Calibration of Photomultipliers of the
MEG LXe Detector
Xue Bai
Feb 2009

Abstract
The MEG experiment aims at discovering the lepton flavor violating decay ofmuon. One of the most important devices in MEG experiment is liquid xenon
γ-ray detector. Equipped with 846 PMTs submerged in 880 liters of liquid
xenon, it provides a precise way to detect the γ-rays produced from decay. The
key to find such lepton flavor violating process with a branching ratio up to
10−13 , is a full understanding and improvement of the detector performance.
Through various ways such as radiative decay, π0 decay, alpha, LED etc., wecalibrate the xenon detector to better understand its sensitivity and find waysof improvement. One of the significant tasks is the measurement of quantum
efficiency, which is not only an important monitor of PMT performance, butalso an indispensable tool for other calibrations. A precise measurement willlead to the enhancement of detector sensitivity. The current accuracy is around
2.8%. The uncertainty of such measurement is mainly due to inconsistency withsimulation, i.e., our lack of knowledge of the properties of liquid xenon. Aftercomparing data with results of simulation, it was concluded that the Rayleighscattering length might be much longer than originally thought, at close to85cm.

Contents
1 Physics Motivation
1.1 Lepton Flavor Violation . . . . . . . . . . . . . . . . . . . . . . .
1.2 Supersymmetry and Standard Model . . . . . . . . . . . . . . . .
1.2.1 SU(5) Supersymmetric Grand Unified Theory . . . . . . .
1.2.2 MSSM with Right-Handed Neutrino . . . . . . . . . . . .
1.3 µ → eγ search experiments . . . . . . . . . . . . . . . . . . . . .

3
3
3
4
5
5

2 The MEG Experiment
2.1 Beam and Target . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Positron Spectrometer . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 COBRA Magnet . . . . . . . . . . . . . . . . . . . . . . .
2.2.2 Drift Chamber . . . . . . . . . . . . . . . . . . . . . . . .
2.2.3 Timing Counter . . . . . . . . . . . . . . . . . . . . . . .
2.3 Liquid Xenon Detector . . . . . . . . . . . . . . . . . . . . . . . .
2.3.1 Liquid Xenon Scintillator . . . . . . . . . . . . . . . . . .
2.3.2 Mechanism of Scintillation Light . . . . . . . . . . . . . .
2.3.3 Photomultiplier . . . . . . . . . . . . . . . . . . . . . . . .
2.3.4 Detection Concept . . . . . . . . . . . . . . . . . . . . . .
2.3.5 The Xenon System . . . . . . . . . . . . . . . . . . . . . .
2.4 Background and Sensitivity . . . . . . . . . . . . . . . . . . . . .

7
9
9
9
11
12
14
15
16
18
20
23
27

3 PMT Calibration
30
3.1 Gain Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.1.1 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.1.2 Accuracy and Stability . . . . . . . . . . . . . . . . . . . . 33
3.2 QE Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.2.1 Alpha sources . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.2.2 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.2.3 Accuracy and stability . . . . . . . . . . . . . . . . . . . . 40
3.2.4 Application of QE correction . . . . . . . . . . . . . . . . 41
4 Study on improving accuracy of QE measurement44
4.1 Determining Factors . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.2 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.3 Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
5 Conclusion

52

1

Introduction
One of the greatest success of the twentieth century physics is the establishmentof the Standard Model, which explains the interactions of fundamental particles
and has successfully predicted the outcome of a large variety of experimentsthat have been carried out. However, there are limitations to it and physicists
around the world are motivated to search for new physics beyond the Standard
Model.
One effective method for such a challenging quest lies within Lepton Flavor
Violation. The MEG experiment aims at discovering a lepton-flavor-violating
decay with a sensitivity of 10−13 . Recent theoretical studies on theories such
as SUSY-GUT suggest that occurs with a decay branching ratio around 10−14 .
Therefore there is a good chance of discovery with MEG.
To make a discovery of such a rare reaction, we need detectors with extremely
high sensitivity. One of the most important devices in this experiment is liquid
xenon detector for detecting gamma rays. Comprised with 846 photomultipliertubes (PMTs) submerged in 800l liquid xenon, it is a novel detector and provides
a high sensitivity. Operating PMTs in such an environment is difficult andchallenging, and studies on performances of PMTs in liquid xenon are of great
importance. One of the properties of PMTs is quantum efficiency (QE) and an
accurate measurement is needed in order to better understand the detector andto improve its performance.
In this thesis, calibrations of liquid xenon detector, in particular, measurement of QE and its accuracy is discussed. In Chapter 1, the physics motivationof the MEG experiment is discussed and an overview of the MEG experimentis described in Chapter 2. Chapter 3 explains the method of PMT calibration,in particular, how to measure QE and its significance to the experiment, while
the details of improving QE measurement are discussed in Chapter 4. The
conclusion is written in Chapter 5.

2Chapter 1

Physics Motivation
1.1

Lepton Flavor Violation

In the minimal Standard Model, neutrinos are assumed to be in one helicity
state and hence considered to be massless. This assumption causes the conservation of lepton flavor. So all lepton flavor violating processes, such as µ → eγ
and τ → µγ, are strictly forbidden.
With the introduction of neutrino mass, lepton flavor violating process canoccur at a unmeasurably small branching ratio (O(10−40 )). However, in theories such as SUSY-GUT, LFV is predicted to be at a measurable level thatis quite close to the current experimental limit. Therefore LFV process suchas µ+ → e+ γ is a promising method to testify theories like SUSY-GUT and a
gateway to new physics beyond the Standard Model.

1.2Supersymmetry and Standard Model

In Standard Model, the interaction between fermions are mediated by gaugebosons W ± , Z 0 and electroweak sector, and the interaction between quarks are
mediated by gluons of the strong sector. The electroweak sector is described
by SU (2) ⊗ U (1) symmetry, while the strong sector is described by SU (3) color
symmetry. Such framework has been in great agreement with experiment. However, when one attempts to unify the electroweak and strong interactions at highunification energy (EGU T ∼ 1016 ), difficulties arise, which is called the hierarchy
problem. Assuming that Higgs mass is around electroweak scale, there would
have to be an incredible fine-tuning cancellation between the quadratic radiative
corrections and the bare mass for the Standard Model to apply at GUT scale.
An elegant solution of the hierarchy problem is the introduction of supersymmetry, which is a symmetry that relates fermions and bosons. A generator of supersymmetry is an operator which transforms a bosonic state into a fermionic state,
and vice versa. The simplest way of incorporating supersymmetry into Standard Model (Minimal Supersymmetric Standard Model) introduces one particle
that differs by half a unit of spin to each existing fundamental particle. Thesepairs, or supermultiplets, consist of both fermionic and bosonic states, which are3known as superpartners of each other. Supersymmetry reduces the size of thequantum corrections of Higgs mass by having automatic cancellations between
fermionic and bosonic Higgs interactions and thus solve the hierarchy problem.
With regards to µ → eγ, the introduction of supersymmetry enhances thebranching ratio significantly by bringing additional sources of flavor mixing
from sleptons. The branching ratio predicted by either of the following models
is reachable by experiments.

1.2.1

SU(5) Supersymmetric Grand Unified Theory

In order to unify strong interaction and electroweak interaction, a single groupthat embeds bothSU (2) ⊗ U (1) electroweak symmetry and SU (3) color symmetry. The simplest of such groups is SU (5) which is spontaneously broken atvery high energy scales. In SU (5)SUSY-GUT, leptons are quarks belong to thesame multiplets and slepton mixing at GUT scale occurs naturally. The LFVprocess, µ+ → e+ γ, is thus enhanced through loop diagrams shown in Fig.1-1.
SU (5)SUSY-GUT only allows LFV through right-handed sleptons. The predicted branching ratio is shown in Fig 1-2.

Figure 1.1: Feynman diagrams of µ+ → e+ γ in SU(5)SUSY-GUT

Figure 1.2: Predicted branching ratio of µ+ → e+ γ in SU(5)SUSY-GUT

4

1.2.2MSSM with Right-Handed Neutrino

To explain to small mass of neutrinos, the seesaw mechanism introduces a heavy
right-handed neutrino into the Standard Model, which also relates to LFV process. The branching ratio in this scenario depends on the Majoron mass of theright-handed neutrino. In fig1-3, the branching ratio of µ+ → e+ γ in MSSR
with right-handed neutrino in the case of MSW large angle solution, a possible
solution to solar neutrino mixing.

Figure 1.3: Branching ratio of µ+ → e+ γ according to MSSMRN in the caseof MSW large angle solution. The three lines represent where tanβ = 30.10, 3
respectively.

1.3µ → eγ search experiments

As discussed above, µ+ → e+ γ decay is a way to examine many interesting
theories beyond the SM in physics such as super-symmetry and its breaking
mechanism, GUT theory and the origin of neutrino mass. Thus many experiments have been conducted so far. The major experiments are listed below.

5The current limit is set by MEGA.

Year
1977
1977
1979
1986
1999

Experiment

Site
SIN(presently PSI)TRIUMF
Crystal Box
MEGA

LANL
LANL
LANL

Upper Limit
1.0 × 10−9
3.6 × 10−9
1.7|times10−10
4.9 × 10−11
1.2 × 10−11

Reference[6,7][8][9,10][11][5]

Table 1.1: Branching ratio of major µ+ → e+ γ experiments in the past years

6Chapter 2

The MEG Experiment
The MEG experiment takes place at Paul Scherrer Institut (PSI) in Switzerland.
In order to reduce background events, precise measurement of energy, emission
angle and time of positron and gamma are very important.

Figure 2.1: An event display during MEG physics run. Reconstructed hits andtracks are shown.

7

The detectors of MEG consist of positron detector and gamma-ray detector,
for the detection of the two products of µ+ → e+ γ, respectively. The cut viewof the detectors is shown in Figure 2.2.

Figure 2.2: Schematic view of MEG detectors

8

2.1

Beam and Target

For muon beam, the πE5 beam line at PSI, the most intense DC beam in theworld with an intensity of 2 × 108 µ+ /s is used. A surface muon beam is produced from pion decays on the surface of the production target.
Muons are transported to the stopping target through Triplet I (quadrupole
triplet), a Wien filter, Triplet II (quadrupole triplet) and a beam transportsolenoid(BTS). The target is a polyethylene/polyester sandwich foil supported
by a Rohacell frame. The target is in an ellipse shape (Figure 2.3) and put at aslant angle of 20.5◦ in the middle of the COBRA magnet, as shown in Figure 2.4.

Figure 2.3: A picture of the stopping target.

2.2

Positron Spectrometer

The positron spectrometer consists of a magnet specially designed to form a
gradient field, a drift chamber system to measure the positron momentum andscintillation counters to measure the positron timing.

2.2.1

COBRA Magnet

A COBRA (COnstant Bending RAdius) magnet is used to produce a gradient
field. Compared with a simple uniform solenoidal field, it has the following advantages:• Positrons are swept away much more quickly, which contributes to theminimization of backgrounds.
• The positrons follow trajectories with a constant projected bending radius
independent of the emission angle. This allows us to define the absolute
momentum window of positrons to be detected.

9Figure 2.4: (a)Muon beam carried to target inside the COBRA magnet by theBeam Transport Solenoid (BTS). (b)COBRA magnet.

Figure 2.5: Comparison between uniform and gradient magnetic field.

102.2.2Drift Chamber

Positron tracks are measured by a drift chamber system consisted of 16 chamber
sectors aligned radially at 10 intervals in azimuthal angle. Each sector is madeup from 2 staggered arrays of drift cells which measure the time and r-coordinateof positrons simultaneously. The chamber walls are made of thin plastic foils.
A thin layer of aluminum deposit on the four cathode foils is shaped to makea Vernier pattern. By comparison of the charges induced on the two sets ofVernier pads of each cell, it is possible to determine the z position with an accuracy of about 300µm.
The chamber sectors and the volumes between them are filled with 50%He
50%C2 H6 gas mixture at 1 atm, in order to minimize multiple Coulomb scattering of tracks.

Figure 2.6: Schematic view of the drift chamber system.

Figure 2.7: Cross view of the drift chamber and reading from Vernier pads.

11

2.2.3

Timing Counter

The positron timing is measured by timing counter, which consists of two arraysof scintillation hodoscopes (composed of ∼ 5cm wide scintillator bars) orthogonally placed along the φ and z directions, respectively. The outer layer will be
used for timing measurement while the inner one will serve mainly for triggering
purposes.
φ counters are straight plastic scintillatior bars lying along z direction as shownin Figure 2.8. Two inch fine-mesh PMTs are attached to both ends. While a z
counter is a curved scintillation fiber put perpendicular to φ counters as shownin Figure 2.9. The timing resolution is expected to be 100ps FWHM.

Figure 2.8: A picture of timing counters (φ-measuring counters).

12Figure 2.9: A picture of timing counters (z-measuring counters). 256 curved
scintillators are put on top of φ-measuring counters. Also seen are the attachedreadout cards.

13

2.3

Liquid Xenon Detector

The gamma ray detector for the MEG experiment is a liquid xenon scintillation
detector that is a 0.8 m3 volume of liquid Xe viewed by arrays of 846 photomultipliers (PMTs) from all side. A schematic view of the detector is shown in
Figure 2.10. Definition of six faces of the PMT holders (inner, outer, upstream,
downstream, top, bottom) are shown in the figure. The PMTs are immersedin the liquid xenon to observe scintillation light directly. Gamma rays from thetarget enter the detector through an entrance window consisting of an aluminumhoneycomb and carbon fiber plates. Then a gamma ray interacts with the liquid
xenon and deposit energy to excite xenon molecules, resulting in emission of alarge amount of scintillation light.

Figure 2.10: Schematic view of the MEG gamma ray detector. (a) Side view.
(b) Top view.

142.3.1Liquid Xenon Scintillator

The characteristics of liquid xenon as scintillator has been studied for a longtime , but rarely has it been used in such a great volume before due to thedifficulties of handling. There are many advantages of using liquid xenon as a
scintillator:• High light yield• Fast signal• Large proton number• Uniformity

Figure 2.11: Typical waveforms of LXe and NaI(Tl) from 320keV γ rays. It isclear that liquid xenon has a much faster response compared to NaI.
These properties of liquid xenon have the benefits of :• increasing statistics and thus enhancing resolution• good time resolution and reduction of pile-up effects• enablement of construction of large homogeneous detectors with a large
acceptanceOn the other hand, using liquid xenon also has some complications:• vacuum ultraviolet light(VUV)• low temperature(165K)• high purity required• high costs
The properties of liquid xenon are shown in Table 2.1.

15

Material Properties
Atomic Number
Atomic Weight
Density at 161.35K
Boiling Point
Melting Point
Triple Point(temperature)
Triple Point(pressure)
Triple Point(density)
Radiation Length
Critical Energy
Mollier Radius
Scinti. Wavelength(peak±FWHM)
Refractive Index at 175nm
Wph for electron
Wph for α particles
Decay Time (recombination)
Decay Time (fast components)
Decay Time (slow components)
Absorption Length

Value & Unit54
131.292.98g/cm3
165K
161K
161K
0.805atm
2.96g/cm3
2.77cm
10.5MeV4.1cm(178±14nm)
1.57 to 1.72
12.6eV
17.9eV
45ns
4.2ns
22ns
>100cmTable 2.1: Properties of Liquid Xenon

2.3.2

Mechanism of Scintillation Light

The origin of scintillation light from liquid xenon is de-excitation process of
excited dimers of xenon, Xe∗2 . Figure 3.1 shows scintillation signals of liquid
xenon by various particles. There are mainly two different processes for thede-excitation;
1.excitation process :Xe + Xe∗ → Xe∗2 → 2Xe + hν

(2.1)

2. recombination process :+∗∗Xe+ + Xe → Xe++ XeXe∗∗ → Xe∗
2 Xe2 + e → Xe

(2.2)

The wave length of the scintillation light emitted from both of these two processes are in the vacuum ultra-violet(VUV), 178nm(±FWHM), and the decay
time constant is relatively short, 45nsec in the recombination process.

16

Figure 2.12: Signal of liquid xenon scintillation.

17

2.3.3

Photomultiplier

We cooperated with R&D Hamamatsu Photonics and developed PMT R9288.
The photo-cathode material is K-ScSb. This is designed so that it can observe
scintillation light of liquid xenon directly while immersed in it. To achieve that,
the PMT has the following properties that are crucial to the experiment.

Detecting scintillation light from liquid xenon. A high sensitivity to VUVof 178nm wavelength thanks to the use of a quartz window that is 80%
transparent to the scintillation light.
Operational in liquid xenon. Stability at low temperature of 165K.
Ability to withstand pressure up to 0.2 MPa.
Little production of impurities.
Reduction of heat load from PMT base.
Short PMT length. In order to reduce thickness of front face as well as minimize the detector volume.
Operational under magnetic field. The use of metal channel dynode structure.
Good energy resolution. Keeping of QE at low temperature.
Good timing resolution. Fast response and little time transit spread (TTS).

Figure 2.13: Hamamatsu R9288. Aluminum strips are attached on the surfaceof cathode to avoid increasing of surface resistance in low temperature.

18

The circuit diagram is shown in Figure 2. and the properties of R9288 areshown in Table 2.2 .

Figure 2.14: Circuit diagram of R9288.

Size
Active Area Size
PMT Length
Photocathode Material
Dynode Type
Number of Dynodes
Typical HV
Typical Gain
Typical QE
Rise Time
Transit Time
TTS

57mm φ45mm φ32mm
K-Cs-Sb
Metal Channel
121000V
1 × 10615%
2.3nsec
16.5nsec Typ.
0.75nsec Typ.

Table 2.2: Properties of R9288

19

PMT Test
About 1000 PMTs were tested before installed into the liquid xenon detector. In
the test, gain at 800V of HV, QE and dark current were measured. Bad PMTs
(problems of base circuit, low gain or low QE) were repaired or eliminated. In
Figure 2.15 , measured gain and QE of currently installed PMTs are shown. To
make the response of the detector as uniform as possible, center part of the QE
distribution was chosen for inner face.

Figure 2.15: Measured gain and QE. Hatched part is PMTs used in inner face.

2.3.4

Detection Concept

Scintillation light from liquid xenon is detected by arrays of 845 PMTs locatedon all the walls of the calorimeter in the liquid without any transmission window. The detection principles are as following:• The interaction position of gamma rays are determined from the light
distribution observed by the PMTs.
• Energy is calculated by the light yield detected from all directions.
• The interaction time is determined by the timing information of pulses
from each PMT.
The solid angle is ∆Ω/4π ≈ 9%(0.08 < |cosθ| < 0.35, 120◦ in φ). The
distribution of PMTs on each surface is shown in Figure 2.18.

20

Figure 2.16: Light distribution of the PMTs.

Figure 2.17: (a) Shallow event. (b) Deep event.

21

Figure 2.18: Distribution of PMTs.

22

2.3.5The Xenon System

Cryostat
The cryostat is made of non-magnetic materials with low permeability. Deformation and stress of the cryostat was studied taking into account of the weightof liquid xenon. The cryostat has an inner and outer vessel. The volume between the two layers is evacuated and installed with super insulation layers.
Xenon is liquified by a pulse-tube refrigerator and a liquid nitrogen cooling pipe
equipped at the top of the cryostat. The liquid xenon is kept in a stable condition by the refrigerator. Another line of LN2 is attached on the outside of theinner vessel to directly cool the vessel. This is used mainly for pre-cooling of
the vessel before starting liquefaction.
Pictures of the second LN2 line is shown in Figure 2.19.

Figure 2.19: Liquid nitrogen pipe attached on inner vessel.

Handling of Xenon
The gamma ray detector for MEG uses around 1000 litters of liquid xenon andsince xenon is expensive and takes time to produce, the xenon system was designed to store the xenon not in use as well. Figure 2.20 shows a schematic viewof the xenon system of MEG. There are two types of storage. The GXe storage
consists of eight tanks with 250 litters of volumes each. And the LXe storage(1000L storage dewar) can store about 1000 litters of liquid xenon. A purification system is installed between these two to purify GXe when it is transferedto the LXe storage tank or to the detector.
For measuring the level of the LXe, a capacitance level-meter is installed.
The temperature of the xenon is measured by 27 pt-100 sensors located at various positions. Additional temperature sensors are attached on the outside of
the inner vessel to monitor temperature of the cryostat. All the cables from
PMTs and sensors installed in the inner vessel go to feedthroughs attached on
chimneys at the top of the detector.
A heated purication getter is equipped in the purication system. The purifier removes H2 O, O2 , CO, CO2 , H2 , N2 and hydro carbon molecules from GXe
23

Figure 2.20: Schematic view of the xenon line.
down to 1.0 ppb. Gas purication test with 100 liters of xenon. It was confirmedthat the impurities, mainly water, were successfully reduced, and an adequate
performance for the MEG photon detector could be achieved. However, purification in gas phase is relatively slow, hence it is not suitable for the final gamma
ray detector, which utilizes much more xenon. Therefore a purication systemwith circulation of xenon in liquid phase was developed. A similar system wasrstly tested by using the large prototype detector. And it was found that thesys- tem reduces amount of impurities from 250 ppb to less than 40 ppb in 5
hours operation for 100 litters of xenon. Figure 2.20 is a picture of the liquid
phase purifier equipped to the final detector. In the purifier vessel, centrifugal
pump and purier (moleculsar sieves) are installed. The system is connected withthe detector by vacuum insulated pipes to circulate xenon through the purier inliquid phase. The pump has a capability to flow xenon up to 71 liters per hour.
The speed is much faster than gas purication (60 c.c. liquid per hour).

24

Figure 2.21: Liquid phase purification system.

25

Figure 2.22: A picture of liquid xenon detector with the cryostat installed.

26

2.4

Background and Sensitivity

Sensitivity
The sensitivity of MEG experiment can be expressed by the following formula.

Br(µ+ → e+ γ) =1
1
· T · (Ω/4π) ×Nµe · γ · sel

(2.3)

where Nµ is the stopping rate of µ; T is time of measurement; Ω is solid
angle; e is the detection efficiency of positron; γ is the detection efficiency of
gamma ray, and sel is the efficiency of event selection.
The solid angle, positron and gamma detection efficiency and event selection
efficiency are estimated as 0.09, 90%, 40%, and 70% ,respectively.
Assuming the muon stopping rate to beNµ = 0.35 × 108 /s(2.4)

and time of measurement to be 2 years, then the expected branching ratio is:Br(µ+ → e+ γ) = 3.1 × 10−14
These sensitivities can be converted to 90% confidence level upper limits, incase of no signal observed, by using the background rate estimates in the following section. The upper limits we obtain for the 108 /s muon beam intensity
is ,1.7 × 10−13 .
The estimated sensitivity of MEG detectors are shown in Table 2.3.
Gamma Energy(%)
Gamma Timing(nsec)
Gamma Position(mm)Positron Energy(%)
Positron Timing(nsec)
Positron Position(mrad)

6
0.15
9
0.9
0.1
10.5

Table 2.3:

Background
There are mainly two types of backgrounds in µ+ → e+ γ experiment.
Prompt Background or physics background from radiative muon decays,µ+ → e+ νe ν µ γ.
This type of background can be identified by energy of the products.
With the aforementioned resolution, prompt background can be reduced
to around 3 × 10−15 .
Accidental Background with the following sources of gamma rays:27• photons from radiative muon decays• photons from annihilation-in-flight• photons from positron interactions with surrounding materials• neutron induced background
The accidental background is the dominant background in MEG experiment.

Figure 2.23: Signal and backgrounds in MEG experiment.
R1
Figure 2.24 shows the integral yield of gamma rays, fγ (y) = y dy 0 gγ (y 0 ).
Here y ≡ 2Eγ /mµ and y = 1 is the energy of signal. fγ (y) is the number ofmgamma rays with energy greater than 2µ y per muon decay. As shown in theplot, the energy of gamma rays in accidental background are lower than that ofa signal. With an energy resolution of 2%, the background rate is 4 × 10−6 fory > 0.98, with annihilation-in-flight the main source.
In the case of a pile-up event, however, the energy of gamma rays may surpass
that of a signal. Figure 2.25 shows the integrated pile-up yield fγγ (y). With theassumed resolution values and muon stopping rate of Nµ = 1 × 108 , the pile-up
gamma rays have an occurrence rate of 1.5 × 10−6 per muon decay.

28

Figure 2.24: Integrated photon yield per muon decay fγ (y).

Figure 2.25: Integrated pile-up photon yield per muon decay fγγ (y).

29Chapter 3

PMT Calibration
In order to detect the signal from µ+ → e+ + γ with a branching ratio up
to 10−14 , high resolutions of detectors are crucial. Especially for liquid xenon
detector, a precise knowledge of PMT gains and quantum efficiency (QE) is
necessary for reaching an excellent energy resolution and reconstruction accuracy of the first conversion point in LXe. Hence this chapter is dedicated to thecalibration of PMTs.
The LXe detector is equipped with multiple LEDs to measure gains of each PMT
and 241 Am sources to measure QEs. Gain adjustment is for converting ADC
count to the number of photoelectrons (Npe ) and QE values of each PMTs arenecessary for converting Npe to the number of photons (Nph ) and, in particular,
for position reconstruction.

3.1

Gain Calibration

Figure 3.1: LED

3.1.1

MethodGains of PMTs are estimated by using LEDs installed in the detector. During
the measurement, several LEDs are flashed so that all the PMTs are illuminated.
Data is taken by changing the intensity of LEDs. PMT gains were by using blue
light LEDs which are covered with Teflon sheets with some small pinholes toattenuate emitted light so that the statistical fluctuation of LED light intensity
can be small. Daily calibration was performed during data taking.
We assume that LED output is constant and the statistics of Npe obeys Poisson30

distribution. Some of those photons reach the quartz window of a PMT andtransmit it, so that photoelectrons are generated by photoelectric effect witha certain efficiency (QE), and hit the first dynode with a collection efficiency(CE). Both obey binomial distribution. Then the photoelectrons are ampliedby dynodes.
The distribution of Npe becomes a convolution of binomial distributions andPoisson distribution. In that case, the upper tail is broader than lower tail.
When Npe is large enough (10 photoelectrons at least), the contribution of binomial distribution is negligible. Therefore the spectrum after amplication canbe Poisson distribution scaled by gain. The gain can be given by the following
equation:
cσ 2
(3.1)
g=
eM
where g is the gain, c is the ADC least count (200 fC/ch), σ and M are
the standard deviation and the mean of ADC spectrum tted with a Gaussian,respectively, and e is the elementary electric charge, assuming that the numberof photoelectrons (Npe ) observed on a PMT is so large that the ADC spectrum
can be regarded as a Gaussian. In practice we have to consider a contribution
from the deviation of pedestal to it as the following equation:e
σ 2 = g (M − M0 ) + σ02
c

(3.2)

where M0 and σ0 are the mean and the standard deviation of the pedestal
spectrum, respectively. The gain estimate becomes more reliable by using thisequation. By changing the intensity of the LED the PMT outputs vary as shownin Fig. 3. Fig. 3. shows an example of the linear relation between σ0 and M .
The gain of the PMT is proportional to the slope of the fitting function. Thus
the precision of gain determination can improve by using data for various yieldof photons.

Figure 3.2: Spectrum of charge of a PMT. Intensity of LEDs are changed in 7
steps.

31

Figure 3.3: Mean and σ 2 of fitted Gaussian functions. Gain can be estimatedfrom the slope of the plot.

32

3.1.2

Accuracy and Stability

The adjustment of gains, as shown previously, depend on the stability of LEDs,
which is proven to be great in the long run. It was found that the gain determination can be reproduced within an accuracy of 1% in sigma and gains remain
stable within 2% in the long term.

Figure 3.4: History of gain. Red and black dots represent values from trigger
and DRS data respectively.

33

3.2

QE Measurement

3.2.1

Alpha sources

In order to measure QE, we use the same wavelength of light as Xe scintillation
light since QEs highly depend on wavelength. Therefore, α particle appears tobe the most reliable light source for this purpose. Alpha ray from 241 Am has analmost monochromatic energy spectrum (5.443MeV(83%) and 5.443MeV(15%))
with lower tail caused by energy loss in the source material itself and its range
in liquid xenon is benecially short as 40µm. In addition it is very stable evenat low temperature in LXe. The half life of 241 Am is long enough that thesource intensity can be regarded as constant. Therefore the α source is a good
point-like light source for estimating QEs.
Alpha sources are put on wires, each of the size 1mm. Diameter of a wire is
100µm. In total 25 alpha sources on five wires were installed as shown in Figure3.5. A picture of an alpha source wire and LED bundle is shown in Figure 3.7.

Figure 3.5: Alpha source on a wire. Length of the source is 1mm, and diameterof the wire is 100 µm.
There are three advantages of wire sources compared to plate sources:• More scintillation light is observed by PMTs as a wire source can be seenfrom virtually all directions, while in the case of a plate source, half of thesolid angle is covered.
• A plate source can be only put on the PMT holders, while a wire source canbe put at any place without making shadows in gamma ray measurements,
making it possible to illuminate all the PMTs with smaller number of alphasources.
• Wire sources are located in the fiducial volume so the geometrical relation
between PMTs and light sources is closer.

34

Figure 3.6: Positions of alpha sources in the detector. Solid and dashed boxesin the left figure are outer and inner faces respectively.

35

Figure 3.7: Alpha source wire and LED bundle.

36

Figure 3.8 shows the weighted mean of PMT positions in alpha events. In
liquid xenon, weighted mean positions make rings shown. The range of an alphaparticle is comparable to the thickness of the wire, so the wire makes shadow,
as shown in Figure 3.9. The radius of the ring depends on thickness of the wireand scattering length of xenon.

yfave_w

yfave_w:xfave_w {qsum2>0&&yfave_w>-200&&qsum2<10000}

80
60
40
20
0
-20
-40
-60
-80
-100

-90

-80

-70

-60

-50
xfave_w

Figure 3.8: Weighted mean position of PMT outputs in alpha events in liquid
xenon.

Figure 3.9: Alpha particle and the wire. Diameter of the wire is 100 µm andthe range of alpha particle in liquid xenon is about 40 µm.

373.2.2

Simulation

QE is measured by comparing the charge spectra from a given alpha source withthose from simulation. The outcome of such simulation depends largely on the
optical properties of liquid xenon, such as absorption length, scattering length,
refractive index, group velocity of scintillation light.

Rayleigh Scattering Length
Rayleigh scattering length can be estimated by comparing data observed foralpha source wires., whose reconstructed positions make rings. This is due toa shadow effect of wires as shown in Figure 3.9. A PMT observes more lightfor events where an alpha particle is emitted to the direction of the PMT thanevents where the particle is emitted behind the wire. These two cases maketwo peaks in the distribution of number of photoelectrons. The ratio of the two
peaks is sensitive to scattering length. Using data from the large prototype, theratio was compared with simulated data by changing scattering length in MC.
The Rayleigh scattering length was estimated to be 45cm.

Absorption Length
Absorption length of scintillation light in liquid xenon has been estimated bycomparing output of each PMTs for alpha source events with MC simulation as afunction of the distance between the PMTs and alpha sources. Scintillation light
can arrive at PMTs indirectly because of Rayleigh scattering. Therefore, theactual path length of light is not exactly same as the distance between the source
and PMT, and the effective distance needs to be estimated from MC simulation
by taking into account Rayleigh scattering. If we do not take into account ofRayleigh scattering effect in the simulation, the correlation between observed
charges of PMTs and absorption length can de described as e−d/λabs where dis the distance between PMT and source. On the other hand in a realistic casewith a finite Rayleigh scattering length, such dependence changes and thus theeffective distance needs to be estimated by fitting with an exponential function
with d as a free parameter. Using the effective distance estimated in this way
as a distance between the PMTs and alpha sources, the absorption length wasestimated in MC simulation for various cases and compared with the input
values to the simulation. Before applying the method to the real data, PMT
output was corrected with QE estimated with alpha data in cold gas xenon.
The ratio of PMT output to MC simulation with infinite absorption length is afunction of the effective distance between the source and PMTs. By fitting the
distribution with an exponential function, it is found that the absorption lengthwas 233+193−72 during the measurement in 2003. The absorption corresponds toabout 80 ppb of water contamination. In this analysis, scintillation efficiency
of xenon (the W value) was assumed as 17.9 eV and 49.6 eV in liquid and gas
respectively, and the scattering length was assumed as 45 cm against 175 nm
ultraviolet light.

38

Comparing data with simulation
Figure 3.8 shows the observed charge of a PMT from a certain alpha source.
To compare the data with the result of Monte Carlo, a fitting function is used.
For number of photoelectrons less than 10, a simple gaussian function is used.
While for more photoelectrons, we use an exponential function convolved witha Gaussian which has a spread of square root of the number of photoelectrons
spread of pedestal distribution.
After fitting data with the aforementioned functions, the mean values ofphotoelectrons of each PMTs are compared with those of simulation and QE is
estimated from the slope, as shown below.

Figure 3.10: (a)An example of charge spectrum from a given alpha source observed by a PMT. (b)The mean value of the fitting function is compared withsimulation. QE can be estimated from the slope.

39

3.2.3

Accuracy and stability

The uncertainty of QE is estimated by the error of fitting function mentioned
above. The current accuracy of QE estimation is around 3%.

Figure 3.11: (a)Distribution of measured QE values. (b)Relative errors of QE
measurement.
The long term stability is monitored and proven to be quite good. Since wealways used the same gains in calculating QE, the overall equalization factor,
which is the quantity of 1/(gain × QE), is not affected by the gain measurement
at all. The uncertainty of the equalization factor is dominated by the inconsistency with MC, i.e., lack of our knowledge of the LXe property.

40

3.2.4

Application of QE correction

As mentioned before, a better QE measurement improves our understanding of
the performance of detectors and accuracy of other calibrations as well. One
example of QE correction is the application on π0 runs. The position resolution
has been significantly improved after applying QE correction.

π0 calibration
Calibration measurements had been performed in August 2008 for about amonth in order to estimate responses of the liquid xenon photon detector, especially energy, position, and timing resolutions to 55MeV gamma rays, which
is close to 52.8MeV signal energy. Gamma rays from π0 decays (π0 → γγ) produced by charge exchange reaction (π − → +p → n + π 0 ) were used. NaI arrayand plastic scintillator detector was placed opposite to the liquid xenon detector
to select back-to-back photons which have almost monochromatic 55MeV, and
83MeV energy. In order to study relative timing resolution between γ ray of
LXe detector and e+ of timing counter and drift chamber, Dalitz decay eventsof the π 0 (π 0 → e+ + e− + γ, BR= 1.12%) are used. Negative pion beam introduced into the E5 area induce the charge exchange reaction in the LH2 target
prepared for this purpose.
Pb collimators are prepared for estimation of position reconstruction andresolution. Figure 3.12 shows the geometry and photo of Pb collimators. Left
figure shows the lead collimator, whose depth is 1.8cm, with three horizontal
slits of them. Right photo shows the lead collimator with three vertical slits
and three horizontal slits.
These collimators were installed to four different positions in front of LXe
detector as shown in Figure 3.13, and each position has two lead plates withvertical slits, or horizontal slits. Lead collimators with horizontal slits are installed to upper two locations, and those with vertical slits are installed to lower
two locations. The centers of the four lead collimators are aligned to 52.3◦ , 0◦ ,-15.69◦ , and -52.3◦ , respectively.
Four Pb collimators were installed just before the measurement. LXe self trigger data with 1.1M events for each Pb collimator were taken independently byusing software collimator, and it took 15 hours per each position.
Event selection criteria is following. Xenon detector single trigger (#9) is selected. Depth of the first conversion point in LXe detector is more than 2cm,
and energy is more than 45MeV and less than 60MeV.

41

Figure 3.12: Left: geometry of Pb collimator with three horizontal slits; Right:
Pb collimators with vertical and horizontal slits.

Figure 3.13: Places where Pb collimators were installed.

42Figure 3.14 shows 2D reconstructed position distribution of one Pb collimator before and after applying QE correction. Horizontal axis shows u direction,and vertical axis shows v direction. The collimator has three slits at horizontal
direction. Compared with the one before QE correction, the one after has abetter resolution.
Figure 3.15 shows 1-D projection to the vertical axis with a horizontal vertex
position slice of |u| <1.55cm. We can see three peaks from the three slits andtwo upper and lower edges. We can get five position resolutions from this 1D
histogram and two gaussian fits are shown in the figure, σs are shown as 8mm
and 7.2mm, respectively.
From these figures, the position resolution is evaluated to be 4∼6mm at theedge events, and 6∼8mm at 1cm slits.

Figure 3.14: 2D vertex distribution with horizontal lead collimator before andafter QE correction.

Figure 3.15: 1D vertex distribution with horizontal lead collimator.

43

Chapter 4

Study on improving
accuracy of QE
measurement
The current accuracy of QE estimation in LXe is 2.83% on average, which remains to be improved. The accuracy of QE measurement is determined by theerror of fitting function, as shown in Figure 3.10 (b). Figure 4.1 below is andexample of fitting. While ideally, all points should form a straight line, for some
PMTs, there are some discrepancies between different points, i.e. differences indata and simulation.
Hence the current inaccuracy arises from the difference between simulation anddata. In other words, our lack of understanding of LXe properties. By studying how to improve the accuracy of QE measurement, hopefully we will learn
more about the properties of liquid xenon as well as enhance detector sensitivity.

Figure 4.1: Example of QE fitting. All points are not on the same line.

44

4.1

Determining Factors

The current default setting in Monte Carlo is listed in table 4.1.

Parameter
Refractive index of liquid xenon
Wavelength
Rayleigh scattering length
Absorption length
Reflection on PEEK
Reflection on Aluminium
Reflection on KOVAR
Refractive index of quartz
Transmittance rate of quartz

Value(for λ=178nm)
1.61
178nm
45cm
∞
0.10
0.2
0.2
1.62
0.8

Table 4.1: Parameter setting in simulation.
Another relevant value is the cut we apply to the incidence angle. As forlarge angles, the scintillation light mostly come from indirect sources and canbe difficult to evalue. The current cut is set as 74◦ Together the crucial factors
in measuring QE can be summarized as:• absorption length• scattering length• reflection• incidence angle cut
The ratios between the mean values of data and MC for each PMT are plottedin relation to distance and angle, as shown in Figure 4.2 and Figure 4.3.

45

Figure 4.2: Ratio between data and simulation in relation to distance.

Figure 4.3: Ratio between data and simulation in relation to incidence angle.
Two traits can be observed from these plots.
• When the distance is small (< 60cm), the data/MC ratio remains relatively constant except for large incidence angles, where there appeared to
be a slight drop followed by a slow climb in the ratio when angles arelarger than 60◦ .
46

Figure 4.4:
• When the distance is large (> 60cm), the data/MC ratio increased inrelation to distance drastically.
In light of these conclusions, the study was focused on the scattering length andreflection factor on various materials inside the detector. A stricter incidence
angle cut was also considered. The current cut was 74◦ , which is quite close
to the total reflection angle (around 80◦ assuming the refractive index of liquid
xenon is 1.61).

4.2

Simulation

A set of Monte Carlo simulation was made in regard to each of these factors
by increasing scattering length and turning off/increasing reflection from eachmaterial (quartz, Kovar, peek, aluminum). 50000 events were created for eachsetting. The comparison between these settings and the default one (MC -302)
is shown in Figure 4.5. to Figure 4.10.

47

Figure 4.5: Data/MC ratio in relation to distance. Several simulations weremade by changing the scattering length from 45cm to 60cm, 85cm, 100cm.

Figure 4.6: Data/MC ratio in relation to incidence angle. Several simulations
were made by changing the scattering length from 45cm to 60cm, 85cm, 100cm.

48

Figure 4.7: Data/MC ratio in relation to distance. Several simulations weredone by turning off reflection on each material.

Figure 4.8: Data/MC ratio in relation to incidence angle. Several simulations
were done by turning off reflection on each material.

49

Figure 4.9: Data/MC ratio in relation to distance. Several simulations weredone by increasing reflection on each material.

Figure 4.10: Data/MC ratio in relation to incidence angle. Several simulations
were done by increasing reflection on each material.

50

4.3

Result1. When scattering length was increased, the data/MC ratio in large distance
dropped significantly and accuracy improved.
2. The climbing up in large angles worsened when increasing scattering length.
3. Turning off or increasing reflections on each material did not render muchchange in relation to distance or incidence angle.
The incidence angle was then set to 60◦ to make the data/MC ratio more uniform.
Judging from overall accuracy, the scattering length is believed to be close to
85cm.

51

Chapter 5

Conclusion
From the result mentioned in the last chapter, it can be concluded that thecurrent most suitable setting for simulation would be for scattering length to be
85cm. Also the incidence angle cut is better reduced to 60◦ due to the inconsistency in large angles.
With this new setting of parameters, the uncertainty of QE measurement dropped
from 2.82% to 2.32%. For PMTs in each locations (inner, outer, upstream,
downstream, top, bottom), the uncertainty of QE dropped 4%, 16%, 26%, 19.6%, 36%, 43%
respectively.

QE

h1
Entries
Mean
RMS

45
QE (MC -302)

846
22.11
4.58

40
QE (SL 85, angle cut 60)

35
30
25
20
15
10
5
0
0

5

10

15

20

25

30

35

40
QE(%)

Figure 5.1: Distribution of QE with old simulation and QE with longer scattering length (85cm) and lower incidence angle cut (60◦)

52

QE Uncertainty
QE Uncertainty (MC -302)

h4
Entries
842
Mean
2.231
RMS
0.864150
QE Uncertainty (SL 85, angle cut 60)

40

30

20

10

0
0

1

2

3

4

5

6

7
8
9
10
Relative Uncertainty(%)

Figure 5.2: Error of QE measurement with old simulation and error of QE
measurement with longer scattering length (85cm) and lower incidence angle
cut (60◦)

53

Unfortunately, the improvement on PMTs located in the inner part of thedetector is rather small, which makes its effects difficult to be seen on position
resolution, etc . But it did give us an interesting insight into the properties ofliquid xenon. As mentioned in Chapter 3, Rayleigh scattering length can be
estimated by measuring the shadow effects of alpha wires. Such study is yet to
be done with the current LXe detector. If scattering length is confirmed to beclose to 85cm rather than 45cm as previously thought, the causal relationshipwith other properties of liquid xenon, such as absorption length, refractive index, group velocity of scintillation light need to be studied as well.

54

Acknowledgment
First of all, I would like to thank my advisor Prof. Toshinori Mori for his
guidance and support throughout the past two years. I also thank Dr. Wataru
Ootani who has given me so many great advices and has helped me throughout
all my work. Without them this thesis could not have been completed.
I would also like to express my gratitude to Dr. Ryu Sawada, who has helpedme tremendously on the analysis of quantum efficiency, as well as Mr. Yusuke
Uchiyama.
I would like to thank Prof. Satoshi Mihara and Dr. Toshiyuki Iwamoto, fromwhom I have learned a great deal in physics and experimental skills.
I would like to thank Mr. Hiroaki Natori, who has helped me with the position
analysis of collimator runs.
I would like to especially thank Mr. Yasuhiro Nishimura, who has offered meso much support and has been a great friend since I joined the experiment.
To all the members in the MEG Collaboration, thank you for all the supportand help. It has been a great pleasure and inspiration to work with all of you.
Last but not least, I would like to thank my parents and dear friends for theirunconditional love throughout all my life.

55

Bibliography[1] T.Mori et al. Research Proposal to PSI, May 1999
[2] Y.Kuno and Y.Okada, Rev. Mod. Phys. 73, 151 (2001)[3] J. Hisano et al., Phys. Lett. B391 (1997) 341[4] M.L.Brooks et al., Phys. Rev. Lett. 83(1999) 1521
[5] S.Mihara et al., MEG Technical Note No. 24 (2004)[6] K. Ozone, Liquid xenon gamma-ray detector for the newµ → eγ searchexperiment (2005)[7] Y.Hisamatsu, Master thesis (2005)[8] Y.Uchiyama, Master thesis (2006)[9] R.Sawada, Doctoral thesis (2009)56