Doctor Thesis

Search for a Lepton Flavor Violating Muon Decay
Mediated by a New Light Neutral Particle
with the MEG Detector

byHiroaki Natori

Department of Physics, School of Science,
the Univeristy of Tokyo

2

Abstract
A discovery of a new particle, which mediates avor violating decay of charged leptons,
would unambiguously establish existence of new physics beyond the Standard Model (SM)of particle physics, because charged lepton avor violation (cLFV) is extremely suppressedin the SM. A rst dedicated search for a lepton avor violating muon decay, + ! e+ ,
mediated by a new light neutral particle, , which decays into two photons,  ! , wasperformed by the MEG experiment. The new particle  is expected to have a long lifetime
and its decay into e+ e may possibly be strongly suppressed. Although the experiment is
optimized to detect another cLFV decay, + ! e+ , it also has a good sensitivity to the-mediated cLFV decay, + ! e+ ;  !
. The liquid xenon photon detector has acapability of reconstructing multiple photon with precise measurements of their energies,
positions and timings within its large acceptance. By analyzing the data taken in 2009
and 2010, which corresponds to 1:8  1014 muon decays in the target, no evidence wasfound for the -mediated decays. Upper bounds on the branching ratio were obtained forvarious mass values 10{45 MeV and lifetimes  10 ns. In particular, for the lower mass
region M , this result exceeds the bound set by the generic search for + ! e+ by the
Crystal Box experiment, and thus established the most stringent limits on the -mediatedcLFV decays.

i

ii

Abstract

Contents

AbstractiContentsiii

I Introduction

1

1 Introduction
1.1 Theoretical background of light (pseudo-)scalar particle . . . . . . . . . . .
1.2 Muon decay experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.1 Muon decay modes . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.2 Constraints on + ! e+ ;  ! by Crystal Box result . . . . . .
1.3 Overview of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3
4
6
6
7
9

II The MEG experiment11

2 Experimental installation
13
2.1 Detectors overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1.1 MEG coordinate system . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 Beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2.1 Proton ring cyclotron at PSI . . . . . . . . . . . . . . . . . . . . . . 15
2.2.2 E5 beamline and surface muon beam . . . . . . . . . . . . . . . . 16
2.2.3 Beam transport system . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2.4 Muon stopping target . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.3 Positron spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3.1 COBRA magnet . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3.2 Drift chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3.3 Timing counter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.4 Liquid xenon gamma-ray detector . . . . . . . . . . . . . . . . . . . . . . . 24
2.4.1 Property of liquid xenon . . . . . . . . . . . . . . . . . . . . . . . . 24
2.4.2 Photomultiplier tube . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.4.3 Design of the MEG liquid xenon gamma-ray detector . . . . . . . . 28
2.4.4 Puri cation system . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.5 Calibration and monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.5.1 LED . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.5.2 241 Am alpha source . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.5.3 17.6 MeV gamma-line from 73 Li(p; )84 Be reaction . . . . . . . . . . . 33
iii

iv

CONTENTS

2.5.4 55 MeV gamma-ray from  Charge exchange reaction . . . . . . .
2.6 Electronics and data acquisition . . . . . . . . . . . . . . . . . . . . . . . .
2.6.1 Data acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.6.2 Trigger system . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

III Reconstruction, simulation and the performance

34
36
36
37

39

3 Analysis software and simulation
41
3.1 The MEG software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.2 + ! e+ ;  ! Monte Carlo event generation . . . . . . . . . . . . . . 42
3.3 Reconstruction sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.4 Waveform analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.4.1 Waveform analysis of drift chamber . . . . . . . . . . . . . . . . . . 45
3.4.2 Waveform analysis of timing counter . . . . . . . . . . . . . . . . . 45
3.4.3 Waveform analysis of gamma-ray detector . . . . . . . . . . . . . . 46
3.5 Reconstruction of positron tracks . . . . . . . . . . . . . . . . . . . . . . . 47
3.5.1 Hit reconstruction and track nding . . . . . . . . . . . . . . . . . . 47
3.5.2 Tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.5.3 Positron time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.5.4 Positron correction . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.5.5 Positron selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.6 Reconstruction of two gamma-rays . . . . . . . . . . . . . . . . . . . . . . 50
3.6.1 Scintillation photons . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.6.2 Pileup identi cation . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.6.3 Position reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.6.4 Time reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.6.5 Energy reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.7 Combined analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.7.1  decay vertex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.7.2 Momentum reconstruction . . . . . . . . . . . . . . . . . . . . . . . 57
3.7.3 Relative time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4 Detector performance and Monte Carlo simulation
59
4.1 Positron spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.1.1 Double turn method . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.1.2 Smearing of positron spectrometer reconstruction . . . . . . . . . . 59
4.2 Liquid xenon gamma-ray detector . . . . . . . . . . . . . . . . . . . . . . . 63
4.2.1 Detector eciency . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.2.2 Energy and position resolution . . . . . . . . . . . . . . . . . . . . . 64
4.3 Time reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

IV Analysis

69

5 -mediated decay search analysis
71
5.1 Signal event selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.2 Backgrounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

CONTENTS

5.3 Observed events in signal region . . . . . . . . . . . . . . . . . . . . . . . .
5.4 Normalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.1 Positron momentum selection . . . . . . . . . . . . . . . . . . . . .
5.4.2 Relative acceptance for positron . . . . . . . . . . . . . . . . . . . .
5.4.3 Acceptance for two gamma-rays . . . . . . . . . . . . . . . . . . . .
5.4.4 Direction match trigger eciency . . . . . . . . . . . . . . . . . . .
5.4.5 Positron relative eciency . . . . . . . . . . . . . . . . . . . . . . .
5.4.6 Gamma-ray eciency . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.7 Event selection eciency . . . . . . . . . . . . . . . . . . . . . . . .
5.4.8 Gamma-ray trigger eciency . . . . . . . . . . . . . . . . . . . . . .
5.4.9 The number of measured Michel positrons . . . . . . . . . . . . . .
5.4.10 Systematic uncertainties . . . . . . . . . . . . . . . . . . . . . . . .
5.4.11 Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.12 Single event sensitivity . . . . . . . . . . . . . . . . . . . . . . . . .
5.5 Upper bounds on the branching ratio . . . . . . . . . . . . . . . . . . . . .

v
82
84
86
87
87
88
89
90
91
91
92
93
93
95
95

6 Conclusion

99

A Normalization Factor

101

B Upper limits for each set of mass and lifetime values

107

Acknowledgment

109

Bibliography

111

vi

CONTENTSPart I
Introduction

1Chapter 1
Introduction
The aim of science is to understand and reveal the law of nature. With many experiments
and theoretical investigations, physicists have constructed the Standard Model (SM) of
elementary particle physics. It can describe the elementary particles and forces, the mostfundamental components of the nature. The SM is a great success. Its predictions are
so powerful that no experiment nds fatal aws in it so far. Nevertheless, scientists do
not believe that the SM is the ultimate goal we have been aiming at, because its many
elements are determined arbitrarily without any theoretical justi cations, just to t theexperimental observations.
Many extended models from the SM have been proposed, and experimental physicists
are now trying to nd a clue to physics beyond the SM. Finding deviations from the SM
prediction is the key. Lepton avor violation (LFV) of charged lepton (cLFV) is thought
to be a clear deviation from the SM. In this thesis, we searched for a new light neutral
particle, , which causes cLFV in the muon decay.  is a light neutral particle, whichis expected to have a large lifetime and to decay into two photons. Searching the decay
mode, + ! e+ ;  ! , was performed using data taken by the MEG experiment in2009 and 2010, which corresponds to 1:8  1014 muon stop in the target.
The experiment is dedicated to the search for another cLFV decay, + ! e+ . A
huge number of muon decays with gamma-ray and positron signals are recorded in theexperiment. As the MEG is designed to search for + ! e+ decays, it is not optimized
to detect other decay modes. For example, we have very small eciency for generic threebody decays such as + ! e+ , because the momentum of positron from this mode is
expected to have a peak around 30 MeV which is out of the range of geometrical acceptanceof the positron spectrometer, and the limited solid angle of the gamma-ray detector gives
very small acceptance to detect both gamma-rays from generic + ! e+ decays.
However, we have good detection eciency for + ! e+ ;  ! decay mode whenthe mass of  is about a few tens of MeV. Positron momentum becomes approximately
the same as that of + ! e+ decay when the mass of  is small, which leads to good
detection eciency by the positron spectrometer. Small mass of  makes generated  totravel nearly with relativistic speed. It makes opening angle of two gamma-rays in theexperimental frame to be small by the e ect of Lorentz boost. This enables to detect both
two gamma-rays within gamma-ray detector acceptance. It also makes the opening angle
between the positron and the gamma-ray approximately back-to-back, which helps us totrigger + ! e+ ;  ! decay with the same trigger setting for + ! e+ search.
In the following sections, theoretical background of such a particle is discussed.
3

4

1.1

Chapter 1.

Introduction

Theoretical background of light (pseudo-)scalarparticle

There are well-motivated theoretical arguments that favor the existence of a very light
scalar or pseudo-scalar particle, which remains undetected because it interacts very weakly
with ordinary matter [1, 2].
It is known that when a global symmetry is spontaneously broken, a massless NambuGoldstone boson appears. But if the symmetry is not exact but only approximate, amassive state arises, which is naturally light [3]. A famous example is pions. They are relatively light compared to the other hadrons, because they are thought to be pseudo-NambuGoldstone bosons generated by spontaneous breakdown of approximate SU (2)L  SU (2)Rchiral symmetry. In many extensions of the SM, the electroweak symmetry breaking sector
includes additional weak doublets or singlets. New CP -even, CP -odd or charged scalarstates may be present in the physical spectrum. If the theory possesses an approximate
global symmetry, a CP -odd scalar may acquire light mass.
Examples of such light particles are axion [4], Familons [5], and Majorons [6], which
are associated with spontaneously broken Peccei-Quinn [7], family and lepton number
symmetries, respectively. Another candidate is a pseudoscalar boson \A" in the twoHiggs doublet model (THDM) which acquires a mass proportional to the small parameter:m2A = 5 v2 , with v = 246GeV the electroweak scale, and 5 ! 0 corresponds to exact
global U (1)  U (1) symmetry. Phenomenology of \A" with mass below 200 MeV is
described in Ref. [1, 2, 8, 9]. According to Ref. [9], the muon anomalous magnetic
moment and other low energy processes give a tight constraint on the parameter spaceof this class of models, but the existence of a very light scalar with a mass at the MeVlevel is still possible by ne-tuning the model parameters. According to Ref. [10], a light
pseudoscalar is allowed also in the minimal composite Higgs model. In the frameworkof the next-to-minimal supersymmetric Standard Model (NMSSM), Ref. [11] shows a
CP-odd Higgs should either be heavier than 210 MeV or have couplings to fermions 4orders of magnitude below those of the SM.
A possible additional scalar that introduces cLFV at the tree level and its implications
on the li ! lj and li ! lj e+ e transitions are investigated in Ref. [1], where li is acharged lepton of i-th generation. Suppose that a very light pseudoscalar boson  mediate
cLFV. When it is lighter than the muon, the only kinematically allowed tree-level decay
mode is  ! e+ e , and a one-loop induced mode  ! can also be competitive sincethe  e+ e vertex is expected to be highly suppressed in general. Figure 1.1 shows the
Feynman diagram for the muon decay through this particle, + ! e+ ;  ! .

Figure 1.1: Feynman diagram for + ! e+ ;  !
fermion loop.

decay. Large circle represents a

Section 1.1.

Theoretical background of light (pseudo-)scalar particle

5

The decay width of  is calculated in Ref. [1]. We assume that the couplings of to the leptons are naturally suppressed by introducing the Cheng-Sher ansatz [12] , andYukawa coupling li lj is written as:
p
Mi Mj
ij
(1.1)
5
v
where  is a dimensionless nondiagonal matrix de ned in the avor space and 5 is thefth gamma matrix [2]. The decay width into an electron pair is given by
! 32
 2
2
2
M
4
M
j

j
M
e
ee

e
(1.2)
1
( ! e+ e ) =
2s22W
MZ
M2 ;
with s2W = 2 sin W cos W and W is the weak angle. The decay width for the two photon
mode is given by
3 M  M 2( ! ) =jF j2;(1.3)
162 s22W MZ
with
X f 2
F=
NC Qf f f xf (x);(1.4)
f =l;qand82< arcsin p1
x  1;x
2(1.5)
f (x) =: arccosh p1 i
x < 1;
xx

where x = 4Mf2 =M2 , NCf is the color index, and Qf is the electric charge in units ofthe positron charge [13]. The result of numerical calculation of the decay width for thecase that f f = 1 is shown in Figure 1.2. We observe that  is of the order of 10 14
GeV at most, and   M holds. This means that  is a long-lived particle, and thenarrow-width approximation can be used. The process in Figure 1.1 thus goes throughon-shell . Branching ratio of + ! e+ ;  ! is then,B( ! e;  !

) ' B( ! e)B( ! )   2Mj
e j2 Me(1 y2 )2  B( !
' 4s2
MZ

2W

)

(1.6)

with y = M =M . Becausemode is a loop e ect, ee mode is usually more favoredthan mode. But this does not hold if ee is strongly suppressed; it would only decay
into in this case.
Possibility to have a \leptophobic" pseudoscalar is discussed in Ref. [2]. The patternof the pseudoscalar couplings to the SM fermions is quite model-dependent. One can employ simple discrete symmetries to construct three-doublet models in which two doublets
couple to quarks while the third doublet couples to leptons and does not mix with theother doublets. In this case, the pseudoscalar in the rst two-doublet sector is entirely
leptophobic. The leptophobic pseudoscalar decays entirely into photon pairs and its lifetime generally becomes 2{3 times larger than the usual case. It is noted that o -diagonal
leptonic couplings must exist for cLFV processes such as shown in Figure 1.1.

the li ! lj e e reaction can be induced at the tree level. It
is worth emphasizing that (9) is only true under the as(4)sumption that ee ’ 1. If the very light  was leptophobic,
it would only decay into a photon pair, in which case theinequality(9) would not hold.
Chapter
1.
Introduction

li ! lj e e ;

6



2
4m2e 3=2
;
1 2
m

−13

(5)

10

−14

10

angle being W . One two photon mode is

e+e−

−15

10

γγ

−16

φ

γ

Γ (GeV)

10

−17

10

φ
γ

10

lj

10

−18

i
−19

−20

10

(b)

0

0.01

0.02

0.03

0.04

0.05
m (Gev)

0.06

0.07

0.08

0.09

0.1

φ

1.2: 2.Decay
widthsfor themodes
 !ee!andng to the li ! lj eFigure
e
FIG.
Decay
widthsfor themodese e !
and when! f f = 1 [1]resents a fermion loop.
as function of m .

1.2

Muon decay experiments

1.2.1117701-2
Muon decay modes
Table 1.1: Decay modes and branching fraction of muon
Decay mode
Branching ratio
+ ! e+ e   100%++
 ! e e  (1.4  0.4) 10 2 [14]+++
 ! e e   e e(3.4  0.4) 10 5 [15]Decay mode
Upper Limit (90% C.L.) ! e e  < 1:2  10 2 [16]
+ ! e+< 2:4  10 12 [17]
+ ! e+ e+ e
< 1:0  10 12 [18]++
 !e
< 7:2  10 11 [19]
+ ! e+ X 0< 1:1  10 9 [19]1
+ ! e+ X 0< 3  10 4 [20]2++0
 !e X< 2:6  10 6 [21]3
+ ! e+ X 0 ; X 0 ! e+ e
< 1  10 10 [22]4
Leptons are elementary fermions that do not interact strongly. There are three typesof charged leptons with di erent masses, electron, muon, and tau, and the corresponding
1 mX 0 < 2 me
2 Valid when mX 0 = 0-93.4, 98.1-103.5 MeV.
3 Limit for neutral massless Goldstone boson
4 Limits on the branching fraction depend on the mass and and lifetime of X0 . The quoted limits arevalid when X0 < 3:  10 10 s if the decays are kinematically allowed.

Section 1.2.

Muon decay experiments

7

neutral leptons are electron-, muon-, and tau-neutrino. Decays of charged leptons (muonsand taus) have been extensively studied, which contributed to the establishment of theSM. The results of the past experimental studies on the muon decay modes are summarizedin Table 1.1.
Upper three decay modes conserve lepton avor and nite branching ratios are experimentally determined, but the other modes are cLFV phenomena and are not discovered
yet. Lower four modes include a exotic particle X0 which induces cLFV and whose massis smaller than that of muon. There is no upper bound on the branching ratio for the
decay mode + ! e+ ;  ! because no experiment has been performed to search forthis decay mode.
The upper limit of + ! e+ X 0 ; X 0 ! e+ e strongly constrains existence of (pseudo-)
scalar that couples to e+ e . But as mentioned in Section 1.1, depending on the model,
branching fraction into
can be much higher than that of ee mode. In particular for
leptophobic pseudoscalars it does not pose any constraint on + ! e+ ;  !
. The
+
+
bound on  ! e
set by the Crystal Box experiment [19], however, constrain somekinematics region of the -mediated cascade decay. This topic is discussed in more details
in the next section.

1.2.2 Constraints on +! e ;  !
+by Crystal Box result

Crystal Box experiment [19] gives an upper limit of the branching ratio of generic + !
e+ decay as 7:2  10 11 . The nal state is the same for both decay modes + !
e+ and + ! e+ ;  ! , but their kinematics are di erent. The result of Crystal Box
experiment can be converted to the upper limit of the branching ratio of + ! e+ ;  !
decay mode by multiplying the relative eciency of the Crystal Box experiment for
generic + ! e+ and for + ! e+ ;  ! mode,(1.7)
B ( ! e;  ! ) = B ( ! e )  !e :!e;!
Figure 1.3 shows a schematic of the Crystal Box detector. Trajectories of positron were
determined with the multilayer drift chamber. No magnetic eld was applied. Energies
of positron and gamma-ray were determined by 396 NaI(Tl) crystals. Crystals located at
the four quadrants are stacked in 9 raws transverse to the beam axis, and in 10 columns
along the beam axis. The size of the crystal is 2:5  2:5  12:0 inch.
The relative eciency was evaluated from the geometrical acceptance and the detection
requirements of the Crystal Box experiment. The following criteria de ne the Crystal Box
acceptance in this evaluation:

 jzj < 10=2  2:5 inch when a particle reaches jxj = 9=2  2:5 inch or jyj = 9=2  2:5
inch,

 E > 20 MeV for each gamma-ray,
 Reject events with two gamma-rays in the same quadrant, The (pseudo-)scalar  decays before entering the crystal,{ jxdecay j < 9=2  2:5 inch,

8

Introduction

Chapter 1.

{ jydecay j < 9=2  2:5 inch,
where the z coordinate goes along the beam axis and y along vertical direction.
The result is shown in Figure 1.4. Note that this is just a rough and approximate
evaluation and we did not try to simulate the detector performance. Estimation is performed using only true values of emission directions, vertex positions, and energies ofparticles. In the Crystal Box analysis, they also applied cuts for momentum conservation.
If the lifetime of the (pseudo-)scalar  is long, it travels long before it decays, thus themomentum conservation cuts could drop the event, lowering the eciency. Therefore, theactual Crystal Box bounds would be worse than shown in Figure 1.4 for longer lifetime.

Branching ratio upper limit

Figure 1.3: A schematic cutaway diagram of the Crystal Box detector [19]

τφ = 10 psec
τφ = 100 psec
τφ = 1 nsec
τφ = 10 nsec

10-7

10-8

10-9

10-10

10

20

30

40
Mφ [MeV]Figure 1.4: Crystal Box + ! e+ Branching ratio upper limit scaled to represent
Branching ratio upper limit for + ! e+ ;  ! modeSection 1.3.

1.3

Overview of this thesis

9

Overview of this thesis

The theme of this thesis is searching for a new light neutral particle , which induces
cLFV muon decay,  ! e, and decays into photon pair,  ! , using the MEG datataken in 2009 and 2010. In the second Chapter, details about the MEG experiment andthe MEG detectors are described. We describe event reconstruction and Monte Carloevent generation for + ! e+ ;  ! decay in Chapter 3. Chapter 4 describes detector
performance and consistency between the experiment and Monte Carlo simulation. The
analysis to search for the signal event is described in Chapter 6, and the conclusion is
given in the last Chapter 6.

10Chapter 1.

IntroductionPart II
The MEG experiment11

Chapter 2
Experimental installation

2.1

Detectors overview

The design of the MEG experiment is optimized to search for + ! e+ . This is a clear
two-body decay, and the event signature for a muon at rest is a positron and a -rayemitted back-to-back, coincident in time, and both with monochromatic energy of 52.8
MeV, which corresponds to approximately half the muon mass.
The key elements of the MEG experiment can be classi ed to the following three: Muon beam Positron spectrometer Gamma-ray detector
The experiment is performed at Paul Scherrer Institut (PSI) in Switzerland. The
world's most intense positive DC muon beam is available in PSI. Transported muon is
stopped at a thin target located at the center of a super conducting magnet called COBRA.
a positron from a muon decay makes helical trajectory in the COBRA magnetic eld andleaves hits in the drift chambers and reaches timing counters. Gamma rays are measured
by a liquid Xenon (LXe) detector located outside of the COBRA. Geometrical acceptanceof the positron spectrometer and the gamma-ray detector is =4  0:1 for the 52.8 MeV
positron and gamma-ray. Schematic view of the detectors is shown in Figure 2.1.

2.1.1 MEG coordinate system
We de ne here the global and local coordinate system, which we use throughout thisthesis.
The origin of the global coordinate system is at the center of the muon stopping target.
The z-axis is in the same direction as the muon beam direction; the y-axis is vertical; andthe x-axis is the remaining axis of right handed coordinate system. , and ' is the polar
and azimuthal angle of spherical system with z-axis as polar axis and x-axis as azimuthalaxis.
A special (u, v, w) coordinate system is used for the LXe detector. It is based on the
inner face of the detector. The origin of (u, v, w) coordinate is (x, y, z) = (-67.85, 0, 0)[cm], which is the center of the inner face. Its de nition is as follows:13

14

Chapter 2.

Experimental installation

Rinner = 67:85 (cm);u = z;
v = Rinner  arctan (y=x);pw = x2 + y2 Rinner :

(2.1)
(2.2)
(2.3)
(2.4)

The coordinate system is shown schematically together with the detector in Figure
2.1.
y

COBRA Magnet
x

Drift Chamberzy COBRA Magnet+µ Beamθe+Timing Counterzv

Stopping Target

e+
ϕ

w

γ

x

u
w

Liquid Xenon
γ-ray Detectorγ
Timing Counter
Drift Chamber

1m

Figure 2.1: Schematic of the MEG detector and coordinate system

2.2

Beam

Requirement for the beam is High muon intensity, Low background.
To search for the rare muon decay, we need as many statistics as possible. In the sametime, the instant intensity of the beam is preferred to be low, because the rate of theaccidental background is positively correlated with it. So, a direct current (DC) muon
beam is preferable to a pulsed beam.
MEG is conducted at the 590 MeV proton ring cyclotron facility of PSI in Switzerland,
which provides the worlds most intense DC muon beam.

Section 2.2.

Beam

15

2.2.1 Proton ring cyclotron at PSI
The core of the PSI beam facility is 590 MeV proton ring cyclotron (Figure 2.2). The 870
keV proton beam from Cockcroft-Walton Pre-Injector (Figure 2.3(a)) is accelerated to 72
MeV by PSI Injector 2 cyclotron(Figure 2.3(b)) to feed into this ring cyclotron.
The accelerator delivers 2.0 or 2.2 mA protons, sometimes 1.8 mA, and it is planned
to reach 2.6 mA in a few years, and 3.0 mA some years thereafter with some resonators'
upgrade for the Injector 2 and cyclotron [23]. Characteristics of the 590 MeV proton ring
cyclotron is summarized in Table 2.1.

Table 2.1: Characteristics of 590 MeV Proton Ring Cyclotron [24]Characteristics
Value
Injection Energy
70-72 MeV
Extraction Energy
590 MeV
Extraction Momentum
1.2 GeV/c
Energy spread(FWHM)
ca. 0.2%
Beam Emittanceca. 2 mm  mrad
Beam Current
2.2 mA DC
Accelerator Frequency
50.63 MHzTime Between Pulses
19.75 ns
Bunch Width
ca. 0.3 ns
Extraction Losses
ca. 0.03 %Mass of Sektormagnet
8  250.000 kg
Magnetic eld (Sti ness T  m, middle) 0.9 T (4.0, 0.6 T)
Radius at injection
2100 mm
Radius at extraction
4460 mm
Mass of Resonator
4  25.000 kg

Figure 2.2: 590 MeV proton ring cyclotron at PSI

16

Chapter 2.

Experimental installation(a) 870keV Cockcroft-Walton PreInjector(b) 72 MeV Injector 2 cyclotron

Figure 2.3: Injection acceralators

2.2.2 E5 beamline and surface muon beam

E-target

We use one of the secondary beamlines called E5 (Figure 2.4) which provides low-energy(10 { 120 MeV/c) pions and muons as daughter particles of the pions at an angle of 175with respect to the primary proton beam.
The production target (Target-E, Figure 2.5) is made of polycrystalline graphite. Its
length along the proton beam direction is 40 mm, and it rotates to avoid overheat and to
make the duration of replacement longer. The target cone is subdivided into 12 segmentswith gaps of 1 mm at an angle of 45 to the beam direction. This allows unconstrained
dimensional changes of the irradiated part of the graphite. At the normal operating
temperature, the gaps in the beam direction narrow down to about 0.5 mm.

p-beamπE5-2 Experimental Area
(U-branch)

πE5-1 Experimental Area
(Z-branch)

To MEG Detector
Beam Transport System
First degrader

Figure 2.4: E5 beamline

Figure 2.5: Target E

Section 2.2.

Beam

17

Charged pions produced inside the graphite target decays,  !   , with the
lifetime about 26 ns, emitting polarized muons and neutrinos. This generates a quasicontinuous muon beam, by smearing the 19.75 ns cycle of the initial proton pulses. The
momentum of muons from pion decay at rest is 29.8 MeV/c. Therefore, the muons fromthe pions stopped near the surface of the production target have a regulated momentum
of approximately 29.8 MeV/c. This is called as surface muon [25]. Muon from a pionying outside the target has higher momentum, and it is called as cloud muon. Figure 2.6
shows the pion and muon beam ux available at E5 Beam line. Pion beam is used forcalibration run. The intense surface muons are used for the + ! e+ search and also
for calibration of detectors.
10 11
10 10

-1 -1

N (mA s )

10 9
10 8
π+
πmeasured pointsµ+µmeasured points

10 7
10 6
10 5
10 4
0

20

40

60

80

100

120

140

160

P (MeV/c)

Figure 2.6: Pion and muon beam intensity at E5 beamline

2.2.3 Beam transport system
The muon beam from the E5 beam channel is transported to the stopping target througha beam transport system which is shown in Figure 2.7 schematically. It is composed of aquadrupole triplet (Triplet I), an electrostatic separator (Wien lter), a second quadrupole
triplet (Triplet II), and a beam transport solenoid (BTS) with superconducting magnet.
In the original beam from the beam channel, the quantity of the positron contamination is eight times larger than that of positive muons. The Wien lter separates positroncontamination spacially by 7.5  with its horizontal magnetic eld of 133 Gauss and a
vertical electric eld of 195 kV. Triplet I, II refocus the beam after a bending magnet
and the Wien lter. The BTS is used as a coupling element to the high magnetic eld of
the COBRA. A momentum degrader made of Mylar with a thickness of 200 or 300 m
is placed at the center of the BTS to increase stopping eciency on the stopping target
with less backgrounds. The beam spot size at the center of the target is x = 9.5 mm
and y = 10.2 mm and the typical stopping rate was 3  107 + s 1 .
Note that we set the beam rate lower than the maximum capability of the channel( 1:5  108 ) by the limitation from the detector performance. From the beam point ofview, there is a room for improvement.

18

Chapter 2.

Experimental installation

MEG Beam Transport System

Wien Filter
Triplet I

Collimator
System +steering
magnetSteering
Magnets

COBRA
Insertion
SystemDegraderSystem inbeam vacuum

Triplet II

BTS

Muon beam
Scale ~ 1m

TC

DC

TC

Target

LXe CalorimeterTo
CockcroftWalton
accelerator

Figure 2.7: Schematic view of MEG beam transport system

2.2.4 Muon stopping target
The picture of the muon stopping target is shown in Figure 2.8. It is made of a sheet ofpolyethylene/polyester with a thickness of 205 m (18 mg/cm2 ). It has an ellipse shapewith the length of 79.8 mm along the vertical axis and 200.5 mm for the major axis.
The target should be thick along the beam direction to increase the stopping eciency
and thin along the direction of the signal positron from the muon decay to minimize thescatter and the annihilation in ight (AIF) of positron. Slant angel is optimized to 20.5
relative to the beam axis. Stopping eciency is estimated to be 82 % using MC simulation.
The target has six holes of 10 mm diameter, which is used to align the target and to
estimate the resolution of the vertex position reconstruction. The support frame of thetarget is made of Rohacell whose density is 0.895 g/cm3 . It is lled with a mixture ofhelium gas and a few percent of air around the target to minimize scattering of positrons.
The target can be removed from the center position to do the background study without
target or the calibration runs using the di erent targets.

(a) Stopping target and hole position in cm(b) Installed position viewed from downstream. 16 drift chamber modules are seen
below the target.

Figure 2.8: Muon stopping target

Section 2.3.

2.3

Positron spectrometer

19

Positron spectrometer

Positron spectrometer for the MEG experiment is designed to satisfy following requirements.

 Good momentum, direction and timing resolutions for the positrons with the energy
around 50 MeV.

 Good performance under very high rate environment.
 Low material to suppress multiple scattering of positron and -ray background forthe photon detector.

It is composed of a solenoidal magnet with graded magnetic eld, 16 segmented drift
chambers to track the positron trajectory to measure momentum, direction and time ofight of positron, and timing counter made of scintillation bars to measure the timing of
positron hit.

2.3.1 COBRA magnet
We developed a thin-wall superconducting magnet with a gradient magnetic eld for the
positron spectrometer in the MEG experiment [26].

Central coil
Gradient coil

φ70
φ81

End coil

φ92Compensation coil
GM Refrigerator

1m(a) Sectional drawings of the COBRA
magnet(b) Picture of the COBRA magnet

Figure 2.9: COBRA magnet
The main coil consists of ve coils with three di erent radii as shown in the Figure 2.9(a). The gradient magnetic eld produced by this step structure have two features.
The rst is much quicker sweep of positrons than in the conventional uniform solenoidal
eld as described schematically in the Figure 2.10(a, c), which allows a stable operationof the spectrometer in a high rate muon beam. The second is COnstant Bending RAdius(The name COBRA is named after this). As described in the Figure 2.10(b, d) tracks ofpositrons with the same momentum have the same radius and are independent of emission

20

Chapter 2.

Experimental installation

angles. Because of this feature, we do not loss eciencies of the + ! e+ positron by
not covering the small-radius region with the drift chambers. The pro le of the magnetic
eld is shown in the Figure 2.11. In a normal operation at 360 A current, the central eld
is 1.27 T at z = 0, and 0.49 T at the edge.

Bz (T)

Figure 2.10: Positron trajectory in a uniform and the COBRA magnetic eld

1.2
1.1
1
0.9
0.8
0.7
0.6
0.5
0

0.2

0.4

0.6

0.8
1
1.2
Distance along axis (m)Figure 2.11: Pro le of the magnetic eld along the axis of the magnet
Gamma-ray from the muon decay passes through this magnet before entering the
gamma-ray detector, so the magnet is desired to be thin. A high-strength conductor wasdeveloped so as to minimize the thickness of the coil between the target and photon detector. The superconducting cable is made from NbTi multi lament embedded in copper
matrix with a 0.59 mm diameter and covered with high-strength aluminum stabilizer with
a 0.8  1.1 mm2 dimension, which is insulated with a Kapton plyimide [27]. Nickel of5000 ppm is added into the aluminum stabilizer to reinforce it mechanically. The totalSection 2.3.

Positron spectrometer21

thickness of the magnet including its cryostat is 0.197 X0 and the transmission eciencyof gamma rays with the energy of 52.8 MeV is 85 %.
A pair of normal conducting compensation coils is implemented to cancel stray eld
around the photon detector which is placed close to the magnet. The Contour plot of thefringe eld is shown in the Figure 2.12. The stray eld is decreased with this compensationcoil to be less than 50 Gauss , so that the PMT performance of the gamma-ray detector
will not be worsened.

Compensation coil

[Tesla]Center of magnet

End coil
Gradient coil
Central coil

Liquid xenon

Relative output [%]Figure 2.12: Contour map of fringe eld around the gamma-ray detector

140

x-axisYZy-axis120

z-axis

X

100

80

60

40

20

0
-300

-200

-100

0

100
200
300
Magnetic flux density [ Gauss]

Figure 2.13: Responce of PMT used in the gamma-ray detector in magnetic eld

22

Chapter 2.

Experimental installation

2.3.2 Drift chamber
To suppress multiple scattering and annihilation in ight of positrons, we developed avery thin drift chamber system with approximately 2  10 3 X0 in total along a positron
trajectory.
Helical trajectories of positrons are measured with drift chambers, and the momentum,
direction and time of ight of positron are reconstructed. It consists of 16 modules radiallyaligned with 10.5 intervals in ' direction. The radius from the beam axis which it covers
is from 19.3 to 27.9 cm, and it measures only positrons with momentum larger thanapproximately 40 MeV. A picture of installed modules is shown in Figure 2.8(b).
Each module is composed of two layers, and each layer has nine drift cells; nine sense
wires and ten potential wires (Figure 2.14(c)). The con guration of two types of wires is
set inversely on each layer to resolve ambiguity along a radial direction. The two layers
are separated by two inner cathode foils and enclosed by outer cathode foil. 3 mm gap
between inner cathode foils is for cross talk suppression. They are supported by a carbon
ber frame with an open frame structure as illustrated in Figure 2.14(a) to decreasematerials along positron path.

(a) Anode wire and Frame (unit: mm)(b) A completed module
Radial direction

Drift Cell
Outer cathode foil
7.0mm
Inner cathode foil

3.5mm
Support frame

4.5mm

3.0mm
7.0mm

Charged particle

Sense wire
Potential wire(c) Sectional drawing of drift chamber module

Figure 2.14: Schematics of a drift chamber module
The potential wires and cathode foils are grounded, and positive high voltage (1850 V)
is applied to the sense wires. The sense wire and the potential wire are made of 25 mdiameter Ni/Cr (80:20) wire and 50 m Be/Cu (2:98) wire respectively. Resistance ofSection 2.3.

Positron spectrometer23

the sense wire is 2200 /m. Cathode pads are made of thin 12.5 m-thickness polyimide
sheet with aluminum deposition. Because of the frame shape, drift chamber has only
wires alined along z-axis and no crossing wires. To measure precise z position, cathodepads have 5 cm period zig-zag shape strip as shown in Figure 2.14(b). This is calledvernier-pattern structure. A rough position is determined by signals at the both end of asense wire, and a precise position by 2  2 cathode pad signals. A detailed explanationof vernier pad method is done in Section 3.5.1.
The active gas is He:C2 H6 = 50:50. Outside of the module is ushed with a mixtureof helium gas and a few percent of air. Pressure of the gas should be controlled better
than 1 Pa to keep the shape of the chamber, and it is controlled within 0.005 Pa stability.
Detailed description about the design, construction, and performance in 2007 engineering
run are found in Ref. [28].

2.3.3 Timing counter
Timing counters (TIC) are installed at the both upstream and downstream side of thedrift chamber system (Figure 2.1). TIC consists of two layers of plastic scintillators. The
rst layer is along z direction and detect hit time, rough z position and position in '(TICP). The second layer is on the TICP along ' direction and detect z position (TICZ).
They are inside a plastic bag ushed with nitrogen gas to protect PMTs of TICP fromhelium gas.
Figure 2.15 shows a picture and a design of TICP. It is made of 15 plastic scintillator
bars (4  4  80 cm3 , Bicron BC-404 [29]) , each with 10.5 intervals in ' direction ata radius of 32 cm, and covers -150 < ' < 10 in total. Only positrons with highmomentum hit the bars. The scintillation bars are mounted with a slant angle at 20
to make the path lengths of positrons inside the bar uniform. Hexagonal shape of thebar is to avoid positron passing edge of these bars. 2-inch ne-mesh PMTs (R5294 by
Hamamatsu Photonics [30]) are attached at the both sides of the bar with a slant angle
at 10 with respect to the z-axis and  30 with respect to the magnetic eld to recover
their operation in a magnetic eld.

(a)

(b)

Figure 2.15: Picture (a) and Design (b) of Timing '-counter.

24

Chapter 2.

Experimental installation

TICZ is mounted on the TICP as shown in Figure 2.16. It is made of bending 128
scintillating bers (6  6mm2 Saint-Goban BCF-20). Each ber is separated optically at
the center and read out independently at the both ends by a 5  5 mm2 silicon avalanche
photo-diode (APD) (Hamamatsu S8664-55). The z-counters are mounted on the -countersat a radius of 29 cm. The ber is optically separated at a center. In the 2009, 2010 run
TICZ was not used, because of some troubles with APDs. So, TICZ is not used in theanalysis of this thesis.
Details of the design, construction, and performance in beam tests are described inRef. [31, 32].

Figure 2.16: Exposed timing z counter mounted on timing ' bars.This picture is before
light shielding.

2.4

Liquid xenon gamma-ray detector

For the + ! e+ search, gamma-ray detector is very important. We developed a novel
detector using liquid Xenon (LXe) as a scintillator.

2.4.1 Property of liquid xenon
Property of LXe is summarized in Table 2.2. Liquid xenon has good property as scintillator as follows: Large light yield (80 % of NaI(Tl)), High density (2.95 g/cm2), short radiation length X0 = 2.77 cm,
 Fast decay time of scintillation light(45 ns for gamma-ray interaction), No self absorption of scintillation light,
 Uniform because it's liquid, Incident particle identi cation by decay time of scintillation light.

Section 2.4.

Liquid xenon gamma-ray detector

25

Large radiation length helps to detect gamma-ray eciently. Large light yield (80 % of
NaI(Tl)) and no self-absorption produce good energy resolution. Because it's liquid andhas no self-absorption, we can construct a big and uniform detector whose response havesmall dependence to incident position. We can do puri cation of xenon to recover good
response when it's needed. Fast decay time of scintillation light is helpful in high rateenvironment to minimize pile up events. It is also free from aging or damage by radiation.

Table 2.2: Properties of Liquid Xenon
Material Properties
Value & Unit
Atomic Number
54
Atomic Weight131.293 [33]Density at 161.4 K
2.978 g/cm3 [34]Boiling point
165.1 K [33]Melting point
161.4 K [33]Triple point161.3 K 0.805 atm [35]Radiation length
2.77 cm [33]Critical Energy
14.5 MeV [36]Mollier radius
4.2 cm [36]Scinti. wavelength (peak  FWHM)(178  14) nm [37]Refractive index at 175 nm
1.57 to 1.72 [38, 39, 40]
Wph for electron
21.6 eV [41]Wph forparticle17.9 eV [41]Decay time (recombination)
45 ns [42]Decay time (fast component)
4.2 ns [42]Decay time (slow component)
22 ns [42]Absorption length> 100 cm
Scattering length
29 cm to 50 cm [40, 43, 44]
Because of its good property, there are many projects to utilize LXe, such as a dark
matter search, a neutrinoless double beta decay search, a gamma ray astronomy, medical
applications such as positron emission tomography (PET) and so on. However, there arediculties as follows: Expensive, Stabilization of the temperature around 165 K (Phase diagram is shown in Figure 2.18),

 Decontamination of particles which absorb or decrease scintillation light (Section 2.4.4),
 Photon detector development which is sensitive to vacuum ultraviolet (VUV) scintillation light (Section 2.4.2).

Many studies were done with prototype detectors [45, 46], and we succeeded to constructand operate the MEG LXe detector [47].

26

Chapter 2.

Experimental installation

Scintillation process [48, 49]
When a charged particle passes in LXe, it produces excited atoms (Xe ) or ions (Xe+ ).
In case of the excited atom, following scintillation process is known.
Xe + Xe ! Xe2
Xe2 ! 2Xe + hExcited atoms instantly form excimers and emit photons. The excimer has mainly two
kinds of excited state; 1 +u (decay time: 4.2 ns) and 3 +u (decay time: 22 ns); and theintensity ratio of 1 +u and 3 +u depends on deposited energy density.
In case of the ions, scintillation process is as follows.
Xe+ + Xe ! Xe+2
Xe+2 + e ! Xe + Xe
Xe ! Xe + heatXe + Xe + Xe ! Xe2 + Xe
Xe2 ! 2Xe + hAttenuation Coefficients [cm / g]This process is slower because of the additional recombination process, and the decay
time depends on the incident particles. The decay time of recombination process is 45 ns
for electron. As shown in Figure 2.17, gamma-ray with energy > 10 MeV interact with
LXe via electron pair production, so the time structure of scintillation light is the sameas electron. When the incident particle is or ssion fragments, decay time is faster thanthe case of electron because of lager deposited energy density. This di erence of the time
structure of scintillation light is useful for particle identi cation.
In both of two processes, scintillation photon is emitted by a excimer Xe2 , not bya excited atoms Xe , thus there is no absorption by itself. This feature is very helpful
to have good energy resolution and small dependence between reconstructed energy andincident position.
2

Total Attenuation

Photoelectric Absorption

Scattering

Pair
Production

Pressure [atm. absolute]

2

10

solid

Figure 2.17: Photon interaction in LXe [50]

gas

1

10

−1

120

Photon Energy [MeV]

liquid

10

140

160

180

200

220

240

260

Temperature [K]Figure 2.18: Xe phase diagramLiquid xenon gamma-ray detector

Section 2.4.

27

2.4.2 Photomultiplier tube
Photomultiplier tubes (PMTs) of the MEG gamma-ray detector is used in LXe, so it isoperated at low temperature and should sensitive to VUV. We developed a new model of
PMT (R9869) with Hamamatsu Photonics.
A photo of the PMT is shown in Figure 2.19. The window of the PMT is made ofsynthetic quartz glass which is 80 % transparent to the scintillation light of liquid xenon.
The photo-cathode material is bi-alkali (K-Cs-Sb). Aluminum strips are attached on thephoto-cathode, because resistance of bi-alkali increase a lot at low temperature. This
strip pattern covers 4 % of e ective aria and supplies photo-cathode with electrons forthe photoelectric e ect. Quantum eciency (Q.E.) is estimated to be approximately 15 %at 165 K. Metal channel dynode is adopted to make the PMT low material and tolerant
to 50 Gauss stray eld of the COBRA magnet. Figure 2.20 shows the voltage divider
circuit of the PMT. To keep Xenon to be liquid stably, high resistance resistors are used
to minimize heat generation. This unfortunately causes gain instability under high rateenvironment because the ampli ed electrons ying between dynodes make the ratio ofthe voltage division di erent. So zener diodes are inserted in parallel with the last two
dynodes to make the voltage stable. Low noise zener diode RD-S series of NEC Co. is
adopted. Selection is done taking the decrease of zener voltage due to low temperature
into account. A resistor inserted in series with each zener diode makes low pass lter toprevent noise from the zener diode from having an e ect on signal output.

Figure 2.19: Photo of R9869
K

DY1

DY2

DY3

DY4

DY5

DY6

DY7

DY8 DY9 DY10 DY11

R14
R1

R2

R3

R4

R5

R6

R7

R8

R9

R10

R11

R15
R12
R20

C1

P

DY12

C2

R16

C4

R17

R19

R13
R21
C3

C5
R18

R1,R12,R13 : 2MΩ(±1%,1/8 W)
R2-R11 : 1MΩ(±1%, 1/8 W)
R14-R16 : 51Ω(±1%,1/8 W)
R17 : 10kΩ(±1%,1/8 W)
R18 : 10kΩ(±1%,1/4 W)
R19-R21 : 100kΩ(±1%,1/8 W)

C1-C3 : 0.022 µF (1kV)
C4,C5 : 0.01 µF (2kV)
Z1 : R068S
Z2 : R082S+HV(RG-188A/U)

Figure 2.20: Voltage divider circuit of R9869

signaloutput(RG-194A/U)

28

Chapter 2.

Experimental installation

2.4.3 Design of the MEG liquid xenon gamma-ray detector
Design of MEG LXe detector is shown schematically in Figure 2.21, 2.22. De nition ofeach face and local coordinate system(see Section 2.1.1) are also shown. Liquid Xenon
is used as scintillator. The active volume is approximately 800 liter and 900 liter liquid
Xenon is used. The scintillation light is collected by 846 PMTs surrounding the active
volume. The detector is C-shaped and covers the region approximately 30 <  < 120 ,120 < ' < 240 and in total 11 % of the solid angle from the center of the stopping target.
Outside the active volume, aluminum spacers are installed to save expensive xenon. The
depth of the active volume is 38.5cm and it corresponds to approximately 14 X0 .
Gamma-ray from the target passes through a entrance window and inner face PMT.
The entrance window for the gamma-ray should be thin and mechanically strong. The
window is made of 0.7 mm thickness stainless steel plate reinforced with aluminum honeycomb covered with carbon ber plates. The window corresponds to 0.075 X0 in total.
The cryostat is made of non-magnetic materials. It has two layers of vacuum-tightvessels to apply vacuum thermal insulation. Xenon is cooled by A 200 W pulse-tube refrigerator, which is specially developed for this liquid xenon calorimeter [51]. Temperatureof xenon is controled using this refrigerator with help of heater. Cooling pipes of liquid
nitrogen are also available when a high cooling power is needed. A capacity level meter,
several pressure sensors and Pt-100 temperature sensors are installed for monitoring thecondition of xenon. We have two storages for xenon, 1000 liter LXe dewar [52] and highpressure gas tanks.

Liquid xenon
Top face
Level meter

Upstream face

PMTγ

Stopping target

Outer face

67.85cm
125.5 deg.
Inner faceγ

Stopping target

1m

Outer face
1m

Inner face

Bottom face

Downstream(a) side view(b) top view

Figure 2.21: Sectional drawings of the MEG LXe detector. Blue circle shows a PMT

Section 2.4.

Liquid xenon gamma-ray detector

top

100

29

outer

downstream

upstream

80
60
40
20

v-axis148.6cm0

w-axis
inner

.5

38

58cm

cm

z

u-axisbottom96cm

Figure 2.22: Development view of the MEG LXe detector

Figure 2.23: Picture of the LXe detector before closing outer and inner vessel covers.

30

Experimental installation

Chapter 2.

2.4.4 Puri cation system
Scintillation light from LXe is vacuum ultra violet, which is easily absorbed and does not
penetrate air as the name indicates. Fig. 2.24 shows absorption of the scintillation lightby water vapor and oxygen. Water absorbs VUV light by the photo-dissociation process.
H2 O + h ! H2 + O
(2.5)
ARTICLEPRESS
Air inside the detector is pumped
out by aINturbo-molecularpump before letting xenon
in. Because some of the components inside the detector cannot be heated, we cannot
perform baking procedure. Especially a small amount of water remains at the surface ofthe components inside and it causes scintillation light absorption.
OxygenAbsorption Coefficient [m-1]�

Xe Scintillation Spectrum���
Water Vapor

����
���

���

���

���

���

���

(a)
Absorption in H2O-doped Xe������Wave length [ n m ]Absorption in O2-doped Xe�������

���������
������������
�����I / I0I / I0���������� �������

��� �

�����
�����
������

��� �
�

(b)

��

��

��

��

Distance [cm]

��

��� �
�

��

(c)

��

��

��

��

��

Distance [cm]Figure 2.24: (a) Absorption coecients for 1ppm water vapor and 1ppm oxygen. Xenon
scintillation spectra is superimposed [53]. (b)(c) Scintillation light intensity and distancefrom a light source for di erent concentrations of water vapor and oxygen [46].
In addition to the absorption problem, there might exist contaminants which disturb
scintillation process. For the case of liquid Argon, Nitrogen is considered to quench liquidargon by a following kinetic collision [54].
Ar2 + N2 ! 2Ar + N2
(2.6)

Calibration and monitoring

Section 2.5.

31This can change time structure of scintillation light, because excimer with longer life timeis thought to be a ected more. It is reported that suppression of slow component of theliquid argon scintillation light was observed when concentration of nitrogen increased [54].
This kind of quenching process is not well studied for LXe, but similar process can happen
also in LXe.
To draw out LXe's high performance, several test was done using a prototype detector,
and we developed two types of puri cation system [55, 56]. One is a gas-phase puri cation.
Gas xenon is send to heated metal getter by a diaphragm pump. The speed of puri cation
corresponds to be less than 0.1 liter/hour in liquid xenon. The puri er removes H2 O, O2 ,CO, CO2 , H2 , N2 and hydro carbon molecules from gas xenon down to 1.0 ppb level.
The other is a liquid-phase puri cation. Molecular sieves removes water contaminantand copper beads, which was developed for LAr TPC at CERN, removes oxygen byoxidization process. The speed of puri cation is 180 liter/hour.
Getter1000 litter
LXe storage tank

Liquid phase purifier /Liquid circulation pumpGas circulation pump

LXe detector

250 litter × 8 gas xenon
storage tanks

Figure 2.25: Schematics of puri cation line. Blue line shows pipe line for liquid xenon.

2.5

Calibration and monitoring

2.5.1 LED
PMT gain was measured by using LEDs installed in the LXe detector. The stability ofgain was monitored daily by the calibration with LEDs. We applied attenuation of lightto get stable light intensity. Principle of it is schematically shown schematically in Figure
2.27. Attenuated LED needs higher voltage to obtain the same amount of light. Whenthe uctuation of voltage is about the same, uctuation of output light is smaller in caseof the attenuated LED.
LED is covered with aluminum foil with small pinhole to attenuate its emission of light(Figure 2.26(a)). Te on sheet is attached as a di user (Figure 2.26(b)). LEDs with three
di erent attenuations are prepared. Picture of the installed LEDs are shown in Figure
2.28.

32

Chapter 2.

Experimental installation

Nph

Naked LED
Attenuation

(a)

ΔNph

(b)

Figure 2.26: LED covered with aluminum foil with pinhole (2.26(a)),
te on sheet is attached for di usionof light (2.26(b)). They are xed byheat shrinkable tube

Attenuated LED

ΔV

ΔV

VLED

Figure 2.27: Schematics of how the attenuation of light works to make the uctuationof the output light small. Curved line shows
LED light intensity versus applied voltage, orange for naked and blue for attenuated LED.

Figure 2.28: Alpha wires (blue arrow) and three LEDs with di erent attenuation (orange
circle) installed between and on the lateral upstream and downstream face of the detector

2.5.2

241 Amalpha source

We install 241 Am alpha source inside the LXe detector. It emits alpha-ray at 5.485 MeV(84.5%) and 5.443 MeV (13.0%), and its life time is 432 years. Since the rage of thealpha-ray is as short as 40 m, it can be used as a point-like light source placed at aknown position. We developed a thin tungsten wire of 100 m diameter on which vealpha sources are deposited with interval of 12.4 cm. The source is protected by a thingold layer ( 1:5m) (Figure 2.29). Five wires are installed in the detector; a lattice of 25

Section 2.5.

Calibration and monitoring

33

alpha-source spots is formed in LXe detector. Figure 2.28 shows a photograph of alphawires and LEDs installed in the detector. The activity of each source is about 200 Bq.
Daily calibration with alpha source was used to measure and monitor Q.E. of PMTs.

Figure 2.29: Microscope photograph of the 241 Am source on a wire. Diameter is 100
m and longitudinal dimension is about 2 mm.

2.5.3 17.6 MeV gamma-line from 73Li(p; )84Be reaction
A 17.6 MeV gamma-line is used to monitor and calibrate the LXe gamma-ray detector
light yield. It is produced by a nuclear reaction; 73 Li(p; )84 Be. The reaction is resonant at
Tp = 440keV with resonance width R ' 15keV and cross section R ' 5mb.
To produce proton-beam required to excite the reaction, we installed a CockcroftWalton (CW) proton accelerator at the downstream side of the experimental area (Figure2.30(a), 2.30(b)). The properties of MEG CW accelerator is shown in Table 2.3. A part ofthe proton beamline is made of metallic bellows and the beam target can be moved at thecenter of the COBRA magnet. As the proton beamline does not interfere with the muon
beamline and moving the muon stopping target and the CW beam target takes less thanhalf an hour, taking data with CW proton beam can be performed frequently. The target
is made of a thick lithium tetraborate (Li2 B4 O7 ) crystal disk. We can select the reaction
12of 73 Li(p; )84 Be or 11
5 B(p; )6 C with the same target by changing the proton kinematicenergy. The latter reaction gives coincident 11.7 MeV and 4.44 MeV gamma-rays, which
can be used to calibrate timing between the gamma-ray detector and the timing counters.
Energy spectrum of 17.6 MeV gamma-line seen by the LXe detector is shown in Figure
2.31. Also visible is the broad 14.3 + Tp MeV gamma-line, corresponding to the 8 Be
transition to the rst excited state of 8 Be( 1).

Table 2.3: Properties of MEG CW accelerator
Nominal Measured at PSI
Terminal energy range (keV)
300 { 900
200 { 1100
< 500
< 500
Energy ripple (RMS eV)
Angular divergence (mrad  mrad)
55
44Spot size at 3 m (cm  cm)<33<1
Energy setting reproducibility (%)
0.1
OKEnergy stability (FWHM %)0.1
OK
Range of current (%)
1 { 100
0.1 { 135
Current stability (%)
3
OK
Current reproducibility (%)
10
OK
Duty cycle (%)
100
OKStart-up time (min)
< 20
< 15

34

Chapter 2.

Experimental installation

Number of events

Figure 2.30: CW accelerator and its beam line at the downstream side of the MEG.

450
400
350
300
250
200
150
100
50
0
5

10

15

20

25
Eγ [MeV]Figure 2.31: Energy spectrum of CW run

2.5.4 55 MeV gamma-ray from  Charge exchange reaction
 beam and hydrogen target
We perform dedicated calibration run of the LXe detector for a certain period once or twice
per year. During this period, E5 beamline is tuned to provide  beam to the centerof the COBRA magnet, where we place liquid hydrogen as the target. The momentumof the pion beam is set to 70 MeV/c, which is optimal in our set up to remove electrons
and muons. Expected pion rate at the center of COBRA magnet is 1.6MHz at 1.8mAprimary proton current. Measured pion pro les in vertical and horizontal direction was
8mm in . Liquid hydrogen target is a cylindrical cell of 50mm diameter, 75 mm length,closed on the entrance side by a thin 135 m mylar window. Hydrogen is liqui ed andmaintained in a stable state with a liquid helium.
When a negative pion collide with hydrogen, following two kinds of process can occur. One is radiative capture reaction ( p ! n), which gives a gamma-ray of energy
129.4MeV. Anther is a charge exchange (CEX) reaction ( p ! 0 n), which gives twoSection 2.5.

Calibration and monitoring

35

gamma-rays by the decay of neutral pion. The ratio of the two channels is known as
Panofsky ratio [57, 58],
( p ! 0 n)= 1:5:(2.7)
P=( p ! n)
The neutral pion produced by CEX has momentum of 28 MeV/c in laboratory frame,
and 98.8% of that decays into two gamma-rays (0 ! ) immediately with life time
8:4  10 17 . Because it's two body decay, both gamma-rays have half the 0 mass (=67:49MeV) in the rest frame of 0 , and because of the e ect of Lorentz boost, the energyof a gamma-ray distribute at between 54.9 MeV and 82.9 MeV in the laboratory frame.
Relation between energy of a gamma-ray and opening angle between two gamma-raysin laboratory frame is shown in Figure 2.32. This plot shows that we can obtain quasimonochromatic gamma-ray with energy 54.9 or 82.9 MeV when we select gamma-rays
with opening angle near 180 degree.

Figure 2.32: Energy and opening angle ofgamma-ray from CEX 0 decay.

Figure 2.33: NaI mover andhousing box for the NaI.

NaI detector
By selecting events in which a gamma-ray with energy of 82.9 MeV is emitted at the
opposite of the LXe detector, we can obtain quasi-monochromatic 54.9 MeV gamma-ray
events with the LXe detector. At the opposite side of the LXe detector, NaI gamma-ray
tagging detector is placed.
NaI detector is composed of 3  3 crystals of NaI (62:5  62:5  300:5mm3 ) viewed by
Avalanche Photo Diode (1cm  1cm, S8664-1010 made by Hamamatsu) readout. When
we perform timing calibration run, a lead converter (50  50  5mm3 ) and two plastic
scintillators (60  60  7mm3 ) viewed by 2  2 ne-mesh PMTs (Hamamatsu H6152-70)
are attached in front of the NaI detector.
NaI tagging detector is mounted on a mover (Figure 2.33) to cover the whole acceptance of the LXe detector.

36

Chapter 2.

2.6

Electronics and data acquisition

Experimental installation

2.6.1 Data acquisition
In the MEG experiment, waveforms of each detector are recorded. We have two di erent
waveform samplers. One is ash analog to digital converter (FADC) with 100 MHz
sampling and 10 bits resolution, which is used for trigger system. The other is Domino
Ring Sampler (DRS) [59] developed in PSI, which is a waveform digitizer with switchedcapacitor arrays (SCAs). DRS has 950 MHz bandwidth at a variable sampling rate up to
6 GHz with 1024 cells. The waveform stored in the sampling cells is read out by a shift
resistor at lower frequency (33 MHz) and digitized externally by a 12-bits commercial
FADC. We set the sampling frequency to 1.6 GHz for the outputs from the gamma-ray
detector and the TICP and 800 MHz for the outputs of the drift chambers.
The data ow from detectors to digitizers is shown in Figure 2.34.
Output of LXe PMT is put in active splitters. Input signal is received by a di erential
ampli er, then the output of an ampli er with 1.9 GHz bandwidth goes to DRS and theoutput of an ampli er with 320 MHz bandwidth or analog sum of four waveform goes totrigger.
TICP PMT output is divided by a passive splitter at the ratio of 8 : 1 : 1. The largest
signal is put into double-threshold discriminator (DTD), and NIM signal is obtained. The
lower threshold of DTD makes a good timing performance with a less e ect of a time walk,and the higher threshold ensures the signal to be a positron hit event, not a fake signal
due to noise or delta-ray hits. One of smaller outputs of the passive splitter and DTD
NIM output are put in the active splitter and goes to DRS and trigger. The other outputof the passive splitter goes to current monitor to check the PMT lifetime.
DCH outputs are rst ampli ed by a preampli er attached at the chamber frame
structure. Anode wire signal is then resistively divided at the ratio of 9 : 1. Larger
output of anode wire and cathode pad go to DRS. Sum of several smaller output of anodewires goes to the trigger.
Detector

LXe

Active splitter

Digitizer
Trigger

Inner PMT
(216)

Sum

Other PMT
(630)

DRS
Trigger
DRS

Double-thresholddiscriminator

TIC

8
1
1
Passive splitter
Current monitor

φ PMT
(60)

DCH
Anode wire
(576)
Cathode pad(1152)

Preamplifier

1

Sum

9

DRS
Trigger
DRS
TriggerDRS
DRS

Patch panel

Figure 2.34: Schematics of data ow and electronics.

Section 2.6.

Electronics and data acquisition37

2.6.2 Trigger system
In the trigger system, the output of FADC is processed by eld programmable gate arrays(FPGAs). Online reconstruction and trigger selection are programed on FPGA. Several
trigger settings can be used simultaneously. Trigger rate is controlled by pre-scale factor.
When pre-scale = 100, one per 100 triggered events is recorded. We count the number oftriggered events and record live and dead time for each trigger type. For + ! e+ search
trigger, DAQ live time is  84 % and the trigger rate is 5 Hz.
A example of trigger types and the selection criteria in the + ! e+ search run islisted in Table 2.4. + ! e+ ;  !
dedicated trigger is not prepared, and we use
the + ! e+ search data to search for + ! e+ ;  !
decay mode. Direction++
match is the tightest trigger condition for  ! e ;  !
event. It is based on acomparison of the emission direction estimators of the positron and the gamma. For the
+ ! e+ event, positron and gamma-ray are back to back and have monochromaticenergy, so the hit position in LXe and TICP are related. A look up table of the index
number of inner face PMT with the highest output and z position of the TICP bar that
positron hits rst is made using + ! e+ MC simulation.
Because the sum of the energies of gamma-rays of + ! e+ ;  ! is larger than
52.8 MeV, E threshold is justi ed, but if the mass of the  is large enough, the sum of
the energies of gamma-rays can become close to the cosmic veto threshold.
Detailed description about the trigger system is found in Ref. [60].

Table 2.4: Trigger setting for + ! e+ search run at one period of 2010. Pre-scale
factor can be changed according to request. E Threshold low  40 MeV, high  44 MeV,
CR veto  62 MeV(2009), 75 MeV (2010), Te narrow  20 ns, wide  40 ns
Id
Trigger typePre-scaleE THR
Te Direction match
0MEG
1high & CR veto narrow
narrow
1 MEG Low E
60
low & CR veto narrow
narrow
2 MEG Wide DM
550high & CR veto narrowwide
3 MEG Wide T
250high & CR veto wide
narrow
4 + ! e+ e  
1100
low & CR veto narrow
9
LXe alone
20000 high & CR veto
Id
Trigger typePre-scale
Selection criteria
12
22000
Pulse shape discrimination
14LEC
6
1 Hz pulse from LED driver module
718
DC alone
1:5  10
DC hit multiplicity
22
TIC alone1  107
TIC multiplicity
27
LXe Cosmic
2500
Threshold on E
31
Pedestal
20000
Random trigger

38

Chapter 2.

Experimental installation

Part III
Reconstruction, simulation and theperformance39Chapter 3
Analysis software and simulation

3.1

The MEG software

We developed three packages of softwares; MEGMC, MEGBartender and MEGAnalyzer.
Relation of each software is shown in Figure 3.1.
MEGMC is GEANT3.21 [61] based Monte Carlo simulation program, which simulates
kinematics of events, interaction of particles with materials of detectors, propagation of
scintillation photons in the LXe detector, number of photons entering TIC PMTs, anddrift of electrons and ions in the drift chambers. We change event types and the detector
settings modifying parameters in the con guration le for the simulation. All parts ofpositron spectrometer and LXe detector are represented with actual dimensions, materials,
and arrangement. Electrical eld of drift chamber is calculated with GARFIELD [62].
MEGBartender simulates electronics and waveform. It can also simulate pileup eventsby mixing MEGMC data sets.
MEGAnalyzer does waveform analysis and event reconstruction for both MC simulation data and experimental data. MEGAnalyzer can also process output of itself. In
the second process, we can skip time-consuming waveform analysis, or select events withrough reconstruction to perform precise reconstruction.
MEGAnalyzer and MEGBartender are are organized by the analysis framework toolkit,
ROME [63]; ROOT [64] based Object Oriented Midas Extension.
Experiment
MIDAS.mid file•Data acquisition•Raw data (MIDAS format)
MEGAnalyzer.root file

Simulation
MEGMC
.rz
file
.rz
.rzfilefile•Event generation•Detector simulation•ZEBRA format

MEGBartender.root file

•Event mixing•Electronics simulation•Trigger simulation•Digitization•ROOT format•Waveform analysis•Event reconstruction•Event selection•Event display•ROOT format

MEGAnalyzer.root file

•Second process•ROOT format

Figure 3.1: Structure of the MEG Software41

42

Chapter 3.

3.2

+

Analysis software and simulation! e+;  !

Monte Carlo event generation

In this section, event kinematics of + ! e+ ;  ! decay and its generation in Monte
Carlo (MC) simulation are discussed. Rn represents a random number from 0 to 1.
MC event is generated assuming + ! e+ ;  !
to be two sets of clear two
body decay and each particles are emitted isotropically in the center of mass system of
decaying particle. One e+ and two gamma-rays are generated in the program. Mass (M )and lifetime ( ) of  are set as input parameters by a con guration le.
Extracted e+ has a monochromatic momentum equal to that of ;qP = Pe+ = ((M2 + Me2 M2 )2 4M2 Me2 )=(2M ):(3.1)
e+ is generated on the muon stopping target taking the beam spot size into account, andthe direction is set isotropically within a region set by the con guration le. Then speedof  is calculated byqM2 + P2 ;
=
P
=


q
(3.2)
2
:
 = 1= 1

By relativistic e ect, e ective lifetime of  in the experimental system becomes   , sotime and position di erences between e+ and gamma-ray generation aret =position = ln (Rn); ct:

(3.3)
(3.4)

 

Gamma-rays are generated at opposite side of e+ direction with the distance position
apart from e+ generation point with a time di erence t later than e+ .
γ1

γ1
ϑeγ1
ϑrest

φ

φ
γ2
Experimental frame

Lorentz boost

γ2Rest frame of φ

Figure 3.2: Kinematics of two gamma-rays
In the rest frame of , energy of gamma-rays are both M =2, and the direction of
gamma-ray can be described as cos #rest =Rn when gamma-rays are generated isotropically. Then, energy of gamma-rays in the experimental frame is calculated as

E 1 =  M =2 +   cos #rest M =2
E 2 =  M =2   cos #rest M =2(3.5)

And angles between e+ and 1, 2 direction (#e 1 , #e 2 ) in the experimental frame havefollowing correlations from momentum conservation.
cos #e 1 = (E 22 E 21 Pe2+ )=(2E 1 Pe+ )(3.6)
cos #e 2 = (E 21 E 22 Pe2+ )=(2E 2 Pe+ )Section 3.2.

+ ! e+ ;  !

Monte Carlo event generation

43

Direction of each gamma-ray is determined by this relative angle, and is rotated isotropically around e+ direction. Then, these directions are checked whether within a region set
by the con guration le or not, and if they are, the event is generated.

Figure 3.3: An example of generated + ! e+ ;  !

MC event (M = 20 MeV).

44

Chapter 3.

3.3

Reconstruction sequence

Analysis software and simulation

Reconstruction sequence for + ! e+ ;  !
Timing φ counter
Waveform analysis

Sec. 3.4.1

Drift chamber
Waveform analysis

search is shown in Figure 3.4.
Gamma-ray detector

Sec. 3.4.2

Sec. 3.4.3
PMT calibration Sec. 3.6.1

Waveform analysis

PMT analysis
Matching
PMT calibration

Hit reconstruction

Sec. 3.5.3

Hit timez-position reconstruction

Clustering

Sec. 3.5.3

Apply gain, QE,
time offset

Sec. 3.5.1
z-position reconstruction

Hit reconstruction

Avalanche time

Position reconstruction

Sec. 3.5.1

Clustering

Track finding

Sec. 3.6.2

Reconstruct gammainteraction position

t0 information

Pileup searchSec. 3.5.1

r-position reconstruction
Track candidates

Track fitting

DCH-TIC interconnection
Matching between TIC hits and tracks
Refine TIC timing by combining several hits
Calculate muon decay time

Sec. 3.5.2 Time reconstruction

Reconstruct gamma
Reconstruct trajectoryinteraction time
Trace back to target
Energy reconstruction
Reconstruct positron on target(momentum, emission angle, vertex)
Reconstruct gamma
energySec.
Sec. 3.5.3
3.5.5

Sec. 5.1
MEG Preselection

MEG Preselected Data

Sec. 5.1µ→eφ,φ→γγ Preselection
Two gamma reconstruction
Combined reconstruction

Sec. 3.7

Sec.
3.6.3
Sec.
Sec. 3.6.4
3.6.5

Reconstruct interaction positions,times, energies of 2 gammas

Reconstruct vertex position of 2 gammas
Reconstruct timing at the target position

Figure 3.4: Reconstruction sequence and section number in which each item is described.
Just after the physics data is taken, the rst processing; waveform analysis (Section 3.4) and rough reconstructions; are done. Then preselection for + ! e+ search is
performed to reduce the data size. In this stage, the quality of calibration is not supposed
to be excellent, so the preselection is determined to be enough loose not to discard any
good events. After that, second processing is done taking all the calibrations into account.
We use this second-processed data for + ! e+ ;  ! search.
Because the data in this stage contains a lot of events not needed for + ! e+ ;  !
search, preselection for + ! e+ ;  !
is performed. The selection criteria is
described in Section 5.1. The selected events are then processed with third-process toreconstruct position, time and energy of each two gamma-rays (Section 3.6) and thevertex position of  decay point (Section 3.7). Reconstruction of positron track (Section
3.5) is already done, so the reconstruction is skipped and the values processed in thesecond-process is copied to be used in the combined reconstruction.

Section 3.4.

3.4

Waveform analysis

45

Waveform analysis

We record signals of the detectors in the format of waveform. Extraction of time andcharge is performed for each detector according to the characteristics and requirementsof the detector.

3.4.1 Waveform analysis of drift chamber
As mentioned in Section 2.3.2, we have 16 drift chamber modules (DCH), 18 wires for each
module, and 6 readout channels for each wire (2 from both ends of anode wire. 4 fromcorresponding cathode pads, that is inner pads and outer pads with two vernier-patternpads). All in all, we have 16 (modules)  18 (wires)  6 (channels) = 1728 readout
channels. In order to reduce the data size, we apply zero-suppression by discarding zerosignal waveform without recording at the online data taking stage. We can also reduce
data size of recorded waveform by re-binning the part of the waveform outside the region
around the signal peak.
Informations of hits on DCH are extracted from the recorded waveform of wires andcathode pads. A pulse identi cation is done by searching for the maximum peak bigger
than a certain threshold. The width of the pulse is extracted by pursuing the waveformfrom the peak in the both directions until it crosses the another threshold. Then, thispulse range is masked and the pulse search is repeated because multiple hits on the samechannel can happen.

Time extraction
Time of each pulse is determined by a single-threshold crossing time.
Charge extraction
Charge is extracted by integrating each pulse in a integration window. This window is determined by the anode wire waveform, and used also for the waveform ofcorresponding cathode pads. The window width is set to 50 ns, which was tuned to
optimize the signal-to-noise ratio.

3.4.2 Waveform analysis of timing counter
We record two types of waveforms for timing ' counter (TICP), raw PMT signal and
DTD-output NIM pulse, as described in Section 2.6.2.

Time extraction
Information of hit time is obtained by tting a NIM pulse with a template waveform,
which is prepared in advance for each channel by averaging many pulses.
Charge and amplitude extraction
From the raw PMT signal, we get an amplitude and a charge. The amplitude is
obtained by comparing the estimated baseline and the pulse peak voltage. Thisis used for time-walk correction of the NIM-pulse time. The charge is obtained byintegrating a pulse with 30 ns integration window. This is used to measure the gains
to equalize raw PMT waveforms.

46

Chapter 3.

Analysis software and simulation

3.4.3 Waveform analysis of gamma-ray detector

10

Amplitude (mV)

Amplitude (mV)

We record waveforms of the 846 PMT outputs of the LXe detector. To reduce the data
size, we perform re-binning outside the region of interest at the online data taking stage
by recording one point per eight sampling points with the average of them. Reduction is
not done for leading edge, peak, and the region just before the leading edge. The region
to be reduced can be changed by trigger types.
We observed noises originating from the data acquisition DRS chips. Template waveform is made for each channel and subtracted for the noise reduction.

50 ns

0
-10

0
-5
-10

30%

-15
-20
-25
-30

-20

-35
-30
Mov-Ave(high-pass) 89pnts

-600

-500

-400

-300

Time (nsec)(a) The digital-constant-fraction method

-40
-600

-500

-400

-300

Time (nsec)(b) High pass ltered waveform

Figure 3.5: LXe waveform
Time extraction
Digital-contant-fraction method is applied to extract time for each PMT. In thismethod, we can reduce the time-walk e ect. Time is determined by the point where
the leading edge crosses 30 % of the full pulse height (see Figure 3.5(a)). Here,
we do not use the actual pulse height. We measure the relation between the pulse
height and the charge in advance. Amplitude is calculated by the charge according
to this relation to reduce the e ect of noise and the statistical uctuation of thepulse shape. No ltering is performed not to distort the leading edge shape.
If two gamma-rays are coming close in time and position, time of an earlier gammaray or a gamma-ray with larger pulse height will be extracted. Time extraction
method dedicated to the pileup event is not prepared.
Charge extraction
High-pass ltered waveform is used for charge extraction of gamma-ray events.  1
MHz noise was observed on PMT waveform, and this noise component is eliminatedwith this ltering. As shown in Figure 3.5(b), the pulse shape becomes sharper andthe baseline becomes at at zero. Fluctuation of the baseline calculation disappears.
The window for the charge integration is determined by using summed waveform,
and is used for each PMT commonly. The width of window is set to 48 ns. The
narrower time window is e ective to reduce pileup gamma-ray coming with sometime di erence. When a gamma-ray interacts very near to a PMT, the output

Section 3.5.

Reconstruction of positron tracks

47

voltage exceeds a dynamic range of the electronics, and the recoded waveform issaturated. The charge of such PMTs are estimated by time-over-threshold (ToT)
method. The time width that a pulse exceeds a given threshold is measured andconverted to the charge by using an average pulse shape of gamma-ray interaction
events.

3.5

Reconstruction of positron tracks

Positron trajectory is reconstructed using drift chamber modules (DCH). Hit position
on a module is reconstructed using signals on anode wires and cathode pads. Then
Kalman lter track tting is performed to reconstruct the track. Muon decay vertex
position, positron emission direction, positron momentum and time of ight of positronare extracted from the tracking. Positron hit time is measured by timing ' counter , andtogether with the reconstructed time of ight, muon decay time is reconstructed.

3.5.1 Hit reconstruction and track nding

Figure 3.6: Schematic view of the vernier pad method
At rst, positron hit z position in a drift cell of a DCH is roughly reconstructed withan accuracy of 1 cm by the ratio of charges measured at both ends of the sense wire, thenis reconstructed more precisely using the vernier pad information. Vernier pad method isshown schematically in Figure 3.6. Phases of the Vernier pattern are shifted by 1/4 of aperiod between inner and outer pads. We measure charges of four vernier pads in a drift
cell; outer cathode readout at upstream/downstream(QOU ; QOD ), inner cathode readoutat upstream/downstream(QIU ; QID ). The normalized charge ratio for outer cathode pads
(1 ) and inner cathode pads (2 ) is written as follows.
Q
QID
Q
QOD
; 2 = OU(3.7)
1 = IUQIU + QIDQOU + QOD
Figure 3.7(a) shows a scatter plot of 1 versus 2 the phase of the vernier pattern; =arctan 2 =1 . Each line in Figure 3.7(b) indicates the n-th vernier periods on versus
charge division plane. z is reconstructed byl(3.8)
z =  + pad2where l is the pattern pitch (5 cm) and pad is a center position of the pad cycle where
the hit exist. The resolution of z is estimated approximately 700 m.

48

Chapter 3.

Analysis software and simulation(a) Vernier circle.

(b) Phase on vernier circle and anode charge division.

Figure 3.7: Muon stopping target
Because each DCH module is composed of two layers, one module has more than one
hit when a positron crosses the module. The clustering of hits in each module is done usingz and drift chamber hit time information. Then, we start to nd track. First, we searchfor clusters with the distance from the beam axis larger than 24 cm, because we want tond positron with high momentum eciently for the + ! e+ search. Then we perform
circle t with three clusters and search for the hit clusters for the same positron trackwith the smaller distance from the beam axis. Using relative position of hits, the angle
that the positron passes the DCH is estimated. This incident angle and an estimation ofdrift time are used for the reconstruction of the distance between the sense wire and thepositron track.

3.5.2 Tracking
Track tting is performed by means of the Kalman lter technique [65]. It is e ective
for tracks with small number of hits or noisy environment, thus suitable for the positron
tracking in MEG experiment. The features of the Kalman lter are as follows.

 E ects of multiple scattering, energy loss of positron and non-uniform magnetic eld
are handled correctly.

 Three-dimensional and complex trajectory can be reconstructed.
 Error propagation is taken into account.
#” , '#”The muon decay vertex ( #”x decay ), direction of positron emission (rec;dir
rec;dire+ ) ande+the momentum of the positron (Prec;e+ ) are tted by this track tting.

3.5.3 Positron time
Time walk of TICP NIM pulse is corrected using pulse height of the PMT waveform anda lower threshold in double-threshold discrimination. The hit position in z-coordinate
is reconstructed by the time di erence between the two PMTs at the both sides of theSection 3.5.

Reconstruction of positron tracks

49bar. Then, TICP hit time is reconstructed using the corrected NIM pulse time of the two
PMTs and the hit z position. Positron with high momentum often put hits on some ofbars. In this case, hits associated with a positron track are clustered by their time and z
hit position. Then the timing counter hit time (tT IC ) is given by the time of the rst bar
hit.
The time of ight (TOF) of positron is estimated from the length of the reconstructed
positron trajectory. Then the time of muon decay is estimated by subtracting TOF fromthe timing-counter hit time.
te+ = tT IC ttof;e+(3.9)

3.5.4 Positron correction
An error on energy reconstruction of positron corresponds to an error on trajectory diameter. So reconstruction of muon decay vertex position especially in y coordinate andpositron emission angle especially in ' coordinate are in uenced by an error on energy
reconstruction. Coecients of the correlation function between Pe+ and 'e+ or ydecay
are extracted using + ! e+ MC simulation data, and con rmed with + ! e+ e   datataken with the MEG detector and + ! e+ e   MC simulation data.
As the correction coecients are derived for the positron with energy equal to half
the muon mass, correction for + ! e+ ;  ! positron is done scaling the coecients
according to the expected positron energy. In the + ! e+ ;  !
search analysis,
positron energy is constant for a certain M (Equation 3.1). Correction is done each time
while scanning M in the analysis.

3.5.5 Positron selection
To ensure the quality of positron reconstruction, we set several cuts for the positron
selection. The positron selection criteria consist of basic track cuts, track tting quality
cuts, decay vertex cuts, DCH-TIC matching cuts, and ghost track cuts.

Basic track cuts
Basic track cuts examine the number of hits used for the Kalman lter tracking,which exclude abnormal tracks.
Track tting quality cuts
Tracks with large uncertainties in momentum and direction evaluated from the
Kalman lter are eliminatedDecay vertex cuts
Decay vertex cuts ensure the positron is from a muon which decays on the stopping
target. If a event is originated from a muon decaying in the helium atmosphere,
we can not identify the precise position of the decay vertex, which leads to large
uncertainty in decay time and emission direction reconstruction of both positronand gamma-ray.
DCH-TIC matching
In the DCH-TIC matching cuts, we compare the hit position on TICP bar that is
expected from Kalman lter tracking by drift chambers (DCH) and that is reconstructed by TICP PMT signals. In addition to this, we compare hit time of DCH

50

Chapter 3.

Analysis software and simulation

and TICP. These cuts eliminates events with uncorrelated positrons for track and
TICP hit, and events that positrons hardly scattered by some materials between
DCH and TIC.

Ghost track cuts
In a high rate environment, sometimes di erent positrons hit the same DCH module
at close in time and position. In such cases, di erent reconstructed trucks may sharesome hits for the trajectory reconstruction. On the other hand, sometimes tracking
process recognize multi-turn events as di erent tracks. Ghost track cuts select themost probable track out of these tracks.
The selection criteria is the same as the case of + ! e+ analysis except energy selection.
In + ! e+ search, positron momentum is equal to half the muon mass. In + !
e+ ;  ! search, positron momentum is expected to be lower and it depends on M .

3.6

Reconstruction of two gamma-rays

The original MEG reconstruction tool kit o ers pileup identi cation, but does not reconstruct each gamma-ray with good resolutions, so reconstruction dedicated to two
gamma-rays is developed. Section 3.6.1 and 3.6.2 describes fundamental method usedin two gamma-ray reconstruction. Section 3.6.3{3.7.3 describe reconstructions dedicatedto + ! e+ ;  ! search.

3.6.1 Scintillation photons
The charge extracted from a PMT can be converted to the number of photo-electrons(Npe ) emitted when photons hit the photo-cathode by

Npe;i = C  Qi =(Gi  CCE;i  e):(3.10)

Then, the number of the photons hitting the photo-cathode (Npho ) is reconstructed by

Npho;i = Npe;i =(CQE;i ):(3.11)

Here, i is the index number of the PMT, Qi , Gi , CCE;i , and CQE;i are charge, gain,
collection eciency, and quantum eciency of the PMT respectively, C is an attenuation
due to electronics, and e is the elementary electric charge.

3.6.2 Pileup identi cation
Pileup identi cation task searches the number of incident gamma-rays by looking forpeaks in the light distribution observed by PMTs on inner and outer faces. Peaks in
two dimensional histogram of Npho which exceed a threshold are searched for each face.
Threshold is set to be 200 photons. Details of the algorithm is described in Ref. [66]. The
number of found peaks and the peak bins are obtained. interaction position in u,v plane
can be known roughly with the resolution of bin width, here the distance between PMTs(= 6:2 cm for inner face). Then comparison of peak position is done to eliminate the same
incident. The identi cation eciency depends on the distance between two gamma-rays

Section 3.6.

Reconstruction of two gamma-rays

51

Entries [a.u.]

as shown in Figure 3.8. This gure is made using MC simulation with two gamma-rays
generated on the muon stopping target with isotropic direction distribution. It is shownthat the identi cation needs at least 3 bins ( 20 cm), unless it fails.
npeakld>1
npeakld=180

Isotropic two
MC

70
60
50
40
30
20
10

0
0
50
100
150
Distance between conv. point of two γ in uv plane[cm]Figure 3.8: Distance between interaction positions of two gamma-rays in uv plane. Red
histogram shows that for pileup search fails and blue shows that for pileup is identi ed.

3.6.3 Position reconstruction
PMT selection
PMT selection is done to minimize the uctuation by the shower developing behind the
rst interaction point since we assume in the reconstruction the scintillation light comesfrom a point-like source. Interaction points of gamma-rays in u,v plane are roughly obtained by the pileup identi cation. Only the events in which pileup is found are processed.
The nearest approximately 16 or 25 PMTs to the interaction position of each gamma-ray
are selected from the inner face PMTs. When the interaction positions are close enoughthat the selected PMTs are overlapped, they are merged. Larger number of the used
PMTs is applied for the case that the interaction position in w coordination is larger than
12 cm.
Then Precise three dimensional position is reconstructed by tting the light distribution observed by inner face PMTs. The rough u,v positions are used as initial values in
the reconstruction.

Reconstruction
The rst interaction position and the expected number of photons by two gamma-rays( 1; 2), all in all 8 parameters (3  2 + 1  2) are tted at the same time by minimizing

2position =X (Npho;inP MT
iNpho; 1  i ( #”x 1 ) Npho; 2  i ( #”x 2 ))2
(Npho;i )2:(3.12)

Here, Npho;i is a measured value, (Npho;i ) is calculated using measured values, #”x andNpho; are tted values, and iP MT ( #”x ) is calculated using tted value. nP MT is thenumber of the selected PMTs. Npho; is the expected number of photons generated by

52

Chapter 3.

Analysis software and simulation(= 1 or 2), #”x is the rst interaction position of , i ( #”x ) is the solid angle ofphoto-cathode of i-th PMT seen from interaction position and (Npho;i ) is statisticaluncertainty of the number of photons seen by the PMT, which is calculated by
1

CQE;i  pe;i(Npe;i)
p
1
=

Npe;i
C

(Npho;i ) ==(3.13)sQE;iNpho;i

CQE;i :

3
2.5

+ ! e+ ;  !

MC

25
20

2
1.5

15

1

3
2.5

+ ! e+ ;  !

MC

18
16
14

2

12

1.5

10
1

10

0.5
0

5

-0.5
-1
10

wrec - wtruth [cm]wrec - wtruth [cm]If initial value of Npho; is much apart from the actual value, position reconstructionin the direction of w can be mis-reconstructed. We perform position reconstruction again
after energy reconstruction to use the reconstructed energy for the initial value of Npho;so as to improve reconstruction eciency.
Then we perform correction on reconstructed position according to observed bias using
MC simulation. Figure 3.9 shows bias in reconstructed position in w coordinate related
to energy and reconstructed position. In + ! e+ ;  !
decay, gamma-ray energy
and its emission angle have strong relation, so the correlation between energy and w may
contain the e ect by incident angel. The correlation with reconstructed position andenergy are studied using + ! e+ ;  ! MC simulation and w is corrected.
Gamma-ray interaction positions are reconstructed in xyz coordinate, then they areconverted into uvw coordinate system which is described in Section 2.1.1. Shift in u iscorrected with 6.2 mm according to alignment calibration (Section 4.2.2). The resolution
is expected to be approximately 5.5mm in u, v coordinate, and 6.5mm in w coordinate.

20

30

40

50
Erec
γ [MeV](a) Energy dependence of w reconstruction

0

8
0.5

6

0

4

-0.5

2

-1
0

2

4

6

8

10
12
wrec [cm]0(b) Depth dependence of w reconstruction

Figure 3.9: Correlation between bias in w reconstruction and reconstructed energy, orreconstructed w.

Reconstruction of two gamma-rays

Section 3.6.

53

3.6.4 Time reconstruction
PMT selection
Time measured by one PMT have not ecient resolution, so we t interaction time using
PMTs selected from all the faces of the detector. For the interaction time extraction of
two gamma-rays, we rst speculate which PMT have the information of the interaction
time of which gamma-ray using the information obtained from the interaction position t.
We use the expected number of incoming photons to the PMT for the selection. Selection
criteria are that, Expected number of photons by , Npho;  i( #”x ) is more than 100,
 The ratio of the expected number of photons by and 0;(Npho;  i ( #”x ))=(Npho;  i ( #”x )) is more than 5,00where is the gamma-ray to be reconstructed, 0 is Npho; is the expected number ofphotons generated by obtained from the position t and i ( #”x ) is the solid angle ofi-th PMT from the reconstructed gamma-ray interaction position. The selection and thereconstruction is performed for each gamma-ray individually.

Reconstruction
Time measured by i-th PMT (tP MT;i ) and interaction time (thit;i; ) of
supposed to have following relation.
thit;i; = tP MT;itdelay;i;

tof f set;i(= 1 or 2) is(3.14)

Here, thit;i; is the gamma-ray interaction time expected from i-th PMT. tP MT;i is the timeof the PMT measured by the constant-fraction method described in Section 3.4.3, tdelay;i;is time delay during the scintillation light propagation to the PMT in LXe and the delaycaused by time walk, and tof f set;i is a constant time o set of the readout channel of the
PMT.
The delay time is estimated from the e ective velocity of scintillation light in LXe,
the number of photo-electron measured by the PMT, and the distance and the angle
between the PMT photo-cathode and the gamma-ray interaction position. Calibrationof tdelay;iP MT is done using CEX data, and the detail is described in Ref. [67]. In thereconstruction for one gamma-ray, the estimation of the delay time includes e ect ofshower using averaged e ective shower length of 52.8 MeV gamma-ray, but the length
should be di erent according to energy of gamma-ray, so this component is not includedin this study. The e ect is supposed to be small because only PMTs that shower pointis nearer than the rst interaction position are a ected and the di erence is supposed tobe small.
Then we de ne the 2time for the time t as follows.
X (thit;i; tLXe; )2;time =
t;i (Npe; )2
i

2

nP MT

(3.15)

where Npe; is the number of photoelectrons expected from the gamma-ray to be
p re2
constructed. t;i (Npe; ) corresponds to time resolution of each PMT, which is 1= Npe

54

Chapter 3.

Analysis software and simulation

corrected with calibration result. PMT selection is done for each gamma-ray and the interaction time (tLXe; ) is reconstructed minimizing 2time for each gamma-ray. During thetting process, PMT selection is performed again removing PMTs whose time information
di ers from the reconstructed interaction time and the minimization is iterated.
In the analysis for one gamma-ray, correction by the sum of the photoelectron is
performed, but the energy range is di erent in the analysis of + ! e+ ;  !
from++that of  ! e , and the calibration does not suit for the lower energy, so this correction
is not performed in this study.

3.6.5 Energy reconstruction
In the reconstruction of energy, we rst reconstruct the ratio of the number of photons
emitted by two gamma-ray interactions. Fitting is performed minimizing the same 2 as
position t (Equation 3.12) tting only Npho; 1 , Npho; 2 , xing the interaction positions.
Though we selected limited numbers of PMTs only from the inner face for the position t,
we select PMTs from all the faces for this t removing PMTs with small output. During
the t, PMTs which cause large 2 are removed and the tting is iterated.
After tting the ratio of the number of photons, we divide reconstructed number ofphotons of each PMT to reconstruct the number of photons derived from each gamma-ray
as follows,
Npho;  i ( #”x ) Npho;i;(3.16)
Npho;i; =#”Npho;  i ( x ) + Npho;  i ( #”x )where Npho;i; is the number of photons induced by and i ( #”x ) is the solid angle of i-th
PMT viewed from the reconstructed incident position of (= 1 or 2). When the solid
angles of both gamma-rays are equal to 0, square of the distance between gamma-ray
interaction position and PMT is used instead of the solid angle.
Then, the total number of photons emitted by each gamma-ray is reconstructed by,
0

Nf; =

Xth face

P MT 2fiNsum; =

allX
faces
f

0

wi  Npho;i; ;wf (u; v; w)  Nf; ;(3.17)

where f indicates inner, outer, lateral upstream, lateral downstream, top, or bottom facethat PMTs are located, Nf; is the total number of photons collected by PMTs in f th face, wi is a weight factor which is inverse of photo-cathode coverage of i-th PMT(see Figure 3.10), wf (u; v; w) is a weight factor to sum each face which is a function of
the reconstructed interaction position of a gamma-ray, and Nsum; is the total numberof photons emitted by the interaction of . All the PMTs are used in the summation.
wf (u; v; w) is optimized to make the energy resolution better using 0 -55 MeV peak data.
We did not apply the technique of the face factor for the data taken in 2009, so wf = 1 forthe analysis of the 2009 data and the face factor technique is only applied to 2010 datain this thesis. Because Nsum; calculated here have better resolution than the result ofenergy t (Npho; ), we repeat this procedure from the division of the number of photonsof each PMT replacing Npho; with Nsum; in Equation 3.16 and iterate.
0Section 3.6.

Reconstruction of two gamma-rays

55

Figure 3.10: Photo-cathode coverage on di erent faces. From the left, inner, outer and
top faces are shown. The circle is area of PMT photo-cathode and gray lled area iscoverage of the PMT.
Then the energy of a gamma-ray is reconstructed by,

E = F (u; v; w)  T (t)  C  Nsum; ;(3.18)

where F (u; v; w) a non-uniformity correction factor, T (t) is a correction to compensate
the change of light yield, and C is conversion factor from the number of photons to energy.

Non uniformity correction: F (u; v; w)
The LXe detector has non uniform response because scintillation photon collectioneciency depends on where the gamma-ray convert. Moreover, additional nonuniformity can be introduced in reality by several e ects, such as deformation of
detector, local bias of PMT calibration, and the face factors. Thus, we calibrate forthe overall e ects by scanning the real response of detector to calibration data over
all acceptance. The non uniformity correction factor F (u; v; w) is obtained using
17.6 MeV gamma-line from 73 Li(p; )84 Be reaction with help of 0 -55 MeV gamma-ray
events.
Light yield: T (t)Light yield is monitored with several calibration methods. In 2009 and 2010, thelight yield was very stable, and the stability of 17.6 MeV gamma-line peak is 0.3 (0.2)% in RMS for 2009 (2010). Calibration with 17.6 MeV gamma-line is performed 2-3
times per week during the data taking period. Light yield correction factor T (t) is
prepared using 17.6 MeV gamma-line and cosmic ray data as well as 0 data during
the CEX runs. The possible errors in the correction are estimated and assigned tothe energy scale uncertainty.
Conversion factor from the number of photons to energy: C
The linearity between Nsum and gamma energy E was checked using gamma-ray
with several energy available from our calibration methods. The conversion factor
from Nsum to energy is given from calibration run using 55 MeV gamma-ray. Figure
3.11 shows the linearity of the detector checked with several calibration sources.
Resolution of the sum energy of two gamma-rays is estimated using MC simulation to
be approximately 2 %, and the resolution of the ratio of the energy of two gamma-rays(E 1 =(E 1 + E 2 )) is 1:9  10 2 (here E 1 > E 2 ). Then resolution of each gamma-ray
energy is approximately 1 MeV.

Analysis software and simulation

Chapter 3.

Reconstructed Energy (MeV)

56

140
120
100
80
60
40
20
0
0

20

40

60

80

100 120 140
Truth Energy (MeV)

Figure 3.11: Linearity of reconstructed energy.

3.7

Combined analysis

3.7.1  decay vertex
 decay vertex position is required to estimate momentum of gamma-rays and relative
time between two gamma-rays or a positron and a gamma-ray. The decay vertex isreconstructed using the kinematics of + ! e+ ;  !
decay. Kinematics of the
decay is described in Section 3.2. When M is determined to a certain value, the decay
kinematics is determined according to the equations described in the Section 3.2.  decay
vertex is reconstructed by using muon decay vertex position ( #”x decay ), opposite direction#”#”of positron ( dire+ ; ' dire+ ), and energy (E ) and position (u; v; w) of gamma-ray. The 
decay vertex position ( #”x vtx t ), and gamma-ray emission angles (' ; #rest ) are tted using
these measured values. #rest is gamma-ray emission angle in the rest frame of , which isshown schematically in Figure 3.2 in Section 3.2. ' is angle along the traveling directionof . Fitting is done minimizing 2 setting M as a xed parameter, and it is performed
several times changing M to a various values.
The 2 is de ned as,X(E E vtx t (M ; #rest ))2 =E2
2vtx t == 1; 2

vtx
t #”
#”
#”
# ” ( x vtx t+ ( dirdirx decay ))2 =2e+(3.19)t #”#”#”# ” ( x vtx t+ (' dir'vtx
x decay ))2 ='2
dir
e+
X X
+
(X X vtx t ( #”x vtx t ; #e (M ; #rest ); ' ; r ))2 =X2 := 1; 2 X =u;v;w
vtx
t vtx t
vtx t are values calculated using the tting values. E vtx t# ” , ' # ” , and X
Here, E vtx t , dirdirt and 'vtx
t are
#”
#”
is expected gamma-ray energy calculated according to Equation 3.5, vtx

angles of  travel ( #”
x

#”
x

dir

dir

vtx t decay ), r is the distance that travels before the rst interaction in the LXe detector which is set to be j #”x #”x vtx t j, and X vtx t is expected gamma-ray
interaction position calculated from the + ! e+ ;  ! kinematics. Gamma emission
angle relative to positron direction in the experimental frame (#e ) is calculated with M
and #rest as described in Equation 3.6. Then gamma-ray interaction position can be cal-Section 3.7.

Combined analysis

57

culated using #e , the emission angle (' ) along the axis of  travel and the distance (r )gamma-ray travels before the interaction in LXe. Then, 2vtx t is obtained by Equation
3.19 as a sum of position, energy di erence of positron and gamma-rays with weight factors. These weight factors are determined taking resolutions of the detector into account.
Because E has asymmetric distribution, we assign di erent values on E according tosign of E E vtx t .
 and e+ are emitted coincident in time, and two gamma-rays are coincident, too. So it
is possible to use time information in the tting. However, this can make bias in the time
structure of accidental backgrounds. We estimate the number of background events using
time sidebands, which we will describe in the Section 5.2. The estimation of backgrounds
fails if bias exists in the time structure, so we do not include time information in the 2for the  decay vertex t.

3.7.2 Momentum reconstruction
Direction of gamma-rays are reconstructed connecting the reconstructed interaction position in the LXe detector and the reconstructed  decay point.

x
vtx t )=j #”And we can estimate momentum of gamma-ray as,#”n= ( #”
x

#”
x

#”
x

vtx t j#”P = E  #”n :(3.20)(3.21)

Using directions of gamma-rays, we can de ne following vectors,
#”

#”

#”

#”

= (P 1  P 2 )=jP 1  P 2 j;
#”
#”
#”
#”
#”
(3.22)n para = (P 1 + P 2 )=jP 1 + P 2 j;#”#”#”n orth = n perp  n para ;where #”n perp is a normal vector perpendicular to the plane which #”n 1 and #”n 2 makes,#”
n para is a direction parallel to the sum of momentum of two gamma-rays, and #”n orth is adirection which is on the plane of #”n 1 and #”n 2 and orthogonal to #”n para .
#”
n

perp

nperp
Pγ1
npara
Pγ2

north

Figure 3.12: Coordination of direction for the sum of momentum.
Then the sum of the momentums of a positron and two gamma-rays and components
in the direction de ned in Equation 3.22 are estimated with
#”

#”

#”

#”

P sum = P e+ + P 1 + P 2 ;#”Psum;perp = #”n perp  P sum ;#”Psum;para = #”n para  P sum ;#”Psum;orth = #”n orth  P sum :(3.23)

58

Chapter 3.

Analysis software and simulation

Psum should be zero for the signal + ! e+ ;  ! from the conservation of momentum.
In the nal state, all the tree particles are on one plane, and the reconstruction of #”n perpdoes not depend much on the resolution of gamma-ray energies, so we can expect better
resolution for Psum;perp than Psum;para and Psum;orth .

3.7.3 Relative time
The time of ight of a gamma-ray and  is estimated according to the expected M as,

ttof; = j #”x#”x

x vtx t
vtx t j=c + j #”#”x

vtx j=(   c):

(3.24)

Then, relative time of reconstructed muon decay time is calculated by
t e+ = (tLXe; ttof; ) te+
t 1 2 = (tLXe; 1 ttof; 1 ) (tLXe; 2

ttof; 2 )(3.25)

Chapter 4
Detector performance and Monte
Carlo simulation
In this chapter, the consistency of detector performance between Monte Carlo simulationand the actual detector is discussed.
We perform detector simulation with MEGMC and simulate waveform outputs ofdetectors with MEGBartender. The simulation program is carefully constructed to reproduce the actual detector, nevertheless there is small di erence in resolutions between thesimulation and the real detector. It is because we sometimes su er trips of drift chamber
HV and instability of muon beam, there might be some small misalignments or uncertainty of position in the actual detector, some of the optical properties of liquid xenon has
uncertainties, and the noise situation cannot be perfectly reproduced in the simulation.
We use Monte Carlo simulation to estimate sensitivity for the + ! e+ ;  ! decay. We describe here how we smear the simulation data to make it consistent with theexperimental data.

4.1

Positron spectrometer4.1.1 Double turn method
In the MEG experiment there is no direct way to measure the positron resolutions, so wedeveloped a method to evaluate them using tracks which make two turns inside the drift
chamber. On average, each track makes 1.5 turns inside the spectrometer. In order toevaluate resolutions, we use tracks which make 2 turns inside the drift chambers.
When a positron makes 2 turns inside the drift chambers, we obtain hit clusters for eachturn. We reconstruct each turn as an independent pseudo-track from each hit clusters.
Each pseudo-track is then projected, after the rst turn, to a ctitious plane on the beamline with the same inclination as the original target and the di erence is used to measure
resolutions. Energy, emission direction of positron and muon decay vertex resolutions canbe obtained by this technique.

4.1.2 Smearing of positron spectrometer reconstruction
To reproduce the actual performance of the positron spectrometer with MC simulation,
smearing of positron reconstruction is performed with two steps for MC simulation.
59

60

Chapter 4.

Detector performance and Monte Carlo simulation

First, we randomly move interaction time and z position in each cells of drift chamber modules according to gaussian distribution. After this smearing, reconstruction of
positron trajectory of MC simulation data come closer to the real data, but resolutions
are still better in the case of MC simulation data.
Then the remaining small discrepancies are corrected by smearing the reconstructed
position, energy and direction to be the same resolution as the case of the experiment.
Comparison is done using + ! e+ ;  ! MC data of the case of M = 25MeV andexperimental data of + ! e+ e   positron with momentum between 49:87  1MeV.

120
100

χ2 / ndf
const1mean1
sigma1const2mean2
sigma2Data

80

112 / 9485.68 ± 8.83
-0.01254 ± 0.02322
0.4841 ± 0.0307
141.1 ± 8.6-0.01387 ± 0.03308
1.328 ± 0.051

Entries [a.u.]

Entries [a.u.]

Smearing on hit reconstruction of drift chamber

1000

χ2 / ndf

MC

800

163.9 / 94

Const1

695.3 ± 29.4

Mean1

-7.238e-05 ± 7.817e-03

Sigma10.4764 ± 0.0141

Const21224 ± 27.8

Mean2
Sigma20.008471 ± 0.012185
1.421 ± 0.024

600

60
400
40
200

20
-2

-1

0

Entries [a.u.](a) Michel data with energy selection250

χ2 / ndf
const1mean1
sigma1const2mean2
sigma2

Data

200

0
-3

1
2
3
hitZ - trkZ [mm]107.1 / 88
153.5 ± 6.3-0.0167 ± 0.0078
0.2802 ± 0.0100
90.23 ± 5.84
-0.02496 ± 0.02592
0.9315 ± 0.0373

2500

1500

100

1000

50

500

-2

-1

0

1
2
3
hitR - trkR [mm](c) Michel data with energy selection

-1

0

0
-3

MC

-2

1
2
3
hitZ - trkZ [mm]MC (M = 25 MeV)
χ2 / ndf

162.8 / 89

Const11649 ± 23.5

Mean1

-0.004189 ± 0.002037

Sigma1

2000

150

0
-3

-2

(b) + ! e+ ;  !
Entries [a.u.]

0
-3

-1

(d) + ! e+ ;  !

00.2787 ± 0.0029

Const2366.5 ± 21.8

Mean2
Sigma20.02188 ± 0.01043
0.6978 ± 0.0177

123
hitR - trkR [mm]MC (M = 25 MeV)

Figure 4.1: Drift chamber hit position from hit reconstruction minus that from tracktting. Upper gures show those for Z position and lower show those for distance fromsense wire. Right gures are from experimental Michel data, and left ones from MC
simulation with hit reconstruction smearing. Solid curve shows double gaussian t line.
Hit position resolution is estimated from the di erence between hit position and track.
Hit position in each cell of the drift chamber modules obtained from the tted track havebetter resolution than that obtained by the hit reconstruction, so the di erence between
these roughly represents the hit resolution. The amount of smearing of z position and hit

Section 4.1.

Positron spectrometer

61

time are adjusted comparing this estimator with + ! e+ ;  !
MC simulation of
the case of M = 25MeV and experimental Michel data selecting positron energy between
49:87  1MeV. The result is shown in Figure 4.1. Z position and hit time are smearedwith 220m and 7 ns respectively.

χ2 / ndf30

17.77 / 25
Constant
28.58 ± 1.85
Mean
-0.04374 ± 0.14197
Sigma
2.737 ± 0.158

Data

25

Entries [a.u.]

Entries [a.u.]

Smearing on reconstructed track
We estimate the amount of smearing needed to compensate remaining di erences after
the hit smearing from the resolutions estimated by double turn method. Figure 4.2 and4.3 show double turn resolutions after hit smearing. Resolutions and its tting errors of
positron energy (Ee ), positron emission angle ('e , e ), and muon decay vertex (radiusfrom beam axis:Re , distance in z direction:Ze ) are summarized in Table 4.1.
Di erence of each resolution is used to smear reconstruction of MC simulation andtting error is counted as systematic uncertainty.
30
25

χ2 / ndf
15.3 / 17
Constant
23.65 ± 1.99
Mean
0.1082 ± 0.1184
Sigma
1.735 ± 0.112

MC

20

20
15
15
10

10

5

5
0
-20

-10

0

10

0
-20

20
∆ Re [mm]-1025

χ2 / ndf
52.92 / 41
Constant
19.04 ± 1.11
Mean
-0.2012 ± 0.2208
Sigma
4.322 ± 0.204

Data

10

20
∆ Re [mm](b)20

Entries [a.u.]

Entries [a.u.]

(a)

0

22
20
18
16
14

χ2 / ndf
60.74 / 36
Constant
14.28 ± 1.23
Mean
-0.4319 ± 0.1908
Sigma
2.969 ± 0.192

MC

12
10

15

5

8
6
4

0
-20

0
-20

10

2
-10

0

(c)

10

20
∆ Ze [mm]

-10

0

10

20
∆ Ze [mm](d)Figure 4.2: Resolution of position on the stopping target plane obtained by double
turn method. Distribution of the radius from the beam axis and that of z position
are shown. Figure 4.2(a), 4.2(c) show these for experimental data of positrons with
momentum between 49:87  1MeV, and Figure 4.2(b), 4.2(d), 4.3(d) show these for + !
e+ ;  ! MC data of the case of M = 25MeV after smearing of the hit reconstruction.

Entries [a.u.]

Chapter 4.

Detector performance and Monte Carlo simulation

45
40
35

χ2 / ndf

48.35 / 21
Constant
31.06 ± 2.12
Mean
-0.04417 ± 0.01251
Sigma
0.2313 ± 0.0141

Data

30

Entries [a.u.]6225

χ2 / ndf

25

17.04 / 17
Constant
20.39 ± 1.81
Mean
0.02479 ± 0.01582
Sigma
0.2148 ± 0.0189

MC

20
15

20
10

15
10

5

5
0
-2

-1

0

1

0
-2

2
∆ Ee [MeV]

-1

30
25

χ2 / ndf

52.67 / 37
Constant
17.72 ± 1.22
Mean
0.00105 ± 0.00110
Sigma
0.01978 ± 0.00124

Data

1

2
∆ Ee [MeV]

(b)

20

Entries [a.u.]

Entries [a.u.]

(a)

0

18
16

χ2 / ndf

MC

39.08 / 36

Constant
12.93 ± 1.11
Mean
-0.002385 ± 0.001025
Sigma

14

0.01531 ± 0.00097

12
10

15

8
10

6
4

5

2
0
-0.1

-0.05

0

0.05

0
-0.1

0.1
∆ ϕe [rad]

-0.05

40
35

χ2 / ndf

Data

49.75 / 55

Constant
26.99 ± 1.50
Mean
0.001285 ± 0.000717
Sigma

0.01687 ± 0.00063

30
25
20
15
10
5
0
-0.1

-0.05

0

(e)

0.05

0.1
∆ φe [rad]

(d)

0.05

0.1
∆ θe [rad]Entries [a.u.]

Entries [a.u.]

(c)

0

24
22
20
18
16
14
12
10
8
6
4
2
0
-0.1

MC

-0.05

0

χ2 / ndf

39.29 / 42

Constant

18.7 ± 1.4

Mean0.0002473 ± 0.0007792

Sigma

0.01307 ± 0.00064

0.05

0.1
∆ θe [rad](f)Figure 4.3: Energy (4.3(a), 4.3(b)), direction (4.3(c), 4.3(d), 4.3(e), 4.3(f)) resolutions
obtained by double turn method. Figure 4.3(a), 4.3(e), 4.3(c) show these for experimental
data of positrons with momentum between 49:87  1MeV, and Figure 4.3(b), 4.3(f), 4.3(d)show these for + ! e+ ;  ! MC data of the case of M = 25MeV after smearingof the hit reconstruction.

Section 4.2.

Liquid xenon gamma-ray detector

63

Table 4.1: Double turn resolutions
Data
MC
Di erence Uncertainty
Ee (keV) 231  14 215  19
8661
'e (mrad) 19:8  1:2 15:3  1:0
12.5
2.3
10.7
1.3
e (mrad) 16:9  0:6 13:1  0:6
Re (mm) 2:7  0:2 1:7  0:1
2.1
0.2
3.1
0.3
Ze (mm) 4:3  0:2 3:0  0:2

4.2

Liquid xenon gamma-ray detector

In this section, we discuss about gamma-ray detector in MC simulation and experiment.
We don't have proper calibration source for two gamma-ray reconstruction, so we can notestimate the resolution of it with experimental data. As basis of reconstruction algorithm
for two gamma-ray is the same as that for one gamma-ray, we compare resolution of one
gamma-ray reconstruction between experimental data and MC simulation, and obtained
di erence is used for smearing the resolution of two gamma-ray. Pseudo two gammaray events are generated superposing photon distribution of Li gamma-ray calibration
data (Section 2.5.3). Di erence between one gamma-ray reconstruction and two gammaray reconstruction was compared and the obtained di erence is assigned as systematic
uncertainty.

1800
1600

MC, reconstruction

1400

Entries [a.u.]

Entries [a.u.]

4.2.1 Detector eciency
14000
12000

MC, true energy deposit

10000

1200
1000

8000

800

6000

600

4000

400
2000

200
0
0

10

20

30
40
50
60
Reconstructed energy (MeV)(a) Reconstructed energy.

0
0

10

20

30

40
50
60
Energy deposit (MeV)(b) Distribution of the energy deposit in LXe.

Figure 4.4: Distribution of energy for 52.8 MeV gamma-ray MC simulation.
Figure 4.4 shows distributions of reconstructed energy and MC truth energy deposit
in LXe. Figure 4.5 shows distribution of gamma-ray rst conversion point. These threegures are obtained using 52.8 MeV gamma-ray MC simulation.
Gamma-ray passes through COBRA magnet, honeycomb window, inner face PMT.
Lower tail of the energy histogram is mainly due to energy loss by interactions before
entering the detector active volume, or shower escape in case that gamma-ray interact
close to the detector face.

4500
4000
3500

MC

3000

Window
PMT
LXe

Detector performance and Monte Carlo simulation
COBRA magnet

Chapter 4.

Entries [a.u.]

64

40

60

2500
2000
1500
1000
500
0
0

20

80
100
Radius (cm)Figure 4.5: Distance from beam axis to gamma-ray rst conversion point. Blue lled:energy deposit in LXe < 48 MeV. blank: all events.
Gamma-ray detector eciency agrees well with experiment and MC simulation. When
we de ne the eciency to be the probability that reconstructed energy of 52.8 MeV
gamma-ray is larger than 48 MeV, it is estimated to be 65 % from MC simulation and
64-67 % from experimental data.

4.2.2 Energy and position resolution
Energy and position resolutions of the LXe detector are estimated using calibration data of
55 MeV gamma-ray from  charge exchange reaction (Section 2.5.4). Di erence between
experimental data and MC simulation is estimated, and the obtained values are used toreproduce the actual detector resolution by MC simulation.

EnergyEnergy resolution is studied using 55 MeV gamma-ray. Study on MC simulation withthe same situation shows that gaussian smearing on the reconstructed energy randomly
with 1.15% reproduces the resolution by experimental data. As the total energy of two
gamma-rays with the + ! e+ ;  ! decay is about the same, and the same amountof smearing on the total energy is adopted for MC simulation.
Uncertainty of the energy scale in the experiment is estimated with several calibration
data. We monitor light yield of LXe using cosmic ray muon and 17.6 MeV gamma-ray
from Li nuclear reaction (Section 2.5.3). Gain is monitored using LED. Huge numberof 17.6 MeV gamma-ray data gives dependence of reconstructed energy on interaction
position. Combining the result of gain and light yield monitoring, dependence on interaction position, and statistical uncertainty of tting, we assign 0.33 % to the energy scale
uncertainty.

Position
Position reconstruction is studied using 55 MeV gamma-ray and putting lead collimatorin front of the entrance window of the detector. Shape of the collimator used in 2008 run
is shown in Figure 4.6. Three slits parallel to the u direction are formed on the collimator.

Section 4.2.

Liquid xenon gamma-ray detector

65(a) Design of lead collimator. Width of slit is 1 cm. (b) Picture of lead collimator. A 2-inch
Thickness is 1.8 cm.
PMT is put for a reference of size.

Figure 4.6: Lead collimator
Distribution of reconstructed position in v direction is shown in Figure 4.7(a). That forthe same setting with MC simulation is shown in Figure 4.7(b). Gamma-rays which passthrough slits of the collimator make three peaks. Fitted sigma of each peak is compared
between experimental data and MC simulation, and the di erence is estimated to be 1.8
mm. Reconstructed position with + ! e+ ;  ! MC simulation is smeared randomly
with gaussian distribution with width of 1.8 mm.
1800
500

1600

450

1400

400

1200

350

1000

300

800

250

600

200

400

Data

200
0
-15

-10

-5

0

5

(a) Data in 2008 run

10

15
v(cm)

150

MC

100
50
-15

-10

-5

0

5

10

15
v(cm)

(b) MC

Figure 4.7: Distribution of reconstructed position in lead collimator run. Red line showst curve.
Alignment
We measured the LXe detector alignment with three ways.
One is a measurement of cosmic ray. The trajectory of high energy cosmic ray isapproximately straight when the magnets are turned o . Reconstructing the trajectoryof cosmic ray which penetrates both the LXe detector and the drift chambers gives relativealignment information.
Second measurement is done placing lead cubes in front of gamma ray entrance windowusing 17.6 MeV gamma-line from Li nuclear reaction (Section 2.5.3). Lead cubes make

66

Chapter 4.

Detector performance and Monte Carlo simulation

shadows in reconstructed gamma-ray incident position. Comparison of the positions oflead cubes and the shadows gives absolute position information.
Third measurement is done placing AmBe 4.4 MeV gamma-ray source in front of
gamma-ray entrance window. We compare the placed position and reconstructed gammaray position.
We combined the results of these three measurements and evaluated the LXe detectoralignment to be z = 6:2  2:3(mm).
In this thesis, the LXe detector is placed 6.2 mm shifted position in the event generation of MC simulation. 2.3 mm is treated as systematic uncertainty in z.

Two gamma-ray reconstruction
As we do not have suitable two gamma-ray calibration data, performance of two gammaray reconstruction is examined by making pseudo two gamma-ray events from two sets of
one gamma-ray data. As shown in Figure 2.31 in Section 2.5.3, Li gamma-ray spectrum
have 17.6 MeV gamma-line and broad 14.7 MeV gamma-ray, which are a bit small but
near to the energy of + ! e+ ;  ! gamma-ray. Pseudo two gamma-ray events are
made superposing photon distributions from two sets of Li gamma-ray data. One example
is shown in Figure 4.8

Superpose
pseudo pileup event

Figure 4.8: Pseudo pileup event generation.
Ordinary one gamma-ray reconstruction used for + ! e+ search is applied before
mixing. Performance of one gamma-ray reconstruction is con rmed with several calibrations, and the result of two gamma-ray reconstruction after the mix is compered with thereconstruction done before the mix. In this way, e ect of noise is also accumulated, so theresolution is supposed to become worse than the actual resolution. The result is shownin Table 4.2. Here, EnergyRatio is de ned as E 1 =(E 1 + E 2 ); (E 1 > E 2 ). Because
the sum of the energies of two gamma-rays is almost the same as the total number ofobserved photons, it is thought to have good resolution. Loss of energy resolution stems
in the separation of energies, so we compare the resolution of separation here. It is shownthat two gamma-ray reconstruction on pseudo pileup event reproduces one gamma-ray

Section 4.3.

Time reconstruction

67

reconstruction applied before the mix. One big di erence is that shift of mean of w is seen
with data. This is probably because of insucient knowledge on optical property of thedetector, for example dependence of PMT Q.E. on incident angle of incoming scintillation
photon. Quadratic di erence between the result of data and MC simulation is counted assystematic uncertainty. This di erence should be bigger than the true value because ofaccumulation of noise.

Table 4.2: Di erence between one and two gamma-ray reconstruction
DataMCEnergyRatio (%) 2:3  0:1
2 :0  0:1
0:78  0:03 0:63  0:04
u1 (mm)0:74  0:03 0:59  0:04
u2 (mm)v1 (mm)0:77  0:03 0:60  0:03
0:64  0:02 0:63  0:04
v2 (mm)w1 (mm)2:5  0:1
2 :2  0:1
w2 (mm)2:2  0:1
2 :4  0:1
w1 (mm)1:69  0:07 0:45  0:09
w2 (mm)1:28  0:06 0:61  0:11
Table 4.3: Systematic uncertainty in two gamma-ray reconstruction
Systematic uncertainty
Energy Scale(%)
0.33
Energy Ratio(%)
1.1
0.5
u ; v (mm)1.2
w (mm)w (mm)1.6

4.3

Time reconstruction

Table 4.4: Time resolution
2009 2010 MC
t (ps) 96
67 61
te (ps) 146 122 94

Table 4.5: Time smearing
for 2009 for 2010
Smearing on t (ps)7428Smearing on te (ps)8473

Table 4.4 shows time resolution of the LXe detector and positron gamma relative time
resolution estimated from the data taken in 2009, 2010 and + ! e+ MC. The di erence
between MC simulation and the experiment is calculated and the result is summarized inTable 4.5. Amount of smearing on gamma-ray time reconstruction needed to adjust time
resolution of MC events is estimated from the di erence of t . Then the smearing factor
for positron reconstruction for MC is is estimated from the di erence of e taking thesmearing factor of LXe detector into account.
Time reconstruction for two gamma-rays is based on the same algorithm as the reconstruction for one gamma-ray except for the PMT selection criteria and energy range

68

Chapter 4.

Detector performance and Monte Carlo simulationof reconstructed gamma-ray, so we can expect that smearing factors for one gamma-ray
work also for two gamma-ray reconstruction. As calibration for time reconstruction of
gamma-ray is made by 0 -55 MeV gamma-ray to suit for the analysis of + ! e+ decay, we observe shift of mean in the time reconstruction of gamma-ray with low energy.
Calibration for MC is also made in the same procedure using 55 MeV MC simulationdata.
As we do not have proper calibration data for two gamma-ray time reconstruction,
we can not compare di erence between one gamma-ray reconstruction and two gammaray reconstruction with experimental data. Superposing light distribution of two setsof one gamma-ray events do not work on time reconstruction, and we need to go backto waveform analysis. But the superposition of waveforms of experimental data is notdeveloped yet. Systematic uncertainty is set to be 150 ps ( 2  smearing) for mean andsigma of time reconstruction for a conservative estimation.

Table 4.6: Systematic uncertainty in timete (ps) 150
te (ps) 150

Part IV
Analysis69

Chapter 5

-mediated decay search analysis
This chapter presents the analysis of searching for lepton avor violating decay mediatedby a (pseudo-)scalar particle . We use data pre-selected for + ! e+ search taken
in 2009 and 2010. The analysis is based on a simple cut analysis. The pre-selection
and the signal selection cuts are described in Section 5.1. We estimate the number ofbackground events in Section 5.2 and that of observed in the signal region in Section 5.3.
Normalization is discussed in Section 5.4. Bounds on the branching ratio are shown in
Section 5.5.

5.1

Signal event selection

The rst processing is done just after the physics data is taken. Then preselection is
performed to reduce data size for more precise analysis with the second processing. The
preselection criteria for + ! e+ search are de ned as,i)

6:875 ns < tii) jttracktT ICHIT < 4:375 ns,

tT ICHIT j < 50 ns,

where t is the reconstructed gamma emission time with an assumption that one gammaray is coming from the origin, and tT ICHIT is TICP (timing  counter) hit timing without
subtraction of the time of ight Thus we did not use precise tracking information for thepreselection. The reason of the asymmetric window for preselection i) is to acquire themulti-turn events; because of the absence of the tracking, we do not know the numberof turns before the hit on the timing counter. The second criterion requires at least one
track associated with the trigger is found. With this preselection, the data size is reduced
by a factor about 0.3-0.4. The selected events are reprocessed when the calibration or thereconstruction algorithm is updated.
We use this preselected data to search for the -mediated decay. In addition to thiscriteria, another pre-selection dedicated to the + ! e+ ;  !
search is applied
subsequently. This selection criteria are de ned as follows, npeakld > 1,
 At least one good positron track, jE normal + Ee+ Mj < M  20%,71

72

Chapter 5.

-mediated decay search analysis

 E normal > 40 MeV,
where npeakld is the number of peaks found by pileup identi cation on the LXe detector(Section 3.6.2), good positron is a positron track passing MEG positron selection criteria(Section 3.5.5) except the energy selection, and E normal is a reconstructed total energy
deposit in the LXe detector without unfolding pileup.
After these preselection, second processing is done to perform reconstructions dedicated to + ! e+ ;  ! search. Then analysis cuts are applied to select signal eventsand eliminate background events. The de nition of the cut is as follows.

Gamma-ray acceptance ju j < 25cm ^ jv j < 71cm for each gamma-rays
Cut for pileup identi cationp (u 1 u 2)2 + (v 1 v 2)2 > 20cm
Energy selection

 jE 1 + E 2 + Ee+ Mj < M  10%
 E 1 > 10MeV, E 2 > 10MeV
 jPe+ Pj < 1MeVTime selection

 jt 1e+ 0:1nsj < 0:5ns (E 1 > E 2)
 jt 1 2j < 0:5ns
Certi cation for the quality of  decay vertex t

 4MeV < E E vtx t(M; #rest) < 2MeV forvtxt#”# ” j < 30mrad
 j dir
dir
e+

t
#”
# ” j < 30mrad
 j' dir
'vtx
dir
e+
q

 (u uvtx t)2 + (v vvtx t)2 < 2 cm for jw wvtx tj < 1 cm for = 1; 2Momentum conservation

 jPsum;perpj < 1:5MeV
 5MeV < Psum;para < 2MeV
 jPsum;orthj < 3MeV

= 1; 2= 1; 2Section 5.1.

Signal event selection

73

The acceptance region is based on interval of inner face PMTs, which excludes a half
size of PMT interval around edges of u and v. Position reconstruction is done using PMTs
only on the inner face, so the resolution become worse at the edge. Energy resolution also
become worse at the edge because of higher probability of shower escape. Acceptanceregion is determined to exclude such events.
Pileup search fails when the distance between incident positions of two gamma-rays inu,v is smaller than 20 cm which corresponds to approximately three times PMT intervals
as mentioned in Section 3.6.2. Figure 5.1 shows the distribution of this distance in u,v.
We observe decay of stopped muon, so the sum of the energies of the nal threeparticles should be the same as the muon mass, and the momentum of the positron shouldbe the same as that of . Events with either gamma-ray with reconstructed energy lessthan 10 MeV are eliminated because we have more backgrounds in the lower energy region.
Eciency of reconstruction is also a ected in the low energy region. These cuts and the
distributions of the estimator are shown in Figure 5.2, 5.3, and 5.4.
A example of time structure of B.G. and signal is shown in Figure 5.5. There is asmall shift about 100 psec in gamma-ray time reconstruction. This is because calibrationof time reconstruction for gamma-ray with low energy is not prepared and gamma-ray
position correction with incident angle is not performed. So the cut for t 1e+ is set to be
shifted. Main B.G. is the events that two gamma-rays coming approximately the same intime and one positron overlap in time accidentally. Distribution of time di erence of two
gamma-rays is broader for B.G. events than the signal.
Distributions of estimators for the cuts to certify the quality of  decay vertex t andcut for for momentum conservation are shown in Figure 5.6{5.9 together with the cut
region shown with red lines. De nition of the estimator of the  decay vertex t is thesame as discussed in Section 3.7.1. Coordination of the momentum sum vector is de ned
in Section 3.7.2. Cut region is determined taking resolutions and B.G. distributions into
account. For example, gamma-ray energy cut is set to be stricter compared to the otherestimators so as to eliminate the B.G. events.

Entries [a.u.]

Chapter 5.

-mediated decay search analysis

Entries [a.u.]74

signal MC
100 M = 15 MeV
120

80
60
40
20
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20

p

30
40
50
distance between 2γ in uv plane [cm](a) (u 1 u 2 )2 + (v 1signal by MCv 2 )2 distribution of (b)

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

Data

20

30
40
50
distance between 2γ in uv plane [cm]p(u 1 u 2)2 + (v 1 v 2)2 distribution of

data

220
200
180
160
140
120
100
80
60
40
20
0
90

Entries [a.u.]

Entries [a.u.]p
Figure 5.1: Distribution of (u 1 u 2 )2 + (v 1 v 2 )2 . Distribution of this for signal
events depends on M . When M is light, peak position comes closer to 0. Preselection,
acceptance cut, energy sum cut, and gamma-ray energy cut are applied. Red line shows
cut line.

signal MC
M = 15 MeV

Data

4000
3500
3000
2500
2000
1500
1000
500

95

100

105

110
115
120
Eγ 1+Eγ 2+Ee+ [MeV](a) Distribution for energy sum of signal by MC

0
90

95

100

105

110
115
120
Eγ 1+Eγ 2+Ee+ [MeV](b) Distribution for energy sum of data

Figure 5.2: Distribution of energy sum of three particles. Preselection, acceptance cut,energy sum cut, and gamma-ray energy cut are applied. Small tail outside the cut region
is made by a pileup positron. Red line shows cut region.

signal MC
M = 15 MeV

160
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Entries [a.u.]

Entries [a.u.]

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75

Data

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0

60
Eγ [MeV](a) Distribution of E of signal by MC

10

20

30

40

50

60
Eγ [MeV](b) Distribution for E of data

Entries [a.u.]

Entries [a.u.]

Figure 5.3: Distribution of energy of a gamma-ray. Preselection, acceptance cut, energy
sum cut, and gamma-ray energy cut are applied. Red line shows cut line.

450

signal MC
350 M = 15 MeV
400

2500

Data

2000

300
250

1500

200
1000

150
100

500

50
0

-4

-2

(a) Distribution for Pe+

0

2
4
Pe+ - Pφ [MeV]P of signal by MC

0

-4

-2

0

(b) Distribution for Pe+

2
4
Pe+ - Pφ [MeV]P of data

Figure 5.4: Distribution of di erence of gamma-ray energy between reconstructed andthat from  decay vertex t. P is calculated expecting M to be 15 MeV for both data
and MC. Preselection, acceptance cut, energy sum cut, and gamma-ray energy cut are
applied. Red line shows cut region.

Entries [a.u.]

Chapter 5.

-mediated decay search analysis

Entries [a.u.]

76

250

signal MC
200 M = 15 MeV


250
200

150

150

100

100

50

50

0
-2

-1

0

1

Data

0
-2

2
Tγ 1 e [nsec]

220
200
180
160
140
120
100
80
60

signal MC
M = 15 MeV

1

2
Tγ 1 e [nsec]

800
700

Data

600
500
400
300
200

40
20
0
-2

0

(b) Distribution for t 1e of data
Entries [a.u.]

Entries [a.u.](a) Distribution for t 1e of signal by MC

-1

100
-1

0

1

2
Tγ 1 γ 2 [nsec](c) Distribution for t 1 2 of signal by MC

-2

-1

0

1

2
Tγ 1 γ 2 [nsec](d) Distribution for t 1 2 of data

Figure 5.5: Distribution of relative times. Vertex t is done expecting M to be 15 MeV
for both data and MC. Preselection, acceptance cut, energy sum cut, and gamma-ray
energy cut are applied. Red line shows cut region.

Signal event selection

Entries [a.u.]

Entries [a.u.]

Section 5.1.

200

signal MC
160 M = 15 MeV
180
140
120

3500
3000

77

Data

2500
2000

100
1500

80
60

1000

40

500

20
0
-20

-15

-10

-5

0
-40

0
5
10
vtx fitErec[MeV]
γ 1 - Eγ 1

300
250

signal MC
M = 15 MeV

0

20

40
60
vtx fitErec[MeV]
γ 1 - Eγ 1(b) Distribution for E 1 of data
Entries [a.u.]

Entries [a.u.](a) Distribution for E 1 of signal by MC

-20

5000
4000

Data

200
3000
150
2000
100
1000

50
0
-20

-15

-10

-5

0
5
10
vtx fitErec[MeV]γ 2 - Eγ 2(c) Distribution for E 2 of signal by MC

0
-60

-40

-20

0

20
40
vtx fitErec[MeV]γ 2 - Eγ 2(d) Distribution for E 2 of data

Figure 5.6: Distribution of di erence of gamma-ray energy between reconstructed andthat from  decay vertex t. Vertex t is done expecting M to be 15 MeV. Red line
shows cut region. Preselection, acceptance cut, energy sum cut, and gamma-ray energy
cut are applied. Original distribution of gamma-ray energy of the background is a broad
one peak distribution, and that of signal is narrower, so the di erence of them makes two
peaks.

Entries [a.u.]

Chapter 5.

-mediated decay search analysis

Entries [a.u.]

78

1200
1000

signal MC
M = 15 MeV

800

9000
8000

Data

7000
6000
5000

600

4000
400

3000
2000

200
1000
0
-30

-20

-10

0

0
-200

10
20
30
∆ θrec - vtx fit [mrad]

1200

10000

signal MC
1000
M = 15 MeV

0

100
200
∆ θrec - vtx fit [mrad](b) Distribution for  of data
Entries [a.u.]

Entries [a.u.](a) Distribution for  of signal by MC

-100

Data

8000

800
6000
600
4000
400
2000

200
0
-30

-20

-10

0

10
∆φ

20

rec - vtx fit

30[mrad](c) Distribution for ' of signal by MC

0
-200

-100

0

∆φ

100

rec - vtx fit

200[mrad](d) Distribution for ' of data

Figure 5.7: Distribution of di erence of  and  between reconstructed and that from 
decay vertex t. Vertex t is done expecting M to be 15 MeV. Preselection, acceptancecut, energy sum cut, and gamma-ray energy cut are applied. Red line shows cut region.
Initial values of  and ' for  decay vertex t is equal to that of e+ , so if there is a local
minimum around the initial value of the t, it makes sharp peak at 0 in the distribution
shown above. Cut region is set to be 3  of the resolution of the positron spectrometer.

Signal event selection

Entries [a.u.]

Entries [a.u.]

Section 5.1.

signal MC
600 M = 15 MeV
700

500

6000

79

Data

5000
4000

400

3000

300
2000
200
1000

100
0
0

5

10

15

0
0

20
25
∆ uvrec - vtx fit [cm]

5

10

15

20
25
∆ uv rec - vtx fit [cm]

1000
800

Entries [a.u.]

Entries [a.u.](a) Distribution for incident position in uv of sig- (b) Distribution for incident position in uv ofnal by MC
data

10000

signal MC
M = 15 MeV

6000

600
400

4000

200

2000

0

Data

8000

-4

-2

0

2
4
∆ wrec - vtx fit [cm]

0

-4

-2

0

2
4
fit
wrec
- wvtx[cm]
γ1γ1(c) Distribution for incident position in w of sig- (d) Distribution for incident position in w bynal by MC
dataqFigure 5.8: Distribution of (u uvtx t )2 + (v vvtx t )2 and w wvtx t . Vertex t
is done expecting M to be 15 MeV. Preselection, acceptance cut, energy sum cut, andgamma-ray energy cut are applied. Red line shows cut region.

Entries [a.u.]

Chapter 5.

350
300
250

-mediated decay search analysis

Entries [a.u.]

80

signal MC
M = 15 MeV

200

3000
2500

Data

2000
1500

150
1000
100
500

50
0
-10

-5

0

0

5
10
Psum perp [MeV]140

signal MC
120
M = 15 MeV
100

-20

0

20
40
Psum perp [MeV](b) Distribution for Psum;perp of data
Entries [a.u.]

Entries [a.u.](a) Distribution for Psum;perp of signal by MC

-40

4000
3500

Data

3000
2500

80

2000
60

1500

40

1000

20
0
-10

500
-5

0

0

5
10
Psum para [MeV]signal MC
160 M = 15 MeV
200
180
140
120

1600
1400

0

20
40
Psum para [MeV]

Data

1200
1000

100

800

80

600

60
40

400

20

200

0
-10

-20

(d) Distribution for Psum;para of data
Entries [a.u.]

Entries [a.u.](c) Distribution for Psum;para of signal by MC

-40

-5

0

5
10
Psum orth [MeV](e) Distribution for Psum;orth of signal by MC

0

-40

-20

0

20
40
Psum orth [MeV](f) Distribution for Psum;orth of B.G. by data

Figure 5.9: Distribution of the sum of momentum vectors of positron and two gammarays. De nition of coordination used here is discussed in Section 3.7.2. Vertex t isdone expecting M to be 15 MeV. Preselection, acceptance cut, energy sum cut, andgamma-ray energy cut are applied. Red line shows cut region.

Section 5.2.

5.2

Backgrounds

81

Backgrounds

We estimate the number of background (B.G.) events which can be misidenti ed as + !
e+ ;  ! using time sideband. B.G.s are classi ed to four types by the time structure
as follows.
i) Two s induced from one muon decay & coincident Michel e+(a) Two s from annihilation in ight (AIF) & Michel e+(b) + ! e+ e   , e+ ! by AIF or bremsstrahlung & Michel e+ii) e+ and one from one muon decay & one from another(a) + ! e+ e   & + ! e+ e  (b) + ! e+ e   & from AIF or bremsstrahlung of Michel e+iii) Triple accidental coincidenceMichel e+ & each from + ! e+ e   , AIF or bremsstrahlungiv) All the e+ and two s induced from one muon decay(a) Generic + ! e+(b) + ! e+   e
B.G. iv) is negligible, because of the limited acceptance of the MEG detector and thesmall branching ratio. Only e+ with large momentum hits the timing counter (TIC) andthe acceptance of the gamma-ray detector is small. The branching ratio of the generic+ ! e+ decay is less than 7:2  10 11 [19]. The decay + ! e+   e is not wellstudied and the branching ratio of this decay is not listed on the PDG [33]. But we can
expect the probability of misidentifying + ! e+   e to be + ! e+ ;  ! is quite
small because both the neutrinos should have very small momentum, the gamma-rays
should be emitted near to each other and the momentum of e+ should be high.
The time sidebands for the B.G. estimation are de ned as follows.
(A) (jt 1 2 j < 0:5 ns) ^ (1 ns < jt 1 e+ j < 3:6 ns) for type i) + iii)(B) (1 ns < jt 1 2 j < 3:6 ns) ^ (jt 1 e+

0:1 nsj < 0:5 ns) for type ii) + iii)(C) (1 ns < jt 1 2 j < 3:6 ns) ^ (1 ns < jt 1 e+ j < 3:6 ns) for type iii)
Scatter plot of time di erence between a gamma-ray with higher energy ( 1 ) and a
gamma-ray with lower energy ( 2 ) versus that between 1 and a positron is shown in Figure5.10(a) together with the de ned time sideband. Preselection, acceptance cut, energy sum
cut, and gamma-ray energy cut are applied on this plot, without the other signal cuts.
From the Figure 5.10, we can see that the event type i) is the major background.
The number of events in each time side band (Nobs:(A) ; Nobs:(B) ; Nobs:(C ) ) is counted
by applying the signal cut with changed time cut. Estimation of the number of eventsare done at grid point of M . They are plotted on the Figure 5.10(b). Because the typeiii) B.G. events are included in the time side band regions (A) and (B), and the number ofChapter 5.

-mediated decay search analysis" T! 1e+ [nsec]

5

60

Data
3

4

2
1

(C)

(A)

(B)

0

(C)
(B)

50
40
30

-1

(C)

-2
-3

(A)

(C)

20
10

-4
-5

-4

-2

0

2

4
" T! 1! 2 [nsec]

0

Entries82

65Number of event in sideband (A)Data

Number of event in sideband (B)Number of event in sideband (C)

4
3
2
1
0
10

20

30

40
Mφ [MeV](a) Time structure of preselected events. Most of (b) Distribution of the number of observed events inthe signal cuts are not applied.
each time sideband

Figure 5.10: Time sideband and the number of backgrounds. Red shows signal region.
Blue, orange, and green represent time sideband regions (A), (B), and (C) respectively.
events can not be negative, the number of each B.G. type of events (NB:G:i) ; NB:G:ii) ; NB:G:iii) )is calculated by,
NB:G:i) = Max(0; Nobs:(A) (0:5=2:6)  Nobs:(C ) );NB:G:ii) = Max(0; Nobs:(B) (0:5=2:6)  Nobs:(C ) );(5.1)
NB:G:iii) = Nobs:(C ) :Then the number of expected B.G. in the signal region is calculated as follows,
NB:G: = (0:5=2:6)  NB:G:i) + (0:5=2:6)  NB:G:ii) + (0:5=2:6)  (0:5=2:6)  NB:G:iii) : (5.2)
When we have nite B.G. events in all the sideband regions, Equation 5.2 is written
as NB:G: = (Nobs:(A) term)+(Nobs:(B) term) (Nobs:(C ) term). Tail of NB:G:i) in Nobs:(B)is canceled by subtraction with Nobs:(C ) . As shown in Figure 5.10(b), Nobs:(B) is zero
most of the cases. Then term of Nobs:(C ) is canceled and the Equation 5.2 becomes
NB:G: = (Nobs:(A) term). We have another case that both Nobs:(A) and Nobs:(B) are zero. In
this case, NB:G = (Nobs:(C ) term). Because NB:Gi) is negligible, its tail is also negligible.
All in all in the region of 10MeV < M < 50MeV, the total number of observed eventsin each time sideband was 14, 2, 11 for region (A), (B), (C) respectively, so the total
number of expected number of background in the signal region is 2.7 events.

5.3

Observed events in signal region

The number of observed in the signal region is summarized in Figure 5.11. The total
number of observed events in the signal region is 4. This is consistent with no signal
event.
Error for the number of events in each time sideband is estimated by square-root of thenumber except the case the number is zero, in which case 1 is assigned as error for conservative estimation. Then, total error is calculated adding each error values quadraticallynormalizing with time width.

Section 5.3.

Observed events in signal region

83

Entries

Table 5.1 shows 90 % con dence level (C.L.) interval by Feldman Cousins method [68].
The number of signal event is zero consistent at all the grid points of mass of . Note that
this includes neither systematic uncertainties nor Poisson statistical errors in the numberof observed events. We will estimate bounds on branching ratio later in Section 5.5 taking
systematic errors into account.
6

Number of obeserved event

5

Expected number of B.G. event

4
3
2
1
0
10

20

30

40

M! [MeV]Figure 5.11: The number of observed events (red circle) and expected number of B.G.
events (blue triangle) in the signal region. Black bar with red star is mass of each observed
event. Red star is the mass that 2 of  decay vertex t was the smallest. Total numberof observed events in the signal region was 4.
Table 5.1: 90 % C.L. interval by Feldman Cousins method
M [MeV] 10 11 12 13 14 15 16 17 18
Upper
1.53 4.61 4.95 4.95 4.95 3.59 1.74 1.63 1.63
Lower
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
M [MeV] 20 21 22 23 24 25 26 27 28
Upper
3.59 3.40 3.40 3.79 2.06 2.06 2.06 2.25 2.25
Lower
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
M [MeV] 30 31 32 33 34 35 36 37 38
Upper
2.25 2.25 2.20 2.25 2.40 2.44 2.44 2.44 2.40
Lower
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
M [MeV] 40 41 42 43 44 45 46 47 48
Upper
2.40 2.40 2.40 2.44 2.44 2.44 2.44 2.44 2.44
Lower
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

19
1.63
0.00
29
2.25
0.00
39
2.40
0.00
49
2.44
0.00

-mediated decay search analysis

84

Chapter 5.

5.4

Normalization

The number of signal events (Ne;! ) observed with a certain combination of M and
 is proportional to the branching ratio, and the relation can be written as,

B(+ ! e+;  !

)=Ne;!
:
k(5.3)

The normalization parameter k is equal to the inverse of the single event sensitivity(S.E.S.). In the experiment, we sometimes su ered from instabilities such as unstablebeam intensity or trips of DCH high voltages. Condition of the experiment was not always
the same. The normalization factor was evaluated taking these e ects into account. We
describe here how we extracted it.
The total number of signal events observed in the data taken with + ! e+ search
trigger is calculated by,Ne;! = B(+ ! e+ ;  ! )  N+
 Aee;!  Ae;!
1:0 trge;!  trg :0Pe+
 e;!  e;!
 cute;! ;

(5.4)

where

B(+ ! e+;  !

) : The branching ratio of + ! e+ ;  !

N

: The total number of muons stopped on the target during thelive time,+Aee;
! ; Ae;!

: Acceptance of the positron spectrometer and the LXe gammaray detector for + ! e+ ;  ! decay,

:0
trg
e;!

: Trigger eciency for the + ! e+ ;  !
e+ trigger (id=0),

P trg:0: = 1, Pre-scale factor of + ! e+ trigger (id=0) which is described in Section 2.6.2,+
ee;
! ; e;!

: Reconstruction eciency of positron and two gamma-rays,

cut
e;!

: Eciency of signal cut.

decay,

events by + !

As mentioned in Section 2.6.2, we take Michel decay (+ ! e+ e   ) data withTIC self-trigger (id=22) in parallel with + ! e+ trigger data. The number of Michel

Section 5.4.

Normalization

85

positrons with momentum in a certain range can be written in a similar way to Ne;!
as follows.

Ne = B(+ ! e+ e   )  N
Pe selection
 fe
 Aee+1:22
 trge  trg :22Pe+ e ;

(5.5)

where
B(+ ! e+e ) :  100%, The branching ratio of + ! e+e  decay,
Pe selectionfe: The fraction of Michel spectrum in a certain momentum range,

+
Aee

: Acceptance of the positron spectrometer for + ! e+ e   decay,

:22
trg
e

: Trigger eciency of TIC alone trigger (id=22),

P trg:22: = 107 , Pre-scale factor of TIC alone trigger (id=22),

+
ee

: Reconstruction eciency of positron.

Here, N is the same as that of Equation 5.4 as we use the data taken in parallel. From
Equation 5.3, 5.4, and 5.5, we can obtain the normalization factor as follows.
+:22
Ee selection
Ae
fe
ee
1
1
1
trg
1
e
e+




:
1=k =



+
trg
:0
cut
e;
!
e;
!
Ne
P trg:22e;!
e;!
ee;!
e;!
Ae+A(5.6)
We evaluate the normalization factor with the product of the number of the Michel
positrons, the relative acceptance and eciency of the positron spectrometer, and acceptance and eciency of the gamma-ray detector. Ne is measured using the experimental
data, and the other parameters are estimated by using MC simulation of signal events fordi erent sets of mass and lifetime values.
We select Michel positron momentum near the target momentum of + ! e+ ;  !
positron according to M . The behavior of the positron with the same momentum is
expected to be the same for the Michel decay and the signal. Ne is evaluated from thedata taken in parallel with the physics data, so we can evaluate the periodical changes inthe beam and positron spectrometer conditions. Eciency of the positron
spectrometer+ e+
di ers accoriding to the data taking period, but relative eciency (ee=e;! ) can bestably estimated with the help of the energy selection. The combination of the estimationof the number of Michel positrons taken in parallel and its momentum selection gives
stable evaluation of the normalization factor.
Eciencies and acceptances were evaluated for the mass values between 10 and 40
MeV with an interval of 5 MeV and for the lifetime of 10 ps, 100 ps, 1 ns, 10 ns, using
MC simulations. Then interpolation is performed for the masses in-between. This is

86

Chapter 5.

-mediated decay search analysis

because MC simulation needs a lot of time and disk space. The reconstructed values wereconservatively smeared to reproduce the detector performance of the 2009 experiment.
In the following sections, we are going to see fraction of the positron momentum selection (Sec. 5.4.1), acceptance of the positron spectrometer (Sec. 5.4.2) and the gamma-ray
detector (Sec. 5.4.3), eciency of the direction match of trigger setting (Sec. 5.4.4), efciency of the positron selection (Sec. 5.4.5) and the gamma-ray reconstruction (Sec.
5.4.6), signal cut eciency (Sec. 5.4.7) and trigger eciency of gamma-ray energy selection (Sec. 5.4.8). Selection is performed according to the order of the section number.
Applied requirements of the former sections are applied to the following sections.

5.4.1 Positron momentum selectiona.u.

In this section, we estimate the fraction of momentum selection on Michel positron.
The number of DCH hits used for track tting is smaller for low momentum positrons
because of smaller radius of the helical trajectory. Therefore track tting su ers morefrom trips of DCH HV for low momentum positrons. Eciency of positron spectrometer
depends on run period. However, behavior of positrons with the same momentum is expected to be the same both for the Michel decay and + ! e+ ;  ! decay. Therefore
proper selection of the positron momentum helps stable estimation of the normalization.
Positron momentum of -mediated muon decay is monochromatic which is calculated
by Equation 3.1 for a given M . On the other hand, Michel positron momentum follows
a certain spectrum. Figure 5.12 shows momentum spectrum of Michel positron. Red lineis theoretical spectrum, green one is smeared spectrum with energy resolution, and blue
one is that containing geometrical acceptance and track t eciency of the MEG positron
spectrometer. Upper tail is made by the energy resolution, and lower one is mainly bygeometrical acceptance.
1
0.8
0.6
0.4
0.2
0

46

48

50

52

54

56

58
Ee [MeV]Figure 5.12: Momentum spectrum of Michel positron. Red line: theoretical Michel spectrum including radiative correction. Green line: red one smeared by detector resolution.
Blue line: \good" positron detected by the MEG spectrometer. Blue hatched region: themomentum selection region for M  20MeV=c.
If M is very light, momentum of signal positron come closer to the upper edge of theMichel spectrum. In this case, we set energy selection region between 50 MeV and 56
MeV to include the tail made by momentum resolution. On the other hand, in the casethat M is large enough, we select momentum for the estimation of the number of Michel
positron in the region that is within jP j  1MeV.

Section 5.4.

Normalization

87

When M = 20MeV, P ' 51MeV, and when M = 25MeV, P ' 50MeV. We use theenergy region 50MeV < Pe < 56MeV when M  20MeV, and jPe P j < 1MeV whenM  25MeV. The fraction is estimated with Michel positron MC simulation applying
energy selection for each cases of M . Only the selection of momentum is performed here,
and no acceptance cut or so is performed for the estimation of the fraction. The result
appears in Table 5.2. Energy selection is done using energy of simulation truth, thencorrected taking the energy resolution into account.

Table 5.2: The fraction of Michel spectrum
M [MeV]10, 15, 20
25
30
Ee selection [MeV]
50 < Ee < 56
jEe 49:9j < 1:0 jEe 48:6j < 1:0
Ee selection2fe(9:9  0:2)  10
(7:1  0:2)  10 2 (6:8  0:2)  10 2M [MeV]35
40
45
Ee selection [MeV] jEe 47:0j < 1:0 jEe 45:3j < 1:0 jEe 43:2j < 1:0
Ee selectionfe(7:2  0:2)  10 2 (6:9  0:3)  10 2 (8:1  0:7)  10 2

5.4.2 Relative acceptance for positron! is de ned as the probability of
Positron acceptance for + ! e+ ;  ! event; Ae;
e+having at least one timing-counter hit for isotropically generated signal events. Positron
acceptance for + ! e+ e   event; Aee+ is de ned as the same probability for isotropicallygenerated + ! e+ e   positrons with the energy written in Table 5.2.
Relative acceptance for positron does not depend on the lifetime of  ( ), but on themass of  (M ), so it is estimated for each M . As we compare acceptance for positrons
with similar energy, the relative acceptance is near to 100% as shown in Table 5.3. Listed
error is statistical error.

Table 5.3: Relative acceptance for positronM [MeV]
10
15
20
25
e;!
e
(Ae+ )=(Ae+)(%) 89:9  1:0 95:1  1:1 105:6  1:2 101:1  1:5
M [MeV]
30
35
40
45
e;!
e
(Ae+ )=(Ae+) (%) 101:7  1:7 98:6  2:0 96:9  2:5 87:7  3:1

5.4.3 Acceptance for two gamma-rays
We estimate here the acceptance for two gamma-rays. Estimation is performed using MC
truth of gamma-ray emission direction and energy deposit in liquid xenon. Estimation byreconstructed values will be done in the Section 5.4.6. Acceptance for two gamma-rays isde ned here as follows.

 Energy deposit of each gamma-ray in liquid xenon > 5 MeV
 Total energy deposit in liquid xenon > 40 MeV

88Chapter 5.

-mediated decay search analysisq  decays before passing inner face of the LXe detector; x2decay + y2decay < 67:85cm
 Gamma direction is within the extended detector acceptance; ju j < 28:1 cm ,jv j < 74:1 cm at w = 0 cm for each gamma-ray.
Acceptance of the incident position in the analysis is de ned that ju j < 25 cm,
jv j < 71 cm, and we require here the direction of gamma-ray is within the extended
range; ju j < 28:1 cm, jv j < 74:1 cm, which are set large enough taking the detector

resolution into account. Here, u and v are estimated extending the gamma direction ofMC
p truth from the generating point until it reaches the inner face of the LXe detector( x2 + y2 = 67:85 cm). As the positron direction is limited to the acceptance of positron
spectrometer which is back to back to the LXe detector, center of the two gamma-rays
should be already restricted around the acceptance, so the estimated values here canbecome larger than the solid angle of the LXe detector ( 10%).
The estimation is done for each M and  sets. The result with statistical error islisted in Table 5.4.

Table 5.4: Acceptance for two gamma-rays
M [MeV]
10
15
20
25
( = 10ps) 24:2  0:2 16:6  0:2 10:4  0:2 7:5  0:1
100ps) 28:6  0:2 20:2  0:2 13:0  0:2 9:0  0:2
Ae;! (%) (( ==1ns)13:6  0:2 16:1  0:2 16:1  0:2 15:4  0:2
( = 10ns) 1:7  0:1 2:3  0:1 2:7  0:1 2:9  0:1
M [MeV]
30
35
40
45
( = 10ps) 5:8  0:1 4:1  0:1 2:7  0:1 1:8  0:1
100ps) 6:2  0:1 4:7  0:2 3:5  0:2 2:1  0:2
Ae;! (%) (( ==1ns)13:6  0:2 11:3  0:2 8:8  0:3 6:9  0:3
( = 10ns) 2:8  0:1 3:1  0:1 3:0  0:2 3:2  0:2
Longer lifetime makes the probability that  decays near the detector bigger, whichmakes the acceptance better, however, too long lifetime makes it worse because the probability that  penetrates the detector without decaying into gamma-rays increases.
Smaller M makes the angle between two gamma-rays smaller with the Lorentz boost
e ect, and larger M makes this opening angle bigger. So, the acceptance is better incase that  has smaller mass. But when the mass is too small, e ective lifetime of  inthe experimental frame becomes longer by the Lorenz boost e ect, and this makes ight
length longer and e ects on the acceptance.

5.4.4 Direction match trigger eciency
We discuss about trigger eciency in this section. Trigger settings for trigger id=0, 22
are described in Table 2.4. Trigger id = 0 is the trigger for + ! e+ search and id =22 is the trigger for Michel decay ( ! e  e ). Trigger eciency is estimated for the
events which satisfy acceptance requirements. Acceptance is discussed in Section 5.4.2
and 5.4.3.
Positron acceptance is already satis ed, so the trigger eciency for trigger id = 22
trg :22(e ) is equal to 1.

Section 5.4.

Normalization89:0 = E T HR TeDM
Trigger id=0 is composed of three components; trg
e;!
e;!
e;!  e;! ,HReDM
where Ee;T!
, Te;! and e;! represent the trigger eciency of gamma-ray energy
selection, gamma-ray positron coincident event selection and the direction match selection
respectively. Because time window of trigger id=0 is large enough for + ! e+ ;  !
eevent, Te;
! is equal to 1. So we should estimate eciency of direction matchand gamma-ray energy thresholds. Eciency of direction match is estimated here, andestimate eciency of gamma-ray energy selection of trigger later in Section 5.4.8.
Direction match is designed to trigger back to back positron and gamma-ray with theenergy equal to half the muon mass. Look up table for the direction match; i.e. thePMT with the largest incoming photon and z of the TICP rst hit position; is madeusing + ! e+ MC simulation. We check if the event satis es the look up table.
Table 5.5 summarize the eciency of the direction match. Longer lifetime makes theprobability that  decays near the detector bigger, and this helps to make the direction
match eciency better. Smaller M also results in better direction-match eciency,
because stronger Lorentz boost makes the opening angle between gamma-ray and positronnear back to back. Larger M makes positron momentum smaller, which makes the radiusof positron trajectory smaller and hit position on TIC bar di erent from the case of 52.8
MeV positron.

Table 5.5: Direction match eciency
M [MeV]101520( = 10ps) 61:0  0:6 45:0  0:5 36:3  0:5( = 100ps) 68:1  0:6 51:0  0:5 39:7  0:5
DMe;! (%) ( = 1ns)
73:9  0:6 67:0  0:6 59:5  0:6
( = 10ns) 75:0  0:6 68:8  0:6 61:6  0:6
M [MeV]30
3540( = 10ps) 22:9  0:5 18:1  0:5 14:4  0:6( = 100ps) 24:8  0:5 20:5  0:5 18:2  0:6
DMe;! (%) ( = 1ns)
42:7  0:6 33:9  0:6 27:7  0:7
( = 10ns) 47:0  0:6 38:0  0:6 31:3  0:7

25
28:3  0:5
31:5  0:5
51:7  0:6
54:5  0:6
45
13:0  0:7
15:0  0:8
23:2  0:9
26:1  0:9

5.4.5 Positron relative eciency
We discussed about the selection criteria to ensure the quality of positron track t in
Section 3.5.5. We check the eciency of the selection in this section. The eciency ofthe selection is estimated using the events which satisfy the detector acceptance cut andtrigger setting.
The result is shown in Table 5.6. From this table, we can see that the positron selection eciency for + ! e+ ;  ! decay is better than that for + ! e+ e   decay.
As described in Section 5.4.3, both two gamma-rays are requested to be inside the extended detector acceptance. This decreases events near the edge of positron spectrometer
acceptance, which result in better eciency for the + ! e+ ;  ! decay.

90

Chapter 5.

-mediated decay search analysis

Table 5.6: Positron relative selection eciency
M [MeV]
10
15
20
25
( = 10ps) 69:7  1:3 71:4  1:5 72:9  1:6 74:0  2:1(
 = 100ps) 70:3  1:3 70:6  1:4 72:6  1:6 74:7  2:1++
ee =ee;! (%) ( = 1ns)
70:8  1:3 71:2  1:3 73:3  1:4 72:8  1:8
( = 10ns) 71:2  1:3 71:3  1:3 73:2  1:4 73:8  1:8
M [MeV]
30
35
40
45
( = 10ps) 72:0  2:5 73:5  3:5 69:1  5:2 81:2  10:9
( = 100ps) 70:3  2:4 73:6  3:4 63:5  4:4 67:3  8:2++
ee =ee;! (%) ( = 1ns)
73:7  2:2 80:9  3:2 78:2  4:9 93:2  10:6
( = 10ns) 73:9  2:2 82:9  3:2 75:1  4:5 97:2  10:7

5.4.6 Gamma-ray eciency
Gamma-ray eciency is de ned here as the probability that reconstruction of two gammarays satisfy following requirements.

 Position, energy and time t do not diverge and are successfully nished,p (u 1 u 2)2 + (v 1 v 2)2 > 20cm,
 ju j < 25cm ^ jv j < 71cm for each gamma-rays,
 E 2 > 10MeV (E 1 > E 2),
 E 1 + E 2 > 40MeV.
The result is summarized in Table 5.7.

Table 5.7: Gamma-ray eciency
M [MeV]101520( = 10ps) 58:3  0:8 59:9  1:0 61:5  1:2(
e;! (%)  = 100ps) 32:8  0:6 56:2  0:9 56:9  1:1( = 1ns)
10:4  0:3 22:5  0:5 29:5  0:6( = 10ns) 8:6  0:3 18:6  0:4 24:5  0:5
M [MeV]30
3540( = 10ps) 62:0  2:0 62:6  2:8 58:8  4:6(
e;! (%)  = 100ps) 61:3  1:9 59:8  2:6 61:9  4:0( = 1ns)
41:4  1:1 46:7  1:8 53:9  3:1( = 10ns) 35:8  1:0 41:7  1:5 43:1  2:4

25
60:8  1:5
59:5  1:4
36:4  0:8
29:7  0:7
45
60:0  8:4
67:2  7:6
57:0  6:2
54:5  5:7

Loss of the eciency stems from the requirement of the distance between interaction
positions of two gamma-rays. We can see from the Table 5.7 that eciency is smaller
for the case of smaller M , because of smaller angle between two gamma-rays. Longer
lifetime make the  decay vertex position to distribute near the detector , which also
makes the distance between incident positions of two gamma-rays smaller and makes theeciency smaller.

Section 5.4.

Normalization

91

5.4.7 Event selection eciency
De nition of analysis cuts is shown in Section 5.1 As we already estimated the e ect of
the acceptance cuts, gamma-ray energy cut, and cut for pileup search quality, we estimate
here the eciency for positron energy cut, cuts for  decay vertex t quality, and cut of
momentum and energy conservation. The result is summarized in Table 5.8.
As shown in the Figure 5.5{5.9 in Section 5.1, loss of eciency stems in the energy
loss of gamma-ray by shower escape.
In case that  is long or M is large, more gamma-rays are expected to enter thedetector with large incident angle , which are expected to be reconstructed with worse
resolutions.

Table 5.8: Cut eciency
M [MeV]1015( = 10ps) 43:8  0:9 47:0  1:2( = 100ps) 44:6  1:2 45:8  1:1
cute;! (%) ( = 1ns)
43:2  1:9 46:3  1:4
( = 10ns) 43:5  2:0 44:0  1:5
M [MeV]3035( = 10ps) 47:3  2:2 40:8  2:9( = 100ps) 45:1  2:1 43:8  2:9
cute;! (%) ( = 1ns)
33:5  1:6 29:9  2:0( = 10ns) 32:0  1:5 25:4  1:8

20
48:1  1:4
45:2  1:3
41:3  1:3
40:4  1:4
40
37:1  4:7
31:4  3:6
24:3  2:8
22:5  2:7

25
50:0  1:8
46:5  1:7
39:1  1:4
36:9  1:4
45
23:5  6:8
29:5  6:1
22:4  5:1
23:1  5:0

5.4.8 Gamma-ray trigger eciency
We changed trigger setting of gamma-ray energy selection three times during 2009 and2010; gamma-ray threshold is lowered a bit during 2009, gamma-ray energy online estimator is changed at the beginning of 2010, and cosmic ray veto threshold is raised earlyin 2010. For the convenience, we name here each period 2009a, 2009b, 2010a, and 2010b.
Total energy of two gamma-rays of + ! e+ ;  ! decay is larger than the caseof + ! e+ decay, so the trigger threshold which is aimed to trigger + ! e+ decay is
not a big problem, but cosmic-ray veto threshold except the period of latter part of 2010
can a ect if M is large.
Gamma-ray eciency curve of trigger for each period is made using 0 -55 MeV gammaray calibration data (Section 2.5.4) which is triggered with gamma-ray energy thresholdlower than that of trigger id = 0 without veto threshold. Although original energy of the
gamma-ray is xed approximately 55 and 83 MeV, some of the gamma-rays lose someenergy before entering the detector with reaction with the material of magnet and soon. Then, collected data contains gamma-ray events of various energies lower than 55
or 83 MeV. We record also the information used for trigger, so we can check how thetrigger setting works afterwards. The eciency curve histogram is obtained comparing
the reconstructed energy spectrum with and without trigger gamma-ray energy selection
settings. Figure 5.13 shows the obtained curve. Gamma-ray energy estimator of trigger
have worse resolution than that of the analysis, which makes this curve.

92

-mediated decay search analysis

Chapter 5.

∈γ , trg∈γ , trg

The eciency is estimated multiplying the histogram with energy spectrum of + !
+e ;  ! data which survived all the cuts. Eciencies for the period 2009a, 2009b,
2010a and 2010b are 79{88, 81{89, 86{96 and 91{97 % respectively.
0.9

0.9

0.8

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
40

50

60

0
40

70
80
Eγ normal [MeV]

50

1

1

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

0
40

50

60

(c) 2010a

70
80
Eγ normal [MeV](b) 2009b∈γ , trg∈γ , trg(a) 2009a

60

70
80
Eγ normal [MeV]

0
40

50

60

70
80
Eγ normal [MeV](d) 2010b

Figure 5.13: Trigger eciency of gamma-ray energy selection. E normal is a reconstructed total energy deposit in the LXe detector.

5.4.9 The number of measured Michel positrons
The number of Michel positrons is counted selecting its energy as described in Section
5.4.1. As mentioned in Section 5.4.8, there are four periods with di erent gamma-rayeciency. Then the number of measured Michel positrons is counted separately according
to the change of trigger setting of gamma-ray energy selection.
Table 5.9 shows the number of Michel positrons for each period.

Table 5.9: The number of measured Michel positronsM [MeV] 10, 15, 20 25
30
35
40
45
Ne in 2009a
10047
6208 4799 3091 1619 670
2009b
5627
3390 2738 1770 976 380
2010a
1179
684
550 321 155 57
2010b
29562
16493 11769 7172 3459 1287

Section 5.4.

Normalization

93

5.4.10 Systematic uncertainties
Systematic uncertainties mainly come from incompleteness of MC simulations and smearing. Systematic error is estimated adding following two components.

Gamma-ray detector eciency
As described in the Section 4.2.1, gamma-ray detector eciency is estimated to be
65 % in MC and 64-67 % in the experiment. We observe two gamma-rays, so squareof the di erence gives the e ect of the uncertainty of gamma-ray detector eciency.
The e ect is then estimated to be 6.2 %.
Detector resolutions and calibrations
Smearing factors and their uncertainties are discussed in the Chapter 4. E ect of
the uncertainties in the reproducibility of the resolutions and the calibrations are
estimated by adding the uncertainties to the smearing parameters and shifting thereconstructed values with uncertainties in mean. We estimate the normalization
factor for whole the period and compared the results with and without the additional smearing, changing scales, and shifting the reconstructed position with theuncertainty in the alignment.
Contribution of uncertainty in positron spectrometer performance is small because weuse relative eciency of  ! e e   and + ! e+ ;  ! by the MEG detector, andbehavior of positrons with approximately the same momentum are expected to be thesame. Systematic uncertainty stems the resolutions of the detectors and the eciency of
the gamma-ray detector, especially uncertainty in gamma-ray time reconstruction because
we assign large value for a conservative analysis.

5.4.11 Interpolation
We can now calculate the normalization factor k of each period combining the result of
the Section 5.4.1{5.4.8 according to the equation 5.6. We separate the estimation of theeciencies and acceptances to see each contribution, but in the analysis, we apply all theselection criteria at once, and use overall eciency. The normalization factor for all the
period (ktotal ) can be calculated by adding them as,

ktotal = k2009a + k2009b + k2010a + k2010b ;(5.7)

where k2009a and so on represent the normalization factor for each period. Then the
single event sensitivity for each period is obtained from the inverse of ktotal . 1=ktotal withstatistical error is shown in Figure 5.14.
We generate MC with a Interval of 5 MeV for M . Points in-between are interpolated
by tting nearest four points with exponential of third order polynomial function. We
also perform tting nearest three points with exponential of second order polynomial
function, and the di erence is taken as systematic error of interpolation. An example ofthe interpolation is shown in Figure 5.15.

94

-mediated decay search analysis

10-8

1/ktotal

1/ktotal

Chapter 5.

10-9
-9

10

10-10

10-10

10-11

10-11
10

20

30

40
Mφ [MeV]

10

30

40
Mφ [MeV](b)  = 100ps
1/ktotal

1/ktotal(a)  = 10ps

20

10-9

10-9
10-10

10

20

30

10-10

40
Mφ [MeV](c)  = 1ns

10

20

30

40
Mφ [MeV](d)  = 10ns

1/ktotal

Figure 5.14: 1=ktotal with statistical error for each lifetime and mass of .

10-10

10

15

20

25
Mφ [MeV]Figure 5.15: An example of interpolation. Red and blue lines are exponential of 2nd
and 3rd polynomial function respectively. The region M  17 [MeV] is interpolated withblue line in this case. The di erence between blue and red is counted as systematic error.

Section 5.5.

Upper bounds on the branching ratio

95

5.4.12 Single event sensitivity

1/ktotal

The result of the estimation of the single event sensitivity (= 1=ktotal ) is summarized in
the Figure 5.16 and the values are listed in Table A.1{A.4. Systematic errors of the casewith M = 10; 15; : : : ; 45 MeV are the sum of the two components described in Section
5.4.10 ; 6.2 % from uncertainty in gamma-ray detector eciency, and the other from thee ect of uncertainty in resolutions and calibrations.
For the interpolated points, bigger value of the sum of statistical and systematic errorsof the nearest two points is assigned as systematic error. The sum of this systematic error
and the error for interpolation is counted as the total systematic error in the nal analysis.
10-8τφ = 10 psec
τφ = 100 psec
τφ = 1 nsec
τφ = 10 nsec

10-9

10-10

10-11
10

20

30

40
Mφ [MeV]Figure 5.16: 1=ktotal v.s. M for each  settings. The error bar shows the sum ofsystematic error and statistic error.

5.5

Upper bounds on the branching ratio

To extract the 90% con dence level interval (C.I.) of branching ratio, Rolke's method[69] is adopted. Con dence intervals can be extracted nding the points where the 2log
likelihood function increases by a factor de ned by the required con dence level in ln L +1=2 method, which used to be used widely in high energy physics. This method is basedon large-sample theory, and it has under-coverage in certain circumstances, but it can beadapted to treat problems with several nuisance parameters which are not known exactly.
Rolke's method combine the ln L +1=2 method with the pro le likelihood method in which
the multi-dimensional likelihood function is reduced to a function that only depends on
the parameter of prime interest. The method is generalized to the problem of a signal
with a Poisson distribution, a background with either a Poisson or a Gaussian distribution
and an eciency with either a Binomial or a Gaussian distribution. It is examined tohave very good coverage even in cases when the parameters lie close or at the physicalboundaries.

96

Chapter 5.

-mediated decay search analysis

B(µ→ e φ,φ→ γ γ ) upper limit

In this thesis, we treat expected backgrounds in the signal region and overall eciency
as Gaussian distributions. Background events are classi ed to three types from the time
structure as described in Section 5.3. The number of each types of backgrounds are
estimated from three types of time sidebands; category (A), (B), and (C). Then the
expected number of backgrounds in the signal region is calculated with equation 5.1 and5.2. Error of the expected background is estimated adding Poisson errors of the number ofobserved event in (A), (B) and (C) quadratically normalizing with time width. Although
it is exact to treat the expected backgrounds as a sum of three Poisson distribution, we
treat it as a Gaussian distribution because of o ered option of Rolke's method. We also
tried backgrounds with a Poisson distribution with a Poisson error equal to the estimatedone, and the di erence is estimated to be much smaller than 1%. Therefore the e ect of
the background distribution shape is expected to be negligible.
The result is shown in the Figure 5.17 and the values are listed in Table B.1. The
result of the number of the signal events was consistent with 0, and we only get the upper
limit for the branching ratio of + ! e+ ;  !
decay. When the lifetime of  is 10
psec,  travels only a few mm, and di erence of the eciency is expected to be very small.
Therefore the result of the case  = 10 psec is expected to be valid for shorter lifetime,
too. However, if the life time is too short and   M does not hold, we can not assume
+ ! e+ ;  ! mode as on-shell process. This result does not hold in this case.
When the mass of  is smaller than  25 MeV and its lifetime is shorter than 1 ns,
we get the upper limit of the order of 10 11 . Obtained upper limits are better than the
expected upper limit from the Crystal Box which is estimated in Section 1.2.2 when M <30{40 MeV.

10-6

τφ = 10 psec
τφ = 100 psec
τφ = 1 nsec
τφ = 10 nsec

10-7
10-8
10-9
10-10
10-11
10

20

30

40
Mφ [MeV]Figure 5.17: Upper Limit of B(+ ! e+ ;  ! ) at grid points of M and  (90%C.L.).Solid black line with blank marker is upper limit from Crystal Box experimentestimated in Section 1.2.2. Marker color represent lifetime of . Red points are expected
to be valid for shorter lifetime as long as   M holds.

Section 5.5.

Upper bounds on the branching ratio

97

From the obtained upper bounds, we can obtain constraints for e . Equation 1.6 canbe calculated as follows,pjej  B( !

vuu) ' tB( ! e;  !

)  1:7  10 7 = 1



 !2
M 2
:
M

(5.8)

|λ µ e| B(φ→ γ γ )The result is shown in Figure 5.18.

τφ = 10 psec
τφ = 100 psec
τφ = 1 nsec
τφ = 10 nsec

10-7

10-8

10-9
10

20

p
Figure 5.18: Upper Limit of je j B( !
.

30

40
Mφ [MeV]) at grid points of M and  (90% C.L.).

98

Chapter 5.

-mediated decay search analysis

Chapter 6
Conclusion
A rst search for a new light neutral particle , which causes lepton avor violating(LFV) muon decay and decays into a pair of photons, + ! e+ ;  ! , was performedby the MEG experiment. The experiment is designed to search for another LFV decay,
+ ! e+ , and collect gamma-ray and positron signals from muon decays with a novel
gamma-ray detector and a positron spectrometer. Although the detectors and trigger
settings are not optimized to detect other decay modes, we have good detection eciency
for + ! e+ ;  ! mode when the mass of  is small.
We assume  to be a (pesudo)scalar particle with long lifetime and small mass, which
decays into gamma-ray pair isotropically in the rest frame of itself. The search was
performed using data taken in 2009 and 2010, which corresponds to 1:8  1014 muon stopin the target.
The + ! e+ ;  !
decay was not detected and we set upper limit on the
branching ratio of it for various mass values 10{45 MeV and lifetimes  10 ns. Obtained
upper limits are better than the expected constraints from the bound on generic + !
e+ set by the Crystal Box experiment [19] when  is lighter than 25{40 MeV. The
upper limits are about the order of 10 11 when 10  M  26 MeV and   1 ns. Thisestablished the most stringent limits on cLFV decay mediated by , which decays into
two photons.
The sensitivity is now limited by statistics, so we can expect improvement collecting
more data. In 2011 the MEG experiment collected about the same statistics as the sum of
2009 and 2010, and we are planning to collect data until 2013. The sensitivity is expected
to improve approximately by a factor of 3 using all the data taken from 2009 to 2013.

99

100

Chapter 6.

Conclusion

Appendix A
Normalization Factor
Values of normalization factor and their errors are listed in Table A.1{ A.4.

101

102

Chapter A.

M [MeV]
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45

Normalization Factor

Table A.1: Normalization factor for  = 10 ps
1=ktotalstatistical error systematic error error of interpolation
12
4:09  10
2:2%
10:8%
12
4:58  10
14:5%
0:7%
5:17  10 12
14:5%
0:9%
12
5:88  10
14:5%
0:8%
12
6:74  10
14:5%
0:4%
7:75  10 12 2:4%
12:1%
8:96  10 12
16:5%
0:4%
1:04  10 11
16:5%
0:8%
11
1:21  10
16:5%
0:8%
11
16:5%
0:4%
1:40  10
1:63  10 11 2:7%
13:8%
1:88  10 11
16:5%
0:2%
11
2:20  10
16:5%
0:4%
2:49  10 11
16:5%
0:4%
11
2:86  10
16:5%
0:2%
3:30  10 11 3:3%
10:4%
3:76  10 11
14:8%
1:4%
11
4:30  10
14:8%
2:6%
4:97  10 11
14:8%
2:5%
11
5:81  10
14:8%
1:4%
6:91  10 11 4:1%
10:7%
8:57  10 11
23:4%
1:0%
10
1:08  10
23:4%
1:8%
1:38  10 10
23:4%
1:8%
10
1:79  10
23:4%
1:0%
2:34  10 10 5:8%
17:6%
3:00  10 10
23:4%
1:8%
10
3:87  10
23:4%
3:2%
5:09  10 10
23:4%
3:1%
10
6:81  10
23:4%
1:8%
10
9:35  10
9:7%
11:5%
1:32  10 9
27:4%
1:8%
9
1:93  10
27:4%
3:2%
2:93  10 9
27:4%
3:7%
9
4:63  10
27:4%
2:7%
9
7:68  10
20:7%
6:7%

Chapter A.

M [MeV]
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45

Normalization Factor

103

Table A.2: Normalization factor for  = 100 ps
1=ktotalstatistical error systematic error error of interpolation
12
5:46  10
2:5%
11:2%
12
5:10  10
13:7%
3:7%
5:02  10 12
13:7%
5:0%
12
5:16  10
13:7%
4:4%
12
5:53  10
13:7%
2:5%
6:12  10 12 2:3%
10:4%
6:96  10 12
14:4%
2:4%
8:08  10 12
14:4%
4:2%
12
9:53  10
14:4%
4:4%
11
14:4%
2:5%
1:13  10
1:35  10 11 2:7%
11:7%
1:56  10 11
14:4%
0:5%
11
1:80  10
14:4%
0:9%
2:07  10 11
14:4%
0:9%
11
2:39  10
14:4%
0:5%
2:75  10 11 3:3%
8:9%
3:18  10 11
20:7%
0:6%
11
3:70  10
20:7%
1:1%
4:33  10 11
20:7%
1:1%
11
5:11  10
20:7%
0:6%
6:09  10 11 4:0%
16:7%
7:40  10 11
25:9%
0:5%
11
9:10  10
25:9%
0:8%
1:13  10 10
25:9%
0:8%
10
1:41  10
25:9%
0:5%
1:77  10 10 5:4%
20:5%
2:20  10 10
30:4%
1:3%
10
2:75  10
30:4%
2:3%
3:48  10 10
30:4%
2:3%
10
4:47  10
30:4%
1:3%
10
5:84  10
8:9%
21:5%
7:81  10 10
32:6%
1:3%
9
1:07  10
32:6%
2:3%
1:51  10 9
32:6%
2:7%
9
2:19  10
32:6%
2:0%
9
3:30  10
15:7%
16:9%

104

Chapter A.

M [MeV]
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45

Normalization Factor

Table A.3: Normalization factor for  = 1 ns
1=ktotalstatistical error systematic error error of interpolation
11
3:48  10
3:6%
9:6%
11
2:60  10
14:8%
4:1%
2:08  10 11
14:8%
5:5%
11
1:76  10
14:8%
4:8%
11
1:56  10
14:8%
2:7%
1:46  10 11 2:8%
12:0%
1:41  10 11
15:7%
2:6%
1:40  10 11
15:7%
4:5%
11
1:43  10
15:7%
4:8%
11
15:7%
2:7%
1:49  10
1:56  10 11 2:8%
12:9%
1:59  10 11
15:7%
1:0%
11
1:63  10
15:7%
1:7%
1:69  10 11
15:7%
1:7%
11
1:77  10
15:7%
1:0%
1:88  10 11 3:1%
12:3%
2:05  10 11
19:7%
0:02%
11
2:27  10
19:7%
0:04%
2:55  10 11
19:7%
0:04%
11
2:92  10
19:7%
0:02%
3:40  10 11 3:9%
15:8%
4:05  10 11
24:5%
0:8%
11
4:89  10
24:5%
1:4%
5:98  10 11
24:5%
1:4%
11
7:39  10
24:5%
0:8%
9:20  10 11 5:3%
19:2%
1:13  10 10
31:7%
1:2%
10
1:40  10
31:7%
2:2%
1:75  10 10
31:7%
2:1%
10
2:23  10
31:7%
1:2%
10
2:90  10
8:6%
23:1%
3:84  10 10
31:7%
1:2%
10
5:21  10
31:7%
2:2%
7:27  10 10
31:7%
2:5%
9
1:05  10
31:7%
1:9%
9
1:56  10
16:6%
8:0%

Chapter A.

M [MeV]
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45

Normalization Factor

105

Table A.4: Normalization factor for  = 10 ns
1=ktotalstatistical error systematic error error of interpolation
10
3:39  10
4:4%
8:6%
10
2:51  10
14:6%
3:1%
1:96  10 10
14:6%
4:2%
10
1:62  10
14:6%
3:7%
10
1:39  10
14:6%
2:1%
1:25  10 10 3:5%
11:1%
1:16  10 10
14:6%
2:0%
1:11  10 10
14:6%
3:5%
10
1:09  10
14:6%
3:7%
10
14:6%
2:1%
1:09  10
1:11  10 10 3:5%
9:9%
1:11  10 10
15:0%
0:1%
10
1:13  10
15:0%
0:2%
1:15  10 10
15:0%
0:2%
10
1:19  10
15:0%
0:1%
1:25  10 10 3:8%
11:2%
1:31  10 10
18:2%
0:5%
10
1:40  10
18:2%
0:8%
1:51  10 10
18:2%
0:8%
10
1:65  10
18:2%
0:5%
1:84  10 10 4:4%
13:8%
2:12  10 10
18:2%
1:2%
10
2:47  10
18:2%
2:1%
2:91  10 10
18:2%
2:1%
10
3:46  10
18:2%
1:2%
4:14  10 10 6:0%
8:8%
4:84  10 10
18:3%
1:1%
10
5:69  10
18:3%
1:9%
6:73  10 10
18:3%
1:9%
10
8:04  10
18:3%
1:1%
10
9:73  10
9:2%
9:1%
1:20  10 9
45:1%
1:1%
9
1:49  10
45:1%
1:9%
1:91  10 9
45:1%
2:2%
9
2:49  10
45:1%
1:6%
9
3:34  10
16:2%
28:9%

106

Chapter A.

Normalization Factor

Appendix B
Upper limits for each set of massand lifetime values
Values of upper limit are listed in Table B.1.

107

108

Chapter B.

Upper limits for each set of mass and lifetime values

Table B.1: Estimated upper limit for each M and M [MeV]  = 10ps
100ps
1ns
10 ns
12
12
11
10
3:8  10
5:1  10
3:2  10
3:1  10 10
1:9  10 11 2:2  10 11 1:1  10 10 1:1  10 09
11
12
2:4  10 11 2:3  10 11 9:7  10 11 9:1  10 10
2:7  10 11 2:4  10 11 8:2  10 11 7:5  10 10
13
14
3:1  10 11 2:5  10 11 7:2  10 11 6:4  10 10
15
2:3  10 11 1:8  10 11 4:4  10 11 3:8  10 10
16
1:1  10 11 8:9  10 12 1:8  10 11 1:5  10 10
1:1  10 11 8:8  10 12 1:5  10 11 1:2  10 10
1718
1:3  10 11 1:0  10 11 1:6  10 11 1:2  10 1019
1:5  10 11 1:2  10 11 1:6  10 11 1:2  10 1020
4:9  10 11 4:1  10 11 4:7  10 11 3:3  10 1021
5:3  10 11 4:4  10 11 4:5  10 11 3:1  10 1022
6:1  10 11 5:1  10 11 4:7  10 11 3:2  10 1023
8:0  10 11 6:6  10 11 5:5  10 11 3:7  10 1024
4:7  10 11 3:9  10 11 2:9  10 11 2:0  10 1025
5:4  10 11 4:5  10 11 3:1  10 11 2:1  10 1026
6:2  10 11 5:3  10 11 3:4  10 11 2:2  10 10
3:1  10 10 2:8  10 10 1:7  10 10 1:0  10 927
28
3:6  10 10 3:2  10 10 1:9  10 10 1:1  10 929
4:2  10 10 3:8  10 10 2:1  10 10 1:2  10 930
4:9  10 10 4:5  10 10 2:5  10 10 1:3  10 931
6:5  10 10 5:7  10 10 3:1  10 10 1:6  10 932
8:1  10 10 6:9  10 10 3:7  10 10 1:8  10 933
9:9  10 10 8:7  10 10 4:6  10 10 2:1  10 934
1:4  10 9 1:1  10 9 5:9  10 10 2:7  10 935
1:9  10 9 1:4  10 9 7:4  10 10 3:1  10 936
2:4  10 9 1:9  10 9 9:9  10 10 3:8  10 937
3:2  10 9 2:4  10 9 1:2  10 9 4:4  10 938
4:1  10 9 3:0  10 9 1:5  10 9 5:2  10 939
5:4  10 9 3:8  10 9 1:9  10 9 6:2  10 940
7:3  10 9 4:9  10 9 2:5  10 9 7:4  10 941
1:1  10 8 6:9  10 9 3:3  10 9 1:4  10 842
1:6  10 8 9:6  10 9 4:6  10 9 1:9  10 843
2:5  10 8 1:4  10 8 6:5  10 9 2:4  10 844
3:9  10 8 2:0  10 8 9:3  10 9 3:1  10 845
6:3  10 8 2:9  10 8 1:3  10 8 3:9  10 8

Acknowledgment
The MEG experiment is a project performed by a collaboration of University of Tokyo,
KEK, Waseda University, Paul Scherrer Institut, INFN and Pisa, University of Genova,
University of Pavia, University Rome Sapienza, University of Lecce, BINP Novosibirsk,
JINR Dubna and University of California Irvine. Research and development works took
over a decade, and we started taking physics data from 2008. This work could be nishedwith many helps and e orts by the MEG collaborators.
I am deeply grateful to my supervisor, Prof. Toshinori Mori who provided carefully
considered feedback and valuable comments. He is one of the spokespersons of the MEG
collaboration and gave me chances to work for the MEG experiment.
I am thankful to Prof. Satoshi Mihara, who accepted me as co-operative researcher of
KEK after I left the University of Tokyo. His daily guide was hard, but indispensable tonish this work.
During my research in PSI, I get ill and supports from Japanese collaborators wasvery grateful. Especially I can not thank enough for Prof. Wataru Ootani's help when I
stayed in a hospital in Baden, Switzerland. I want to thank his suggestion to study about
generic + ! e+ decay, which was starting of this work.
I would like to express my gratitude to Prof. Toshiyuki Iwamoto, Dr. Ryu Sawada
and Dr. Yusuke Uchiyama, who worked together in the same oce room. Their opinions
and information have helped me very much throughout the production of this study.
I would also like to thank Dr. Hajime Nishiguchi, Mr. Yuki Fujii, Dr. Elisabetta
Baracchini, Dr. Cecilia Voena and Dr. Francesco Renga for giving me informations
about analysis of the positron spectrometer. I appreciate Dr. Marco Grassi, Dr. Donato
Nicolo and Dr. Luca Galli for useful informations about trigger system. I would like toexpress my appreciation to Dr. Stefan Ritt, Dr. Peter R. Kettle, Dr. Malte Hildebrandt
for supporting me in PSI. I appreciate Dr. Yasuhiro Nishimura, Dr. Shuei Yamada,
Dr. Yasuko Hisamatsu, Dr. Kenji Ozone, Prof. Akihiro Maki, Prof. Tom Haruyama,
Mr. Katsuyu Kasami, Ms. Bai Xue, Mr. Daisuke Kaneko and Ms. Miki Nishimura forgiving me valuable advices and pleasant research time. I thank Dr. Giovanni Signorelli,
Dr. Angela Papa, Mr. Emanuele Ripiccini, Dr. Paolo W. Cattaneo for meaningful
discussions.
I would also like to express my gratitude to my family for their support and warm
encouragements.

109

110

Acknowledgment

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