). When all cooling systems were
stopped, the pressure was increased from 0.11 MPa to 0.2 MPa in 43 hours. So,
the cryogenic system is safe even when there is no electric power and control for
certain period.
Xenon in the GXe storage tanks can be transferred to the LXe storage tankor the detector by making use of a pressure difference. When GXe is transferredto the LXe storage tank, GXe is liquefied in the LXe storage tank continuously,
and the pressure is kept to be around 0.1 MPa. Xenon can be transferred until
an equilibrium is established between the pressure of LXe storage tank and the3.2 Liquid xenon gamma ray detector of MEG

47

Figure 3.13: GXe storage tanks in the experimental area

120

100

Pressure [bar]

52

C 7C
4 C
42
C
37

80
32 C
27 C
22 C

60

17 C
Critical Point
58 bar, r = 1.1 g/cm 3@ 17 C

40

20

0
0

0.4

0.8

1.2

1.6

2.0

3

Density [g/cm ]Figure 3.14: Temperature and density of gas xenon.

3.2 Liquid xenon gamma ray detector of MEG

48

Figure 3.15: (a) Schematic view and picture of the LXe storage tank. (b) A
photograph of LXe storage and gas purification system.

Dimension
VolumeDesign pressure (DP)Hydrostatic test pressure
Air test pressure
Design temperature
operation temperature
Material
Designed heat income
Inner surface treatment

φ1400 × 2570mm2
1110 L(Max storage 1000L)
0.6013 MPa
0.91 MPa (1.5 x DP)
0.67 MPa (1.1 x DP)-196 ∼ 40 ◦ C
165 K
SUS304< 20 W
electrochemical
polishing

Table 3.5: specification of LXe storage tank3.2 Liquid xenon gamma ray detector of MEG

49

GXe storage tanks where about 1.5 kg of GXe remain in the GXe storage tanks.
The LXe storage tank is connected to the detector by vacuum-insulated pipes totransfer the xenon in the liquid state by making use of a pressure difference. It
makes the transfer much faster than that in gaseous state. The speed of transferring xenon in gaseous state is limited by the cooling power for liquefactionof xenon. Xenon will be kept in either the detector or the LXe storage tankwhile MEG experiment is running. However during long-term shutdown of theexperiment such as a detector upgrade, xenon will be stored in the GXe storage
tanks because no control systems or electric power are needed. In order to recover xenon to the GXe storage tanks, GXe storage tank is cooled by LN2 filledin Dewar in which tanks are located, and the LXe storage tank is pressurized up
to 0.18 MPa by using heaters installed at the bottom. Then,evaporated xenon
is transferred to GXe storage tank, and solidified continuously. After recovering
all xenon from the LXe storage tank, and valves of the GXe storage tanks areclosed, the cooling of the GXe storage tanks is not necessary any longer. Suppose that the temperature of the xenon inside the GXe storage tanks reaches
low enough (less than 100K), xenon remained in the LXe storage tank can be
expected to be negligible.
A heated purification getter[45] is equipped in the purification system. The
purifier removes H2 O, O2 , CO, CO2 , H2 , N2 and hydro carbon molecules fromGXe down to 1.0 ppb. Gas purification test with 100 liters of xenon by using
a similar purifier is described in ref.[46][47]. It was confirmed that the impurities, mainly water, were successfully reduced, and an adequate performancefor the MEG photon detector could be achieved. However, purification in gas
phase is relatively slow, hence it is not suitable for the final gamma ray detector, which utilizes much more xenon. Therefore a purification system withcirculation of xenon in liquid phase was developed[48]. A similar system was
firstly tested by using the large prototype detector. And it was found that thesystem reduces amount of impurities from 250 ppb to less than 40 ppb in 5 hours
operation for 100 litters of xenon. Figure 3.16 is a picture of the liquid phase
purifier equipped to the final detector. In the purifier vessel, centrifugal pumpand purifier (molecular sieves) are installed. The system is connected with thedetector by vacuum insulated pipes to circulate xenon through the purifier inliquid phase. The pump has a capability to flow xenon up to 71 liters per hour.
The speed is much faster than gas purification (60 c.c. liquid per hour).

3.2 Liquid xenon gamma ray detector of MEG

Figure 3.16: Liquid phase purification system

50

3.2 Liquid xenon gamma ray detector of MEG

3.2.4

51

PMT test

About 1000 PMTs were tested before installed into the gamma ray detector. The
half of them were tested at PISA test facility[49] and the others were tested at
PSI with using the large prototype detector. In the test, gain at 800 V of H.V.,
Q.E. and dark current was measured. Bad PMTs (problem of base circuit, lowgain or low Q.E.) were repaired or eliminated from the list of usable PMTs.
In addition, shape of glass tube was measured in a precision of a few ten µm,
because a PMT may not fit to the PMT holder of the inner face if the shape
is too much different from the typical one. PMT holders of the inner face havemore fine structure than other faces.
Since PMTs in the inner face is important, we have chosen suitable PMTs
for the part. In figure 3.17, measured gain and Q.E. of currently installed PMTs
are shown. To make response of the detector as uniform as possible, center partof Q.E. distribution was chosen for inner-face. For low gain PMT, H.V. will behigher when gain is adjusted to be a certain value. In general, higher H.V. gives
better linearity and smaller transit time spread (TTS). By this reason, low gain
PMTs were chosen for inner face.
50
50
40

40

30

30

20

20

10

10

0
0

100

200

300

400

500

600 700 800 900 1000
Relative gain at 800 V (a.u.)

0
0

50

100

150

200

250
300
Relative Q.E. (a.u.)

Figure 3.17: Measured gain and Q.E. in PMT test. Hatched part is PMTs used
in inner face.

3.2 Liquid xenon gamma ray detector of MEG

3.2.5

52

Alignment

Before installing PMTs. In the cryostat, targets to measure positions are attached to rails for PMT holders. The position was measured by using laser.
Correct position was marked on the platform for locating the detector after
installing PMTs. It was done with accuracy better than 1 mm and the error
is negligible compared to position resolution of the detector. Figure 3.18 isphotographs during the alignment.

Figure 3.18: Photographs during alignment of the gamma ray detector. A target
for the alignment is attached to the rail on the inner face.

3.2.6

Installation of PMT

PMT holders consist of several slabs, as shown in fig.3.20, so that the assembly ofslabs can be done separately. In inner and outer faces, 9 PMTs are in a slab. In
lateral faces, 6 PMTs are in a slab. Top and bottom faces are each one big platecontaining 54 PMTs. Holders except for the inner face are made of aluminum.
PMTs and holders are electrically isolated by Teflon parts to make the groundlevel of PMT independent of cryostat’s level. The holder of the inner face ismade of PEEK to decrease material between the active volume and the target.
The design of the inner PMT holder is carefully done not to make rooms whereliquid xenon can enter. Spaces behind PMTs were filled Delrin parts and small
grass beads to avoid base circuits are destroyed by deformations of materials ina low temperature. Cables are embedded in STYCAST as shown in fig.3.19 to
fit the shape of holder. If there is a void in STYCAST used to form a cablestructure, air inside the void can leak during experiment, and it can contaminate
liquid xenon. To void it, STYCAST is put in vacuum before it is hardened toeliminate air contained in it. The cable structure was made carefully not tomake voids. Assembled slabs are mounted as shown in fig.3.20. Gaps between

3.2 Liquid xenon gamma ray detector of MEG

53

inner surface of cryostat and holders smaller than 0.75 mm were filled by using
Teflon sheets of 250 µm thickness.

Figure 3.19: Installation of PMTs in inner a face holder.

After the slabs were mounted, cables were connected to inside-patch-panels,
then to feedthroughs. All the electrical connections were checked, and PMT
signals were checked by using an oscilloscope. Other components for monitoring
and calibrations such as alpha sources, LEDs, temperature sensors, level meters
were installed. As shown in fig.3.21, after installing all the parts, aluminum
blocks were put to reduce empty spaces so that necessary amount of xenon was
decreased.

3.2 Liquid xenon gamma ray detector of MEG

(a)

54

(b)

Figure 3.20: Installation of PMT holders. (a) Inner face. (b) Lateral and outerface.

3.2 Liquid xenon gamma ray detector of MEG

Figure 3.21: A picture after installing every part to the cryostat.

55

3.2 Liquid xenon gamma ray detector of MEG

3.2.7

56

Slow control of the system

The slow control system in MEG is controlled by electronics using the MSCB[50]system developed in PSI. Each control node connected to MSCB bus has a
micro-controller. A picture of two SCS-2000 nodes is shown in fig.3.22. Up toeight daughter cards can be inserted in a module. Several daughter cards areavailable such as ADC, DAC, capacitance meter, current source and relays. One
node has up to 64 I/O channels.

Figure 3.22: A picture of a SCS-2000 node. The right one is used as a LED
pulser and has LEMO connectors instead of normal back-plane.
They control the xenon system by making use of proportional-integral-derivative(PID) control algorithm which is a generic control loop feedback mechanism
widely used in industrial systems. The control nodes handle valves (open/close),equipments such as pumps, and acquires the system status (temperatures, pressures and so on). Firmwares were developed specially for the xenon system.
Variables in the processor can be overwritten either through front panel of eachnode, or through MSCB bus without interrupting the operation. MSCB bus
can be connected to computers with USB or Ethernet adaptor.
Status of the system is monitored by using LabVIEW[51] panels running ona remote computer. The panels are prepared to show the status graphically,
to change control parameters, and to use alarm system. Control nodes have aconnection to the computer over Ethernet by using MSCB bus adapters. The
system is not affected even if the computer on which LabVIEW program isrunning has some problems, because algorithms and all the variables are on thememories of micro controllers in the control nodes. A part of the LabVIEW
panel is shown in fig.3.23. An alarm system is implemented in the LabVIEW
panels so that emails are sent to mobile phones when the pressure of LXe storagetank or the temperature of LXe becomes out of a certain range or the connection
between the computer and the control nodes is lost. The status of almost all
valves can be changed through the panel so that the storage system can be fully
controlled remotely even when the beam area is closed.

3.2 Liquid xenon gamma ray detector of MEG

57

Control of xenon system consists of four sub-systems. Namely, the detector,
the LXe storage, the GXe storage and GXe purification system as shown in
fig.3.24. The LXe purifier is included in the detector’s part. All the necessary
values for controlling each sub-systems are read in the node so that each subsystem works independently.

Figure 3.23: A part of LabView control panel. All the valves drawn here canbe controlled from the panel. Pressures and status of heaters are shown in thispart.
Relation between pressure and temperature of xenon is shown in fig.3.25.
During the experiment, pressure is controlled to be stable around 0.13 MPa.

3.2 Liquid xenon gamma ray detector of MEG

58

Human interface

Network
Logging and alarm

Bus adapter

Detector

Liquid storage

Gas storage

Gas purifier

Sensors, Valves, Heaters, Compressors, Pumps...

Figure 3.24: Slow control system of the gamma ray detector. Four SCS-2000
control nodes read sensors and handle valves, heaters and so on. Variables in
the nodes can be monitored or changed from computers over network by using
several interfaces.

3.2 Liquid xenon gamma ray detector of MEG

59

2

Pressure [atm. absolute]

10

liquid

10

1

solid

gas

−1

10

120

140

160

180

200

220

240

Temperature [K]Figure 3.25: Phase diagram of xenon

2603.2 Liquid xenon gamma ray detector of MEG

3.2.8

60

Electronics

Figure 3.26 is a schematic view of the connection from PMTs to DRS, trigger
system and H.V.. Coaxial cables from PMTs are connected to a patch panel
located in the cryostat. Here, lines for signals and high voltages are separated
and go to each feedthrough. Signal cables are connected with active splittersthrough a patch panel. After the splitters, signals are sent to trigger and DRS
boards. DRS and trigger boards are described in section 2.4. High voltage
cables are connected with voltage dividers through patch panels. Pictures ofoutside a patch panel and a feed through is shown in fig.3.27.

FeedthroughPatch Panel

Trigger

Computer

DRS

Computer

Splitter

Inside cryostat
Flat

Co−axial (4 m)Flat

Co−axial (4 m)

PMTPatch Panel

Signal line
H.V. line

Voltage divider

Power supply

Figure 3.26: Connection from PMT to electronics

(a)

(b)

Figure 3.27: Picture of (a) outside patch panel and (b) feedthrough.

Chapter 4

Simulation
Simulation of MEG experiment is done by two programs. The one is basedon Geant3, and it includes event generation starting from a muon decay on thetarget or a muon beam, particles tracking and sub-detector responses simulation.
The other was written from the scratch in MEG collaboration with using ROOT
package. This program reads several output files from the detector simulator,
merges several events to simulate accidental pileups, and makes waveforms bysimulating electronics devices. Digitization of waveforms are also simulated, andthe result is written in the same format with experimental data.

4.1

Scintillation photon tracking in the gamma
ray detector

At each energy deposit position in the active volume of the gamma ray detector, scintillation photons are generated isotropically according to the energy
deposits and assumed scintillation efficiency. Scintillation efficiency is different
depending on particles. During the tracking, several optical processes such as
Rayleigh scattering, absorption by impurities, reflection on walls or PMT windows, transmittance of PMT window and efficiency of photoelectric effect on
cathodes are simulated. Arrival time of photons at each PMTs are recorded in
output files.

4.2

Gamma Ray Detector waveform simulation

Waveform simulation includes multiplication in PMT, attenuation of pulses incables, reflection by impedance mismatching, clipping and smearing in electronics and digitization on read out chips. It is done by using photon arrival time
information from the detector simulator.
Two ways were prepared for the simulation. In one method, each processes
are parametrized and simulated separately. Namely, transit time spread of PMT
is simulated by a Gaussian distribution, attenuation is done by software filteringwith assumed frequency cut off and so on. In the second method, simulation isdone by convolution of photon arrival time with a known impulse response. The
impulse response is obtained from real waveform and distribution of PMT hit4.3 Response of the gamma ray detector

Impulse Response[a.u.]XEC Template Waveform[a.u.]

62

0

0.008

-50

0.006

-100
-150

0.004

-200
-250

0.002
-300
-350

0

-400
0

0.1

0.2

0.3

0.4

0.5
[sec]

×10

-6

×10

-6

-450
-0.1

0

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18
[sec]

(a)

(b)

−0.5

[mV]

[mV]

[mV]

Figure 4.1: (a) Template waveform created from real data. (b) Impulse response.

0

0
−50

−1

−2

−1.5

−100

−4

−2

−150

−6

−2.5
−8

−200

−3
−10
−600

−500

−400

−300

−200

−100

−600

[nsec]

−500

−300

−200

−100

−600

[nsec]

−500

2
1.5

−400

−300

−200

−100

-200

-100

[nsec]

(c)
[mV]

(b)
[mV]

[mV]

(a)

−400

4

0
-50

2

1

-100

0

0.5

-150

-2
0

-200

-4
-0.5

-250

-6
-1

-8
-600

-500

-400

-300

(d)

-200

-100

[nsec]

-300
-600

-500

-400

-300

(e)

-200

-100

[nsec]

-600

-500

-400

-300

[nsec](f)

Figure 4.2: Waveform of real data(a)(b)(c) and simulation(d)(e)(f). Rebinning
except around the peak is done for large pulses for data reduction.

time in MC simulation assuming scintillation decay time of 45 nsec. Deconvolution was done by Fourier-transform. Once we obtain the impulse response from
data, the second method reproduces the data well. Template waveform createdfrom real data, and impulse response created from the template is shown in
fig.4.1 Gaussian noise can be simulated. Also for noise simulation, frequency
dependent attenuation is taken into account. Figure 4.2 shows waveforms ofreal data and simulation for different pulse heights.

4.3

Response of the gamma ray detector

Figure. 4.3 shows the energy deposit in the active volume for signal gamma
rays generated in the detector acceptance. The lower tail is due to gamma ray
interaction before the active volume, and escape of gamma rays from the active
volume. The probability of escape is larger in the shallow and very deep part.
The detection efficiency calculated from the simulation of signal events is shownin fig. 4.4. About 40 % of gamma rays from muon decays impinge to the active
volume without interacting with COBRA magnet or materials before the active
volume. However due to escape, the efficiency depends on the energy threshold.

4.3 Response of the gamma ray detector

63

25000

20000

15000

10000

5000

0
40

42

44

46

48

50

52
54
56
Energy deposit [MeV]Event fraction

Figure 4.3: Energy deposit of simulated signal events in the acceptance.

0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
46

47

48

49

50

51
52
53
Energy threshold [MeV]

Figure 4.4: Efficiency of the gamma ray detector as a function of energy threshold.

Chapter 5

Prototypes
Before constructing the final gamma ray detector, a small prototype with 2.3
litters of fiducial volume and a large prototype with 68.6 litters of that wereconstructed. It was confirmed by the small prototype that the newly developed
PMTs work with expected performance, and the detector has a good performance of gamma ray measurement for low energy gamma rays up to 4.4 MeV.
The large prototype was build to check the performance for gamma rays of similar energy to the µ+ → e+ γ signal. Figure 5.1 shows the comparison of thesize of the final detector and the large prototype. The area of acceptance ofthe large prototype is much smaller than that of the final detector, however,the length along the direction of impinging gamma rays is almost same as the
final one so that it has a similar performance to the final detector within theacceptance. During the large prototype experiment, techniques to handle andto purify a large amount of xenon were developed. Two kinds of beam tests
were carried out, and it was confirmed that the performance of the prototype
satisfies requirements of the experiment.

5.1

Small prototype

From 1998 to 1999, a performance test of the same type of detector was donewith using a small prototype for low energy photons. The prototype consists of
32 PMTs surrounding 2.3 litters of active volume. Old type of PMTs(R6041Q)
were used in this prototype. Figure 5.2 shows the schematic view of PMTs andthe holder. The performance was estimated by using several radio active sources
with various energies up to 4.4 MeV. Results are described in ref.[52] and [53].
Resolutions for various energies are shown in fig.5.3.

5.2

Large prototype

From 2000 to 2004, the large prototype was build and several beam tests wereconducted in order to gain experience of the detector operation and to investigate its performance. Figure 5.4 shows cross-sectional views of the prototype.
The cryostat consists of inner and outer vessels. The volume between the twovessels is evacuated for thermal insulation. Super insulation layers are installed
between the two vessels to suppress heat income caused by radiation. Xenon is5.2 Large prototype

65

Figure 5.1: Comparison of the final detector and the large prototype

Al plate

ga mma source

H AMAMATU
R6 0 4 1 Q

226 mm178mm
Active region
116 116 174 mm

YZ
X

Figure 5.2: Schematic view of the small prototype

5.2 Large prototype

66

10

Position Resolution (mm)Energy Resolution (%)

20
18
16
14
12

51

Cr

9

8

51

Cr

7

6

10

5

137

Cs
54
Mn

8

137

Cs

4

54

Mn

6

88

Y

3

88

Y

4
2

2
1

0 -1
10

1

0
10

σ [psec]

Energy (MeV)
(a)

-1

1

γ Energy (MeV)

(b)

600
500
400

300

200

100
200

500

1000

2000

Number of photoelectrons(c)Figure 5.3: Resolutions of the small prototype. (a) Energy resolution. (b)Position resolution. (c) Time resolution

5.2 Large prototype

67

liquefied by a pulse-tube refrigerator (Iwatani Co. Ltd) and a liquid nitrogencooling pipe equipped at the top of the cryostat. After the liquefaction, theliquid xenon is kept in a stable condition by the refrigerator.
Signal
HV

1m

LN2
Refrigerator

PMTs

Outer vessel
241

Am
Inner Vessel
blue LEDs

LXe

372

y
372

x

z

y
z
x

Unit: mm

Front View

Side View

Figure 5.4: Liquid xenon gamma ray detector prototype. PMTs are installed on
six faces of a rectangular solid holder. PMTs were not installed in grey circles
in this figure.
The entrance window consists of a 0.1 mm thick aluminum plate and a 20 mm
thick stainless steel honeycomb. The holder for the front-side PMT is made of
G10 and Acrylic plates. The gap around the PMT base circuit is filled withglass beads and epoxy resin to avoid liquid xenon from entering there. This
makes it possible to keep the gamma ray detection efficiency flat, independentlyof the incident location. The total thickness in front of the fiducial volume
corresponds to 0.24 radiation length.
Two kinds of complementary beam tests were performed to study the response of the prototype to gamma rays in a wide energy range. One was doneby using gamma rays from Laser-Compton Scattering (LCS) and the other wasdone by using those from pion charge exchange (CEX).
The LCS beam test was carried out at National Institute of Advanced Industrial Science and Technology (AIST) in Japan. Gamma rays with Compton-edgeenergy of 40 MeV are generated via backward scattering of Nd:YAG pulsed laser
photons of 266 nm by 800 MeV electrons stored in a synchrotron. Gamma rays
with Compton-edge energy of 20 MeV and 10 MeV are also available by using
532 nm and 1064 nm laser photons respectively. The high intensity gamma
beam allows to investigate the position resolution with collimation by using
lead bricks with a 2 mm φ hole. The details of the beam test are described ina thesis[54].
The CEX beam test was conducted at PSI by using a negative pion beam
and a liquid hydrogen target. A negative pion beam stopped in the target
interacts with protons and produces neutral pions and neutrons. A neutral pion
produced in the target has a momentum of 28 MeV/c in the laboratory frameand decays into two gamma rays. Since this process is a two-body decay, energy

5.2 Large prototype

68

and opening angle of the two gamma rays have a correlation. By tagging backto-back decays in the laboratory frame with collimation, almost monochromatic
gamma rays at energy of 54.9 MeV and 83.0 MeV can be obtained.

5.2.1

Optical properties of xenon

Optical properties of liquid xenon used in the gamma ray detector can be extracted from the data. For this purpose, scintillation signal from an alpha source
is useful because it can be considered as a point-like source, and the position
is known. For example, absorption length, scattering length, refractive index,
group velocity of scintillation light could be extracted. Absorption length isstrongly depends on impurities.
Rayleigh scattering length
Rayleigh scattering length can be estimated by comparing data observed foralpha source wires. Figure 5.5 shows number of photoelectrons observed by a
PMT for alpha events. The PMT is located at z = 0, y = 3.1. Reconstructed
positions make rings as shown in the figure. This is due to a shadow effectof wires as shown in fig.7.8. A PMT observes more light for events where analpha particle is emitted to the direction of the PMT than events where theparticle is emitted behind the wire. These two cases make two peaks in the
distribution of number of photoelectrons. The ratio of the two peaks is sensitive
to scattering length. The ratio was compared with simulated data by changing
scattering length in the simulation. In the simulation scintillation spectrum witha peak at 175 nm and FWHM of 13 nm was used. Rayleigh scattering length
varies inversely with fourth power of the wavelength in the simulation. The best
assumption of scattering length in simulation to reproduce an experimental datais 55 cm at 175 nm.
Absorption length
Absorption length of scintillation light in liquid xenon has been estimated bycomparing output of each PMTs for alpha source events with MC simulation as afunction of the distance between the PMTs and alpha sources. Scintillation light
can approach to PMT indirectly because of Rayleigh scattering. Therefore, theactual path length of light is not exactly same as the distance between the source
and PMT. The effective distance was estimated for each PMT and alpha source
pairs from MC simulation by taking into account Rayleigh scattering. Figure
5.6 shows dependencies of observed charge in typical PMTs on the absorption
length. If we do not include Rayleigh scattering effect in the simulation, thosedependencies can be expressed as e−d/λabs where d is the distance between the
PMT and source. On the other hand in a realistic case with a finite Rayleighscattering length, such dependence differs from the above function and thus theeffective distance needs to be estimated by fitting with an exponential function
with d as a free parameter. Using the effective distance estimated in this way
as a distance between the PMTs and alpha sources, the absorption length wasestimated in MC simulation for various cases and compared with the input
values to the simulation as shown in fig.5.7. It can be seen that the input values
are well reproduced in the analysis.

5.2 Large prototype

69

Figure 5.5: Number of photo electrons of a PMT and reconstructed position ofalpha wire source. The PMT is located at z = 0, y = 3.1. Rings of two wires
are shown.

Before applying the method to the real data, PMT output was correctedwith Q.E. estimated with alpha data in cold gas xenon. Figure 5.8 shows theratio of PMT output to MC simulation with infinite absorption length as afunction of the effective distance between the source and PMTs. By fitting the
distribution with an exponential function, it is found that the absorption lengthwas 233+193−72 cm during the measurement in 2003. The absorption corresponds
to about 80 ppb of water contamination. In this analysis, scintillation efficiency
of xenon (the “W value”) was assumed as 17.9 eV[32] and 49.6 eV[55] in liquidand gas respectively, and the scattering length was assumed as 45 cm against
175 nm ultraviolet light.

1

0.9

χ2 / ndf

70

normalized peaknormalized peak

5.2 Large prototype

100.6 / 13
14.47 ± 0.04121

p0

1

0.9

0.8

χ2 / ndf

6.12 / 1345.46 ± 0.268

p0

0.8

0.7

0.7

0.6

0.6

0.5

0.5

0.4

0.4

0.3

0.3

0.2

0.2

0.1

0.1

0
10

10

2

0

3

10
absorption length [cm]

10

10

(a)

2

3

10
absorption length [cm](b)estimated absorption length [cm]Figure 5.6: Expected outputs of PMTs as a function of absorption length foralpha source events located on the bottom face of the large prototype. Two
PMTs, (a) and (b), are located at different distances from the source. The
effective distance was estimated by fitting the shape with exponential functions.
True and effective distances are 14.2 cm and 14.5 cm for (a), 40.8 cm and 45.5 cm
for (b). respectively.

10

10

3

2

10
10

10

2

3

10
true absorption length [cm]Figure 5.7: True absorption length (input value to MC) and estimated one in
MC simulation.

71

data/MC

5.2 Large prototype

1

-1

10

0

100

200

300

400

500

600

effective distance [mm]Figure 5.8: Ratio of PMT output in real data to MC simulation with an infiniteabsorption length as a function of the effective distance.

5.2 Large prototype

5.2.2

72

Purification

Gas phase purification
Figure 5.9 shows the xenon transfer lines of the prototype. When xenon isliquefied into the cryostat of the detector, gas xenon is transferred from a tank
via a purifier. Hence, liquid xenon in the detector must be purified. However,the xenon may not be completely pure due to out-gas from materials inside
the cryostat or cryostat itself. In the cryostat, some materials, such as G10or Acrylic plates, which can absorb water vapor and slowly release it later, areused. In many other applications, out-gas attached on materials can be removed
by heating up them during evacuation. On the other hand, the large prototype
detector has PMTs inside and it is not possible to bake it with high temperature.
As a result, a strong light attenuation due to impurities was observed when thefirst beam test was conducted.

Xe Tank

Gas Purifier

TeflonTube

Molecular
FilterHeat Exchanger

Diaphragm Pump
Gas Xe flow

Figure 5.9: Liquid xenon line.

In order to make xenon transparent, it is necessary not only to purify xenon,
but also to clean materials inside the cryostat. After the cryostat is filled withliquid xenon, a part of it is extracted by a diaphragm pump, and the xenon
is purified, then liquefied into the cryostat. In this process, impurities cameout from materials in the cryostat can be removed by a purifier continuously.
Figure 5.10 shows variations of observed amount of light during purification[46].
It is clearly seen that the amount of light was increased by the purification, andincrease of light observed by far PMTs from a light source is larger than near
PMTs, that implies the increase is due to a improvement of transparency. A flat
period from 700 to 900 hours is because purification was not done. A change
after 1000 hours is due to a instability of electronics. After repeating liquefaction and circulation several times, absorption length stayed long even when
purification is stopped because impurities on materials were almost removed.
Liquid phase purification
Another type of purifier was tested by using the prototype[48] in order to makepurification faster. Limitations of purification speed was conductance of xenon

5.2 Large prototype

������

d =11.6 cm
d = 7.6 cm

�

�����
�����
�����

���
�
���

�����
�
�

(a)

���

TC2(middle) trigger

Relative Peak

Total Number of Photoelectrons������

73

��� ��� ��� ��� ���� ����Elapsed Time [hrs]

�
�

(b)

�

��� ��� ��� ��� ���� ����Elapsed Time [hrs]Figure 5.10: Variations of amount of light during purification. (a) Landau peakof sum of all the PMTs in cosmic ray events triggered by plastic scintillation
counters locate above and below the detector. (b) Relative output of each PMTs
in alpha source events. Different markers are used for different distance between
a PMT and a alpha source.

transfer line and cooling power to re-condensate xenon. To decrease these effects, the new method adopts circulating xenon in liquid phase. In this way, mass
flow in the transfer line becomes faster, and evaporation and re-condensation of
xenon are not needed. A centrifugal pump was adopted to circulate xenon. The
pump can make a flow of 100 l/h with differential pressure of 0.2 MPa. A motor
is put outside of the cryostat and the pump does work for cold liquid without
contaminating it. Since it was found that the main contribution of absorption
is water, molecular sieves (MS13A) was chosen as the filter. The cartridge used
for the test with the prototype can absorb more than 24 g of water. It can beregenerated by heating it with evacuating the cryostat. Figure 5.11 shows theslope of corresponding lines to fig.5.8 during the test of liquid phase purification. For the test, a small amount of water was put in the xenon. Hatchedpart in this plot shows periods when the purification was operated. The staring
point corresponds to 250 ppb of water contamination. It was decreased down
to 40 ppb in 5 hours operation.
In the case of the final detector, the purification system was put in a smaller
separated cryostat, and it was connected with the detector by vacuum insulated
pipes. The operation was successful also for the final detector.

-1

Slope [cm ]5.2 Large prototype

74

0.014
0.012
0.01
0.008
0.006
0.004
0.002
0
-0.002-0.004
0

10

20

30

40

50

60
70
80
Elapsed time [hours]

Figure 5.11: Slope of data v.s. MC of alpha events as a function of time duringliquid phase purification.

5.2 Large prototype

5.2.3

75

CEX beam test

CEX beam tests were done twice at PSI in 2003 and 2004. In 2003, old type
PMTs(R6041Q) were used. In 2004, front half of PMTs were replaced by new
type of PMTs(R9288) which have three times higher Q.E. than the old type.
Setup
Pion beam momentum of 110 MeV/c was adopted to get a maximum TOF
separation of about 8 nsec between electrons and π − s, and µ− s and π − s, that is,so called “magic momentum”. For reducing electron contamination in the beamfurther, we employed a carbon degrader of 4 mm thickness placed, resulting ina π − beam momentum of 107 MeV/c. Beam line elements were tuned so thatthose π − s can be transported to the exit of the beam line where a 190 µm
Mylar window ends the beam line vacuum. A plastic scintillator(S1) is locatedjust after the Mylar window to define the beam and determine the start timing
for electronics. Taking the time difference between the S1 and the RF timingof the cyclotron accelerator, π − could be clearly separated from electrons andµ− s. Although electron contamination in the beam even at this level did notcause any serious background, we could further reduce it by requiring larger
pulse on the S1 counter than certain threshold. π − s were degraded by carbon
plates after leaving the S1 counter so that they could be stopped effectively at
the center of the hydrogen target. Thickness and location of the degrader was
optimized to be 26 mm in order to maximize the π − stopping. Schematic viewsof the liquid-hydrogen target chamber and its cell are shown in fig.5.12. The
dimension of the target cell is approximately 40 mm in diameter and 100 mm
in length, whose window is made of thin aluminum. The cell is supported
by a cylindrical shell attached to the cold head. Hydrogen is liquefied andmaintained in a stable state with a GM-type cryo-cooler, by heat conduction
through the shell, equipped at the end of the target chamber, and a heater whose
power is controlled continuously by monitoring the cell temperature. During
data acquisition, the target stayed quite stable even without paying any special
attention.
The beam profiles were obtained by using a plastic-scintillation countermounted on a beam profile scanner placed at the position of the target cell.
Beam spread is estimated to be 12 mm in sigma both in vertical and horizontal
directions, which means that more than 80 % of beam could enter the cell. By
integrating the profiles in two dimensionally we estimated the maximum beam
intensity to be 2.6 MHz with 1.8 mA primary proton current. Low intensity π −beam data was used to minimize the effect of neutron background, which can
reduce Q.E. of PMTs by too high PMT current. Lead collimators were locatedboth in front of the xenon and NaI detectors to select back-to-back gamma rays
with less ambiguity coming from position reconstruction.
As introduced in the previous section, we employed an NaI array for tagging gamma rays from π 0 decays opposite the xenon detector large prototype.
Details of the modular detector are described in ref.[56]. Signals from the detector was utilized for triggering π 0 events and in the offline analysis they wereapplied for event selections. Performance of the detector will be described in
the later section. For the purpose of estimating the timing resolution of thexenon detector, two different types of detectors were used in 2003 and 2004. In

5.2 Large prototype76

2003, we prepared a scintillation counter, which consists of two sets of timing
counters, each of which consists of a plastic scintillator (5×5×1 cm3 ) viewed by
two PMTs (Hamamatsu R5505) at both ends through light guides. Lead plates
in total 6 mm thick were placed in front of the timing counters for converting
gamma rays. These two counters were set before the NaI detector only whenstudying the timing resolution in order not to deteriorate the energy resolutionof the NaI detector. In 2004, an LYSO(Lu(2−x) Yx SiO5 :Ce) crystal with two
PMTs attached at the both ends was used.
Purification of liquid xenon was performed in prior to the beam test to obtain
longer absorption length.
Timing information was taken from all PMTs by discriminators and TDCs.
One FASTBUS TDC (LeCroy 1875A), four CAMAC TDCs (Phillips 7186H)
and four VME TDCs (CAEN V775) were implemented for this purpose. For
splitting the PMT signal MACRO fan-out splitters that had been used in seriesof studies were prepared for all channels. For measuring pulse amplitude of thePMTs, FASTBUS ADCs (CERN CIA) [57] were used. A new function of the
ADC module was invoked from this test to measure small signals more precisely.
Analog-to-digital conversion is done for raw input and in addition for 8-times
amplified input simultaneously in the module, thus enabling us to measure theamplitude with a 15-bit resolution. Furthermore for central 16PMTs on the front
face, the signal amplitudes were also measured with 10-20 dB attenuation by
utilizing another output from the splitters. This is for treating large amplitude
signals that could be observed when gamma ray interaction occurred near thefront-face PMTs.
Gain of the PMTs in xenon detector was adjusted to be 5 × 106 in 2003.
In 2004, two gain settings, “normal gain” (5 × 105 for R9288 and 1 × 106 forR6041Q) and “high gain” (1 × 106 for R9288 and 2 × 107 for R6041Q), wereused for comparison. Lower gain was used in 2004 because it was expected
the gain would be optimum for the final setup of MEG electronics by using
DRS. Eventually, we decided to set gain to be 2 × 106 in the MEG experiment,
therefore “high” gain mode in the beam test is closer to the setting of the final
experiment.
NaI detector
The NaI detector is an 8 × 8 array of optically isolated NaI(Tl) scintillator bars
encased in an air-tight container. The dimension of each bar is 63.5 × 63.5 × 406 mm3 .
The lateral and rear walls of this box are 19 mm thick aluminum plates. The
front wall is made of a 0.5 mm thick steel sheet, a thermal isolation of 20 mm of
Styrofoam glued to a 2 mm aluminum foil. In the back plate, 64 PMTs (Philips
PM2202) are connected to NaI through 64 Pyrex windows with Plexiglas lightguides (60 mm). In order to avoid thermal drift due to the heating inside theshielding, the last four dynodes are individually powered by a common active
voltage divider, located outside the shielding. The anode pulses are sent to the“signal processor” through tri-axial cables. These signals are shortened to lessthan 600 nsec, and the active stabilizer maintains the output base line close to
zero. Three outputs are obtained from the signal processor. One is the output
through 360 nsec delay and an attenuator for ADC, second one is a 50 nsec
FWHM fast pulse for TDC, and the last one is a signal to the trigger device.
To avoid triggering on low energy multi-particle events, the trigger device se-5.2 Large prototype

77

lects the events whose energy sum in each of the 49 groups of quad NaIs areabove threshold, “quad trigger”. To get back-to-back gamma events from π 0
decay around the detector center, additional trigger signal was prepared, which
is an energy sum of center four NaIs, “center trigger”. Signals for the ADC andtrigger were sent from the signal processor in the area to the electronics hat
through 64 nsec delay cables. High voltage value for each PMT was adjusted byusing cosmic ray spectra. Pedestal subtraction and gain correction were donein the offline analysis. As described in the previous section, an excellent energy resolution is not required for the tagging side counter, NaI detector, but
only a reasonable position resolution to define the opening angle which directly
corresponds to the energy resolution for gamma rays from π 0 decays.
High voltage values of 64 PMTs were adjusted by using the MIP peak bycosmic rays. Eventually, the gain variation over all NaIs was reduced down toabout 3.5 %, with high voltage settings ranging from −1300 to −1700 V. Figure
5.14 shows the energy spectrum of tagging side during CEX beam test. Energy
measured by NaI and LYSO detector are summed in the analysis. The tagging
detector has a good enough resolution as shown in fig.5.15.
Prototype detector analysis
In this section, analysis of xenon detector is discussed by using mainly 2004
CEX test data. The comparison of 2003 and 2004 data will be done later.
Position Reconstruction In this section the position reconstruction algorithm is described and its performance is presented by using MC simulation
data. This is because, contrary to the LCS beam test, the counting rate of
gamma ray injection to the detector was not enough to study the position resolution by placing a collimator with a diameter much smaller than the resolution.
Incident position of gamma rays to the xenon detector was reconstructed witha local-weighted method. In this method the following procedure was taken:
1. Make a 2-dimensional histogram with 6 × 6 bins. Each bin corresponds toa PMT on the front face.
2. Fill the histograms with output of PMTs. Define the starting point(xrec , yrec ) for the following iteration procedure as the mean of the distribution.
3. Re-bin the histogram so that the center of each axis becomes (xrec , yrec )without changing the bin width.
4. Define the next point with taking average in a limited range. The range
is determined as |x − xrec | < f /sx and |y − yrec | < f /sy , where sx and sy
mean the standard deviations of the histogram along x and y directions.
The selection of the range is done to decrease effects from energy deposits
other than the first interaction. The factor f should be optimized as afunction of the incident position. But in this analysis, a constant value(40) was used just for simplicity.
5. Iterate the 3 and 4 processes till (xrec , yrec ) converges.

5.2 Large prototype

78

Figure 5.16 shows a 2-dimensional distribution of differences between true
and reconstructed positions for MC simulation data. The data was generated
under the conditions of (i) Eγ ∼ 54.9 MeV, (ii) first conversion in the fiducial
volume. The position reconstruction resolution is estimated to be about 6 mm
in σ by fitting thep distribution with a Gaussian function including only one
parameter, r ≡ (x − x0 )2 + (y − y0 )2 . In fig.5.17 a comparison between (a)local-weighted method and (b) simple-average method is shown. It is clear thatthe local-weighted method is superior to the simple average method in particularfor deep events. In the simple-average method the reconstructed position is tend
to be pulled to the centers of PMTs while in the local-weighted method not.
Thus we can conclude that the reconstruction of incident gamma ray positions
can be done in a less biased way by employing the local-weighted method.
depth reconstruction When the first conversion of a gamma ray occurs close
to the front face, the distribution of scintillation light detected on the front faceis narrow, and it becomes broader as the first conversion point moves deeper.
The number of PMTs on the front face which occupy a half of Qfront (Nfpmt (0.5))1 was used as a measure for the first conversion depth. Here PMT output issummed in the order of the distance from the reconstructed incident position
until the sum exceeds a half of Qfront . The relation can be expressed in thefollowing equation:
PNfpmt (0.5)
i=0Qfront

Qi

= 0.5

(5.1)

Examples are shown in fig.5.18 for two typical cases, shallow conversion(4.6 cm depth) and deep conversion (13.8 cm depth). The sum of PMT output
in the shadowed region is equal to a half of Qfront . The sum is taken witha weight proportional to the are in the circle, so Nfpmt (0.5) is not an integer
necessarily. It can be seen that the area of the shadowed region is smaller incase of shallow events and it becomes larger for deeper events.
In fig.5.20 relations between the Nfpmt (0.5) and actual first conversion depth
for MC simulation data are shown for different impinging points of gamma rays
whose notations are defined in fig.5.19. By fitting the relation with a secondorder polynomial function, for example for the case of (a), the depth can bereconstructed as
Drec = 1.38201 + 0.246552 × Nfpmt (0.5) + 0.0768057 × Nfpmt (0.5)2
Figure 5.21 (a) shows a relation between the reconstructed depth in thisway and true first conversion depth. From this the depth resolution for MC
simulation data is estimated to be 8.2 mm for 54.9 MeV gamma rays in the rageof 4 cm < Drec < 15 cm as shown in fig.5.21 (b). This relation is employed for
estimating the depth in real data.
Energy Resolution Energy resolution was evaluated using simple sum of all
PMT outputs (Qsum) with correction of the dependence on position. Q.E. andgain correction of PMTs are done before computing Qsum. In this discussion
1Q
front means a sum of output of PMTs on the front face.

5.2 Large prototype

79

Q.E. includes also collection efficiency. Estimation of Q.E. and gain is discussed
in 7.1.1 and 7.1.2 respectively.

Qsum =

238
X

Qi /gain ×

i=0

Q.E.
Q.E.i

(5.2)

Figure 5.22 shows measured number of photons in the xenon and the energy
at the tagging detector. Tails below the gamma ray peaks from π 0 decays are
due to gamma conversions in the lead collimator or vacuum chamber, and toenergy leakage from the front face. When we analyze the data of 54.9 MeV and
83.0 MeV gamma rays, a selection was applied for the measured energy with thetagging detector as 70 MeV< Etag < 105 MeV and 35 MeV< Etag < 70 MeV
The distributions of the number of photons observed in the xenon detector arepresented in fig.5.23. The black histogram is data without cuts and the blue
and red ones are for those after 54.9 MeV and 83.0 MeV selections. Figure5.24 (a) shows a depth dependence of Qsum when gamma rays impinged at thecenter of the detector. Qsum slightly increases depending on the depth aroundthe middle, and decreases at the end. This is because PMT coverage density
is higher in central part than front or back part, and much less at the backside than the other part because PMTs were not installed in the last columnof the prototype detector as shown in fig.5.4. For removing this dependence, inthis analysis, events with Nfpmt (0.5) > 12 were discarded and a correction wasapplied for the other events with a linear function. The distribution after thecorrection is shown in fig.5.24 (b).
To estimate the energy resolution, following function was used as a fit function. Figure 5.25 shows a typical histogram of Qsum overlaid with a fit function.
(
F (x) =−(x−x0 )2

Ae 2σ2t
Ae σ2 (t/2−(x−x0 ))(x > x0 + t)
(x ≤ x0 + t)

Energy resolution was evaluated in two ways, by using FWHM and σ of thisfunction. Discussing the resolution using σ is important for estimating background rejection power against µ+ → e+ γ because gamma rays from accidental
and prompt background has less energy than those from µ+ → e+ γ . In addition σ must improve statistically as the observed number of photoelectrons
increases. On the other hand, FWHM needs to be considered to discuss thedetector efficiency. Because there is always a non-negligible effect of “leakage”
from the front face of the detector, FWHM does not necessarily improve evenwhen the number of photoelectrons increases. Figure 5.26 shows the energy resolutions, expressed in σ and FWHM, as a function of slices of a depth parameter
when gamma rays impinged on IP5. As can be seen in the figure, the FWHM
improves for deeper events, and stays constant in 4.5-5.0% for the events with
Nfpmt (0.5) > 4. This can be simply explained by the fact that the leakage effectis negligible for the deeper events compared to the shallow events. σ is also
constant around ∼1.3% in case Nfpmt (0.5) > 4. For shallow events, resolution
becomes worse because depth and position resolution becomes worse, and Qsum
with after Q.E. correction (N sum) dependence on position is large. An analysis
to solve this problem is discussed in a section for final detector’s analysis.

5.2 Large prototype

80

50.00

3.90

150.50

3.90

90.30

Temperature
SensorHeaterAPD-CryocoolerCold Head
191.30Figure 5.12: A schematic view of the target chamber. The cell sits at the centerof three window flanges. A pion beam comes from the left. The liquid xenon
and the tagging detectors are locate at the upper and lower direction in the
figure respectively.

Figure 5.13: Setup in 2004 CEX beam test. The xenon detector, the hydrogentarget cell and a tagging detector are seen in the left, center and right in thispicture respectively.

5.2 Large prototype

81

1800
1600
1400
1200
1000
800
600
400
200
0
0

20

40

60

80 100 120 140 160
NaI + LYSO Energy [MeV]Resolution (FWHM) [%]Figure 5.14: Spectrum of gamma rays at tagging side. Two peaks (54.9 and83.0 MeV) of back-to-back gamma rays from π 0 decays and 129 MeV peak fromneutron capture process.

20
18
16
14
12
10
8
6
4
2
0
0

20

40

60

80

100

120
140
Energy [MeV]

Figure 5.15: Observed energy resolution of NaI and LYSO detector as a functionof incident gamma ray energy.

5.2 Large prototype

82

Figure 5.16: Distribution of difference between true and reconstructed positions
in simulation.

Figure 5.17: Distribution of the residual between reconstructed and true positions as a function of the first conversion depth for MC simulation data. (a)local-weighted method (b) simple-average method. x0 represents the true incident position.

5.2 Large prototype

83(a) shallow event (4.6 cm)(b) deep event (13.8 cm)

Figure 5.18: Charge distributions on the front face for shallow and deep events.
A sum of PMT outputs in the shadowed region is equal to a half of Qfront .

Thin aluminum beam window

IP1

IP2

IP3

IP5
IP4

IP7

PMT Cathode

IP6

IP8

IP9

3.1 cmFigure 5.19: Notations of impinging points used in this analysis.

5.2 Large prototype

84

(a)

(b)

(c)
Figure 5.20: Relations between the Nfpmt (0.5) and true conversion point in
MC simulation. (a) is for gamma ray impinging at IP5, (b) is for IP 2,4,6, and8, and (c) is for IP 1,3,7, and 9 as defined in fig.5.19

hist

600

EntriesMean
RMS
χ 2 / ndf
Constant
Mean

500

Sigma

400

5950
0.043251.614
602.6 / 85516.6 ± 10.1
0.1711 ± 0.0117
0.8202 ± 0.0114

300
200
100
0
-10

(a)

-8

-6

-4

-2

0

2

z - z 0 [cm]
(b)

4

6

8

10

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

5.2 Large prototype

85

Figure 5.22: Distribution of Qsum vs observed energy with the NaI detector.

3000

2500

2000

1500

1000

500
×10
2000

3

0
0

200

400

600

800

1000

1200

1400

1600

1800

Figure 5.23: Distributions of the number of photoelectrons observed in the xenon
detector for three cases. The black histogram is data without cuts and the blue
and red ones show the distributions after 54.9 MeV and 83.0 MeV selections on
the NaI detector side.

5.2 Large prototype

86

(a)

(b)

Figure 5.24: Distributions of Qsum vs depth. (a) before correcting the depth
dependence. (b)after correcting the depth dependence with a linear function.
nphe
120
100
80

EntriesMean
RMS
χ2 / ndf
Peak
Transition
Height
Sigma

nphe

3018
9.183e+05
3.221e+05708.6 / 169
1.142e+06± 1703
−3723± 623.8
123.5 ± 5.0
1.408e+04± 1051

100
80
60

EntriesMean
RMS
χ2 / ndf
Peak
Transition
HeightSigma

4260
1.228e+06
5.29e+05
89.47 / 43
1.726e+06± 2413
−2990± 519.4
102.1± 4.1
1.723e+04± 1360

200

600

60
40
40
20

20
0
0

×10
1200
1400
number of photons

3

200

400

600

800

1000

0
0

400

×103
800 1000 1200 1400 1600 1800 2000
number of photons

(a)

(b)

Resolution [%]Figure 5.25: Qsum distribution together with a fit function for (a)54.9 MeV and(b)83.0 MeV gamma ray incident. Sigma of right edge of the peak is 1.2 % and1.0 % for (a) and (b) respectively.

25

20

15

10

5

0
0

1

2

3

4

5

6

7

8

9
10
Nfpmt(0.5)

Figure 5.26: Energy resolutions as a function of the depth selection thresholdwhen gamma ray impinged at the center of the detector (IP5).

5.2 Large prototype

87

Timing Resolution
Timing calculation in the large prototype The timing of gamma ray inthe large prototype was calculated in a following way.
1. Time walk correction for each PMT.
2. Adjust offsets so that the mean of each PMT timing is set to be 0.
3. Take a weighted average among PMTs those satisfy following requirements.
• Npe,i > 50.
• |Ti | < 10 nsec.
The weight for each PMT is determined as√

Qi event by event.

T0-TTC [nsec]

4. Correct impinging position and depth dependence.

20
18
16
14
12
10
8
6
4
2
0
0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

1/ Nphe0

Figure 5.27: An example of time walk correction for a certainp
PMT. Timing ofeach PMT was corrected by using a factor proportional to 1/ Npe,i .
Time walk of each PMT was estimated from a plot like fig.5.27. In the figure
time distributionof a PMT relative to the tagging counter is shown as a function
pof 1/ Nphe , where Nphe is number of photoelectrons. Correction factor was
obtained by fitting the distribution with a linear function for each PMT.
Timing resolution was estimated for 54.9 MeV and 83.0 MeV gamma rays.
The event selection was done by observed energy by the gamma ray detector,
and the tagging detector was not used except for a coincidence condition.

5.2 Large prototype88(TR -TL)/2 [nsec]

Intrinsic timing resolution To estimate the intrinsic timing resolution, “LR” analysis was performed. In this analysis, PMTs were divided into right andleft groups by the center plane of the detector. Timing of both groups were
calculated independently. Then the intrinsic timing resolution was estimatedfrom the distribution of (TL − TR )/2, where TL and TR are defined as averaged
timing in the left and right groups respectively. Difference of averaged timing
between right and left groups is largely dependent on impinging position of
gamma rays in x direction. Figure 5.28 shows dependence on reconstructed x.
After correcting the dependence on x evaluated by using the simple weighted
mean with all PMTs, a depth selection was applied with Nfpmt (0.5) . Figure 5.29
shows the time resolution as a function of the depth parameter. The resolution
is not affected by depth.
1
0.8
0.6
0.4
0.2
-0
-0.2
-0.4
-0.6
-0.8
-1
-10

-8

-6

-4

-2

0

2

4

6

8 10
x [cm]

Figure 5.28: x dependence of (TL − TR )/2.

Practical timing resolution We also performed evaluation of practical timing resolution. In this analysis, time difference between the xenon detector andthe tagging detector was used. Note that in this analysis we have to take into
account the effect of beam spread, that is the spread of the π 0 production/decay
point. The relative timing has dependencies on the first conversion depth, Qsum
, and impinging position. The spread includes not only the xenon detector timing resolution but also other fluctuations. Main contributions are from thetiming counter resolution and ambiguity of π 0 decay position. The spread ofπ 0 decay position was estimated by measuring the beam profile on the target.
That contribution is calculated to be 58.8 psec in sigma. After subtracting theseeffects, the timing resolution of the xenon detector was evaluated. The result issummarized in fig.5.30 as a function of the depth selection parameter.

Resolution [psec]

5.2 Large prototype

89

60

50

40

30

20

10

0
0

1

2

3

4

5

6

7

8

9
10
Nfpmt(0.5)

Resolution [psec]

Figure 5.29: Intrinsic time resolution and the depth selection. Resolution without slicing by depth is 43 psec.

140
120
100
80
60
40
20
0
0

1

2

3

4

5

6

7

8

9
10
Nfpmt(0.5)

Figure 5.30: Practical time resolution as a function of the depth selection parameter. These numbers include the time resolution of the tagging detector(64 psec)and decay point fluctuation(58.8 psec). Resolution without slicing by depth is
53 psec after contributions of the tagging counter resolution and the decay point
fluctuation are subtracted.

5.3 Summary of prototypes

90

Comparison of 2003 and 2004 runs
In this chapter resolutions in 2004 was shown. In this section, comparison of2003 and 2004 data is discussed. Between 2003 and 2004 beam test, front halfof PMTs were replaced to new type PMTs. The structure of two types of
PMTs are basically same except for photo-cathode. The old type PMT has a
RbCsSb+Mn photo-cathode which was selected for low temperature operation.
However, it was found that the sensitivity for ultra violet light was not sohigh. And control of gain is not easy. Therefore, KCsSb is used for the new
type. KCsSb have higher resistance than RbCsSb. To reduce the resistance,
aluminum strips are attached on photo-cathode. By the modification, Q.E. andgain control were improved. FWHM of the peaks do not change from 2003 since
the lower tail is due to leakage of gamma rays and interaction before the active
volume. However, the sigma of right edge of the peak was improved due to larger
number of photo-electrons than 2003. Time resolution was much improved in
2004, because number of PMTs with more photo-electrons than a threshold touse for averaging time was increased due to improvement of Q.E..
The comparison is summarized in table 5.1. The difference of energy resolutions due to the difference of Q.E. is reasonable from simulation (1.5 % and1.0 % with 2003 and 2004 Q.E. settings respectively.)

Energy resolution (sigma of right edge) for 54.9 MeV peak
Energy resolution (sigma of right edge) for 83.0 MeV peak
Intrinsic time resolution for 54.9 MeV peak
Intrinsic time resolution for 83.0 MeV peakTime resolution for 54.9 MeV peak

2003
1.6 %
1.2 %
73 psec
59 psec
102 psec

2004
1.2 %
1.0 %
43 psec
36 psec
53 psec

Table 5.1: Comparison of resolutions in 2003 and 2004. Resolutions are written
in σ.

5.3

Summary of prototypes

During the prototype tests, we have learned several technical things to operateliquid xenon detector stable. The large prototype was the largest liquid xenon
detector ever made at that time. Those experiences help a lot for designing andconstructing the final gamma ray detector for MEG. Newly developed refrigerators and PMTs eventually worked fine after modifications. Response of liquid
xenon scintillation detector was studied for low energy up to 4.4 MeV by using
the small prototype and for energy around µ+ → e+ γ signal or even higher byusing the large prototype.
For 54.9 MeV gamma rays, energy and time resolutions were estimated tobe 1.2 % and 53 psec respectively by CEX beam test. Energy and position
resolutions were measured in LCS beam test to be 1.5 % and 4.3 mm for 40 MeV
gamma rays respectively[54]. Figure 5.31 shows energy resolutions as a functionof energy of gamma rays.
The resolutions of the large prototype is compared with the requirement of
the MEG experiment in table 5.2. The angular resolution is slightly worse than5.3 Summary of prototypes

91

Energy resolution (σ) [%]

10

1

10

Energy [MeV]102

Figure 5.31: Energy resolutions as a function of energies. Black points are resultof the LCS beam test and white ones are from the CEX beam test.

the requirement, and the energy and the time resolutions are better. The rateof the accidental background, which is the dominating background, is approximately proportional to (∆Eγ )2 ·∆Ee+ ·(∆θγe+ )2 ·∆Tγe+ [58]. By combining three
resolutions, the performance of the large prototype satisfies the requirement.

∆Eγ [%]∆Ee+ [%]∆θγe+ [mrad]∆Tγe+ [nsec]
Acceptance × Efficiency [%]Muon stopping rate (108 )Running time [weeks]Single event sensitivity(10−13 )90 % C.L. limit(10−13 )MEG goal
4.5∼5.0
0.8
12.4∼16.9
0.18>1.6
0.3(DC)
100
0.5
1.7

Large prototype
4.4
18.8(14.9)
0.16(0.12)-

Table 5.2: Comparison of MEG goal(table 1.3) and the results of the large
prototype. Resolutions are written in FWHM. ∆Eγ of the large prototype is
FWHM of fitting function of fig.5.25-a. For ∆θγe+ and ∆Tγe+ , requirements
for the positron detector (10.5 mrad and 100 psec) are included respectively.
For those resolutions, contributions of the gamma ray detector are written inparentheses.

Chapter 6

MEG run 2007
An engineering run was carried out from Autumn to Winter in 2007. It was
the first beam test with the final gamma ray detector. The main purposes of
the run was investigating the performance of sub-detectors and preparing thetrigger for physics runs. Finally, all the sub-detectors worked, and the MEG
trigger was prepared. Data for physics analysis was taken for a couple of days.
In this chapter, conditions of acquired data in MEG run 2007 are summarized.

6.1

Preparation of gamma ray detector

Before starting liquefaction of xenon, the inner and outer vessels were evacuatedindependently. The final vacuum level of the inner vessel was 6.9 × 10−3 Pa.
Vacuum leaks between the inner vessel and the air was checked by using a helium
leak detector, and all leaks were fixed. Leaks between the inner and the outer
vessel were checked by using residual gas analysis (RGA) of the outer vessel
with filling inner vessel with xenon gas. When we used a recycled gasket as areference, a clear peak of xenon was seen in the RGA result, which corresponds
to 10−4 mbar·l/sec. On the other hand, there was not the peak when we useda new gasket. Very small leaks by pin holes of the cryostat were searched by
nondestructive inspection with eddy current. Pin holes were fixed by additional
welding.
Transfer of liquid xenon from the liquid storage tank to the detector wasstarted on October, 21st and it was finished in three days. In total, 865 littersof liquid xenon was transferred to the detector in a speed of about 10 litters per
hour.
H.V. for PMTs were adjusted to set PMT gain to be about 1.5×106 . Typical
H.V. was 810 V. Gains were measured in almost every day with a method
discussed in 7.1.1. The target gain was determined to be as high as possible forbetter S/N ratio and time resolution, but not to exceed splitter input voltage
limit for typical events. The limitation is the protection clipping of 2.5 V at the
input of the splitter. Waveforms were attenuated by factor 3 at the input of
DRS so that the pulse height is in the dynamic range of DRS for most of events.
During the physics and calibration data acquisition in 2007, there were 17
dead PMT channels out of 846. Two of them were in the inner face. Those were
due to short of the base circuit of PMT through cable bands made of aluminum,6.2 Cockcroft-Walton

93

or bad soldering of base circuit broken in a low temperature. After the dataacquisition in 2007, aluminum cable bands were replaced by cable ties made ofNylon. PMTs with a bad base circuit were replaced with new ones.
Purification of the xenon was done for 205 hours by using the liquid phase
purifier described in 3.2.3. The absorption length was monitored by using analysis discussed in 5.2.1. Initial absorption length was 60 cm and it stayed longer
than 3 m after the purification. During the purification light yield was increasedby 1.6 times, and saturated after 180 hours of purification.

6.2

Cockcroft-Walton

The Cockcroft-Walton (C.W.) accelerator was used mainly with LiF target tomonitor the performance of the gamma ray detector by using 17.6 MeV peak.
For this purpose, PMTs located around the center of the inner face was used
for trigger. Such data was taken typically once per 3 days. Data in the full
acceptance was also taken to study the dependence of energy scale on positions.
A boron target was also used to know the time difference between the gamma
ray detector and the positron timing counters by using a pair of two gamma
rays from a nuclear reaction. C.W. data is used in analysis in chapter 7 forenergy scale calibration.

6.3

Pion charge exchange

A similar beam test to the large prototype test by using gamma rays from pion
charge exchange process was conducted for four days. The purpose was to checkthe performance of the detector and to demonstrate a calibration which will bedone in 2008 and later. In this beam test, events in limited region (2 × 3 PMT
region) were selected by trigger. In 2008, it is planed to scan whole the innerface.
A tagging detector for CEX run consists of nine NaI crystals(62.5 × 62.5 ×
305 mm), two plastic counters(60 × 60 × 7 mm) and a lead plate(60 × 60 × 6 mm)
to convert gamma rays. The lead converter can be removed when better energy
resolution is needed for the tagging side. In fig.6.1-a, the lead converter is notpresent. When it is used, it is put in front of plastic scintillators.
An requirement of the tagging detector in addition to prototype test is thatthe detector needs to work in a magnetic field. To fulfill the requirement,
avalanche photo-diodes (APD) were used instead of PMTs. To gain enoughamount of light, two APDs were attached to each crystal as shown in fig.6.1-b.
For the plastic scintillation counters for time measurement, 1 inch fine-mesh
PMTs were used.
The tagging detector is mounted on a movable stage which allows to movethe detector to r and φ direction, and rotate the detector so that the detector
can be put at a back-to-back position to a triggering region of the gamma ray
detector.
Resolutions of the gamma ray detector are evaluated from CEX data. The
analysis is discussed in chapter 7.

6.4 Michel decay

94

Figure 6.1: Pictures of tagging detector for CEX test. (a) NaI crystals andplastic scintillation counters. (b) APDs to be attached on the back face of NaI
crystals.

6.4

Michel decay

Michel decay data was taken by using the positron timing counter or the drift
chambers for triggering. This data was used to study the performance of thepositron spectrometer and to make probability density functions (p.d.f.) for
physics analysis.

6.5

Radiative muon decay

A large amount of radiative muon decay data was taken mainly for developing
the MEG trigger. The condition of RD trigger is almost same with the MEG
trigger, except that RD trigger does not require any condition of opening angle.
The trigger condition was• Eγ > 40 MeV• |Teγ | < 20 nsec
• At least two timing counter hits
, where Eγ is energy of a gamma ray and Teγ is time difference between a gamma
ray and a positron.

6.6

MEG trigger data

MEG trigger was prepared by adding a requirement of direction matching of a
gamma ray and a positron to the RD trigger. For direction matching, positionof the PMT of the gamma ray detector with maximum charge and reconstructed
position of a positron hit by using charge asymmetry of phi-measuring timing
counter were used. Direction matching table was made based on MC simulation.
triggers listed in table 6.1 were mixed with proper pre-scaling.
Condition of MEG trigger was,
• Eγ > 40 MeV• |Teγ | < 10 nsec

6.6 MEG trigger data95

• At least two timing counter hits
• Direction matching of a gamma ray and a positron.
Name
MEG
MEG Low Q
MEG Wide Angle
MEG Wide TimeRD Narrow Time
RD Wide Time

Pre-scaling
1
2
5
1
15
30

Difference from MEG
Eγ > 35 MeV
Only upstream/downstream correlation|Teγ | < 20 nsec
No check of angle. |Teγ | < 20 nsec
No check angle. |Teγ | < 40 nsec

Table 6.1: Triggers used for 2007 physics data taking
Event rate of MEG trigger was 4 Hz as it had been expected. Live time of
DAQ system was 63 % of real time. In year 2007, 73 % of events were triggeredby other triggers than MEG, and the higher rate made dead time of the system.
In the case of data acquisition in physics runs in 2008 and later, we will use
higher pre-scaling factors for trigger types other than MEG, so most of events
will be triggered by MEG trigger. Therefore dead time will be smaller than thecase of 2007.
In chapter 8, analysis result of 170 k MEG trigger events collected in 23.5 hours
is shown.

Chapter 7

Analysis
In this chapter, performance of the gamma ray detector is discussed by using
data in 2007. We discuss about calibration of PMTs including gain, Q.E. andtime offset measurement. After that, event reconstruction is described and theperformance is evaluated by using CEX data. Finally, event type identification
to reduce background events is described. The measured resolutions are notas good as requirements mainly due to lower scintillation yield than expected
due to contamination of liquid xenon. In following sections, these are discussed
quantitatively.

7.1

Calibration of PMT

In the MEG experiment, quantum efficiency of photo cathode(Q.E.) and PMT
gain are measured separately. Q.E. is supposed to be stable for long term,
therefore it is measured few times. On the other hand, it takes time to stabilize
gain when temperature or H.V. is changed. So gain calibration is done frequently
during experiment. Time offset between PMTs due to variations of path lengthfrom PMT to readout electronics is measured from time difference in LED runs
with taking into account distance between a LED and a PMT.

7.1.1

PMT Gain

Gains of PMTs are estimated by using LEDs installed in the detector. Figure 7.1
shows positions of LEDs on the lateral faces. During the measurement, several
LEDs are flashed so that all the PMTs are illuminated. As it is shown fig.7.2-a,data is taken by changing the intensity of LEDs. Number of photo-electrons canbe calculated from the width of distribution at each step from Poisson statistics.
Figure 7.2-b shows a relation between mean and σ 2 of Gaussian distributions.
PMT gain is proportional to the slope of the fitting function in this figure.
Contribution of noise independent of LED intensity is included in intersectionof the fitting, and it does not affect estimation of gains.
However, when a noise depends on intensity of LEDs, it affects estimation.
To reduce the effect, a new technique was developed. Principle of the modification is increasing voltage for LED, and attenuate light by covering LEDs byfilters. In 2007, LEDs were covered by thin Teflon sheets. When this technique7.1 Calibration of PMT

97

DOWNSTREAM

UPSTREAM

6
18

0
30

12

24

7
19

1
31

13

25

8
20

2
32

14

9
21

26
3

33

15

10
22

27

4
34 11

5
17

23 35

16

28

29

Figure 7.1: LEDs for calibration. Different markers represent different attenuation factors.

is not used, variance of number of photons from a LED can be written as,
2σN= NA +
ph



dN
∆V
dV V0

2
(7.1)

where NA is averaged number of photons, V is applied voltage and ∆V isfluctuation of V .
After the modification, the same quantity is written as,
2σN= NA +
ph



1 dN
∆V
f dV V1

2(7.2)

where f and V1 are adjusted so that NA does not change from eq. 7.1.
When f is large enough and the light intensity of the LED increases as afunction of applied voltage more slowly than an exponential function, the contribution from the noise will be negligible. Figure 7.3 shows measured intensityof LED as a function of applied voltage. Actually, the increase is much slower
than an exponential function.
Geometrical effect(solid angle of PMT viewed from a LED) and quantum
efficiency of PMTs have the same effect with the additional attenuation by thefilter. In total, attenuation of 1000 is possible and it makes the effect of noise
negligible.

7.1.2

Photo-cathode quantum efficiency(Q.E.)

Q.E. is measured by comparing output of PMTs from scintillation by alphasource(241 Am) with simulation. In this discussion, Q.E. includes also collection
efficiency. To estimate Q.E. of each PMT, peaks of PMT outputs for each sourcePMT pair was compared with simulation in which fixed Q.E.(16 %) is used.

Counts

7.1 Calibration of PMT

98

χ2 / ndf
239.8 / 220
Constant
88.18 ± 1.13
Mean
0.9475 ± 0.0007
Sigma 0.06933 ± 0.00060

x10

500

0.005

400

0.004
σ2

300
200

Gain = 5.16 x 10

0.003

6

0.002

100
0

χ2 / ndf
7.941 / 7p0
7.011e−06± 2.443e−06
p10.005156 ± 3.532e−05

18

0.001

0

0.5

1

1.5

2 x10
−Charge (e+)

9

0

(a)

0

0.5

1
Mean

1.5

2

x10

9

(b)

Light intensity [a.u.]

Figure 7.2: LED gain calibration. (a) Spectrum of charge of a PMT. Intensityof LEDs are changed in 9 steps. (b) Mean and σ 2 of fitted Gaussian functions.
Gain can be estimated from the slope of the plot.

10-7

10-8

10-925

30

35

40

45

50
55
60
Applied voltage [a.u.]

Figure 7.3: LED intensity and applied voltage.

7.1 Calibration of PMT

99

In the simulation, reflection on the PMT window was calculated from Fresnel
equation and Snell’s law. Alpha sources are suitable for this purpose since therange is short (about 40 µm in liquid xenon), and they can be considered as
point-like sources. In the large prototype, alpha sources on plates of one inch
diameter were put on PMT holders. For the final detector, alpha sources put
on wires were produced. It was also tested by using the large prototype. In
the final detector, five alpha sources are put on each wire, and the size of eachsource is 1 mm. Diameter of a wire is 100 µm. In total 25 alpha sources on fivewires were installed as shown in fig.7.5. A picture of an alpha source wire anda LED bundle is shown in fig.7.6.

Figure 7.4: Alpha source on a wire. Length of the source is 1 mm, and diameterof the wire is 100 µm.

Front view

Side view

Figure 7.5: Positions of alpha sources in the detector. Solid and dashed boxesin the left figure are outer and inner faces respectively.

7.1 Calibration of PMT

Figure 7.6: Alpha source wire and LED bundle

1007.1 Calibration of PMT

101

There are three advantages of wire sources compared to plate sources.
• In the case of plate sources, a half of solid angle viewed from energy release
position is covered by the plate, hence practical amount of scintillation
light is close to the half of alpha energy. While in case of wire sources,
range of alpha particle and the width of wire are comparable, so more
scintillation light is observed by PMTs.
• A plate source can be put only on the PMT holders, while a wire source
can be put any place in the fiducial volume without making shadows in
gamma ray measurements. It makes possible to illuminate all the PMTs
with smaller number of alpha sources.
• Since wire sources are located in the fiducial volume, geometrical relation
between PMTs and light a source is closer to gamma ray measurement.
Figure 7.7 shows weighted mean of position of PMTs in alpha events. Top
three wires are in gas and bottom two are in liquid xenon. In liquid xenon,
weighted mean positions make rings shown in this figure. In liquid, range ofan alpha particle is comparable to the thickness of the wire, so the wire makes
shadow as shown in fig.7.8. An interesting point is that the radius of the ringdepends on thickness of the wire and scattering length of xenon. An estimationof Rayleigh scattering length by using the rings is described in section 5.2.1.

7.1 Calibration of PMT

102

Figure 7.7: Weighted mean position of PMT outputs in alpha events. Bottom
two wires are in liquid and other three wires are in gas xenon. Middle wire isreconstructed upper than real position due to reflection on liquid surface.

7.1 Calibration of PMT

103α
Source wire
Liquid xenon
Figure 7.8: Alpha particle and the wire. Diameter of the wire is 100 µm andthe range of alpha particle in liquid xenon is about 40 µm.

7.1 Calibration of PMT

7.1.3

104

Time offset

There are systematic time differences in channels due to different path lengthsof signals from the PMTs to the readouts, and due to path lengths of trigger
stop signal from the trigger system to readouts. To calibrate the offsets, LEDs
installed in the gamma ray detector is used. These LEDs are same ones used
for gain calibration.
Measured time of a PMT can be written like equation 7.3.
Tmeasured = Temit + Ttravel + Tstatistics + Ttransit + Telectronics − Ttrigger (7.3)
where, Temit is the time of photon emission, Ttravel is the time for a photon to
travel in xenon to PMT, Ttransit is the time of electron multiplication in a PMT,
Telectronics is the time delay in electronics including cables, Ttrigger is the time
when trigger stop signal comes to a readout channel. Observed time have a delay
when number of photo-electron is small(Tstatistics ). The purpose of time offset
calibration is to estimate Ttransit + Telectronics − Ttrigger , because this number is
independent of light sources.
To investigate time offset, a LED is flashed with rather high intensity during a measurement to make Tstatistics negligible. In principle, by subtracting
Ttravel from Tmeasured , time offsets relative to a reference PMT can be obtained.
However, there are two points to be considered. The one is that velocity of
LED light in liquid xenon is unknown, and the second is that one LED can not
illuminate all the PMTs in the gamma ray detector.
In the gamma ray detector, LEDs were located at twelve different positions
in year 2007 setup. So several measurements can be done where in each measurement, only one LED is flashed. About 5000 events were recorded in eachmeasurement, and mean of time of each PMT is estimated by fitting the distribution of events with Gaussian function.
Connection of two different measurements can be done by using PMTs whichwere illuminated in both the measurements. To align two measurements, ascatter plot of Ti0 − Ti1 v.s. Di0 − Di1 are fit with a linear function, where Tij
is a time of i-th PMT in j-th measurement relative to a reference PMT and Dij
is a distance from a LED to i-th PMT in j-th measurement. Reference PMTs
are not necessary to be same in all the measurements. Intercept of the linear
function is the difference of references in two measurements, and the value isindependent of PMT time offsets or speed of light. The slope represents the
speed of light in liquid xenon.
Figure 7.9 shows measured time as a function of distance from LEDs. One
graph corresponds to a PMT, and a point corresponds to a measurement. White
markers are time before correction, and lines are expectation with assuming
estimated speed of light of 1.43 × 108 m/sec. The difference between whitemarkers and the line is equivalent to the time offset of the channel. Figure
7.10 shows uncertainty of offset calibration of all the PMTs. Many PMTs were
calibrated with uncertainty better than 200 psec.
The method is used to correct large offset like fig.7.9-d. More precise timeoffset is estimated from CEX data by using time difference distribution of each
PMT with respect to a tagging detector with statistical uncertainties better
than 10 psec. Offset calibration by using CEX data could be done only about
100 PMTs because the CEX test was done for a part of the inner face in 2007.
Practically, these PMTs contribute to the time resolution because the time of a

7.1 Calibration of PMT

105

50

50

PMT 219

PMT 275

40

30

30

20

20

Time [nsec]

Time [nsec]

40

10
0
−10

10
0
−10

−20

−20

−30

−30
−40

−40

−50

−50
0

20

40

60

80

100

120

140

160

180

200

0

20

40

60

Distance [cm]

80

(a)

120

140

160

180

200

140

160

180

200

(b)

50

50
PMT 49140

PMT 723

40

30

30

20

20

Time [nsec]

Time [nsec]

100

Distance [cm]

10
0
−10

10
0
−10

−20

−20

−30

−30

−40

−40

−50

−50
0

20

40

60

80

100

120

140

160

180

200

0

20

40

60

80

100

120

Distance [cm]Distance [cm]

(c)

(d)

Figure 7.9: Time v.s. distance for time offset estimation. The difference between
white markers and the line is equivalent to the time offset of the channel, so
PMT 723 has a larger offset than other PMTs in this figure.

120
100
80
60
40
20
0
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time offset calibration uncertainty [nsec]

Figure 7.10: Time offset calibration uncertainty. The number is standard deviation of points in fig.7.9 from a line of speed of light.

7.2 Structure of event reconstruction

106

gamma
p ray is estimated by a weighted mean, and the weight is proportional to1/ Nphe , where Nphe is number of photoelectrons observed by a PMT.

7.2

Structure of event reconstruction

Reconstruction of the gamma ray detector is done in following steps.
1. Decoding and calibration of raw waveform data.
2. Waveform analysis of each PMT. Here, charge and time of each PMT are
extracted.
3. Calibration of each PMT is done for charge and time. All the calibration
parameters are read from a database.
• Attenuation in electronics are corrected.
• Output charge is converted to number of photo-electrons on photocathode by using gain.
• Number of photo-electrons are converted to number of photons byusing Q.E..
• Systematic time offset by different path length from PMTs to thereadout is corrected.
4. Pile-up identification is done by using spatial and temporal distributionof PMT outputs.
5. Several kinds of algorithms are implemented to reconstruct energy, position and time of impinging gamma rays.
As a result, energy deposit, position and time associated with a gamma ray
are filled in a persistent data structure so that they are used for combined analysis with reconstruction of positrons. The gamma ray detector is not sensitive
to the direction of gamma rays, thus combined analysis is done by assuming
gamma rays are emitted at the reconstructed muon decay point by positron
analysis.

7.3

Waveform analysis

In the MEG experiment, all the waveforms of sub-detectors are recorded so that
pileup events can be find in offline analysis. So, the first step of the offline analysis chain is waveform analysis. Not to degrade DAQ speed, all the calibrations
are not done in DAQ frontend, but some of them are done in offline analysis.

7.3.1

Calibration and noise reduction

Voltage calibration
Voltage calibration of ADCs on DRS can vary depending on the temperature of
the chip, and the temperature can be changed by readout event rate. Relation
between ADC value and voltage is not linear. The voltage calibration to correctthese effects is done in DAQ frontend so that the raw waveform data is already7.3 Waveform analysis

107

written in volt. The calibration parameter is obtained by using internal DC
generator on DRS boards.
A response curve of DRS is shown in fig.7.11. The curve is not linear andthe resolution is better for smaller pulse than 500 mV. Typical pulse height ofwaveforms in the MEG experiment is adjusted to be smaller than 500 mV.






















Figure 7.11: Response curve of DRS2.

Time calibration
Time differences between two sampling points depend on delay time of inverters
between sampling cells on DRS chips. The calibration parameters to cancel it
was obtained from a measurement of sine waves, and they are stored in the
database. In this measurement, sine waves with a known frequency(80 MHz)
were measured and the time of each cell was determined so that the measured
data reproduce the known shape of sine waves.
The phase of the stop signal of an event in the domino ring is roughly
determined by using a pulse generated on the DRS board by a trigger stop signal
coming through the back plane of a VME crate. The resolution of the roughestimation is not good enough to use for analysis. And the timing can be affectedby path length from a trigger board which generates the stop signal and each
DRS board. The speed of DRS sampling is regulated, but it is not necessarily
constant. For correction of domino wave speed variation and alignment of chips,
a common clock signal with steep edges is provided to all the DRS chips withthe same length of cables. A typical waveform of the clock signal observed by
DRS is shown in fig.7.12. Time calibration of clock analysis is done in offlinefor each event. The clock waveforms are fitted by template waveform and thetime of each edge is estimated. Time of each sampling points of each channel isreassigned so that time of edges become same for all the DRS chips. Standard
deviation of the time correction by this analysis (difference of time before andafter the correction) around time region of typical pulses is about 0.7 nsec.

7.4 Reconstruction

108

Amplitude [mV]

Cr:4-Sl:7-Bd:2-Cp:1-Clock
600
550
500
450
400
350
300
-600

-500

-400

-300

-200

-100

0
Time [nsec]

Figure 7.12: Typical waveform of clock signals for time calibration.

Noise reduction
It is known that there is a noise by cross-talk with sharp edges of clock signal.
Since the shape of the noise is always same, and the time can be estimated fromthe clock signal, it is possible to subtract it in analysis. A template waveform
was created from random trigger data, and the subtraction of the template
waveform is done for each event.

7.3.2

Charge integration

Number of photoelectrons of a PMT is estimated from an integrated charge of
waveform in a time window. A common time window is used for all the PMTs
in each event, and the time window is determined relative to the time of a peakof sum waveform of PMTs. To cancel an effect of slow component noise, thebaseline voltage is determined for each PMT at every event by using a part ofwaveform before a pulse.
During 2007 run, a slow component noise was observed. The interval of thenoise was the same level of the DRS time window, therefore the effect can not becanceled by baseline subtraction completely. To reduce the effect of the noise,high-pass filtering was done in offline analysis. Figure 7.13 show a raw waveform
and that after the filtering. Effectively, it is decreasing amount of integrated
charge, and it makes the signal to noise ratio (S/N) worse for high frequency
noise.
In the case of 2007 run, the filtered waveform improves energy resolution,
because the effect of slow frequency noise was larger than high frequency one.
Before applying the filter, contribution of noise to 54.9 MeV energy peak was
4.5 % and it is improved to 2.0 % by the filtering. For the analysis in thissection, filtered waveforms were used. The filtering was done by subtractionof a waveform after moving average of 89 sampling points. It corresponds tothe cut off frequency of 10.7 MHz[59]. Charge integration was done in 45 nsec
range.

7.4

Reconstruction

In this section, a local coordinate system for the gamma ray detector is often
used. Figure 7.14 shows the local coordinate system (u, v, w) and the global

109

5

Amplitude [mV]

Amplitude [mV]

7.4 Reconstruction

0
-5

20
15
10
5

-10

0

-15

-5
-10

-20
-15
-25

-20

-30

-600

-500

-400

-300

-200

-100
Time [nsec]

-25

-600

-500

-400

(a)

-300

-200

-100
0
Time [nsec](b)

Figure 7.13: Waveform filtering. (a) Raw waveform. (b) Filtered waveform.

coordinate system (x, y, z). The origin of (x, y, z) is defined from the positionof the COBRA magnet, while that of (u, v, w) is the center position of the innerface of the gamma ray detector. In the case of 2007 run, conversion of the twocoordinates can be written as,
u
v
w

= z

(7.4)
(7.5)

−1

= r0 · tan (−y/x)p=x2 + y 2 − r0

(7.6)

where r0 = 67.85 cm is the radius of the inner face. (u, v) is the projected
position on the inner face, and w is the depth from the inner face.
u

w

y
v
z
x

Inner face

Figure 7.14: Local coordinate system of the gamma ray detector. The target is
located around the origin of (x, y, z) coordinate system.

7.4.1

Position reconstruction

The purpose of the reconstruction is estimating the position of the first conversion point in the active volume, instead of center of the shower. For thispurpose, position reconstruction is done by fitting PMT charge distribution on
the inner face in a limited region around the initial estimated position. (u, v)

7.4 Reconstruction

110

can be estimated from the mean of a fitting function, and w can be estimatedfrom the width of the function. The initial estimation is the center position of
the PMT with the maximum charge at the event. The estimation is improvedat the second step, where the estimation is the weighted mean of the center
position of the max PMT and eight surrounding PMTs. At the third step, projection to u and v are fitted by a function independently. The fitting function
is


cath
cath
tan−1 u−ū−r− tan−1 u−ū+rw
w

f (u, w) =tan−1 −rwcath − tan−1 rcath
w

(7.7)

”
“
”
“



r0 ·sin v−v̄r0 ·sin v−v̄r0 +φcath
r0 −φcath
−1
“
“
””
“
“
””
−
tan
tan
w+r0 · 1−cos v−v̄
w+r0 · 1−cos v−v̄r0 +φcath
r0 −φcath““””f (v, w) =r0 ·sin rv̄ −φcath
r0 ·sin rv̄ +φcath
0“
0“
−1
””
””
“
“
−
tan
tan−1
w+r0 · 1−cos rv̄ +φcath
w+r0 · 1−cos rv̄ −φcath
−1



0

0

(7.8)
where r0 , rcath and φcath are the radius of the inner face, the radius of
the PMT photo-cathode and φ of the PMT photo-cathode respectively. The
average of w estimated at two fittings for u and v projections are used as theinitial value of the fitting at the next step. For the fitting, 4×4 PMTs aroundthe mean position at the previous step are used to eliminate effect of PMT hits
in a distance by Compton scattering and pileups.
At the last step, a three dimensional fitting is done by using all u, v and w
as free parameters with a function based on equation 7.7 and 7.8. In this step,
light attenuation in the liquid xenon is taken into account.
Figure 7.15 and 7.16 shows fittings to simulated µ+ → e+ γ event in the caseof shallow(w=1.44 cm) and deep(w=10.58 cm) conversions. In the plot (a), eachbox represents amount of light of a PMT. (b) and (c) shows the projection tou and v directions and fittings. It is clearly seen that a deep conversion makes
broader light distribution than a shallow one.
Figure 7.17 shows a comparison between the true first interaction depth
and the reconstruction. Resolution is improved from a method used for thelarge prototype, and it does not become worse in the shallow part very much.
When energy deposit distribution becomes broader in u or v direction thantypical events, reconstruction can be deeper than true depth. By the reason,
the distribution of the residual is asymmetric. In fig.7.18, the sigma of residual(reconstructed - MC) for each side of Gaussian is shown as a function of thereconstructed depth.
u and v resolutions for simulated signal events are shown in fig.7.19. Resolution of u looks worth than v, because the coordinate system is a projection to
the inner face. For example, 10 mm difference of u at (u, v, w) = (0, 0, 25) cm
and (u, v, w) = (25, 0, 25) cm correspond to 7.3 mm and 6.8 mm difference ofv at those points respectively. Angular resolutions are shown in fig.7.20 for θand φ. θ and φ correspond to u and v directions respectively. In the plot,
events outside of acceptance are not used. The acceptance is shown in fig.3.7.
Resolutions are almost same for θ and φ in the central region of the detector,

111

v [cm]

7.4 Reconstruction

60

×10

3

140

40

120
100
80
60

20

40
20
0

−20

−10

0

10

20
u [cm]

(b)

0
×10

3

140
120

−20

100
80
60
40

−40

20
0

−20

−10

0

10

20
v [cm]

(c)

−60

−20

−10

0

10

20
u [cm](a)Figure 7.15: Fitting of position for a shallow event for a simulated signal event.
(a) 2D histogram of PMT outputs. (b) Fitting of u projection. (c) Fitting of v
projection.

112v [cm]

7.4 Reconstruction

60

×10

3

140

40

120
100
80
60

20

40
20
0

−20

−10

0

10

20
u [cm]

(b)

0
×10

3

140
120

−20

100
80
60
40

−40

20
0

−20

−10

0

10

20
v [cm]

(c)

−60

−20

−10

0

10

20
u [cm](a)Figure 7.16: Fitting of position for a deep event for a simulated signal event.
(a) 2D histogram of PMT outputs. (b) Fitting of u projection. (c) Fitting of v
projection.

7.4 Reconstruction

113

Sigma of residual [cm]Figure 7.17: True and reconstructed position for µ+ → e+ γ event simulation.
Events in the acceptance are shown.

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0

5

10

15

20

25
30
35
Reconstructed W [cm]Figure 7.18: Sigma of residual of w for upper (triangle) and lower (circle) sides.
Sigma of the upper part is larger due to variation of the shape of shower.

7.4 Reconstruction

114

Sigma of residual [cm]Sigma of residual [cm]while θ becomes worse at the edge of u. This is because reconstruction is doneby PMTs in the inner face, and at the edge the fitting can be done to only apart of the distribution. This is the same for φ at the edge of v.

1.4
1.2
1
0.8

1.4
1.2
1
0.8

0.6

0.6

0.4

0.4

0.2

0.2

0
0

5

10

15

20

0
0

25
30
35
Reconstructed W [cm]

(a)

5

10

15

20

25
30
35
Reconstructed W [cm](b)Sigma of residual [mrad]

Figure 7.19: Resolution of (a) u and (b) v as a function of the reconstructed
depth.

14
12
10
8
6
4
2
0
0

5

10

15

20
25
Reconstructed U [cm]Figure 7.20: Angular resolution for θ direction(circles) and φ direction(triangles)
as a function of reconstructed u.
Differences of position resolutions depending on the position relative to innerface PMTs were studied. The result is shown in table 7.1.
In order to measure position resolution from experiment data in CEX runs,a lead plate of 1.8 cm thickness was put between the detector and the COBRA
magnet. Reconstructed positions are shown in fig.7.22. During the runs, gamma
rays in front of 2×3 PMTs were used for the trigger. Position resolution was
estimated from the shape of a edge in fig.7.22-a. The edge of the plate lies on
the middle of C and D in fig.7.21 horizontally, and the measurement was for φdirection. For events deeper than 2 cm, measured resolution is 7.6± 1.2 mm.
Resolutions for each depth slice is shown in fig.7.22-b. The best value in depth
slices is 5.9 ± 1.4 mm.

7.4 Reconstruction

115

Position A
Position B
Position C
Position D

φ resolution
6.44 ± 0.09
6.64 ± 0.08
7.64 ± 0.09
7.52 ± 0.10

θ resolution
6.66 ± 0.08
7.56 ± 0.10
6.73 ± 0.08
7.92 ± 0.10

Table 7.1: Position resolutions at several relative positions [mrad]. The definition of positions are shown in fig.7.21. 7 mrad corresponds to 4.75 mm on the
inner face.

D

C

D

B

A

B

D

C

D

Position
Entries7517
Mean-22.87
RMS
2.952

350
300
250

Resolution [cm]Figure 7.21: Definition of relative position from PMTs.

2.5

2

1.5
200
150

1

100
0.5
50
0-30

-28

-26

-24

-22

(a)

-20

-18

-16
V [cm

00

2

4

6

8

10

12

14
Depth [cm](b)

Figure 7.22: Measured position resolution. In this plot, events around 54.9 MeV
and deeper than 2 cm were selected. (a) Fit of collimator edge. The data wastaken for v > −19 cm by trigger. (b) Resolution and depth.

7.4 Reconstruction

7.4.2

116

Energy reconstruction

In the case of the large prototype, photo-cathode area coverage of each PMT
were same on all the faces. On the other hand, in the case of the final detector, it
depends on position of PMTs as shown in fig.7.23. For example, the coverage on
the outer face is 2.6 times less than that of inner face. Therefore, a simple sum of
PMT charge depends on the position and the depth of the first conversion point.
In order to cancel the effect, Qsum2 was introduced for energy reconstruction.
X
Qsum2 =
ci · Qi(7.9)
where, ci is a correction factor which is proportional to the inverse of photocathode coverage of a PMT. Qi is PMT charge.

Figure 7.23: Photo-cathode coverage on different faces. The picture shows inner,outer and top faces. The circles are area of PMT photo-cathodes.

Even after the correction, Qsum2 is not completely flat in the fiducial volume
due to geometrical effect (difference of overall PMT coverage depending on
position), and that of dead channels. In fig.7.24, N sum2 (weighted sum of
outputs of all the PMTs after Q.E. correction) dependencies on reconstructed
positions are shown for simulation data. In order to correct such effects, further
correction was done by using measured data. To obtain calibration constants,
gamma rays which satisfy following conditions are needed.
• It must come from the target position.
• It must have a monochromatic energy.
• It must impinge whole the acceptance of the gamma ray detector,
with high enough rate.
Furthermore, if the energy is known, it can be used for calibration of absolute
scale of conversion from Qsum2 to energy. There are two candidates which
satisfy this condition, namely gamma rays from CEX and those from nuclear
reaction which can be produced by the C.W. accelerator.
For the calibration of future physics runs, pion charge exchange could be
used. But in 2007, full scan in the acceptance was not done with pion beam due
to a limited beam time. Hence, in this thesis, C.W. data is used for the energy
scale calibration.
When a gamma ray converts in the shallow part of the detector, Qsum2
depends on the position very strongly because solid angle of the nearest PMT
affects very much. To reduce the effect, a special treatment is done for shallow
events. In this analysis, when the conversion depth is less than 2 cm, Qsum2 −Qmax was used, where Qmax is the charge of the PMT with maximum output inthe event. Scaling factors from number of photons to energy were extracted from

7.4 Reconstruction

117

17.6 MeV peak in C.W. runs for events in w < 2 cm and those for w >= 2 cm
separately. As seen in fig.7.25, connection at w = 2 cm is done smoothly, anddepth dependence is well corrected.
Fittings to evaluate the resolution were done in the same way with the large
prototype. Figure 7.26 and 7.27 show resolution (σ of right edge) dependence
on depth and impinging position for simulated signal events.

(a)

(b)

(c)

Corrected Nsum2

Figure 7.24: Nsum2 and reconstructed positions for simulated signal events.

50000

40000

30000

20000

10000

0
0

1

2

3

4

5

6
Depth [cm]Figure 7.25: Corrected N sum2 and depth for C.W. experiment data withlithium target. The peak of N sum2 = 3200 corresponds to 17.6 MeV. For
shallower events than 2 cm, Qsum2 − Qmax is used.
Real energy resolution of the detector was estimated from CEX data for
54.9 MeV and 83.0 MeV for events deeper than 2 cm. σ of right edge is 2.8 ± 0.1
and 2.9±0.1 % for 54.9 and 83.0 MeV respectively. Figure 7.28 shows histogramsof energy for both energies. The resolution depends on depth as shown in
fig.7.29. The best resolution in slices by depth is 2.1 ± 0.2 %.
Figure 7.30 shows peaks of Qsum2 for various gamma ray energies. The
numbers are normalized for 54.9 MeV peak. 54.9 and 83.0 MeV peaks are
obtained from CEX data. 17.6 and 14.6 MeV peaks are from nuclear reactionof lithium, 6.13 MeV is from that of florin during C.W. beam test with Lithium
fluoride target. 4.4 MeV is from a nuclear reaction of boron. Center values ofσ [%]

7.4 Reconstruction

118

10
9
8
7
6
5
4
3
2
1
0
0

5

10

15

20

25

30
35
Reconstructed W [cm]

4

σ [%]

σ [%]

Figure 7.26: Energy resolution and reconstructed depth for simulated signal
events.

3.5

2
1.8
1.6

3
1.4
2.5

1.2

2

1
0.8

1.5

0.6
1
0.4
0.5
0
0

0.2
5

10

15

20
25
Reconstructed U [cm]

0
0

5

10

15

(a)

20

25

30
35
Reconstructed v [cm](b)

Figure 7.27: Energy resolution and reconstructed position for simulated signal
events.

120

120

100

100

80

80
60

60

40

40

20

20

040

45

50

55

(a)

60
65
Energy [MeV]

060

65

70

75

80

85

90

95
100
Energy [MeV](b)

Figure 7.28: Fitting to estimate energy resolution for 2007 data. In this plot,
events than 2 cm were selected. (a) 54.9 MeV peak. (b) 83.0 MeV peak.

Resolution [%]7.4 Reconstruction

119

8
7
6
5
4
3
2
1
0
0

5

10

15

20

25

30

35

reconstructed w [cm]Figure 7.29: Energy resolution and depth for 54.9 MeV peak for 2007 data.

points in this figure except for 14.6 MeV peak are within ±0.8 % from a fitting
linear line.
14.6 MeV peak is naturally wide as shown in fig.2.18 and the peak is notvery clear compared to other monochromatic peaks.
The response of the detector shows a good linearity in this wide range ofenergy.

7.4.3

Time reconstruction

Time of each PMT is calculated by constant fraction discrimination in offline
analysis so that it does not depend on pulse height very much. Even if the constant fraction algorithm is used, measured time has a delay due to scintillation
photon statistics. Time offset of each PMT is firstly measured by using LED
which is discussed at 7.1.3. More precise time offset and statistical delay are
estimated from CEX data by using time difference distribution of each PMTwith respect to a tagging detector with taking into account distance between
interaction positions in the gamma ray detector and the PMT.
An estimate of a gamma ray’s time by a PMT can be written as
Tγ = TPMT − Tstatistics − Tpropagate − Toffset(7.10)

where TPMT , Tstatistics , Tpropagate and Toffset are -measured time by a PMT,
time delay due to scintillation photon statistics, propagation time from energy
deposit point to the PMT and time offset due to cables and electronics.
Timing of a gamma ray is estimated by taking
pweighted average of each
PMT’s estimate. The weight is proportional to Nphe . PMTs with morethan 200 photo-electrons are used for taking the average. The resolution wasmeasured in two ways as it was done by the large prototype. An intrinsic
resolution was measured from difference of estimation by the top half and thebottom half of the detector. Figure 7.31 shows a distribution of time differenceof the top and the bottom half. For this plot, events deeper than 2 cm andNormalized Qsum2

7.4 Reconstruction

120

1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
00

10

20

30

40

50

60

70 80 90 100
Energy [MeV]

Figure 7.30: Qsum2 peaks of various gamma ray energies.

|v| < 1 cm were selected so that time resolution of the top and the bottom half
are approximately same.
200

200

180

180

160

160

140

140

120

120

100

100

80

80

60

60

40

40

20
0
-2

20
-1.5

-1

-0.5

0

0.5

1
1.5
2
Ttop - Tbottom [nsec]

(a)

0
-2

-1.5

-1

-0.5

0

0.5

1
1.5
2
Ttop - Tbottom [nsec](b)

Figure 7.31: Time difference of top and bottom half. (a) 54.9 MeV peak (b)83.0 MeV peak
The distribution widths are 164 ± 2 and 140 ± 2 psec for 54.9 and 83.0 MeV
peaks respectively. If we assume the resolution is determined by scintillation
photon statistics, the intrinsic resolution(δtintrinsic ) can be written as
δtintrinsic = δ(ttop − tbottom )/2
where δ(ttop − tbottom ) is σ of time difference of estimations by top and bottom
half of the gamma ray detector.

7.4 Reconstruction

121

Resolution [nsec]

Figure 7.32 shows the time difference in 54.9 MeV peak for each slice of
depth. The best in depth slices is 142 ± 4 psec.

0.5

0.45
0.4

0.35
0.3

0.25
0.2
0.15
0.1
0.05
0
0

5

10

15

20

25

30

35
Depth [cm]Figure 7.32: Time difference of top and bottom half for each depth slice.
The practical resolution was measured by comparing the time at the gamma
ray detector and that at the tagging detector.
350

160

300

140
120

250

100
200

80
150

60
100

40

50
0
-2

20
-1.5

-1

-0.5

0

(a)

0.5

1

1.5
2
Txe - Ttc [nsec]

0-2

-1.5

-1

-0.5

0

0.5

1

1.5
2
Txe - Ttc [nsec](b)

Figure 7.33: Time difference of the gamma ray detector and the tagging detector. (a) 54.9 MeV peak (b) 83.0 MeV peak

The distribution widths of fitting functions in fig.7.33 are 205±6 and 197±8
psec for 54.9 and 83.0 MeV peaks respectively. These number includes depth
resolution(35 ∼ 90 psec depending on depth, estimated from simulation), distributions of pion decay position(60 psec), tagging detector’s resolution(90 psec)
and time alignment of the gamma ray detector and the tagging detector. By
subtracting these contributions,p the practical time resolution for 54.9 MeV
gamma ray for w > 2 cm is (205)2 − (60)2 − (90)2 = 175 ± 5 psec. Figure 7.32 shows the time difference in 54.9 MeV peak for each slice of depth.
Atp the best depth, the practical time resolution for 54.9 MeV gamma ray is(162)2 − (60)2 − (90)2 = 121 ± 8 psec. The difference from intrinsic time
resolution (72±2 psec) is due to fluctuations of depth reconstruction and timealignment of readouts(80 psec). Effect from depth reconstruction fluctuation is7.5 Event type identification

122

Resolution [nsec]

estimated to be 51±12 psec from MC simulation. Taking into account theseeffects, practical and intrinsic time resolutions are consistent. Note that DRS
time alignment uncertainty between the gamma ray detector and the tagging
detector is included in 121 psec. The contribution is not subtracted from theresolution because the same contribution is present in physics analysis in timedifference of a gamma ray and a positron. Contribution of the gamma ray detector to the resolution is evaluated to be 90.7 ± 8 psec by subtracting that of
DRS alignment.

0.5

0.45
0.4

0.35
0.3

0.25
0.2
0.15
0.1
0.05
0
0

5

10

15

20

25

30

35
Depth [cm]Figure 7.34: Time difference of the gamma ray detector and the tagging detector for each depth slice. These numbers include tagging detector’s resolution(90 psec) and decay position distribution(60 psec).

7.5

Event type identification

In this section event type identifications of three possible sources of backgrounds
are discussed. Since most of gamma rays from radiative muon decays and AIF
have lower energy than those from signals, events reconstructed higher energy
than actual gamma ray energy can be backgrounds. One is due to too large
output by a PMT, that occurs when there is an energy deposit just in front ofa PMT. Another source is a pileup of two gamma rays. Identification of cosmic
rays is also discussed.

7.5.1

Higher tail identification

The total solid angle of PMT photo-cathode seen from the fiducial volume isalmost uniform, and the sum of number of photoelectrons does not strongly
depend on the shape of electro-magnetic shower in the volume. When thefirst conversion occurs very shallow part, the variance is larger. Therefore such
events are analyzed in a special way which was already discussed. However,with a small probability, the detector can observe a larger amount of light thanthat expected from the position of the first conversion position. The typicalevent display is shown in fig.7.35. In this event, the first interaction occurs in7.5 Event type identification

123

the fiducial volume, then a low energy gamma ray travels and deposits energy
just in front of an outer face PMT. Even with a small energy deposit, the PMT
observes a large amount of light when the deposit point is in front of the photo
cathode. This kind of events can be identified by searching a too sharp peak inspatial distribution of PMT outputs. Too sharp peak was searched from charge
ratio of a PMT and an average of surrounding eight PMTs. Threshold was
adjusted by using MC to be 15 for the outer face and 5 for top, bottom andlateral faces. Figure 7.36 shows the distribution of N sum2 of simulated signal
events with and without cut by too sharp peaks. Miss rejection(inefficiency ofsignal) by this selection is 2 % where ratio of reconstructed energy and true
deposit energy is around one.
21999

6304

1806

517

148

42

12

3

0

50

100

150

200

250

300
1

(a)

(b)

Figure 7.35: Event display of a higher tail event in simulation. In this event,a part of energy was deposit in front of an outer face PMT by a low energy
gamma ray. (a) shows a 2D map of PMT charge on the outer face. (b) is a 3Dview of the event. Color code of energy deposits(small square boxes) represent
time of deposits.

7.5.2

Pile-up identification

Identification of pile-up events where two gamma rays enter the detector will be
important to improve limit of µ+ → e+ γ .
In a simulation assuming a high muon stopping rate (1 × 108 ) 28 % of events
have pileups during the decay time of scintillation, where definition of pile up
is when area of overlap of waveforms corresponds to more than 0.5 MeV. In thecase of a muon rate of 3 × 107 , the probability should be around 8.4 %.
To identifying pile-up events, two complementary types of algorithms weredeveloped. The most case of pile-ups is an accidental coincidence of two gamma
rays from radiative muon decay, annihilation in flight of positrons, bremsstrahlung7.5 Event type identification

124

hist1
Entries
49610
Mean
4.011e+05
RMS
2.205e+04

4

10

103

102

10

1

×10

3

150

200

250

300

350

400

450

500

550
Nsum2

Figure 7.36: Nsum2 distribution of simulation before and after higher tail eventcut.

of positrons and so on. The detection of this type of pile-ups can be done by time
separation. Time separation is done by using time difference of the earliest PMT
hit and the latest PMT hit in an event. When there are not pile-ups, it must be
less than 4 nsec, while in the case of pile-ups, it can be larger than that. Thismethod is sensitive when time difference of two gamma rays are larger than thethreshold, while it can not find a pile-up when two gamma rays impinge almost
at the same time, for example a gamma ray from a radiative muon decay and athat from AIF from the same muon decay. Another type of identification is doneby using spacial hit pattern of PMTs. Figure 7.37 shows a hit pattern and 3D
event display when two gamma rays enter the gamma ray detector. Triangles
in the right figure show detected two peaks in the distribution. Identification
power and miss-identification probability was studied by using MC simulation.
Identification power and miss-identification probability depend on thresholds inthe analysis and those must be adjusted according to noise level of the gamma
ray detector in the experiment. When one uses the lower thresholds, identification power and miss-identification probability become larger. In a simulation
study, when low thresholds were used to detect low energy pileups, identification
power of time and space separations were 76 and 80 % respectively. By combining them, 95 % of pileups could be identified. Miss-identification probabilityof them were 2 and 10 % respectively.

7.5 Event type identification

(a)

125

(b)

Figure 7.37: Event display of pileup events in simulation and pileup identification.

7.5 Event type identification

7.5.3

126

Cosmic ray event rejection

1.8
Entries

58236

1.6
1.4
1.2

Rate [Hz/MeV]

Rate [Hz/MeV]

Figure 7.38-a shows a spectrum of the gamma ray detector measured at thenominal position with beam off and the COBRA magnet on. The data wastaken by the self-trigger of the detector. Since beam was off, most of these
events must be from cosmic rays or secondary particles of a cosmic ray hitting
on a structure in the experimental hall. For comparison, expected gamma ray
spectrum from radiative muon decay(RD) and annihilation in flight(AIF) withassuming 3 × 107 muon stopping rate is shown in fig.7.38-b.

3

10

102

1
0.8

10

0.6
1

0.4
0.2

10-1

00

50

100

150

200

250

(a)

300

350

400 450 500
Energy [MeV]

20

25

30

35

40

45

50

55
60
Energy [MeV](b)

Figure 7.38: (a) Measured cosmic ray spectrum. (b) Simulated spectrum ofenergy deposit in the gamma ray detector, from RD(solid line) and AIF(dashedline), with assuming 3 × 107 Hz muon stopping rate.

The rate of low energy backgrounds from cosmic rays is much lower thanthat from radiative muon decays or AIF. So, the probability of an accidental
pileup of a gamma ray and a cosmic ray background must be much lower thanpileup of two gamma rays. However, since the rate of cosmic rays is almost
constant around the energy of µ+ → e+ γ signal, a probability that a cosmic
mimics a signal is relatively high in a narrow energy window around the signal.
Event rate of cosmic rays observed by the gamma ray detector is comparablewith RD or AIF around the signal region, if we don’t adopt any rejection ofcosmic ray events.
Most of cosmic-ray event can be clearly distinguished from gamma ray eventsfrom the hit pattern of PMTs. Cosmic rays observed by the gamma ray detector
can be classified like followings.
1. It enters from the inner/outer face and exits to outer/inner face.
2. It enters or exists from one of top, bottom, upstream or downstream face.
3. It enters from one of top, bottom, upstream, downstream or outer face,
and it stops in the active volume.
4. It enters from the inner face, and it stops in the active volume.
In the case of (1), the minimum energy deposit is around 160 MeV which corresponds to 38.4 cm of path length (distance of two faces), and 4 MeV/cm energy
deposit, which is reasonable for liquid xenon(z=54). So it does not look like asignal gamma ray because the deposit energy is too high. In the case of (2),

7.5 Event type identification

127

when the energy deposit is close to the signal region, the position must be reconstructed outside of the fiducial volume. Most of all events of (1), (2) or (3)can be rejected with a selection of Qinner2 /Qouter2 > 0.4, even when energy andposition are reconstructed in the signal box. Qinner2 and Qouter2 are weighted
charge sum of PMTs on the inner and outer face respectively with the same
factor of Qsum2.
Figure 7.39 shows Qinner2 /Qouter2 distribution during muon beam on andoff. When muon beam is on, there are two peaks corresponding to cosmic ray
events and gamma ray events. When muon beam if off, in most of events it isless than 0.4. By a cut of Qinner2 /Qouter2 > 0.4, 80 % of cosmic ray events
can be rejected. Most of remaining events are (4). Figure 7.40 shows the same
variable in simulated signal events and its depth reconstruction. The fractionof events cut by the selection is 3.7 %, and those events are mostly deep events
for which resolutions are not as good as those for normal depth events.
hist
Entries
11888
Mean
1.028
RMS
0.4676250

hist
Entries
24227
Mean
0.386
RMS
0.3029

2400
2200
2000
1800

200

1600
1400

150

1200
1000

100

800
600

50

400
200

0
0

0.5

1

1.5

2

2.5

3

(a)

0
0

0.5

1

1.5

2

2.5

3

(b)

Figure 7.39: Qinner2 /Qouter2 distribution during (a) muon beam on, and (b)muon beam off.

500

400

300

200

100

0
0

0.5

1

1.5

(a)

2

2.5
3
Qinner2 / Qouter2(b)

Figure 7.40: (a) Qinner2 /Qouter2 distribution of simulated signal events. (b)Depth dependence of the variable.

Integrated rates of cosmic rays and gamma rays in fig.7.38 from 51 to
55 MeV, are 5 and 20 Hz respectively before the rejection of cosmic ray events.
After the rejection, the rate of cosmic rays is 1/20 of that of gamma rays.

7.6 Summary and discussion on the gamma ray detector

7.6

128

Summary and discussion on the gamma ray
detector

In this chapter, reconstructions and calibrations of the gamma ray detector aredescribed. The performance of the detector and the analysis was evaluated byusing CEX data in 2007. The best resolutions in depth slices are summarisedin table 7.2. With comparing to table 1.3 and table 5.1, all the resolutions are
not as good as the requirements and worse than the prototype. The spacial
resolution(5.9 mm in σ) corresponds to a contribution of 20 mrad. The time
resolution (121 psec in σ) includes DRS time alignment resolution between the
gamma ray detector and the tagging detector. Comparable number to the resultof the large prototype is 0.21 nsec in FWHM with subtracting contribution of
the alignment uncertainty. On the other hand, the uncertainty remains in timedifference between a gamma ray and a positron in MEG physics run, and wehave to compare 121 psec in σ(0.284 nsec in FWHM) with the goal. The rateof the accidental background, which is the dominating background, is approximately proportional to (∆Eγ )2 · ∆Ee+ · (∆θγe+ )2 · ∆Tγe+ [58]. With assuming
goal resolutions of the positron detector, the background event rate with thesemeasured gamma ray resolutions is 4.4 times larger than the goal. The contributions of three resolutions are almost same (1.44, 1.67 and 1.82 by energy,
time and position respectively).

∆Eγ [%]∆Ee+ [%]∆θγe+ [mrad]∆Tγe+ [nsec]
Acceptance × Efficiency [%]Muon stopping rate (108 )Running time [weeks]Single event sensitivity(10−13 )90 % C.L. limit(10−13 )MEG goal
4.5∼5.0
0.8
12.4∼16.9
0.18>1.6
0.3(DC)
100
0.5
1.7

2007 (best)
6.0
23.2(20.4)
0.301(0.284)-

Table 7.2: The best resolutions in depth slices, measured in 2007 (FWHM).
∆Eγ is FWHM of fitting function of 54.9 MeV peak. σ of right edge of thefunction is 2.1 %. For ∆θγe+ and ∆Tγe+ , requirements for the positron detector(10.5 mrad and 100 psec) are included. For those resolutions, contributions of
the gamma ray detector are written in parentheses. 20.4 mrad and 0.284 nsec
in FWHM correspond to 5.9 mm and 121 psec in σ respectively.
There are two major sources which make the resolution worse. Observed
amount of light in the final detector is much lower than expectation from thelarge prototype and MC simulation of the final detector. In 2007, amount oflight was 1/3 of the expectation. According to the result of the large prototype(fig.5.31), when energy of gamma rays is 1/3 of 54.9 MeV, energy resolution can be worse than 2 %. Another factor which makes resolution worse isnoise or instability of electronics. The effect can be evaluated approximatelyfrom the distribution of estimated energy for random trigger events. The dis-

7.6 Summary and discussion on the gamma ray detector

129

tribution width corresponded to 2 % of 54.9 MeV in run 2007. Time resolution
is affected by the low scintillation yield and alignment of time measurementsof several DRS chips. The correction of event by event time jitter is done byusing a common clock signal as described in section 7.3.1. As it can be seenin fig.7.12, the waveform is not very clean, and event-by-event variation of the
waveform makes alignment uncertainty of 80 psec. The problem is a way toread the waveform on DRS chip, instead of the original waveform. Position
resolution can be improved by better gain and Q.E. estimation of PMTs. To
improve gain estimation, LEDs with higher attenuation factor were installed
during a maintenance period after 2007 run. Q.E. estimation can be improvedby optimizing parameters in MC simulation to reproduce alpha source eventsin the final detector well.
A prospect to improve scintillation yield and the DRS time alignment are
discussed in section 9.2.
Three kinds of event type identification (higher tail event, cosmic ray andpile up) are described. In a study of MC simulation, higher tail events are
successfully identified as shown in fig.7.35.
From rejection factor of cosmic ray events, which is estimated from measured
cosmic ray spectrum, and an expected rate of single gamma rays from MC
simulation, single event rate of cosmic ray event is 1/20 of that of gamma rays
around the signal energy after a rejection. So background rate by cosmic rays
will be negligible.
Event rate of pileup events was estimated from MC simulation with assuming
the highest possible muon stopping rate (1 × 108 ) of the MEG. In an energy
deposit region from 51 to 55 MeV, which is 2σ region of 2.1 % resolution, 90 %of events are pileup events. After the rejection, the rate becomes a half of single
gamma events. Since the accidental rate is proportional to the square of thebeam intensity, the fraction with the nominal beam rate(3 × 107 ) is nine times
less than that. So if the performance is realized for experiment data, the rateof pileup events must be much lower than that of single gamma events in 2007
and 2008. The beam rate will be optimized for 2009 run based on the accidental
event rate in 2008 result.
Figure 7.41 shows single spectrum of the gamma ray detector during physics
run in 2007. Histograms for each event types are stacked on each other. Events
included in the top most histogram is used for physics analysis in chapter 8.
Note that the figure is single spectrum of the gamma ray detector, and event
selection by using time and opening angle correlation with a positron is notdone except for trigger requirement. So, absolute number of background event
is much lower than the figure. A discussion after the event selection is done in thefollowing chapter. Tail of the top most histogram is broader than an expectation
based on the measured energy resolution. The broadness is equivalent to anenergy resolution of 7.2 %. Possible reasons are remaining pileup events, or
remaining non-uniformity of energy scale in the inner face. To understand theorigin of those events, further studies are needed. How the spectrum affects
the sensitivity is estimated in the following chapter by estimating number ofbackgrounds with assumed statistics in 2008 with using measured gamma ray
spectrum after these event type identifications.

7.6 Summary and discussion on the gamma ray detector

130

3

10

102

10

1
45

50

55

60

65

70

75
80
Energy [MeV]

Figure 7.41: Spectrum of gamma ray of µ+ → e+ γ trigger data. Four spectra
are shown for different event types identified by analysis. From the bottom,
CR, pileup of two or more gamma rays, higher tail events. White one is after
rejection of these events. Each histogram is stacked.

Chapter 8

The MEG Sensitivity
In the past µ+ → e+ γ search experiments(MEGA and Crystal box), upper limitof branching ratio was calculated by maximum likelihood analysis. Likelihood
analysis allows to take into account the shape of the signal and backgrounds,
including correlation between variables. In this chapter, the upper limit ofbranching ratio from 2007 data is evaluated by using maximum likelihood analysis. In order to check performance of the detector for the sensitivity with morestatistics, the sensitivity with assumed statistics in 2008 is evaluated by using
Feldoman-Cousins approach[60].

8.1

Likelihood analysis with MEG 2007 data

In this section, we tried to estimate the upper limit of branching ratio by using data taken in 2007 engineering run, while it is clear that the statistics is
not enough to improve the current experimental limit. So the purpose of thissection is to demonstrate the physics analysis and understanding the current
capability of the experiment, rather than estimating the upper limit. In thisstudy, some simplification was utilized, because the statistics is much lower andthe likelihood analysis is still under development.
• Only accidental background was considered. Rate of prompt backgroundshould be one order of magnitude less than accidental one from a calculation.
• Events with shallower gamma ray conversion than 2 cm were not used in
the study. The resolutions are worse than normal events, so they shouldbe less significant to sensitivity. In the real physics analysis in 2008 or
later, they can be included with taking into account resolutions.
• It was assumed that pileup, cosmic ray, higher tail event identification
works perfectly for signal events when the probability function is created.
The effect of failure of identification must be taken into account in a real
physics analysis in 2008 by using simulation.
In this analysis, resolutions written in table 8.1 were used for signal probability function(p.d.f.). For energy and opening angle, measured resolutions in8.1 Likelihood analysis with MEG 2007 data132

2007 were used. Since, in this analysis, common probability density functions
are used all over the depth region of the gamma ray detector, resolution functions are broader than those with the best resolutions shown in table 7.2. Whenthe development of the likelihood fit software is completed, the functions foreach depth slice will be prepared. Since statistics in this analysis is very small,the fitting result must not be changed even if functions are prepared for each
depth. Time coincidence resolution was measured in 2008 by using π 0 → γe+ e−
decay. In this analysis, a preliminary result of the measurement is used. The
measuredtime coincidence resolution is worse than an expectation, which isp(0.175)2 + (0.0587)2 × 2.35 = 0.43 nsec in FWHM, from measured time resolutions of gamma ray detector for w > 2 cm, and an expected resolution of
positron detector described in section 2.3.1. This can be due to errors of calibration to correct position dependence of time on the timing counter and/or the
gamma ray detector. The investigation is still being done. To be conservative,
the measured time resolution is used in this analysis.
For the data modeling and fitting, RooFit Toolkit[61] was used.

∆Eγ [%]∆Ee+ [%]∆θγe+ [mrad]∆Tγe+ [nsec]

MEG goal
4.5∼5.0
0.8
12.4∼16.9
0.18

MEG 2007
6.4
2.2
30.2
0.82

Table 8.1: Resolutions of detector used in likelihood analysis, written in
FWHM. Resolutions for positrons are measured in 2007[21]. Those for gamma
rays are measured average resolutions for events deeper than 2 cm, which is
described in section 7. ∆Eγ is FWHM of fitting function of 54.9 MeV peak in
CEX test. The function is shown in fig.8.2-a. Time coincidence resolution is apreliminary result from a measurement of π 0 → γe+ e− decay during CEX testin 2008.
The analysis was done for 21 events in analysis box. Event selection was
done by following conditions.
• 46 ≤ Eγ ≤ 60 MeV• 50 ≤ Ee ≤ 56 MeV• cos θeγ ≤ −0.99145• |∆Teγ | ≤ 1.75 nsec
• Acceptance cut for positrons. | cos θe | ≤ 0.35 and |φe | ≤ 60◦ , where (θe ,φe ) is a direction of a positron at the muon decay point.
• Acceptance cut for gamma rays. |u| ≤ 24.8 cm, |v| ≤ 71.1 cm and w ≥2 cm, where (u,v,w) is a hit position in the gamma ray detector.
• Pileup, cosmic ray and higher tail event rejection described in section 7.
Selections by gamma ray energy(Eγ ), positron energy(Ee ) and time difference(Teγ )correspond to 5σ region of each variable. A selection by opening angle(cos θeγ )8.1 Likelihood analysis with MEG 2007 data

133

60

Time difference [nsec]

Gamma energy [MeV]

was done by wider region than 5σ in order to increase number of events for the
analysis. The result is independent of the size of analysis box. Figure 8.1 showsa distribution of the selected events for four variables.

1.5

58
56

2

1

5

50

7

3

4

8

6

10

51

52

11

53
54
55
56
Positron energy [MeV]

4
8
5

3

10

9

-1

9

6

0

-0.5

48
46
50

11

0.5

54
52

2

1

7

1

-1.5
-1

-0.999 -0.998 -0.997 -0.996 -0.995 -0.994 -0.993 -0.992

cos�

Figure 8.1: Distribution of selected 21 events for gamma and positron energy(left) and time difference and opening angle(right). For some events, event
number is assigned to show correspondence in two plots. Boxes in the plotsshow 1.64σ region.

8.1.1

Building likelihood function

The partial probability to measure i-th observed event with parameters xi canbe defined to be
P (xi )
N

= Nsig S(xi ) + NRD S 0 (xi ) + NBG B(xi )(8.1)= Nsig + NRD + NBG(8.2)

where Nsig , NRD , NBG are number of events of signals, prompt backgrounds
and accidental pileups respectively.
The extended maximum likelihood method is used in this analysis to estimate absolute number of signals, instead of fraction of it. The extended likelihood function can be written as
Y
L(Nsig , NRD , NBG ) = Q(N ; Nexp )P (xi )
(8.3)
Q(N ; Nexp )N −Nexp= Nexp
e
/N !

(8.4)

where Nexp is a fitting parameter to estimate the absolute normalization. In
this analysis following observables were used to build the likelihood function.
Eγ
Energy of a gamma ray
Ee
Energy of a positron
Teγ
Time difference of a gamma ray and a positron(u, v, w)
First interaction position of a gamma ray written in a local
coordinate system of the gamma ray detector(x, y, z)Muon decay vertex position(cos θe , φe ) Initial direction of a positron8.1 Likelihood analysis with MEG 2007 data

8.1.2

134

Probability density functions

p.d.f. of signals
S was defined to be= S1 (Eγ |Ee , u, v, w, x, y, z, cos θe , φe , Teγ ) ·S(Eγ , Ee , u, v, w, x, y, z, cos θe , φe , Teγ )S2 (Ee |u, v, w, x, y, z, cos θe , φe , Teγ ) ·S3 (Teγ |u, v, w, x, y, z, cos θe , φe ) ·S4 (u, v, cos θe , φe |w, x, y, z) ·S5 (w|x, y, z) ·S6 (x, y, z)(8.5)

Projection of signal gamma energy PDF

Projection of signal positron energy PDF

Projection of signal time difference PDF

Probability [/GeV]

Probability [/GeV]

Probability [/sec]

where S6 is muon stopping distribution, and S5 is depth distribution of the firstinteraction position of gamma rays in the gamma ray detector. Each function
from S1 to S6 is normalized. S6 is created from measured beam profile andtarget geometry. S5 is created from measured depth distribution in the gamma
ray detector. S1 , S2 , S3 and S4 are identical to the response functions of thedetector in this study because the kinematics is monochromatic for Eγ , Ee , Teγand θeγ . S2 , S3 and S4 are approximated by Gaussian functions with a varianceof the detector resolutions. S1 is not a Gaussian, but a function written inparagraph 5.2.3. Response functions for gamma rays and positrons were createdindependently. For positrons, response functions were created by using Michel
decay data. For gamma rays, response functions were created from 54.9 MeV
peak of pion charge exchange data. Figure 8.2 shows S1 , S2 and S3 .
0.018
0.016
0.014
0.012

0.025

0.02

0.015

0.01

0.016
0.014
0.012
0.01

0.008

0.008

0.01

0.006

0.006

0.004

0.004

0.005

0.002
0

0.018

0.002
0.048

0.05

0.052

0.054

0.056

0.058
EGamma [GeV]

0
0.05

0.051

(a)

0.052

0.053

0.054

0.055
EPositron [GeV]

(d)

0

-1.5

-1

-0.5

0

0.5

1

1.5
Teγ [sec]

×10-9

(c)

Figure 8.2: Probability density functions of (a)gamma energy, (b)positron energy and (c)time difference for signals. These were created from measured detector responses.

p.d.f. of accidental backgrounds
B was defined to beB(Eγ , Ee , u, v, w, x, y, z, cos θe , φe , Teγ )= B1 (Eγ |Ee , u, v, w, x, y, z, cos θe , φe , Teγ ) ·B2 (Ee |u, v, w, x, y, z, cos θe , φe , Teγ ) ·B3 (Teγ |u, v, w, x, y, z, cos θe , φe ) ·B4 (u, v, cos θe , φe |w, x, y, z) ·B5 (w|x, y, z) ·B6 (x, y, z)(8.6)

8.1 Likelihood analysis with MEG 2007 data

135

For accidental pileup backgrounds, distributions of gamma rays and positrons
must be independent by definition. Hence, p.d.f. can be created separately.
B1 and B5 were created by using off-center events in time from RD trigger
data. B2 and B6 were created from Michel trigger data. B4 was created fromrandom combinations of an off timing gamma ray and a positron. B3 must be
1 by definition. B6 is same with S6 .
Figure 8.3 shows gamma ray spectrum during µ+ → e+ γ data taking. Eventsin the acceptance and deeper than 2 cm are included in histograms. A histogramin 8.3-b is used as B1 .

102

10

1
46

48

50

52

54

56

58

60

62
64
Energy [MeV]

Figure 8.3: Background spectrum of gamma rays. Cosmic ray, pileup andhigher tail event rejections are done. e+ γ coincident events are excluded byrequiring Teγ > 2 nsec to obtain spectrum of accidental pileup events.

8.1.3

Upper limit from 2007 physics run

The mean value of the maximum likelihood fitting of Nsignal is 1.02 × 10−7 .
The 90 % confidence limit is the value of Nsignal where 90 % of the likelihood
distribution is covered. The limit was obtained from integration of a curve in
fig.8.4-c. This value is 2.7 events. Figure 8.5 shows distribution of four variables
together with fitting result.
If we use numbers listed in table 8.2, 90 % C.L. upper limits of the branchingratio of µ+ → e+ γ can be calculated to be 1.2 × 10−10 .

Projection of -log(L)Number of BG events

8.1 Likelihood analysis with MEG 2007 data

25

20

15

136

14
12
10
8
6

10

4
5
2
0
0

0.2

0.4

0.6

0.8

1

1.2

1.4
1.6
1.8
2
Number of signal events002

Likelihood

(a)

4

6

8

10

12

14
16
18
20
Number of signal events

(b)

1

0.8

0.6

0.4

0.2

0
0

2

4

6

8

10

12

14
16
18
20
Number of signal events(c)
Figure 8.4: Result of likelihood fitting. (a) Center value and one sigma region of
number of signal and background events. Sigma is statistical error of likelihood
fitting by MINUIT. (b) Projection of − log(likelihood) as a function of numberof signal events. (c) Projection of likelihood function as a function of numberof signal events.

Running time [weeks]
Number of stopped muons
Acceptance(%)
Gamma detection efficiency(%)
Positron detection efficiency(%)

0.13
1.89 × 1012
9
30.7
43.8

Table 8.2: Numbers used for normalization to translate number of signals into
the branching ratio in this work. Gamma detection efficiency is lower than anormal value, because in this study shallower events than 2 cm was not used.

8.1 Likelihood analysis with MEG 2007 data

137

6
4.5
4

5

3.5
4

3
2.5

3

2
2

1.5
1

1

0.5
0
0.046

0.048

0.05

0.052

0.054

0
0.05

0.056
0.058
0.06
Gamma energy [GeV]

(a)

0.051

0.052

0.053

0.054
0.055
0.056
Positron energy [GeV]

(b)

4.5

4.5

4

4

3.5

3.5

3

3

2.5

2.5

2

2

1.5

1.5

1

1

0.5

0.5
×10

-9

0

-1.5

-1

-0.5

0

(c)

0.5

1
1.5
Time Difference [sec]0-1-0.999 -0.998 -0.997 -0.996 -0.995 -0.994 -0.993 -0.992
cosθ

(d)

Figure 8.5: Projected distributions of 21 events for (a)gamma energy,(b)positron energy, (c)time difference and (d)opening angle. Solid lines show
best fit curves and dashed line show 90 % C.L. upper limit of number of signals.

8.2 Sensitivity estimation for run 2008

8.2

138

Sensitivity estimation for run 2008

In this section, expected sensitivity of MEG run 2008 is estimated by FeldomanCousins approach[60]. It is assumed that bad channels of the drift chambers
would be solved and run with full expected efficiency. For gamma ray detector,
an increase of amount of light by purification is taken into account. Numbers intable 8.3 were used for the estimation. In the estimation, signal region is defined
as a region of 90 % cut determined by the detector resolutions for each variable.
As it is discussed in section 8.1, a preliminary time resolution measured in 2008
is worse than an expectation. To be conservative, the measured resolution isused also in this analysis.

∆Eγ [%]∆Ee+ [%]∆θγe+ [mrad]∆Tγe+ [nsec]
Acceptance × Efficiency [%]Muon stopping rate (108 )Running time [weeks]Single event sensitivity(10−13 )90 % C.L. limit(10−13 )MEG goal
4.5∼5.0
0.8
12.4∼16.9
0.18>1.6
0.3(DC)
100
0.5
1.7

MEG 2008 expectation
6.0
1.5
21.0
0.82
1.7
0.3(DC)
11-

Table 8.3: Expected conservative performance in MEG 2008. Numbers are
written in FWHM. γ efficiency includes cut by w > 2 cm. Resolutions of the
gamma ray detector are preliminary performance measured in 2008. Resolutionsof the positron detector is expectation from MC in full condition[21].

8.2.1

Prompt background

Background event rate of single radiative decay can be calculated using the formula given in [62][63][64][65] with taking into account resolutions of the detector.
With using expected resolutions in 2008, the contribution of prompt backgroundcan be found to be much smaller than that of accidental background.

8.2.2

Accidental backgroundNumber of accidental background can be written asNacc =

nµ · fe0 ·

 
  
Ω
Ω
δω
0
· e · nµ · fγ ·· γ ×· (2δt) · T · fPµ (8.7)
4π
4πΩwhere nµ is muon stopping rate, δt is a timing coincidence resolution, Ω isacceptance of the detector, δω is opening angle resolution and T is DAQ livetime,e and γ are detection efficiency for positrons and gamma rays respectively. fe0
and fγ0 are the fractions of the spectrum within the signal box of the positrons in
the Michel muon decay and photons in the radiative muon decay respectively.
They include their branching ratios. fPµ is a background suppression factor

8.2 Sensitivity estimation for run 2008

139

when a muon is polarized. In this discussion fPµ = 1 is considered. The
effective branching ratio can be obtained by

Bacc =

nµ · T ·

Nacc

Ω
4π

· e · γ= nµ · fe0 · fγ0 ·



δω
4π


· (2δt) .

(8.8)

fe0 is obtained by integrating Michel muon spectrum in the signal region. It
is approximately 2 × δx, where x is positron energy divided by 52.8 MeV anddeltax is resolution of x. nµ · fγ0 is obtained from p.d.f. of background gamma
rays. Normalization can be obtained from single counting rate of the gamma
ray detector with taking into account selection in analysis. By incorporating
above, effective branching ratio is estimated to be 1.2 × 10−13 . In order toestimate sensitivity in 2008, we assume 5 × 106 of DAQ time for physics runs
from September to December. During this period calibration runs are also taken.
DAQ live time would be about 85 % of it. The total livetime corresponds toabout 11 weeks with the same normalization in table 1.3.
Single event sensitivity can be simply calculated from these numbers andefficiencies to be 4.4 × 10−13 . 90 % C.L. upper limit of null experiment can be
estimated by using Feldoman-Cousins approach described in ref.[60]. Numberof backgrounds expected from parameters in this section is 0.27. Using the
expected number of backgrounds, the 90 % C.L. upper limit of null experimentis calculated to be 9.4 × 10−13 .

Chapter 9

Summary and prospects
9.1

Summary

A new type of gamma ray detector where many PMTs surround a single active
volume was developed. The development was done in three steps, the small
prototype, the large prototype and the final detector. During the prototype
test, fundamental techniques for operation of large xenon detector, purification,measurement of scintillation photons and analysis were developed. By using
the large prototype, resolutions of energy and time for 54.9 MeV and position
resolution for 40 MeV gamma ray were measured to be 1.2 %, 43 psec and4.3 mm respectively. Construction of the final detector was started from testing
and measuring properties of all the PMTs individually. The cryostat with thin
and wide entrance window was built and it was passed all the hardware tests.
In 2007, the first operation of the gamma ray detector was done starting frompurification of xenon. After finishing purification, the first engineering run of
MEG with all the sub-detector was conducted. CEX data was taken to evaluate
performance of the gamma ray detector in limited region of the acceptance. The
best resolutions of energy, time and position in depth slices were estimated tobe 2.1 ± 0.2 %, 5.9 ± 1.4 mm and 121 ± 8 psec respectively. A small amount ofphysics data was taken in the engineering run. A simplified likelihood analysis
was done to demonstrate that to be done with much more statistics in 2008.
The 90 % CL upper limit of BR(µ+ → e+ γ ) from 2007 data is 1.2 × 10−10 .
By using measured resolutions and background spectrum, it was confirmed thatthe gamma ray detector has a good enough performance to carry out µ+ → e+ γ
search experiment with a better sensitivity than 1 × 10−12 in 2008.

9.2

Prospects

The resolutions of the final gamma ray detector are worse than the result of
the large prototype, mainly due to low amount of light and noise of electronics.
Observed amount of light in the final detector in 2007 was 1/3 of expectation,
while absorption of scintillation does not seem so much. In 2008, it was foundthat amount of light has a correlation with operation of liquid nitrogen forcooling. So it is most likely that there is a small leak of nitrogen from thecooling pipe only when the part is cooled. Nitrogen contamination can decrease9.2 Prospects

141

amount of scintillation as discussed in section 3.1.1. In 2007, purification was
done by molecular sieves which mainly eliminate water. In addition to that, in
2008, a purifier by using copper beads was introduced to eliminate also oxygen,
which may exist in liquid xenon due to outgas. After finding the possible leak,we stopped using the cooling pipe and started using alternative one. After apurification, amount of light was increase by factor 1.8 with respect to that in2007. Even after the factor 1.8 improvement, it is still increasing by operating
purification. If the amount of light is three times larger, all the resolutions are
expected to be improved significantly.
In 2008, a search of noise sources was done and burst noise from power
supply of VME crates and noise correlated with VME signals were found. It
was found that noise is picked up by flat cables running near VME crates. To
fix the problem, flat cables were shielded and the noise was reduced. Noise
correlated with VME signals were reduced by increasing interval of polling tocheck status of VME modules.
Time resolution is degraded by alignment of time measurements of several
DRS chips. A new version of DRS (version 4) is expected to be introduced from2009 to improve many aspects of readouts, including an improvement of clock
waveform readout. DRS2 has some other problems, noise induced by clock,large cross talks, unstable baseline offsets, temperature dependent response,
fake signals due to calibration variation and remaining charge by large pulsein the previous loop. The collaboration is trying to decrease effect of these
problems both in the operation and analysis, however there are remaining effects
to resolutions. DRS4 is expected to solve some of these problems.
In 2007, because of limited beam time, the study of performance of gamma
ray was done in limited positions in the acceptance. In 2008, the full scan of
all the acceptance is done. Detailed study for non-uniformity and long term
stability will be done. Detection efficiency of the gamma ray detector will bemeasured in 2008 by counting number of hits of the gamma ray detector insingle trigger data by the tagging detector in CEX test.
In 2007, about 25 % of cells of the drift chambers had some problems mainly
due to disconnection of loose connectors or H.V. discharges. Many of them are
fixed in 2008. Further study to fix discharges are being done. z measuring timing
counter was not in operation due to problems of readout electronics. When it isin operation determination of z hit position on timing counter will be improved.
Then reconstruction of muon decay time from positron spectrometer will be
improved.
Calculation of expected sensitivity in 2008 was done with assuming a fullefficiency of the positron spectrometer, and it was calculated to be 9.4 × 10−13 .
The number is one order of magnitude improvement from the current experimental upper limit (1.2 × 10−11 ). MEG will make a new limit in 2008 and willcontinue improvements of apparatus and analysis, and will continue to collect
more statistics after 2008 for even higher sensitivity.

Bibliography[1] Y. Kuno and Y. Okada, Rev. Mod. Phys. 73, 151 (2001).
[2] G. W. Bennett et al., Phys. Rev. Lett. 89, 101804 (2002).
[3] G. W. Bennett et al., Phys. Rev. Lett. 89, 129903 (2002).
[4] G. W. Bennett et al., Phys. Rev. Lett. 92, 161802 (2004).
[5] G. W. Bennett et al., Phys. Rev. D 73 (2006).
[6] W.-M. Yao et al., Journal of Physics G 33, 1+ (2006).
[7] J. Hisano and K. Tobe, Physics Letters B 510, 197 (2001).
[8] M. L. Brooks et al., Phys. Rev. Lett. 83, 1521 (1999).
[9] R. D. Bolton et al., Phys. Rev. D 38, 2077 (1988).
[10] U. Bellgardt et al., Nuclear Physics B 299, 1 (1988).
[11] C. Dohmen et al., Physics Letters B 317, 631 (1993).
[12] W. Honecker et al., Phys. Rev. Lett. 76, 200 (1996).
[13] W. Bertl et al., The European Physical Journal C 47, 337 (2006).
[14] P. Depommier et al., Phys. Rev. Lett. 39, 1113 (1977).
[15] A. van der Schaaf et al., Nuclear Physics A 340, 249 (1980).
[16] W. W. Kinnison et al., Phys. Rev. D 25, 2846 (1982).
[17] D. Anderson, H. Arvela, A. Breskin, and G. Charpak, Nucl. Instr. andMeth. 224, 315 (1984).
[18] D. Green, H. Haggerty, S. Hansen, and M. Takasaki, Nucl. Instr. and Meth.
A 256, 305 (1987).
[19] J. Allison et al., Nucl. Instr. and Meth. A 310, 527 (1991).
[20] Y. Ajima et al., Nucl. Instr. and Meth. A 443, 71 (2000).
[21] H. Nishiguchi, An Innovative Positron Spectrometer to Search for the Lepton Flavour Violating Muon Decay with a Sensitivity of 10−13 , PhD thesis,
University of Tokyo, 2008.

BIBLIOGRAPHY

143[22] S. Ritt, Nucl. Instr. and Meth. A 518, 470 (2004).
[23] D. Zahnow, C. Rolfs, S. Schmidt, and H. P. Trautvetter, Z. Phys. 359, 211(1997).
[24] F. E. Cecil et al., Nucl. Phys. A 539, 75 (1992).
[25] T. Doke, Portugal Phys. 12, 9 (1981).
[26] D. R. Lide, CRC Handbook of Chemistry and Physics 2004-2005 (CRC
Press, Boca Raton, FL, 2004).
[27] J. Jortner, L. Meyer, S. A. Rice, and G. E. Wilson, J. Chem. Phys. 42,4250 (1965).
[28] N. Schwenter, E.-E. Koch, and J. Jortner, Electronic Excitations in Condensed Rare Gases (Springer-Verlag, Berlin, 1985).
[29] L. M. Barkov, A. A. Grebenuk, N. M. Ryskulov, P. Y. Stepanov, and S. G.
Zverev, Nucl. Instr. and Meth. A 379, 482 (1996).
[30] V. N. Solovov et al., Nucl. Instr. and Meth. A 516, 462 (2004).
[31] G. M. Seidel, R. E. Lanou, and W. Yao, Nucl. Instr. and Meth. A 489,
189 (2002).
[32] T. Doke et al., Jpn. J. Appl. Phys. 41, 1538 (2002).
[33] A. Braem et al., Nucl. Instr. and Meth. A 320, 228 (1992).
[34] V. Y. Chepel, M. I. Lopes, R. Ferreira Marques, and A. J. P. L. Policarpo,
Nucl. Instr. and Meth. A 349, 500 (1994).
[35] N. Ishida et al., Nucl. Instr. and Meth. A 384, 380 (1997).
[36] T. Doke and K. Masuda, Nucl. Instr. and Meth. A 420, 62 (1999).
[37] L. Landau and E. Lifshitz, Electrodynamics of Continuous Media, 2ndedition (Pergamon Press, Oxford, 1984).
[38] V. A. Rabinovich, A. A. Vasserman, V. I. Nedostup, and L. S. Veksler,
National Standard Reference Data Service of the USSR. Translation. 10,622 (1988).
[39] K. WATANABE and M. ZELIKOFF, J. Opt. Soc. Am. 43, 753 (1953).
[40] K. Watanabe, E. C. Y. Inn, and M. Zelikoff, The Journal of Chemical
Physics 21, 1026 (1953).
[41] K. Yoshino, J. R. Esmond, W. H. Parkinson, K. Ito, and T. Matsui, Chemical Physics 211, 387 (1996).
[42] K. Yoshino, J. R. Esmond, W. H. Parkinson, K. Ito, and T. Matsui, Chemical Physics 215, 429 (1997).
[43] R. Acciarri et al., Effects of nitrogen contamination in liquid argon, 2008,
nucl-ex/0804.1217.

BIBLIOGRAPHY

144[44] R. Acciarri et al., Oxygen contamination in liquid argon: combined
effects on ionization electron charge and scintillation light, 2008, nuclex/0804.1222.
[45] Omni NuPure III, http://www.nupure.com.
[46] A. Baldini et al., Nucl. Instr. and Meth. A 545, 753 (2005).
[47] S. Mihara et al., Cryogenics 44, 223 (2004).
[48] S. Mihara et al., Cryogenics 46, 688 (2006).
[49] A. M. Baldini et al., Nucl. Instr. and Meth. A 566, 294 (2006).
[50] MSCB, http://midas.psi.ch/mscb.
[51] Labview, http://www.ni.com.
[52] T. Miyazawa,
Development of liquid xenon calorimeter for µ →eγ experiment,
Master’s thesis, University of Tokyo, 1999,
http://meg.web.psi.ch/docs/theses/miyazawa.pdf (in Japanese).
[53] K. Ozone, Timing resolution of liquid xenon gamma-ray detector for µ →eγ decay search experiment, Master’s thesis, University of Tokyo, 2000,
http://meg.web.psi.ch/docs/theses/ozone.pdf (in Japanese).
[54] K. Ozone,
Liquid Xenon Gamma-ray Detector for the New µ →eγ Search Experiment,
PhD thesis, University of Tokyo, 2005,
http://meg.web.psi.ch/docs/theses/ozoned.pdf.
[55] M. Miyajima, S. Sasaki, and E. Shibamura, Nucl. Instr. and Meth. B 63,
297 (1992).
[56] A. Bay et al., Nucl. Instr. and Meth. A 271, 497 (1988).
[57] F. Bourgeois, A. Corre, J. P. Marcelin, A. Meyrier, and G. Schuler, IEEETNS 34, 240 (1987).
[58] M. Toshinori et al., Research Proposal to Paul Scherrer Institut, R-99-05(1999).
[59] W. Xi, Engineering Fracture Mechanics 52, 199 (1995).
[60] G. J. Feldman and R. D. Cousins, Phys. Rev. D 57, 3873 (1998).
[61] W. Verkerke and D. Kirkby, The roofit toolkit for data modeling, 2003,
physics/0306116.
[62] Y. Kuno, A. Maki, and Y. Okada, Phys. Rev. D 55, R2517 (1997).
[63] Y. Kuno and Y. Okada, Phys. Rev. Lett. 77, 434 (1996).
[64] C. Fronsdal and H. Überall, Phys. Rev. 113, 654 (1959).
[65] S. G. Eckstein and R. H. Pratt, Ann. Phys. 8, 297 (1959).

Acknowledgements
The MEG experiment is done by a collaboration of University of Tokyo, KEK,
Waseda University, PSI, INFN Pisa, INFN and University of Genova, INFN and
University of Pavia, INFN and University of ROME I, INFN and University of
Lecce, BINP Novosibirsk, JINR Dubna and University of California Irvine.
The construction of the new liquid xenon gamma ray detector was done on
efforts of many persons. To take physics data, a huge amount of effort for all the
sub-detectors, beam, DAQ and triggers were needed. It was possible to perform
analysis and simulation by gathering implementations by many persons. All
these things were done with a decade of works. Here I can not write all thenames, however I appreciate all the persons contributed MEG experiment, andpersons who supported or educated me.
Prof. Toshinori Mori is one of spokes persons of the MEG experiment. He
gave me a chance to work in MEG experiment for the gamma ray detector
and responsible positions in the collaboration. He always gave me importantsuggestions directly or indirectly, and lead me to the correct direction.
I joined the MEG experiment when I belonged to Waseda University. Prof. Tadayoshi Doke, Prof. Jun Kikuchi and Prof. Satoshi Suzuki are very experts ofany kinds of xenon detectors, and I learned important basics at that time.
Dr. Kazuhiro Terasawa is the first person who taught me about experiment.
From Prof. Masaki Yamashita, I learned many technical things and how interesting experiment is.
Prof. Satoshi Mihara developed the gamma ray detector of the MEG as thegroup leader. I could gain valuable experience when I try to complete tasks
suggested by him. I learned a lot of things during working with Dr. Wataru
Ootani, or enjoying interesting logical discussions. The development and operations of the gamma ray detector wouldn’t be done without Dr. Toshiyuki
Iwamoto’s much reliable works. I learned about software and computers fromDr. Shuei Yamada.
I learned many things from Dr. Kenji Ozone during the prototype tests.
Without his support, I couldn’t have been involved in the experiments as I could.
Dr. Hajime Nishiguchi mainly worked for the development of the drift chamber.
However actually, he contributed also for the development and experiments forthe gamma ray detector very much. I thank him also for his helps in my Swiss
life. Yasuko Hisamatsu made grate contributions to the development of the
PMT. Her contribution for analysis and simulation are also important. I thankher help in Tokyo for my activities in Switzerland. Analysis of the gamma ray
detector would be incomplete without contributions of Yusuke Uchiyama. He
is contributing not only to the gamma ray detector, but also for analysis of
positron spectrometer and physics. Works of Hiroaki Natori may not be highlyvisible necessarily, but his reliable works were important to develop the gamma
ray detector. Calibration of the gamma ray detector by using pion decays could
be done by using a tagging detector developed by Yasuhiro Nishimura. I would
appreciate Toshiya Mitsuhashi and Takefumi Yoshimura for works for the large
prototype tests and PMT development. I would like to appreciate Prof. Satoru
Yamashita for comments and advices.
The operation of the liquid xenon system is done by using refrigerators developed by Prof. Tom Haruyama. He contributed whole the design of the liquid
xenon system. He also supported activities of MEG group during the large prototype tests in KEK. I thank grate technical supports by Katsuyu Kasami. I
would like to appreciate Prof. Akihiro Maki for comments and advices.
The development of the gamma ray detector and its analysis were done bycooperation of Japanese group and INFN Pisa group lead by Prof. Alessandro Baldini. Dr. Donato Nicoló and Dr. Giovanni Signorelli have been working
together with me since the large prototype tests. Dr. Fabrizio Cei has been
contributing analysis and simulations also since the large prototype tests. Giovanni Gallucci participated the construction of the gamma ray detector. Calibration of the gamma ray detector by using nuclear reactions could be done by
a C.W. accelerator proposed, prepared and operated by Prof. Calro Bemporad,
Dr. Giovanni Signorelli and Angela Papa.
Dr. Stefan Ritt was my super visor in Switzerland. He developed great DAQ
system, DRS and slow control system. I learned practice of designing systems
from discussions with him and his works. Dr. Matthias Schneebeli developed
the framework of the MEG analysis software. He improved the framework fromour feedback in the prototype tests. He developed a software library for DRS
readout and analysis of the drift chambers. Analysis of the drift chamber usedin this thesis was done by implementation of mainly by him and Fedor Ignatov. Dr. Jonny Egger and Dr. Malte Hildebrandt developed the drift chambers.
Dr. Malte Hildebrandt helped me not only for experiment, but also for my life
in Switzerland. The muon beam line system was built by Dr. Peter-RaymondKettle and Dr. Dimitri Grigoriev. I thank Dr. Valeri Markshin who has been
supporting the computing system of MEG.
Discussions with Prof. William Molzon and his group members, Dr. Vladimir
L. Tumakov, Paul Huwe, Feng Xiao, Christina Topchan and Ben Golden werevery constructive. The group prepared the gas control system of the spectrometer and the muon target. The timing counter system construction was leadby Prof. Giorgio Cecchet, Dr. Flavio Gatti and Dr. Simeone Dussoni. Analysis
and simulation of the timing counter is done by a coordination of Dr. Paolo
Cattaneo. The trigger system were successfully prepared to take physics data
by great works by Dr. Marco Grassi, Dr. Donato Nicoló and Luca Galli.
There are no words to express my deep appreciation to my parents Tetsuhide
and Reiko Sawada.