R&D studies of Muon Polarimeter
for J-PARC E06
T-Violation Experiment
Master’s Thesis

35-096116
Keisuke Yoshihara

Department of Physics,
Graduate School of Science, The University of Tokyo

20th January 2011

Abstract
The J-PARC E06 experiment, called TREK, aims to measure the transverse muon polarization in K + → π 0 μ+ νμ decay as an indicator of the direct T-violation in weak interaction. From the KEK PS E246 experiment, the result of PT = −0.0017 ± 0.0023(stat) ±0.0011(syst) was obtained, which is consistent with T-invariance. Now the TREK Collaboration intends to continue the PT experiment at J-PARC, where a higher accelerator
beam intensity will be available and a higher experimental sensitivity can be expected, inorder to search for new physics beyond SM. We aim for a sensitivity of δPT ∼ 10−4 , whichmight reveal some new physics beyond the SM in this sensitive region. In order to achieve
this sensitivity, we have to improve some detectors to decrease the systematic errors. The
largest systematic error is the eﬀect of multiple scattering of muons through the Cu degrader in front of the polarimeter. The TREK experiment, however, will be free from thiserror as we will employ an active polarimeter. In order to evaluate the performance of theactive polarimeter, we have performed beam test at TRIUMF in Vancouver, Canada. In
this thesis, the results of this beam test and other studies including an alternative designof polarimeter are presented. Finally the result of the commissioning of K1.1BR beamline
at Hadron Experimental Hall in J-PARC is presented.

Acknowledgements
First of all, I would like to express my sincere gratitude to my supervisor, Prof. T.
Kawamoto, who allowed me to join the TREK experiment and encouraged my research andmy private life. Numerous discussions with him greatly attracted me to particle physics. I
want to express my thanks Prof. S. Asai, who allowed me to join this experiment. I am
deeply indebted to Dr. T. Namba for his valuable suggestions and support. I also owe
him for carefully reading this thesis repeatedly. I greatly want to express my gratitude
to Prof. J. Imazato, who attracted me to this exciting experiment and gave me so many
chances to learn a lot about physics and detectors. He also gave me a lot of helpful advice,also showing me the attitude necessary for a scientist through his daily work. I am muchindebted to Prof. M. Hasinoﬀ for carefully reading this work repeatedly in spite of my poor
English, and also for helping me to do the beam test at TRIUMF. I am grateful to Dr. Y.
Igarashi, who always worked with me in KEK and in J-PARC and taught me about not
only the Data Acquisition system, but also other hardware and software technique. I owe
him for his kindness and his support with regard to my research and the enjoyable working
atmosphere. I would like to express my gratitude to Dr. H. Yamazaki for his advice. A lotof discussion with him greatly promoted my understanding for particle physics. I would
like to express my gratitude to Dr. S. Shimizu for his advice. I could see his passion for
physics experiments and he also gave me many suggestion for my studies. I would like toexpress my gratitude to Dr. A. Toyoda for his support. Without his support, the beamtuning in J-PARC could not have been performed. I would like to express my gratitude to
Dr. K. Horie for her support with regard to my simulation work. I would like to express mygratitude to Dr. M. Uchida for his support with regard to my simulation work. I would liketo express my gratitude to Dr. F. Habermehl for his help for the preparation of K1.1BR
commissioning. I owe him for his kindness. I would also like to thank the other membersof the TREK collaboration. I want to express my gratitude to all the secretaries of ourgroup, R. Anbiru, M. Shiota, N. Kataoka, C. Morita, M, Suzuki. I would like to thankall the students of our group, R. Inoue, S. Kazama, K.K. Siang, Y. Sasaki, A. Miyazaki,
Y. Fuji, T. Kamiya, Y. Ninomiya, K. Bendtz, Y. Yamaguchi, Y. Iiyama, elderly students,
and younger students. Finally, I would like to express my gratitude to my parents, mygirlfriend, and all relatives for their continuous support and encouragement.

iContents
Introduction

1

1 J-PARC TREK Experiment
1.1 Phenomenology of Kμ3 Decay . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Transverse Polarization PT . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 Theoretical Predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3.1 Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3.2 Final state interactions . . . . . . . . . . . . . . . . . . . . . . . . .
1.3.3 Multi-Higgs doublet model . . . . . . . . . . . . . . . . . . . . . . .
1.3.4 SUSY models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4 J-PARC TREK experiment . . . . . . . . . . . . . . . . . . . . . . . . . .
1.5 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.5.1 Overview of TREK detector setup . . . . . . . . . . . . . . . . . . .
1.5.2 Fitch-type Cherenkov counter . . . . . . . . . . . . . . . . . . . . .
1.5.3 Beamline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.5.4 K + stopping target . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.5.5 Photon Counter . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.5.6 Superconducting spectrometer magnet . . . . . . . . . . . . . . . .
1.5.7 Tracking Chamber . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.5.8 Muon polarimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.5.9 Muon polarimeter magnet . . . . . . . . . . . . . . . . . . . . . . .
1.5.10 Electronics and data aquisition . . . . . . . . . . . . . . . . . . . .

5
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2 Muon Polarimeter for TREK Experiment
2.1 Muon polarimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Passive polarimeter for the E246 . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Requirements for an active polarimeter . . . . . . . . . . . . . . . . . . . .
2.4 Concepts of the polarimeter design . . . . . . . . . . . . . . . . . . . . . .
2.5 Requirement for stopper material . . . . . . . . . . . . . . . . . . . . . . .
2.6 Expected performance of the polarimeter . . . . . . . . . . . . . . . . . . .
2.7 Development of the charge division method . . . . . . . . . . . . . . . . . .
2.7.1 Test experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.7.2 Analysis scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.7.3 Result and an additional analysis . . . . . . . . . . . . . . . . . . .
2.7.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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ii

2.8
2.9

Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Read-out system for the polarimeter . . . . . . . . . . . . . . . . . . . . .
2.9.1 16 ch Amp. Shaper Buﬀer card (ASB card) . . . . . . . . . . . . .
2.9.2 VME discriminator board MODEL RPV-240 . . . . . . . . . . . . .
2.9.3 De-coupler card . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.9.4 CAEN ADC V792 / CAEN TDC V1190 . . . . . . . . . . . . . . .

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3 Beam test at TRIUMF
3.1 M11 beamline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Beam tuning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.2 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.3 Degrader tuning . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 Null Asymmetry test . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.2 Analyzing power measurement . . . . . . . . . . . . . . . . . . . . .

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4 Analysis of the beam test data
4.1 Veriﬁcation of data quality . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Wire eﬃciency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 Event selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4 Development of the track reconstruction . . . . . . . . . . . . . . . . . . .
4.5 Spurious asymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5.1 Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5.2 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5.3 Summary of the asymmetry analysis . . . . . . . . . . . . . . . . .
4.5.4 Future plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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5 Design of the Muon Tube Polarimeter
5.1 Estimates of Muon Tube parameters . . . . . . . . . . . . . . . . . . . . .
5.2 Current status of MTP . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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6 K1.1BR beamline for the TREK experiment91
6.1 Expected performance of K1.1BR . . . . . . . . . . . . . . . . . . . . . . . 92
6.1.1 Design of beamline and optics . . . . . . . . . . . . . . . . . . . . . 92
6.1.2 Pion contamination . . . . . . . . . . . . . . . . . . . . . . . . . . .
95
6.1.3 Expected Kaon yield . . . . . . . . . . . . . . . . . . . . . . . . . . 96
6.2 Detectors for the beamline commissioning . . . . . . . . . . . . . . . . . . 97
6.2.1 beam detector elements . . . . . . . . . . . . . . . . . . . . . . . . . 97
6.2.2 Fitch-type diﬀerential Cherenkov counter . . . . . . . . . . . . . . . 99
6.3 Commissioning of the beamline . . . . . . . . . . . . . . . . . . . . . . . . 101
6.3.1 Result of the beam tuning . . . . . . . . . . . . . . . . . . . . . . . 101
Conclusion

106

A Charge division

107
iii

B An estimate of X-T relation
110
B.1 Determination of the X-T relation . . . . . . . . . . . . . . . . . . . . . . . 111
B.2 Iteration method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
C Beam polarization

118

iv

List of Figures
1.1

The intensity distribution (a), and the three components of the muon polarization in the Kμ3 decay of (b)longitudinal component PL , (c)normal com6
ponent PN , and (d)transverse component PT /Imξ as deﬁned by Eq(1.9). .
1.2 Deﬁnition of PT , PN , PL . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
9
1.3 Radiative corrections in the Kμ3 decay . . . . . . . . . . . . . . . . . . . .
em
1.4 (a) One of the diagrams of the ﬁnal state interactions contributing to PT ;from one photon exchange calculated in Ref [28] and (b) one of the diagramsfrom two photon exchanges calculated in Ref [29]. . . . . . . . . . . . . . . 10
1.5 T-violating diagram in the three Higgs doublet model in Kμ3 decay. Interference between (a) W + exchange and (b) charged Higgs exchange is themain contribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12
1.6 T-violating diagram of Minimal Supersymmetric Standard Model in Kμ3 decay. 13
1.7 T-violating diagram of R-parity breaking Supersymmetric Standard Model
in Kμ3 decay, (a) and (b) are possible diagrams , (a) is a slepton exchangeand (b) is a down-type squark exchange. Note that the diagram (c) does
not exist. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14
1.8 Side view (top) and end view (bottom) of TREK detector . . . . . . . . . 17
1.9 T-violating azimuthal polarization PT for the case of the π 0 going in theforward (fwd) and backward (bwd) directions. . . . . . . . . . . . . . . . . 18
1.10 Scintillating ﬁber target for TREK experiment. The active zone has a lengthof 20 cm and a diameter of 7.5 cm. Each of the 489 ﬁbers has 3.0mm×3.0mm
square cross section. The ﬁber bundle is surrounded by 12 ﬁducial counters. 18
1.11 Example picture of scintillating ﬁber with two thin wave length shifter(WLS) ﬁbers although an actual number of WLS is equal to 1. . . . . . . . 18
1.12 CsI(Tl) barrel with 768 crystal modules. There are 12 muon holes. . . . . . 19
1.13 Performance of the CsI(Tl) detector for Kμ3 and Kπ2 in E246. a) Invariant
mass spectrum of two photons of Kμ3 , b) cluster timing distribution alsoof Kμ3 showing the time resolution, c) opening angle distribution of Kπ2
showing the angular resolution, and d) two-photon and one-photon energy
spectra of Kμ3 events. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20
1.14 Readout scheme of the CsI(Tl) calorimeter using APD . . . . . . . . . . . 21
1.15 One sector of the superconducting toroidal magnet. . . . . . . . . . . . . . 23
1.16 Schematics of the tracking system in the E246 setup (left) and the TREK
setup (right) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
25
1.17 Muon ﬁeld magnet one sector test setup. . . . . . . . . . . . . . . . . . . . 26
v

2.1
2.2
2.3

Schematic structure of the muon polarimeter. . . . . . . . . . . . . . . . .
Magnetic ﬁeld distribution on the muon stopper . . . . . . . . . . . . . . .
Incident muon y distribution in the stopper measured by the C4 chamber(top), and the intrinsic geometrical asymmetry for those muons (bottom).
The real stopping distribution has a smearing due to beam divergence andmultiple scattering. The geometrical asymmetry was measured as the null
asymmetry A0 by accepting all π 0 directions. . . . . . . . . . . . . . . . . .
2.4 Muon stopper made of parallel plates which serve also as drift chamber cellstructure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5 Picture of 1/5 prototype polarimeter . . . . . . . . . . . . . . . . . . . . .
2.6 Picture of 1/5 prototype polarimeter . . . . . . . . . . . . . . . . . . . . .
2.7 (a) and (c) are RQ distributions and (b) and (d) are x distributions, respectively. (a) and (b) are ± 5 cm samples and (c) and (d) are ± 15 cm samples.
The RQ distributions are obtained by adjusting the α. The x distributions
are also obtained by adjusting the f parameter. . . . . . . . . . . . . . . .
2.8 The residual distribution before correction (left) and the residual distribution
after applying the additional correction (right) as discussed in the text. . .
2.9 Process of the wire stringing. . . . . . . . . . . . . . . . . . . . . . . . . . .
2.10 Picture of the FSM polarimeter. . . . . . . . . . . . . . . . . . . . . . . . .
2.11 Main ﬂow of the data acquisition system. . . . . . . . . . . . . . . . . . . .
2.12 Top view of ASB cards. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.13 Overview of the modules for DAQ. The silver card on the bottom is one of
the De-coupler cards. The four red modules are the interrupt register (left),the two ADC modules (center) and the TDC module (right), respectively.
All the blue modules are VME-discriminator modules. . . . . . . . . . . . .
3.1
3.2
3.3
3.4
3.5

3.6

3.7

3.8
3.9

Overview of Meson Hall in TRIUMF. . . . . . . . . . . . . . . . . . . . . .
M11 beam rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Layout of M11 beam channel . . . . . . . . . . . . . . . . . . . . . . . . .
Experimental setup for beam tuning. . . . . . . . . . . . . . . . . . . . . .
Pictures of oscilloscope. The top one shows the S0 and the S1 counter signal
which correspond to the yellow line and the blue line, respectively. The S1
counter signals appear 10 ns laterOn the other hand, than theS0 signals.
the bottom one shows the S0 S1 and S0 
S1 RF corresponding to theyellow line and the blue line, respectively. S1 RF coincidence signal has 3components due to the three kinds of positive charged particles. . . . . . .
Pictures of TOF spectrum at 170 MeV/c by using the MCA. The top one
shows the raw TOF spectrum showing three peaks for π, μ, and e. The
bottom one shows the TOF spectrum after the RF cut. In the bottom one,pion peak including a little contamination of muons has been selected. . . .
Timing chart. The ADC gate was made from the coincidence of both thedelayed trigger and the chamber signals. In addition, the TDC stop has thesame timing as the end of the trigger gate. . . . . . . . . . . . . . . . . . .
Conﬁguration of the DAQ system. . . . . . . . . . . . . . . . . . . . . . . .
Typical chamber raw signal. It had an overshoot and some ringing. . . . .
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3.10 Main ﬂow diagram of the logic circuit. . . . . . . . . . . . . . . . . . . . .
3.11 Conﬁguration of the gas system. . . . . . . . . . . . . . . . . . . . . . . . .
3.12 Conﬁguration for degrader tunings. . . . . . . . . . . . . . . . . . . . . . .
3.13 Results of the degrader tuning. Upstream (top), Middle (middle), andDownstream (bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.14 Conceptual diagram for the null asymmetry test. In this measurement, theπ + beam was used. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.15 Conceptual diagram for analyzing power measurement. In this measurement, μ+ beam was adopted. . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1

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Picture of the S1 counter time spectrum. This was used to be the timereference. A 170 ps in σ time resolution was achieved. This is suﬃciently
high in our measurement. . . . . . . . . . . . . . . . . . . . . . . . . . . .
63
4.2 Picture of the muon decay curve. The parameter (1/τ ) corresponds to ∼ 2μs. 64
4.3 Picture of the TDC data corresponding to a single wire. The TDC spectrum
composed of the decay positron hit with a small fraction of the incident particle. 64
4.4 Picture of the ADC data after a pedestal suppression. The ﬁgure corresponds
to a single wire hit. The ADC spectrum is completely composed of the decay
positron due to the delayed trigger as mentioned in Chapter 3. . . . . . . . 65
4.5 Sample track. In this picture, the pion enters into polarimeter and the decay
positron is ﬁnally emitted. . . . . . . . . . . . . . . . . . . . . . . . . . . .
65+
4.6 π stopping distribution. It seems that incident pion stops ASB region withconcentric circles. Its central position tends to concentrate upstream of thefull ASB region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
66
4.7 Conﬁguration of the Al plates (left) and the ASB cards (right). . . . . . . 67
4.8 The ﬁrst results of the wire eﬃciency measurement. These eﬃciencies reliedon the position of a sense wire due to multiple scattering eﬀect. . . . . . . 68
4.9 Schematic view of the Al plates and the new deﬁnition of the wire eﬃciency. 68
4.10 Final result of the detection eﬃciencies in a cell unit. This included thecorrection of the multiple scattering eﬀect. . . . . . . . . . . . . . . . . . . 69
4.11 Schematic view of the track reconstruction. . . . . . . . . . . . . . . . . . . 70
4.12 Sample picture of the decay positron ﬁtting 1. . . . . . . . . . . . . . . . . 72
4.13 Sample picture of the decay positron ﬁtting 2. . . . . . . . . . . . . . . . . 72
4.14 Sample picture of the decay positron ﬁtting 3. . . . . . . . . . . . . . . . . 72
4.15 Sample picture of the decay positron ﬁtting 4. . . . . . . . . . . . . . . . . 73
4.16 Schematic view of the null asymmetry measurement and the deﬁnition of axis. 73
4.17 Result of null asymmetry measurement. A large spurious asymmetry appears. It depend on the wire position. . . . . . . . . . . . . . . . . . . . . . 74
4.18 Schematic view of the decay positron emission. The tendency shows thatthe positron tended to be emitted upward (downward) in case of a vertex
cell located upward (downward). . . . . . . . . . . . . . . . . . . . . . . . . 75
4.19 Schematic view of pion decay in rest frame (left) and laboratory frame (right). 76
4.20 Summary of properties of decay muons. Momentum distribution. . . . . . 77
4.21 Summary of properties of decay muons. Decay-cone aperture angle formuons produced by pion decay in ﬂight. . . . . . . . . . . . . . . . . . . . 77
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4.22 Three types of muon source (surface μ+ , cloud μ+ , and decay μ+ ) produced
by energetic protons from accelerators. . . . . . . . . . . . . . . . . . . . .
4.23 Schematic view of the M11 beamline. BWD muons could be produced after
the B2 magnet. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.24 TOF spectrum. BWD (FWD) muon could be contained in the pion peaktoward the left (right) direction. . . . . . . . . . . . . . . . . . . . . . . . .
4.25 A polarimeter constructed in Geant4 simulation. In addition, main axes
were also deﬁned. Here, the incident beam was incoming toward the −Z
direction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.26 Incident π + beam proﬁles in Geant4 simulation . . . . . . . . . . . . . . .
4.27 Features of the decay positron in Geant4 simulation . . . . . . . . . . . . .
4.28 Result of the spurious asymmetry measurement in Geant4 simulation. . . .
4.29 Schematic view of the cause of a spurious asymmetry. . . . . . . . . . . . .
Schematic view of the constraint against the Muon Tube. The tubes arealigned densely in the left one, while the tubes in the right one are alignedwith a lower packing density. . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 OD : ID = 10 : 9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3 OD : ID = 10 : 8. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4 OD : ID = 10 : 7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5 OD : ID = 10 : 8.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.6 Side view of Muon tube. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.7 End view of Muon tube. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.8 Full volume. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.9 Buﬀer space. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.10 Inner template. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.11 Tube to template connector. . . . . . . . . . . . . . . . . . . . . . . . . . .
5.12 End plate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.13 Feedthrough. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.14 The Al tubes assembling. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.15 End plate connection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.16 Feedthroughs connection. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.17 Process of the wire stringing. . . . . . . . . . . . . . . . . . . . . . . . . . .

78
79
79

80
81
82
82
83

5.1

6.1
6.2
6.3
6.4

Overview of the Hadron Hall at J-PARC . . . . . . . . . . . . . . . . . . .
The layout of K1.1BR . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Beam envelop of the current K1.1BR beamline. The top half and the bottom
half corresponds to vertical and horizontal envelop, respectively. . . . . . .
Picture of the intermediate focusing slits (IF X + IF Y ) and the mass slit
(M S) before installation. Both slits are located at the vertical focusing
point. The IF Y , in particular, has a crucial role for the removal of pionsin spite of the use of a single stage separator. In addition, IF X is useful tocontrol the overall beam acceptance. . . . . . . . . . . . . . . . . . . . . .

viii

87
88
88
88
88
88
88
89
89
90
90
90
90
90
90
90
90
91
92
94

94

6.5

Picture of the horizontal focusing slit (HF OC) before installation. The
HF OC is placed before the ﬁnal doublet Q7 - Q8 and is also useful for theremoval of the pion contamination in the beam. . . . . . . . . . . . . . . . 95
6.6 Picture of the electrostatic separator (ESS) before installation. The ESS
is one of the essential elements for the beamline to extract a clean K + beam. 95
6.7 Detector components for the beam tuning. . . . . . . . . . . . . . . . . . . 97
6.8 Detector elements for the beamline commissioning. . . . . . . . . . . . . . 98
6.9 Picture of the beam Hodoscope. The Hodoscope is composed of 24 scintillators with a thickness of 12 mm in a stainless steel frame. . . . . . . . . . 98
6.10 Top view of the beam Cherenkov counter. . . . . . . . . . . . . . . . . . . 99
6.11 Side view and end view of the beam Cherenkov counter. The beam with
740-800 MeV/c momentum emits Cherenkov light with an angle of 38◦ for
K + and 47◦ for π + . The critical angle of the radiator for total reﬂection is42.2◦ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
6.12 Distribution of PMT-hit K ring multiplicity @ 770 MeV/c in Monte Carlosimulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
6.13 Distribution of PMT-hit π ring multiplicity @ 770 MeV/c in Monte Carlosimulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
6.14 TOF spectrum. A large number of kaons were observed in the separated
beam. We also see pions and protons in the spectrum. In this ﬁgure, theconditions that the π ring and K ring PMT hit multiplicity are equal to zero
hit and more than 1 hit, were required, respectively. . . . . . . . . . . . . . 102
6.15 The performance of the K ring. In this spectrum, the condition of the piontiming conﬁrmed by the TOF spectrum above is required. Thus, the ﬁgureshows the pion fraction in the K ring. . . . . . . . . . . . . . . . . . . . . . 102
6.16 The performance of the K ring. In this spectrum, the condition of the kaon
timing conﬁrmed by the TOF spectrum above is required. Thus, the ﬁgureshows the real kaon events. . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
6.17 The performance of the π ring. In this spectrum, the condition of the piontiming conﬁrmed by the TOF spectrum above is required. Thus, the ﬁgureshows the real pion events. . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
6.18 Mass separation curve obtained with a ESS voltage of ± 300 kV at thebeam momentum of 0.8 GeV/c. . . . . . . . . . . . . . . . . . . . . . . . . 104
6.19 Kaon beam spot at the FF for the best tuning setting of Q7 and Q8, and at
the end of Q8 using a beam Hodoscope. . . . . . . . . . . . . . . . . . . . 105
A.1 The schematic view of charge division system. The distance from avalanche
to wire ends are Z1 and Z2 , and the corresponding resistances of the wire
are R1 and R2 , respectively. The input impedance of ampliﬁers are r1 and r2 .107
A.2 Equivalent electric circuit of the charge division system. The collected charge
on capacitor is discharged through resistances. The experimentally timeintegrated I1 and I2 are observed as the charges Q1 and Q2 . . . . . . . . . 108
B.1 Drift time distribution. The sweep of the drift time distribution corresponded to a cell size. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ix

110

B.2 Schematic view of the deﬁnition of wires for analyzing the X-T relation. The
same conﬁguration of wires was adopted in my analysis. . . . . . . . . . . . 111
B.3 2-Dimensional plot of the X-T relation based on 50 μm/ns drift velocity.
The resulting plot shows that drift velocity was not constant. . . . . . . . . 112
B.4 Sample of projected histogram. These products were ﬁtted by Gauss function.113
B.5 Result of ﬁtting with an assumed parameter. At the same time, the valueof χ2 was recorded every time. . . . . . . . . . . . . . . . . . . . . . . . . . 114
B.6 The variation of χ2 . The value of χ2 converged after several iterations. . . 115
B.7 Final result of parameters corresponding to actual drift velocity. . . . . . . 115
B.8 A ﬁnal set of the projected histograms and the 2-Dimensional X-T plot. The
mean value of the histogram is shifted toward the right direction and thevalue of sigma is becoming smaller. . . . . . . . . . . . . . . . . . . . . . . 116
B.9 The variation of σ. The resulting parameters were adopted as the ﬂuctuationof the equi-drift-time line. . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
C.1 Conceptual diagram of the longitudinal polarization measurement. . . . . . 118
C.2 Asymmetry of the longitudinal polarization measurement. . . . . . . . . . 119x

List of Tables
1.1
1.2
1.3
1.4

Main parameters of the CsI(Tl) calorimeter. . . . . . . . . . . . . . . . . .
Readout scheme using APDs compared with the E246 PIN readout. . . . .
Main parameters of the charged particle tracking . . . . . . . . . . . . . .
Main parameters of the muon ﬁeld magnet . . . . . . . . . . . . . . . . . .

20
22
24
26

2.1
2.2
2.3
2.4
2.5
2.6

Summary of major systematic errors . . . . . . . . . . . . . . . . . . . . .
Parameters of plate and wire . . . . . . . . . . . . . . . . . . . . . . . . . .
List of μSR target . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The main functions of ASB . . . . . . . . . . . . . . . . . . . . . . . . . .
Gain control set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The specs of VME discriminator board . . . . . . . . . . . . . . . . . . . .

33
35
38
45
45
46

3.1

Summary of degrader thickness . . . . . . . . . . . . . . . . . . . . . . . .

60

5.1

Parameter comparisons of the plate type. . . . . . . . . . . . . . . . . . . .

86

6.1

Main parameters of the beam Cherenkov counter. The K + momentum is
expected to be 740-800 MeV/c. The K + eﬃciency is obtained to be higher
than 99 % by setting the threshold multiplicity of N > 6. . . . . . . . . . . 99
Results of the K + beam tuning at 0.8 GeV/c at K1.1BR. . . . . . . . . . . 104

6.2

xi

Introduction
In the ﬁeld of elementary particle physics, it is essential to search for what kinds of materials( or particles) is our universe composed of and how they build up our universe. Forproceeding with our understandings, a lot of elementary particle physics experiments were
performed around the world.
As the results of these investigations, the electroweak model was accomplished as wellas quantum chromodynamics (QCD). Finally, the elementary particle Standard Model(SM) [1, 2] based on the Cabibbo-Kobayashi-Masukawa mixing matrix (CKM matrix)
was proposed. The SM consists of the quarks and the leptons with three generations inaddition to the gauge bosons based on the gauge principle such as W, Z, and γ bosons
for the interactions as the elementary particles. It is generally said that the SM has also
another elementary particle, named Higgs boson for the vacuum description although it
has not yet been discovered. However, it is expected to be probably discovered in themass region of 110 < MH < 200 GeV in the near future. The SM successfully explains thevarious phenomena in our universe, especially regarding the particles and their interactions
precisely, and was consistent with a lot of particle and nuclear physics experiments.
At the same time, it is a well-known fact that the SM can not be the ultimate theory,
namely it may just explain a comparatively low energy scale (∼ T eV ). Thus, particle andnuclear physicists hope that new physics beyond the SM lies at the energy region of a few
TeV, in the light of the following problems given as examples.
• Neutrino mass problem
Neutrinos have actually a small mass (meV-eV) although neutrinos are dealt withmassless particles in the SM. Although the problem was accounted for as the neutrino
oscillation [3], the oscillation parameters have not been determined precisely yet.
• Hierarchy problem [4]This is the question that asks why the Higgs boson is so much lighter than the Planckscale (or the grand uniﬁcation energy scale).
• Baryogenesis problem [5]This is the question that asks why our universe mainly consists of not antibaryons
but baryons.
• Dark matter and dark energy problem [6]Although it is said that our universe mainly consists of the dark matter and the dark1

energy, they have not yet been discovered.
For explaining these unknown phenomena, theoretical physicists have made up a lot of
new theories. As the most important possibility, some of them believe that the existenceof the super symmetry theory (SUSY) [7] which predicts the partner particles for all of theSM particles. The SUSY will be possible to solve all problems above. The existence of the
SUSY particles assumed, for example, the Yukawa coupling of the top quark can generate
electroweak scale naturally.
As well as the theoretical physicists, we, namely experimental physicists, have planned
a lot of new experiments with the aim to search for new physics beyond the SM. One of
the most noteworthy experiments is the Large Hadron Collider (LHC) experiment [8]. In
the LHC, where energy frontier physics can be performed, it is possible to search for the
new particles such as the Higgs boson and the SUSY particles beyond the SM, directly up
to TeV scale. It is said ( and I hope) that the LHC will discover the Higgs boson because
the LHC will be cover the mass region of 110 < MH < 200 GeV in the near future. In
addition, neutrino oscillation experiments and next-generation B factory experiments arealso undertaken.
In Japan, we give high priority to the T2K experiment [9] and the BELLE experiment [10] as the large experimental projects. The T2K project in J-PARC [11] aims tomeasure one of the neutrino oscillation parameters and the experiment has already started.
And the BELLE experiment in KEK, where the highest luminosity beam is available, hasalready measured the CP violation, which was discovered in the neutral kaon system in1964 [12], corresponding to the CKM matrix phase in the asymmetric decay timing of theB 0 system in 2001.
As well as these experiments, it is clear that we should also perform the kind of precise
measurement at J-PARC using kaons such as the KOTO experiment [13], which aims tomeasure the rare decay of neutral kaons KL → π 0 ν ν̄, the TREK experiment [14], which aims
to measure the transverse polarization (PT ) corresponding to the T-violation, and the P36
experiment, which aims to measure the lepton universality using Γ(K+ → e+ ν)/Γ(K + →μ+ ν), are also of great importance not only in the search for new physics but also to proceedwith our understandings of new physics.
Since baryogenesis as a generic term produced an asymmetry between baryons andantibaryons in the very early universe, the universe today is composed of the substantial
amounts of residual matter. In order to generate its term, a set of three conditions, theso-called A. Sakharov conditions, are required.
1)Baryon number violation2)C-symmetry and CP-symmetry violation3)Interactions out of thermal equilibrium
Currently, there is no experimental evidence of the particle interactions, where the2conservation of baryon number is broken. In addition, although the CP violation completely
corresponds to the CKM matrix complex phase in the quark sector, larger CP violations
are required in order to explain baryogenesis. Therefore it is essential to examine new CP
violation sources.
The CPT theorem [15] asserts that a Lorentz-invariant ﬁeld theory is unchanged under
the combined CPT operation, thus conserving CPT. According to the CPT invariance,
however, the observation of the CP violation in the K 0 and B 0 systems requires the existence of T violation. Thus, T violation has a great impact on our understanding of nature.
Before the ﬁrst observation of T-violation by the CPLEAR experiment in 1988 [16], theT-violation was regarded as the kind of statistical ﬂuctuation due to an increase of entropy
in our universe. The observation means that the T-violation can be explained as the resultof particle interactions. I was surprised at this fact, and at the same time I was so shocked
because we have no way to go back to the past of our universe although we can often go
back to the past in some kind of Science Fiction (SF) movie.
A large number of experiments to search for T-violating eﬀects have been performed
such as the particle and the nuclear electro dipole moment (EDM) experiments [17]. On
the other hand, we aim to measure the eﬀect in K + → π 0 μ+ νμ (Kμ3 ). More than 50 years
ago it was suggested by J. Sakurai [18] that the nonzero transverse polarization (PT ) of themuon in Kμ3 decay would be a deﬁnite signature of the T violation. Therefore, we want totest if the polarization of the muons perpendicular to the kaon decay plane is nonzero. The
system has several advantages such as the smallness of the ﬁnal-state interactions which
can mimic T violation by inducing a T-odd eﬀect.
The search of PT has been performed at the KEK-PS North Hall in KEK as the E246
experiment [19]. As the result of the E246 experiment, PT = −0.0017 ± 0.0023(stat) ±0.0017(syst) [20] was obtained as the world record, and the result was consistent with noT-violation.
Now we are preparing to perform the TREK experiment. The TREK experiment aims
to search for the T-violation with a sensitivity of PT ∼ 10−4 . In this sensitivity, we will
be able to discover the new physics beyond the SM. In chapter 1, I will describe the newphysics which will be covered by the TREK experiment, and I will also describe somedetector components for TREK.
For the TREK experiment, the muon polarimeter, which will measure the muon transverse polarization directly, is one of the most essential detectors. The polarimeter has beenstudied in my responsibility such as manufacturing of the prototypes, preparation of thebeam test, as well as analysis of the data including some simulations. Here, I will summarize the status of the muon polarimeter in the chapters as described below.
In Chapter 2, some requirements of the polarimeter will be described.
In Chapter 3, the outline of the beam test in TRIUMF [21] will be described.
In Chapter 4, some analyses based on the beam test data will be described.
3

In Chapter 5, a new design of the polarimeter based on the beam test analysis will be
described.
In fact, I have participated in the other test experiments for the TREK experiment. For
evaluating the kind of APD readout as one of the new candidate for the CsI(Tl) calorimeter,
we have also done a beam test at ELPH in Tohoku University.
Furthermore, I have also taken part in the commissioning of the K1.1BR beamline at
the Hadron Experimental Hall in J-PARC. Last autumn, the K1.1BR beamline started its
operation for the ﬁrst time. There, I have prepared and tuned all the detectors, for example
MWPCs, Gas Cherenkov detector, Hodoscope counter, Fitch Cherenkov detector, and TOF
counters, for measuring the K/pi ratio and the kaon yield. In addition, I have tuned all
the K1.1BR magnets downstream from the proton target along with our collaborators.
Thus, in Chapter 6, I will describe the status and the result of K1.1BR beam commissioning.
It was actually impossible to write everything on which I have worked for the TREK experiment due to time constraints. Thus, I will describe the development of the polarimeter
mainly.

4

Chapter 1
J-PARC TREK Experiment
1.1

Phenomenology of Kμ3 Decay

The matrix element for Kμ3 decay in the standard form of the V-A theory can be written
as [22, 23]
M∝

GF
sin θc [f+ (q 2 )(pλK + pλπ ) + f− (q 2 )(pλK − pλπ )] × [u¯μ γλ (1 − γ5 )uν ],
2

(1.1)

with two form factors f+ (q 2 ) and f− (q 2 ) of the momentum transfer squared to the lepton
pair, q 2 = (pK − pπ )2 . Here, GF is the Fermi constant, θc is the Cabibbo angle, pK , pπ ,pμ , and pν are the four-momenta of the kaon, pion, muon, and antineutrino, respectively.
Using pK = pπ + pμ + pν , Eq(1.1) can be rewritten asM∝GF
sin θc [f+ (q 2 )(pλK + pλπ )u¯μ γλ (1 − γ5 )uν + f− (q 2 )mμ u¯μ (1 − γ5 )uν ]2

GF
sin θc f+ (q 2 )[2pλK · u¯μ γλ (1 − γ5 )uν + (ξ(q 2 ) − 1)mμ u¯μ (1 − γ5 )uν ].
2
The parameter ξ(q 2 ) is deﬁned as=

ξ(q 2 ) = f− (q 2 )/f+ (q 2 ).

(1.2)
(1.3)

(1.4)

The ﬁrst term of Eq(1.2) corresponds to the vector and axial vector amplitude, and thesecond term corresponds to the scalar and pseudo-scalar amplitude. Both f+ and f− can,in general, be complex, but if T invariance holds, then the parameter ξ should be a real
number. Hence, any nonzero value of Imξ would imply T violation. The form factors f−
and f+ depend on q 2 as
f± (q 2 ) = f± (0)[1 + λ± (q/mπ )2 ],(1.5)
where the currently adopted values [23] of λ+ and ξ(0) are
λ+ = 0.0284 ± 0.0027
ξ(0) = −0.14 ± 0.05

5

(1.6)

and λ− = 0, namely, a constant f− .
The Dalitz distribution for Kμ3 decay is given by [23]ρ(Eπ , Eμ ) ∝ f 2 + [A + Bξ(q 2 ) + Cξ 2 (q 2 )],

(1.7)

1
A = mK (2Eμ Eν − mK Eπ ) + m2μ ( Eπ − Eν )4
1
B = m2μ (Eν − Eπ )2
1 2 
C = mμ Eπ4Eπ = (m2K + m2π − m2μ )/(2mK ) − Eπ

(1.8)

with

Here, Eπ , Eμ , and Eν are the pion, muon, and neutrino energies in the kaon center-of-massframe, respectively, and mK , mπ , and mμ are the kaon, pion, muon masses, respectively.
The Dalitz distributions are shown in Fig(1.1)(a).

Figure 1.1: The intensity distribution (a), and the three components of the muon polarization in the Kμ3 decay of (b)longitudinal component PL , (c)normal component PN , and(d)transverse component PT /Imξ as deﬁned by Eq(1.9).

6

1.2

Transverse Polarization PT

In general, one can deﬁne three orthogonal components of the muon polarization vector: thelongitudinal(PL ), normal(PN ), and transverse(PT ) as the component parallel to the muon
momentum Pμ , the component transverse to PL in the decay plane, and the component
normal to the decay plane, respectively. The directions of PL , PN and PT are schematicallyshown in Fig(1.2).
They are expressed as

Figure 1.2: Deﬁnition of PT , PN , PLσμ · pμ
|pμ |
σμ · (pμ × (pπ × pμ ))PN =|pμ × (pπ × pμ )|σμ · (pπ × pμ )PT =|pπ × pμ |
PL =

(1.9)

with the polarization vector σμ . Using the decay probability Eq(1.7), the muon polarizationin the kaon rest frame can be written as [22, 23] A|,σμ = A/|

(1.10)

 is determined as follows:
where A
 = (a1 (ξ) − a2 (ξ)[(mK − Eπ )A
+ (Eμ − mμ )(pπ · pμ )/|pμ |2 ])pμ − a2 (ξ)mμ pμ+ mK mμ Im(ξ)(pπ × pμ ).

(1.11)Here,a1 (ξ) = 2m2K [Eν + Re(b(q 2 ))(Eπ∗ − Eπ )]a2 (ξ) = m2K + 2Re(b(q 2 ))mK Eμ + |b(q 2 )|2 m2μ1b(q 2 ) = [ξ(q 2 ) − 1]2Eπ∗ = (m2K + m2π − m2μ )/(2mK ).
7(1.12)

These three polarization components are shown in Fig(1.1)(b)-Fig(1.1)(d). One has to lookfor PT in the presence of the predominant in-plane component of the polarizations, PL and
PN . PT can be further written as an explicit product of Imξ and a kinematical factor as
PT = Imξ ·|pμ |mμ.
mK [Eμ + |pμ |nμ · nν − m2 μ /mK ](1.13)The quantity Imξ, which is sensitive to T-violation, can be determined from a PT measurement. The advantage of Kμ3 over Ke3 (k + → π 0 e+ νμ ) is apparent as PT is proportional to
the lepton mass.
(1.14)< PT >∼ 0.3Imξ.
It is of interest to establish the connection between the Imξ and eﬀective parameters of
new physics appearing in the coeﬃcients of generic exotic interactions. To this end, aneﬀective four fermion Lagrangian can be used:GF
L = − √ sin θC s̄γα (1 − γ5 )uν̄γ α (1 − γ5 )μ2+ GS s̄uν̄(1 + γ5 )μ + GP s̄γ5 uν̄(1 + γ5 )μ+ GV s̄γα u¯ν γ α (1 − γ5 )μ + GA s̄γα γ5 uν̄γ α (1 − γ5 )μ + h.c..

(1.15)

here, GS and GP are the scalar and pseudo-scalar coupling constants and GV and GA are
the exotic vector and axial-vector coupling constants, respectively. Tensor interactions are
neglected. Imξ is found to be caused only by the interference between the SM term andthe scalar term, namely by the complex phase of GS [24, 25], which can be written asImξ = √

(m2 K − m2 π )ImG∗S,
2(ms − mu )mu GF sin θC(1.16)

where ms and mμ are the masses of the s-quark and u-quark, respectively. Thus, measurements of the PT can constrain the exotic scalar interactions.

8

1.3

Theoretical Predictions

The amplitude of the T-violating transverse muon polarization has been estimated in various theoretical models. In this section, I will brieﬂy describe several models which mightlead to a sizable PT value. I will also give a more general discussion based on the effective ﬁeld theory to clarify the diﬀerence of PT physics from other T and CP violating
observables.

1.3.1

Standard Model

A T-violating amplitude arises from the relative phases between diagrams or complex
coupling constants in a diagram. Since only a single element of the Cabibbo-KobayashiMasukawa matrix Vus is involved in the W-exchanging semi-leptonic Kμ3 decay in theSM, no CP violation appears in ﬁrst order. [26] The lowest order contribution comes fromradiative corrections to the ūγμ (1 − γ5 )sW μ vertex as shown in Fig(1.3) is presented in the
textbook of Bigi and Sanda [27]. This has been estimated to be less than 10−7 .

Figure 1.3: Radiative corrections in the Kμ3 decay

1.3.2

Final state interactions

Strictly speaking, a measured non-zero value of a T-odd observable does not automaticallymean T-violation. Spurious PTem can be induced by electromagnetic ﬁnal-state interactions(FSI). This has been a concern in PT experiments for quite some time. In the case ofKμ3 decays, the FSI are mainly due to electromagnetic interactions. Since the FSI contributions to PT in the present case are much smaller than those in K 0 μ3 decay, where thetwo charged particles can interact in the ﬁnal state and PTem ∼ 10−3 , this eﬀect may limit
the sensitivity for T violation and it has been extensively investigated. The single-photon
contribution to PTem that arises in this decay due to the imaginary part of the two-loop
diagram was estimated more than 20 years ago as PTem ≤ 10−6 [28]. An example is shownin Fig(1.4)(a). More recently, two-photon exchange contributions to PTem have also beenstudied in Ref [29], where the transverse polarization is proportional to the imaginary partof the diagrams shown in Fig(1.4)(b). The average value of PTem over the Dalitz plot was
concluded to be less than 10−5 . Thus, a nonzero PT in the range of ∼ 10−3 − 10−4 would
9

unambiguously imply the existence of a new physics contribution.

Figure 1.4: (a) One of the diagrams of the ﬁnal state interactions contributing to PTem ;from one photon exchange calculated in Ref [28] and (b) one of the diagrams from two
photon exchanges calculated in Ref [29].

1.3.3

Multi-Higgs doublet model

As the minimum and natural extension of the SM with one Higgs doublet, multi-Higgs
doublet models have been considered [30, 31, 32, 33, 34, 35, 36, 37, 38] as one of thepromising candidate theories for non-zero PT . This model was originally proposed by
S.Weinberg [39]. One doublet is for up-type quarks, one for down-type quarks, and one for
leptons. This Higgs generation number does not allow for ﬂavor changing neutral current(FCNC). To avoid the FCNC, Weinberg proposed natural ﬂavor conservation (NFC), which
requires that all fermions couple to only one kind of Higgs doublet. With the NFC, it iswell-known that at least three Higgs doublets are needed to generate CP violation. In theclass of models without tree-level FCNC, new CP violating phases are introduced,
1) in the complex phase of CKM,
2) in the complex charged Higgs mixing matrix,3) in the neutral-Higgs mixing matrix.
Here, 1) and 2) are associated with the CP violation in the Kμ3 decay. The coupling ofquarks and leptons to the charged Higgs boson is expressed in terms of the Lagrangian [30,
31]
2

√
1
2
[αi u¯L V MD dR Hi + + βi u¯R MU V dL Hi + + γi ν¯L ME eR Hi + ] + h.c., (1.17)
L = (2 2GF )i=1

where MD , MU , ME are diagonal mass matrices, V is the CKM matrix, and αi , βi and γi
are the new complex coupling constants associated with the charged Higgs interactions.
For three doublet case the NFC can be arranged. In this model CP symmetry canalso be broken spontaneously due to the complex phases of the vacuum expectation values
10

of the Higgs ﬁelds. The coeﬃcients, αi , βi and γi can have complex phases, and PT is
calculated as
m2 K
Imξ = 2 Im(γ1 α∗ 1 ),(1.18)
mH
where α1 and γ1 are the quark and lepton couplings to the lightest charged Higgs boson.
The E246 result [40] yielded |Imξ(γ1 α∗ 1 )|/mH 2 < 0.066(GeV)−2 (90 % C.L.) as the moststringent limit for this parameter. It is also constrained by the semi-leptonic decay of the
B meson [41], B → τ νX, but the result is less stringent than the PT constraint. The
recent result of B → τ ν published by the BELLE collaboration in Oct 2010 [42] is also lessconstrained due to a large uncertainty of the theoretical calculation for the SM branchingratio. Suppose that the TREK will achieve 20 times higher sensitivity of PT than the E246
result, the TREK will give 10 times stronger constraint directly against this parameter.
Other constraints to this model come from the neutron EDM (dn ), b → sγ [41] andb → sl¯l [43] complementing the PT result in a diﬀerent manner, since these channels limit
Im(α1 β1∗ ).
These two parameters are related as Im(α1 β1∗ ) = −(v3 /v2 )2 Im(γ1 α1∗ ) through the ratioof the vacuum expectation values v2 and v3 . An interesting scenario assumed in Ref [30] isv3 /v2 ∼ mτ /mt ∼ 1/80 thus making PT the most sensitive test of the three Higgs doublet
model over dn and b → sγ.
The important feature of this model is the prediction of PT in the radiative decay
K + → μ+ νγ(Kμνγ ). The following expression was obtained [24],2mK
PT (Kμνγ ) ∼= −0.1 2 Imξ(γ1 α∗ 1 ),mH

(1.19)

with the same parameter as PT (Kμ3 ) but with diﬀerent size and sign. The E246 provided
a result [44] but with less statistics. Although the ﬁnal state interaction is large and on
the order of 10−3 we may purse this mode also at J-PARC in the future.

Furthermore, it is essential to compare the PT with the collider experiments, in particular the LHC. If the LHC ﬁnds the charged Higgs boson, the PT measurement will be
important to look for associated CP violating couplings. Provided that a MSSM Higgs
boson is discovered with 5 σ signiﬁcance after an integrated luminosity of 30 fb−1 , the discovery of this would yield a value of tan β/mH + ≥ 0.06(GeV)−1 . If this limit is applied to
the lightest charged Higgs boson with regard to the multi-Higgs model, the PT corresponds
to |PT | < 3 × 10−4 . This roughly corresponds to the sensitivity of the TREK experiment.

11

Figure 1.5: T-violating diagram in the three Higgs doublet model in Kμ3 decay. Interference
between (a) W + exchange and (b) charged Higgs exchange is the main contribution.

1.3.4

SUSY models

A number of other models also allow PT at observable level without conﬂicting with otherexperimental constraints. Supersymmetric models have attracted many physicist, since itoﬀers the natural uniﬁcation of strong and electroweak interactions, and a natural solution
to the mass hierarchy problem. However, the current experimental information of thesemodels is not suﬃcient. Thus, intensive experimental researches have been devoted to
study the model. Some MSSM models allow sizable values of PT .
In the MSSM, we require R-parity conservation.
R ≡ (−1)3B+L+2S(1.20)

where B, L and S are baryon number, lepton number and intrinsic spin of the particle,
respectively. R = +1 for the ordinary particles and R = −1 for their superpartners are
assigned. Thus, if R-parity is conserved, superparticles are produced in pairs. In addition,
it ensures the stability of the proton and the stability of the lightest superparticle (LSP),
which is one of the candidates for dark matter in our universe.
One interesting case is the MSSM discussed by G.-H. Wu and J.N. Ng [45]. In thismodel the complex coupling constant between the charged Higgs boson and s-quarks andu-quarks is induced through squark and gluino loops. The PT value, when the muon andneutrino momenta are at right angles, is given as+pμ (μ + At cot β)
Eμ
mg
∗
∗
H+
DL
2
(100GeV) Im[V33 V32 V31 UR ]MH2sin θCPT H ≈ 3.5 × 10−3 IH +(1.21)

for tan β ≈ 50. If we allow large ﬂavor mixing coupling in the squark-quark vertices,
there is an allowed parameter region for large PT . The E246 PT upper bound corresponds12to MH > 140GeV. In the view of several assumptions made, this boundary should beconsidered as a qualitative estimate. It is noteworthy that PT (Kμ3 ) and PT (Kμνγ ) have
opposite signs in this model.

Figure 1.6: T-violating diagram of Minimal Supersymmetric Standard Model in Kμ3 decay.

SUSY with R-parity violation
On the other hand, if R-parity is not conserved, the situation is completely changed. Under
such conditions, single production of superparticles becomes possible. According to one of
the R-parity violating models [46], the superpotential which breaks R-parity can be writtenas(1.22)
W = λijk Li Lj Ekc + λijk Li Qj Dkc + λijk Uic Djc Dkc ,where λijk , λijk , λijk are coupling constants with i,j,k being family indices. Li , Ei , Qi ,(Uic , Dic ) denote superﬁelds of the left-handed lepton doublets, lepton singlets, left-handedquark doublets and singlets, respectively. Here, λijk = −λijk and λijk = −λijk . The
ﬁrst and second terms represent lepton-number violation, the third term is baryon-numberviolation. It has been well known that there is a very tight constraint on λijk from nonobservation of proton decay. For this reason, R-parity was originally introduced to the
MSSM. It would be easier to understand the R-parity breaking interaction, if the cor
responding Lagrangian is given from Eq(1.22). First, let us assume λijk = 0, becauseof non-observation of proton decays. For the non-zero λijk and λijk , the corresponding
Lagrangian is given by1ceLj ẽ∗Rk + ēRk νLi ẽLi − (i ↔ j)]
L = λijk [ν̄Li2c+ λijk [ν̄Li
dLi d˜∗Rk + d¯Rk νLi d˜Rj + d¯Rk dLj ν̃Li− ēc uLj d˜∗ − d¯Rk eLi ũLj − d¯Rk uLj ẽLi ] + h.c,
Ri

Rk

13

(1.23)

where the tilde denotes the scalar fermion superpartners. The subscripts of R and L areright-handed and left-handed, respectively. This Lagrangian describes possible R-parity
breaking couplings. Eq(1.23) shows that tree level contributions are allowed in the diagramsof PT in Kμ3 decay. Typical diagrams are shown in Fig(1.7). Thus, it could give large
contributions to PT . Theoretical calculations predict PT of the order of 10−3 .

Figure 1.7: T-violating diagram of R-parity breaking Supersymmetric Standard Model
in Kμ3 decay, (a) and (b) are possible diagrams , (a) is a slepton exchange and (b) is adown-type squark exchange. Note that the diagram (c) does not exist.

14

1.4

J-PARC TREK experiment

Considering the current experimental situation of direct CP violation (or direct T-violation)
studies and searches for new physics, we believe that it is essential to perform a PT mea+
surement in Kμ3
at J-PARC, which oﬀers much superior experimental environment. The
transverse muon polarization (PT ) in Kμ3 decay is one of the best indicators for the direct
T-violation. In addition, it can be a better probe to search for new physics, in particular
new CP violation source, beyond the SM with less background than any other probe of PT .
In terms of the fact that currently there is no PT experiment beyond the E246 limit
around the world, we think that this PT experiment ranks high among the particle physics
experiments in the low energy region. Hence, we should be responsible for the PT experiment as a leading group and we will perform the TREK experiment in J-PARC.
The crucial merits of the TREK experiment compared with the E246 experiment are
as follows.
1)In a case that the TREK experiment runs for nearly 1 year with ∼ 270 kW proton
intensity, a large number of K + events, which corresponds to more than ≥ 100 times ashigh as the E246 experiment, will be available though the E246 experiment was limited by
the statistical error. In addition, as we employ an active polarimeter, the analyzing poweris more than 2 times higher than the E246 experiment. This means that eventually wewill be able to improve the sensitivity of the PT up to more than ≥ 20 times as high as
the E246 experiment even √considering the fact that the statistical sensitivity of asymmetry
measurements scales as 1/ N .
2)Along with an uncertainty of statistics, we must reduce systematic errors in the E246,
which is summarized in Table(2.1), at least by one order of magnitude in order to achieve
the sensitivity of ∼ 10−4 . For accomplishing the sensitivity above, we have to upgrade theE246 detectors.
• New polarimeter system (an active polarimeter + muon polarimeter magnet) is
adopted to reduce the μ+ multiple scattering and an uncertainty of the magnetic
ﬁeld in the polarimeter.
• New electronics and read-out, in particular CsI(Tl) read-out, systems will be adopted
to handle the higher event rates.
• Additional tracking GEM chambers for charged particle is adopted for improving an
uncertainty of the determination of decay planes.
• A slimmer target with ﬁner segmentation is adopted in order to improve an uncertainty of the K + stop position.
We plan to perform the TREK experiment using the K1.1BR beamline at Hadron Experimental Hall in J-PARC in 2015 - 2016. At present we are waiting for the realization15

of accelerator high power operation (currently ∼ 5 kW intensity beam for slow extraction is available.), and after ﬁnishing another experiment (P36) at K1.1BR which can be
performed with lower accelerator power, we will start to perform the TREK experiment.
The preparation of all the detectors is in progress. In the next section, these detectors aredescribed in detail.

1.5

Experimental Setup

In order to overcome the limitations of the E246 experiment, several improvements to thedetector system must be undertaken. In this section, I will present an overview of the
TREK detector system and several important detectors as follows.

1.5.1

Overview of TREK detector setup

The TREK experiment will be performed using a toroidal spectrometer setup in conjunction
with a stopped K + beam at the low momentum separated kaon beamline K1.1BR in the
Hadron Experimental Hall of the J-PARC 50 GeV synchrotron. The spectrometer consistsof an iron-core superconducting toroidal magnet with 12 gaps. The setup is shown inFig(1.8). The K + beam will be stopped in an active target located at the center of themagnet. Kμ3 decays are identiﬁed by detecting a π 0 with a CsI(Tl) barrel surrounding theactive target, a muon with a charged particle tracking system consisting of GEM chambers(C0, C1), MWPCs(C2, C3 and C4) and the target with particle identiﬁcation by meansof time-of-ﬂight(TOF). This arrangement will enable a measurement of the decay pions
ranging over all directions covering all regions of the decay phase space for a given μ+
momentum. As described next, this scheme allows for a “double ratio” measurement and,thus, a number of systematic errors can be suppressed. The CsI(Tl) barrel has 12 holes toadmit charged particles into the magnet gaps. Since the barrel does not cover the full 4πsolid angle, not in all events will the two photons from π 0 decay be detected. However, one
photon with relatively large energy can also be used to determine the π 0 momentum. Muons
are bent by about 90 deg, momentum-analyzed, and then they enter the muon polarimetersystem. After passing through a spectrometer and Cu degrader, the muons are ﬁnallystopped in the active polarimeter. The muon polarization is measured by means of the
decay positron asymmetry. When π 0 s are detected in the forward (FWD) or the backward(BWD) directions relative to the beam axis, transverse component PT lies in the azimuthal
directions in each polarimeter clockwise (cw) or counterclockwise (ccw), respectively, as
shown in Fig(1.9). Thus, the magnitude of the transverse polarization PT ∼ σμ · pπ0 × pμ+can be measured as the azimuthal asymmetry of positron emission, namely, a cw and ccw
emission rate diﬀerence.

1.5.2

Fitch-type Cherenkov counter

The Fitch-type Cherenkov counter will alos be described in detail in Chapter 6.

16

1.5.3Beamline

The K1.1BR beamline for the TREK experiment will be described in detail in Chapter 6.

Figure 1.8: Side view (top) and end view (bottom) of TREK detector

17Figure 1.9: T-violating azimuthal polarization PT for the case of the π 0 going in the forward(fwd) and backward (bwd) directions.

1.5.4

K + stopping target

In order to localize the K + stopping point (decay vertex) and also to help the tracking of
the decay particles, the K + stopping target is an active bundle of scintillating ﬁbers. The
bundle is made of 489 pieces of 3.0 mm rectangular scintillating ﬁbers with a length of 20
cm forming a 7.5 cm diameter cylinder. In each ﬁber a thin wavelength shifter (WLS) ﬁber
is embedded in a groove and the light through the nearly 1.5 m long WLS ﬁber is readby a multi pixel proportional counter(MPPC). The ﬁne segmentation is also necessary to
suppress backgrounds in reconstructed trajectories. The manufacturing of the target has
been started at TRIUMF in Canada.

Figure 1.10: Scintillating ﬁber target for TREK experiment. The active zone has a lengthof 20 cm and a diameter of 7.5 cm. Each of the 489 ﬁbers has 3.0mm × 3.0mm square crosssection. The ﬁber bundle is surrounded by 12 ﬁducial counters.

Figure 1.11: Example picture of scintillating ﬁber with two thin wave length shifter (WLS)
ﬁbers although an actual number of WLS is equal to 1.
18

1.5.5Photon Counter

The photon counter is one of the most important detectors for the TREK experiment. The
muon transverse polarization axis is determined directly whether the π 0 is emitted forward
or backward. To reconstruct the π 0 mass and momentum, 768 CsI(Tl) crystals, which havealready been used in the E246 experiment, with APD readout, will be adopted. These
photon calorimeters make up a barrel surrounding the target region as shown in Fig(1.12).
There are twelve muon holes to allow the charged particles to enter the spectrometer. The
solid angle coverage is therefore less than 4π (∼ 3π if we include the losses due to the K +beam entrance and exit holes). The size of the muon hole was optimized to maximize theKμ3 acceptance. As shown in Fig(1.12), the barrel structure is symmetric for the upstream(forward) and the downstream (backward) side, which is essential in the TREK experiment.
The barrel was assembled very carefully ensuring a local as well as a global precision of
better than 1 mm. The main parameters of the barrel are summarized in Table(1.1). The
calorimeter worked very well in the E246 experiment.
Some valuable features of the photon calorimeter are as follows. First of all, the highlight yield of each crystal is conﬁrmed with a low photon energy threshold (≤ 5 MeV). The
timing information can be also extracted and this will be available in the analysis. Theenergy response function has a signiﬁcant tail on the low energy side mainly due to shower
lateral leakage into the muon holes, but the intrinsic energy resolution of the spectrum isreasonably good. In addition, the angular response of a photon was conﬁrmed to be equal
to 2.40◦ using Kπ2 events in the E246 experiment. These angular characteristics become
more important in the TREK experiment. The typical responses measured in the E246
data are shown in Fig(1.13). The performance related to energy might be diﬀerent after
modifying the readout scheme, but the angular characteristics will remain almost the same.

Figure 1.12: CsI(Tl) barrel with 768 crystal modules. There are 12 muon holes.

19Figure 1.13: Performance of the CsI(Tl) detector for Kμ3 and Kπ2 in E246. a) Invariant
mass spectrum of two photons of Kμ3 , b) cluster timing distribution also of Kμ3 showing
the time resolution, c) opening angle distribution of Kπ2 showing the angular resolution,and d) two-photon and one-photon energy spectra of Kμ3 events.

Table 1.1: Main parameters of the CsI(Tl) calorimeter.
Parameter
Value
Number of CsI(Tl) crystals 768
SegmentationΔθ = Δφ = 7.5◦ .
Inner / outer diameter
41 / 90 cm diameter
Detector length
141 cmSolid angle coverage∼ 75%
Crystal length
25 cm (13.5 X0 )Typical size of crystals
3 ×3 − 6 × 6 cm2
Wave length at peak
560 nmLight decay time
∼ 900 ns20

Avalanche photo-diode readout (APD)
In the E246 experiment, the PIN diode readout was used, but it is impossible to take data
under the higher counting rate condition expected at J-PARC. Considering the higher intensity of the K1.1BR K + beam, it is necessary to use a preampliﬁer which can be operated
under high rate conditions. Thus, we are planning to use avalanche photo-diodes (APD)of reverse type. Such APDs with multiplication factors of about one hundred with reasonably large sensitive areas are commercially available. The conceptual scheme of the APD
readout is shown in Fig(1.14), and the relevant parameters are compared with the PIN
readout in Table(1.2).
The output from the ampliﬁer system will be read by FADCs (65MHz sampling with 12bits) recently developed by the KEK electronics shop. The FADCs are very powerful toresolve pulse pileup. If the photon statistics are large enough, one may in principle analyze pileup events up to the rise time of the FADC input pulse, namely the rise time ofa photon signal as determined by the light emission mechanism, the shower developmentin the crystal, and the light propagation/collection in the crystal. If we apply a simple
current ampliﬁer, the noise is more serious. This point which might lead to pulse height
uncertainty will be solved by the integration (hardware or oﬀ-line) of the signal over thetime window of 900 ns at the cost of pileup resolving capability. In this case, we may
expected the pulse separation of a pileup with a time diﬀerence larger than half of the
decay time (400 ns) is not spoiled. In a conservative estimation, the calorimeter system
can tolerate an average counting rate of 0.1 MHz in each crystal with a loss of 4 %. Sincea photon cluster involves 3 × 3 = 9 crystals, the maximum rate of 0.1 MHz in each crystal
corresponds to a total decay particle rate, of nearly 20 MHz, into the total solid angle of
4π, which is large enough for the beam intensity in the TREK experiment.
To evaluate the performance of the APD read-out and 65 MHz FADCs, we have alreadyperformed a beam test at the Research Center for Electron Photon Science, Tohoku University in June 2010.

Figure 1.14: Readout scheme of the CsI(Tl) calorimeter using APD

21

Table 1.2: Readout scheme using APDs compared with the E246 PIN readout.
Parameter
E246-PIN
APD readout
Diode
1× S3204-03
1× S8148
5 × 5 mm2
Total area
18 × 18 mm2Quantum eﬃciency∼ 0.70> 0.807Photoelectron / GeV
1.1 × 10
4.0 × 106
Diode gain
1
50
6
Electron yield at 100 MeV 1.1 × 10
2.0 × 107
Preampliﬁer
Charge sensitive Current ampliﬁer

1.5.6

Superconducting spectrometer magnet

The superconducting spectrometer magnets will be reused for the TREK experiment. Basically, the performance of the spectrometer expected for the TREK experiment is the sameas the E246 experiment. Hence I will describe the status of E246 spectrometer as follows.
The heart of the muon spectrometer is a superconducting toroidal magnet with 12 ironsectors separated by 12 gaps. Each iron sector is magnetized by a superconducting coil,and a ﬁeld up to 1.8 T can be excited across the 20 cm uniform gaps. At a ﬁeld strengthof 0.9 T, which is used for this experiment, the ﬁeld is nearly completely dipole with aslight toroidal component superimposed. Charged particles from the target located in thecenter of the magnet are bent by ∼ 90◦ and tracked by several chambers at the entrance
and exit of the gap. One sector of the magnet is illustrated in Fig(1.15). In manufacturingof the magnet, special care was taken to assure the dimensional accuracy necessary forhigh precision experiments. Each iron core was machined with a precision of 50 μm. The
positioning of the superconducting coil relative to the core to form a sector was achieved
within an accuracy of 2 mm. Assembly of the entire structure was performed using a
special positioning device ensuring a rotational symmetry of 30◦ . The 12 median planes of
the gaps converge to a virtual central axis with an accuracy of 0.3 mm. The diﬀerence ofthe diameters in the horizontal and vertical directions is less than 2 mm over a diameterof about 4.0 m. As a superconducting magnet this device is unique in its structure. The
coil windings are NbTi monolith stabilized by Cu operated at about half of the criticalcurrent density at 4.5 K and maximum excitation. The windings are cooled indirectly by
two-phase He ﬂow through one turn of cooling channels around the windings. The 12 coils
are connected in series and equal ﬁeld distributions are generated in the 12 gaps. A power
supply with a stability of 5 × 10−5 is used. Because high-quality magnet steel was used forthe cores, there is no signiﬁcant hysteresis in the magnetization. The validity of the map
has been checked using the measured monochromatic momentum spectra of muons fromKμ2 and pions from Kπ2 in the E246 experiment.

1.5.7

Tracking Chamber

E246 tracking system

22

Figure 1.15: One sector of the superconducting toroidal magnet.
In E246, ﬁve diﬀerent tracking elements have been employed, three planar multiwire proportional chambers (MWPC) C2, C3, and C4, a cylindrical drift chamber C1, a scintillatingﬁber target and ring counters surrounding the target as shown in Fig(1.16). For each of
the 12 sectors, positively-charged tracks leaving the target in the transverse direction passthrough the gap of the CsI calorimeter and are bent in the toroidal magnetic ﬁeld by about
90◦ . The track reconstruction has been based on the three planar chambers C2, C3 andC4 and the ring counters. The C2 element is located at the entrance gap of the magnet,
while the C3 and C4 chambers reside near the focal plane at the exit gap of magnet infront of the muon polarimeter. Near the target, another element, C1 drift chamber withcylindrical geometry was installed. However, due to its imperfect high rate performance,
the C1 chamber has not been included in the ﬁnal analysis. Thus, only the ring counter
was used for tracking in the source vicinity, but it had a much worse resolution (6 mm) as
compared to the other chambers. The momentum of the charged particle was deduced fromthe reconstructed momentum corrected for the energy loss in the target. The background
was rejected in the momentum spectrum as well as in the χ2 cuts of the track ﬁtting.

TREK tracking system
At J-PARC, two sources of systematic errors will dominate. While one source is givenby the background contamination from Kπ2 -dif events1 , the other source of systematics isdue to misalignments of the setup, in particular of the muon polarimeter. In the TREK
tracking system, the errors from both backgrounds and the alignment will be improved to1nuμKπ2 -dif is one of the decay mode corresponding to K + → π 0 π + → π 0 μ+23

Table 1.3: Main parameters of the charged particle tracking
Item
TREK
E246(reference)High resolution elements C0, C1, C2, C3 and C4
C2, C3 and C4
Scintillator elements
TargetTarget + Rings
C0 chambercylindrical GEM chamber C1 cylindrical chamber
C1 chamber
planar GEM chamber
C2 chamber
MWPC (the same)
MWPC
C3 chamber
MWPC (the same)
MWPC
C4 chamber
MWPC (the same)
MWPC
C3-C4 distance
30 cm
15 cm
Magnet gap
He gas bag
air
6.6 × 10−3 X0
Total material thickness ∼ 7 × 10−3 X0
meet the requirement of 10−4 for the systematic error in PT . These performance goals will
be achieved both by reducing the material budget along the track and by rearranging thecurrent tracking elements and adding new GEM chambers in replacement of the previous
C1 chamber. The momentum uncertainty of 3.6 MeV/c in E246 can be reduced at leastby one order,
1) by employing a 6 cm instead of 7.5 cm diameter target with a segmentation of 3.0 × 3.0
mm2 ﬁbers instead of 5 × 5 mm2 ,2) by replacing the air volume in the magnet between C2 and C3 and before the C2 chambers with helium bags and by increasing the distance between the C3 and C4 elements to30 cm.
For suﬃcient identiﬁcation and suppression of Kπ2 -dif events we need to build a GEM
cylindrical tracking chamber (C0) with a radius of 10 cm and a spatial resolution < 0.1 mm.
The new C0 chamber will replace the previous cylindrical C1 chamber of the E246 setup.
In order to increase the tracking redundancy we will also add a new planar tracking element(again named C1) with < 0.1 mm resolution to cover each of the 12 gaps at the outer surfaceof the CsI calorimeter. By adding these additional elements to the track ﬁtting procedure,
the resulting χ2 / degree of freedom will be much more eﬀective to distinguish tracks from
Kπ2 -dif from regular tracks which do not have a kink along their path. In combination withthe higher segmentation of the ﬁber target, this will be suﬃcient to suppress the Kπ2 -dif /Kμ3 ratio below 10−3 , rendering a spurious PT < 5 × 10−5 . Fig(1.16) shows a comparisonof the tracking system in the E246 and the TREK experiments. In addition, the tracking
elements parameters compared with the E246 are shown in Table(1.3).

24

Figure 1.16: Schematics of the tracking system in the E246 setup (left) and the TREK
setup (right)

1.5.8

Muon polarimeter

The muon polarimeter for the TREK experiment will be described in detail in the next
chapter.

1.5.9

Muon polarimeter magnet

A uniform muon polarimeter magnet with a large strength is essential for the TREK
experiment, whereas a passive ﬁeld was used by guiding and trimming the main ﬁeld of thesuperconducting magnet in the E246 experiment. The unavoidable consequence was that
there was a non-uniform strength distribution and a curved ﬂux distribution at the stopper.
A uniform ﬁeld parallel to the PT component provides the maximum analyzing power. Somerequirements of the muon polarimeter magnet, size, ﬁeld strength and uniformity, are as
follows.
To accommodate the polarimeter with range stacks on both sides the parallel gap of thedipole magnet must be about 30 cm. The area is determined to produce a uniform ﬁeld
distribution in the polarimeter region. From the point of view of1) spin relaxation suppression,25

Table 1.4: Main parameters of the muon ﬁeld magnet
Parameter
Value
Gap size
70cm(x) × 45cm(z) × 31.4cm(y)Central ﬁeld
0.03 T at I = 12 A
Magnetic motive force 3744 A Turn / coil for 0.03 T
Power consumption
530W /coil at 0.03 T
Assembly precisionbetter than 50 μA2) stray ﬁeld decoupling,a strong ﬁeld is preferable. However, the ﬁeld is limited by the interference with thetoroidal magnet, in particular with its SC coils. Point 2) is regarded as the determining
factor; assuming 0.3 Gauss of an unwanted component in the shielded magnet gap, a ﬁeld
strength of at least 300 Gauss is necessary to obtain a ﬁeld alignment of 10−3 .
The ﬁeld symmetry across the median plane is important but a non-uniformity of 10−2 instrength as well as in vector distribution is tolerable in the positron energy analysis.
A one sector prototype of the muon polarimeter magnet has been tested in the North
Hall of KEK. After the symmetry measurement using the opposite coil-current method of
the pole faces and coils without a return yoke, the magnet is now equipped with the lowweight yokes and a return yoke as shown in Fig(1.17), and normal ﬁeld distribution withnormal coil currents were measured. By installing the shim system, a ﬁeld distribution
with a uniformity good enough for the polarimeter was achieved in the ﬁducial volume.
This magnet can be applied to the TREK experiment. It would be, however, necessary tocompare the distribution with a 3D TOSCA calculation with the ﬁnal realistic geometry.
An improved shim system which realizes a larger ﬁeld-ﬂat volume might be possible. We
don’t know if the perpendicular Bx in the ﬁducial volume is small enough to suppress thesystematic error due to δz rotation, although its detailed estimate depends on the actual
muon stopping distribution in the polarimeter and this is not yet known.

Figure 1.17: Muon ﬁeld magnet one sector test setup.

26

1.5.10

Electronics and data aquisition

In order to overcome the higher counting rate at J-PARC, a much faster ADC system
has to be used. The data-taking speed will be 100 times faster than E246. Currently weare considering a KEK-VME system, which is being developed at KEK. The KEK-VME
is based on the standard VME crate but it is equipped with a power supply for analog
modules and digital signal nets for timing and trigger purposes. The readout modules are
made of 9U type VME modules and are called COPPER. An ADC module, for example,
can acquire data using several kinds of ADC cards (FINESSE) on board with dead timesof only several μs. A FADC COPPER with 65 MHz sampling and a 12-bit range has
already been developed by the KEK electronics shop and they have already been used for
the CsI(Tl) readout test at Tohoku University. This FADC will be used for the CsI(Tl) andmuon polarimeter readout in the TREK experiment. A TDC COPPER/AMT-FINESSE
with a resolution of 0.78 ns/bin with a delaying dynamic range of 17 bits has also beendeveloped. We are considering the possibility of this module for chambers and counters.
In addition, to acquire the data of TOF, which is required for higher time resolution, we
have to consider a high resolution TDC. One possibility is a chip with 50 ps resolution and1.8 ms range, which is now under development. A multi-stop charge-sensitive ADC /ASIC
is also being developed.

27

Chapter 2
Muon Polarimeter for TREK
Experiment
2.1

Muon polarimeter

The transverse muon polarization (PT ) in Kμ3 decay is ﬁnally measured by the polarimeter.
In principle, a decay positron with more than 30 MeV energy from the Michel decay canpreserve the muon spin direction due to the helicity conservation. This is a basic mechanismof the polarimeter. Hence, the polarimeter has to measure an emitted direction of the decay
positron precisely along with the transverse axis, hence the PT is measured as a transverse
asymmetry of the decay positron (AT ).
It is no exaggeration to say that the most important feature of the TREK experimentis the adoption of an active polarimeter with the ability of measuring a trajectory ofparticles in contrast to the E246 experiment which used a passive polarimeter. The passive
polarimeter consists of a separated system of a muon stopper and positron counters. The
advantage of this passive system was the simplicity of the analysis with the consequenceof very small systematic errors associated with the analysis. The systematic cancellation
scheme, namely the asymmetry is summed over the 12 sectors, is also based on the useof both clockwise and counterclockwise counters at the same time. However, the passive
system did not overcome the cost of e+ detection acceptance and polarization analyzing
power. We now aim for higher detector acceptance and higher sensitivity by introducing anactive polarimeter. The suppression of the systematic errors ensured in the E246 passive
polarimeter will be guaranteed by a diﬀerent method.

28

2.2

Passive polarimeter for the E246

A passive polarimeter as shown in Fig(2.1) was used for measuring PT in the E246 experiment. The E246 analysis method will be able to give us some hints about how to improveand build the new polarimeter.
Structure of the E246 polarimeter

Figure 2.1: Schematic structure of the muon polarimeter.
One sector of this polarimeter consisted of the following components,
1) a wedge shaped Cu degrader for decreasing the speed of muons,2) Fe shims for adjusting the magnetic ﬁeld from the toroidal spectrometer,3) one polarimeter trigger counter,4) 8 pure Al plates of 6 mm thickness with size of 16 cm width and 55 cm height with 8mm spacing in between for stopping muons,5) two sets of counters for detecting positrons,6) veto-counter.
The width of the pure Al plates are smaller than the toroidal spectrometer gap of 20
cm and polarimeter trigger counter width of 18 cm so that all the stopped muons would
generate a trigger. The height was chosen to cover the necessary momentum range andthe total Al thickness of 48 mm was enough to stop muons in a wide momentum range
with an eﬃciency of more than 85 %. The spacing lowered the eﬀective average density of29

Al to suppress the e+ interaction creating nearly optimum conditions for the asymmetry
measurement. Veto-counters behind the stopper detected nonstopped muons to suppress
background decays from the surroundings.
The holding ﬁeld strength applied by two iron shim plates aside the stopper varied from
300 to 150 G with a vector direction as shown in Fig(2.2).

Figure 2.2: Magnetic ﬁeld distribution on the muon stopper
The shim plates were aligned with a precision better than 200 μm relative to the magnet gap in order to produce a symmetric ﬁeld distribution across the median plane. A
ﬁeld mapping was performed to check the ﬁeld symmetry and to measure the strength
distribution for all 12 gaps. The ﬁeld vector could be analyzed with a precision of 1 mr.
Positrons were counted by a plastic counter (e+ counter) of 6 mm thickness segmented
in three parts in coincidence with two sandwich coincidence counters of 3 mm thickness.
The counter system was aligned with a precision of a few mm relative to cw as well as
ccw stoppers. One positron counter system served as both the cw and ccw counter withthe same detection eﬃciency. The solid angle of detection (about 10 % on each side) was
determined by the three e+ counters and the detection threshold was set at 5 MeV. The
positron time spectra were measured with a multistop time-to-digital converter (TDC) witha time range of 20 μs relative to the time origin.

30

The analysis method of the E246 polarimeter
The transverse polarization was measured as an asymmetry deﬁned asA=

Ncw − Nccw
Ncw + Nccw

(2.1)

with the clockwise (cw) and counterclockwise (ccw) counts Ncw and Nccw , respectively. A
measurement to determine the null asymmetry A0 , was also needed to ensure an accurate
PT . For measuring the null asymmetry, the data, which did not require the π 0 direction(f wd direction or bwd direction), could be used. In this case, most of the data could include
Kπ2 events. After conﬁrming the data quality from the null asymmetry measurement, thetransverse polarization (PT ) measurement could be performed. In order to take better
quality PT data from Kμ3 decay, a double ratio method was performed for two opposite
kinematic situations which correspond to the π 0 direction, respectively (f wd/bwd). Paying
attention to just one e+ counter, it could count both Ncw and Nccw . This means that theeﬃciency of this counter is canceled out when we sum up the 12 sectors data with 12-foldazimuthal symmetry. This method played an important role in reducing the systematic
errors. However, several diﬃculties still remained. When the transverse asymmetry was

Figure 2.3: Incident muon y distribution in the stopper measured by the C4 chamber (top),
and the intrinsic geometrical asymmetry for those muons (bottom). The real stopping distribution has a smearing due to beam divergence and multiple scattering. The geometricalasymmetry was measured as the null asymmetry A0 by accepting all π 0 directions.
measured, it was essential to consider the fact that the muon stop distribution could aﬀect
31

the asymmetry very strongly. In particular, a shift along the y direction was critical.
The asymmetry A0 (y) for the muons is shown in Fig(2.3). The eﬀect of the shift on theasymmetry is δA = k×δ y with k = 0.015/mm for the average shift δ y . Considering sucha spurious eﬀect, the asymmetry was analyzed diﬀerentially using the y-information fromthe C4 chamber which is in front of the polarimeter. The y dependence of the T-violating
asymmetry AT (y) was calculated as
1
AT (y) = (Af wd (y) − Abwd (y)),
2

(2.2)

with the y-dependent f wd and bwd asymmetries
1 N f wd
Af wd (y) = [ cw
− 1],
f wd
2 Nccw
1 N bwd− 1].
Abwd (y) = [ cwbwd
2 Nccw(2.3)

Here, Ncw (y) and Nccw (y) are the event number distributions from C4-y. The T-violating
polarization at y is then extracted using the relevant analyzing power function of α(y),which is determined by the polarimeter structure, especially detector acceptance, as
PT (y) =AT (y).
α(y) cos θT(2.4)

The attenuation factor, cos θT determined by the average of the angles cos θπ0 is independent of y. This scheme corresponds to the case in which a number of sliced muon stoppers
were inserted and the polarization measurements were done for each stopper. The ﬁnal PT
result for one data set was obtained as the statistical average of PT (y) asPT ≡ PT = PT (y)w(y)dy,(2.5)= −0.0017 ± 0.0023(stat) ± 0.0011(syst),
with the normalized weight function of w(y) ∼ 1/σ 2 PT (y). Thus, PT was unaﬀected by themuon stopping distribution in the stopper.
As mentioned above, it was impossible to avoid the eﬀect of multiple scattering and there
is no way to know the decayed vertex. This means that some systematical uncertainties
are still remaining. Actually, the uncertainty of muon multiple scattering is larger thanany other systematic error as shown in Table(2.1). Considering these points, the E246
polarimeter should be improved in order to achieve the sensitivity of δPT ∼ 10−4 .

32

Table 2.1: Summary of major systematic errors
SourceΣ12 f wd/bwd δPT × 104
e+ counter r-rotation
yes yes0.5+
yes yes0.2
e counter z-rotatione+ counter φ-oﬀset
no yes2.8
e+ counter r-oﬀset
yes yes< 0.1
yes yes< 0.1
e+ counter z-oﬀset
 oﬀset ()Bno yes3.0
 rotation (δr )Bno yes0.37
 rotation (δz )no yes5.3
B+
μ counter y-oﬀset
no yes< 0.1
CsI(Tl) misalignment
yes yes
1.6
yes yes< 3.0
K + stop distribution
MWPC y-oﬀset (C4)no yes2.0
yes no< 1.9
K + DIF backgroundKπ2 DIF backgroundno yes
0.6+
7.1
μ multiple scattering yes no
e+ time spectrum
no yes0.8
1.2
Decay-plane angle (θr ) no yes
Decay-plane angle (θz ) no no
0.66
Uncertainty of α
1.3
3.3
cosθT uncertainty
PT gradient
0.3
Analysis
0.9
total
11.4

33

2.3

Requirements for an active polarimeter

The active polarimeter should have the following functions and advantages.
• Determination of the muon vertices event-by-event
An active polarimeter determines the muon stopping position for each event. Therefore the TREK experiment will be free from the systematic error associated with the
ambiguities in the muon stopping distribution. Since the decay positron tracks, inaddition to muon tracks, are measured, the decay vertices will be determined eventby-event. In contrast to the situation in the E246 experiment, where the positron
signals were associated with non-negligible constant background events, the active
polarimeter data will be relatively background free.
• Higher solid angle acceptance as possible
The detection of decay positrons in all directions by a polarimeter with nearly 4πsolid angle will provide a much larger acceptance. In the E246 experiment, thepositron counter solid angle was limited to about 10% on each side. The active
detector acceptance becomes roughly 10 times larger, even though the sensitivity
does not scale by this factor. The ability to measure the positron emission provides
the possibility to use not only the f wd/bwd π 0 scheme but also the lef t/right pion
scheme which was not possible in the E246 experiment.
• Measurement of the positron emission angle
The asymmetry changes as the function of both the positron emission angle and theenergy. A weighted analysis brings about a signiﬁcant increase in the analyzing power
resulting in higher sensitivity. It is of interest to note that this superior performanceis achieved in case of measuring the positron emission angle precisely.

2.4

Concepts of the polarimeter design

The requirements for the polarimeter design are following below.
• The polarimeter should have a large muon stopping eﬃciency in relatively small
volume. This means that the polarimeter should be made of a material with highaverage density.
• On the contrary, the polarimeter enable clean detection of positrons without interactions such as bremsstrahlung or annihilation in ﬂight. This means that the polarimeter should be made of a material with low average density.

34• A drift chamber makes sense as a detector.
• The cell structure is essentially determined by the ﬁne structure of the stopper. Thus,
the stopper has to be designed taking this point into account.
• Optimization for the azimuthal ﬁeld arrangement sets the highest priority to thef wd/bwd pion analysis. Thus, the stopper structure must be optimized for the
cw/ccw asymmetry measurement.
• Internal cancellation mechanism against any local ineﬃciency is essential for thepolarimeter. The cw/ccw ineﬃciency cancellation scheme of the E246 experiment ismaintained by using the polarimeter.
Considering these conditions, a parallel plate conﬁguration has been proposed as shownin Fig(2.4). The parameters of this polarimeter are also shown in Table(2.2). The tube
polarimeter is actually in progress and it will be described in Chapter 5. Considering the
stopping power and the spin relaxation, we also should have determined the inner material
to be either Al or Mg.
Table 2.2: Parameters of plate and wire
Number of plates
24
Material
Al
Size of plate
700 mm × 300 mm
Plate thickness
2.5 mmPlate gap
8 mm
Average density
0.24ρAl
Stopping eﬃciency
nearly 85 %Number of anode wires
nearly 500
Anode wire
SUS304 / 20μm φAnode wire gap
16 mm
Number of cathode wires nearly 500
Cathode wire
Au-CuBe /100μm φCathode wire gap
16 mm

2.5

Requirement for stopper material

One of the most important issues in designing the active polarimeter is the selection of the
stopper material. The analyzing power, deﬁned as AT /PT , should be as large as possible
to obtain the highest sensitivity in the experiment. This analyzing power is also required
to be independent of environmental conditions such as the ambient temperature, to be35

Figure 2.4: Muon stopper made of parallel plates which serve also as drift chamber cellstructure.
stable during a long-term measurement, and to be uniform over the whole volume of the
12 stopper units. These requirements mean that the polarimeter should not lose the initialpolarization of the incident muons due to some interactions in the stopper material during
the muon stopping phase, and that the spin polarization relaxation due to solid statephysics eﬀects, if any, should be small. Hence, the stopper material should be selected1) without any initial polarization loss during stopping and2) without any signiﬁcant spin relaxation.
Considering the decay positron interactions, the material should also be a light element.
It is known that pure metals such as Al satisfy these conditions at room temperature. Infact for the E246 experiment, a pure Al plate with 99.99 % purity was adopted. In the
TREK experiment, however, pure Al is not suitable, because the muon stopper material
itself constitutes a component of the active polarimeter drift chamber mechanical structure.
Therefore, the stopper plates have to be rigid enough as a structural element and to havea large yield strength. Pure Al, when it is annealed for the highest diﬀusion characteristics
of muons, is too soft and easily deformed. Thus, the best material should be looked
for in a wider range of metals and alloys. The most important prerequisite is the goodspin polarization behavior which could be investigated with a real muon spin relaxation
measurement.
Hence, an experiment was performed at TRIUMF using a surface muon beam at M20
in May 2007 under realistic magnetic ﬁeld conditions. [47] In this study, only pure Al and36

Mg and their alloys were studied. For the muon spin relaxation (μSR) experiment, somesamples were collected as shown in Table(2.3). The criteria for the selection was thatthe concentration of the admixed elements should not be large, in particular, magnetic
impurities like Fe, Mn or Cr. For these impurities the depolarization can be signiﬁcant due
to the large paramagnetic ﬁelds from these elements if the muons are trapped in the sites.
Although the transverse ﬁeld as well as the longitudinal ﬁeld measurement were performed
with an external magnetic ﬁeld of 0.03 T, which is the same ﬁeld strength as designed
parameter for active polarimeter, the longitudinal ﬁeld relaxation rate is relevant if we dothe analysis primarily in the f wd/bwd scheme.
In conclusion, any alloys of Al and Mg could be used except for the Al alloy A2017 andthe Mg alloy AZ31-PE which showed a relatively large relaxation rate in a transverse ﬁeld
and a longitudinal ﬁeld, respectively. Finally, A5052 was selected as the frame material of
the polarimeter and pure Al (JIS1100) was also selected as the stopper. The ﬁnal selection
was done by comparing the characteristics of the surface condition which is important forthe drift chamber electrode.

2.6

Expected performance of the polarimeter

An active polarimeter should have the abilities to measure both the muon and decay
positron tracks with high position resolution, typically 100μm. The coordinate along thewire is determined by charge division at both ends. The coordinates in the y-z plane aredetermined by drift time information. The angular determination of decay positron trackis done after determination of 3-dimensional position.
Considering Michel decay and helicity conservation, selecting high energy (more than
35 MeV) positrons make sense since the low energy (less than 30 MeV) positrons have anegative asymmetry AT . Thus, we should determine the threshold level for positrons using
stoppers to achieve a higher sensitivity of PT . Since we will know the number of plates
that the positron passes through, we can select just high energy positrons.
In order to determine the cell structure including plate thickness precisely, we havecalculated electric ﬁeld distribution of a cell using a Garﬁeld simulation. Although the cellstructure is a rectangle, the drift velocity, which is mostly determined by the kinds of gas,
is a linear function without a neighboring anode wire. The performance will be described
as a drift chamber in detail in Chapter 4.

37

38

Material
AZ31B
Pure Mg
AZ31-PE
AZ61A
AZ91D
AM60B
ZK60A
Mg-6%Zn
A5052
Pure Al
A1050
A6063
A2017
p. Al annealed

Base
Mg
Mg
Mg
Mg
Mg
Mg
Mg
Mg
Al
Al
Al
Al
Al
Al

0.1
0.44
0.66

0.02
0.00
0.49

0.29
0.18
3.8

0.00
0.00
0.47

Al
2.91
0.0064
2.80
6.40
9.22
5.88

Mg

Ti

t[mm]
1.0
1.0
1.0
1.0
1.0
1.0
1.0
<0.001 Bi<0.005 Pb<0.005
1.0
2.5
others<0.15 1.0>99.99
2.0
0.00
99.55
0.01
0.01
1.0
0.00
0.51
0.00
2.0
0.02 <0.01
0.5
0.01
1.0
99.9993.0

Table 2.3: List of μSR target
Si
Cu
Fe
Mn
Ni
Zn
Zr
0.021
0.0011 0.0015 0.4
0.85
0.01
0.0016 0.0046 0.0098
0.011
0.0007 0.006
0.0034 0.0007 0.93
0.015
0.0029 0.002
0.35
0.0012 0.74
0.031
0.002
0.002
0.23
<0.001 0.69
0.008
0.0013 0.005
0.32
0.00085.60 0.52<0.001 <0.005 <0.005
6.2
0.10
0.02
0.27
0.01

2.7

Development of the charge division method

2.7.1

Test experiment

The position resolution along the wire direction is required to be better than 2 mm in σ.
In order to check the performance of the position determination by charge division, a 1/5
prototype chamber as shown in Fig(2.5) was constructed.

Figure 2.5: Picture of 1/5 prototype polarimeter
The test experiment was performed at the Fuji Test Beam Line ( FTBL ) at KEK in
Nov 2008. The detail of this experiment is described in Ref [48]. The e− beam with anaverage energy of 2 GeV hits the vertical center position of the prototype chamber. ADC
and TDC data were recorded by moving the chamber along the wire axis. The data, whichis equal to x = ±15 cm and ±5 cm from the center of the wire, was mainly taken for the
analysis.

Figure 2.6: Picture of 1/5 prototype polarimeter39

2.7.2Analysis scheme

In the method of charge division which will be described in detail in Appendix A , thedistance of the particle hit position from the center of the wire is ﬁnally deﬁned as x,x
r1 + r2 Q2 − Q1 r1 − r2
= (1 +
)
−
,
Z
R
2Q
2R

(2.6)

where Z is the total length of the wire and R is the total resistance of the wire. In addition,
the input impedance of the ampliﬁer and the corrected charge on a capacitor are deﬁned
as r and Q, respectively. In this analysis, the value of r1 − r2 is assumed to be muchsmaller than R and is negligible. As easily understood, the wire length can be regarded to
be extended due to the input impedance of ampliﬁers. In other words, the resolution of x
becomes a factor of 1 + (r1 + r2 )/R worse than that of (Q2 − Q1 )/2Q. It is necessary tocorrect the ampliﬁer gains and the input impedance of the ampliﬁer because only the valuesof Q1 and Q2 can be extracted from the measurement. The gain correction is performed
by introducing a gain ratio parameter α as,
RQ =


1
1
Q2 − Q1
1
Q1
1
1
= −
= −
= −

,
2Q
2 Q1 + Q2
2 1 + Q1 /Q2
2 1 + αQ1 /Q2

(2.7)



where Q1 and Q2 are the output charges from the ampliﬁers. Since α can change run-byrun due to the ﬂuctuation of input impedance, in this analysis we obtained the α values byrequiring the fact that the mean values of the RQ distributions were balanced for symmetricpositional data such as 5 cm / -5 cm. Actually, the value of α is not far from 1.
Next in order to determine x from the RQ distribution, we need to correct for the eﬀectof the input impedance as,
r1 + r2x= (1 +) · RQ = f · RQ,Z
Rx = Z · f · RQ = 65cm · f · RQ.

(2.8)

Since the mean value of the beam proﬁle of each run is known, the x distributions are
obtained to satisfy these mean values by adjusting the f parameter.

2.7.3

Result and an additional analysis

The RQ distribution and x distributions are shown in Fig(2.7). And the resulting residual
distribution which just corresponds to the position resolution is also shown in Fig(2.7).

40

Figure 2.7: (a) and (c) are RQ distributions and (b) and (d) are x distributions, respectively.
(a) and (b) are ± 5 cm samples and (c) and (d) are ± 15 cm samples. The RQ distributions
are obtained by adjusting the α. The x distributions are also obtained by adjusting the fparameter.

Figure 2.8: The residual distribution before correction (left) and the residual distribution
after applying the additional correction (right) as discussed in the text.

41

Here, an additional correction to improve the position resolution is introduced. As
shown in the left ﬁgure of Fig(2.8), a slight shift of the residual distribution can be recognized, and the systematic eﬀect of the ampliﬁer response as a function of pulse heightof the input signal has to be considered. To correct this eﬀect, it is necessary to separate
the ADC regions into 4 regions as 1) Qh < 500 ch, 2) 500 < Qh < 600 ch, 3) 600 < Qh <800 ch, and 4) Qh > 800 ch. The f parameters were ﬁnely tuned to remove the above
correlation with ﬁxed α. The residual distribution after this correction are also shown in
the right ﬁgure of Fig(2.8).

2.7.4

Summary

In conclusion it can be interpreted that the input impedance of the ampliﬁer changes as afunction of the ADC value, and this eﬀect can be corrected by adjusting the f parameters.
As the result of the test experiment, the position resolution of 1/5 prototype chamber was
obtained to be 2 mm in σ which is good enough for our requirement. Indeed we havetested two kinds of sense wires both SUS304, which has 1.9 KΩ intrinsic resistance andStablohm800, which has 2.54 KΩ intrinsic resistance. SUS304 has been ﬁnally adopted as
the sense wire in the TREK experiment.

2.8

Production

After the development of the charge division method, a Full Size Model polarimeter (FSM)
has been made by REPIC Co. During the manufacturing, I went there and checked theprogress of the work. As mentioned in section 2.4, pure Al plates were adopted as the
stoppers and A5052 materials were adopted as the frames of the polarimeter. SUS304
wires with the diameter of 20 μm, which have a large resistance, were adopted as the sensewire and Au-CuBe wires were also adopted as potential wires. Both the potential wires
and the stopper plates work as the cathode. Stringing the wires took more than 3 days
due to the large number (nearly 1000) of wires but also due to their ﬁne structure.
All the sense wires were strung with the same 30 g tension using a weight and thepotential wires were strung with a tension of 80 g. Since the accuracy of the wire position
was determined by the accuracy of the attached feedthrough, these feedthroughs were also
attached very carefully. After the process of stringing the wires, the wire tensions were
tested by using a magnet. First of all, some AC electric currents are input into a drive
wire and its frequency is increased. As the drive wire produces a resonance on its speciﬁcfrequency, an oscillatory wave is transmitted to the other wires. As each wire reaches
its speciﬁc frequency, external force (here, the magnetic ﬁeld’s) also produces resonance.
Finally the current is converted into tension. We are able to measure the tension this way
if the wires have the same speciﬁc frequency. After the tension measurement, the processof assembling was started. The ﬁnal overview of the FSM is as shown in Fig(2.10).
After assembling, a high voltage test was done with maximum voltage. (nearly 2000 V)
42

Although some capacitors had some electric leakage on the printed circuit board (PCB) at
ﬁrst, we ﬁnally succeeded in the normal operation as a drift chamber. It took more than 2
weeks to achieve the normal chamber operation.

Figure 2.9: Process of the wire stringing.

Figure 2.10: Picture of the FSM polarimeter.

43

2.9

Read-out system for the polarimeter

Figure 2.11: Main ﬂow of the data acquisition system.
A polarimeter read-out test was performed at the same time as the polarimeter performance
test at TRIUMF in Nov 2009. A schematic view of the read-out is shown in Fig(2.11).
The main data acquisition stream follows below. First of all, the chamber raw signals
input into an ASB card. The ASB card serves as ampliﬁer(A), shaper(S), buﬀer(B). The
ASB output signal passes through a ﬂat cable and input VME-discriminator board which
requires about ± 5 V for its operation. The VME-discriminator board just works as an
ordinary discriminator. But it has also three kinds of output which are an analog, a LVDS
and a NIM signal, respectively. The analog signal and the LVDS signal are required for
the CAEN ADC and TDC modules. On the other hand, the NIM signal is used in orderto tag the chamber signals. In fact, the trigger logic includes the NIM output signals.
After the VME-discriminator board, the LVDS signals ﬁnally input into the CAEN TDC
modules. The TDC modules are used to take both chamber data and all counters’ data. In
terms of impedance matching for the ADC modules, the De-coupler card are also requiredfor our measurement. The De-coupler cards are connected directly to the CAEN ADC
modules for the adoption of charge division method. The several important parts of thedata acquisition system are summarized below.

2.9.1

16 ch Amp. Shaper Buﬀer card (ASB card)

This ASB card as shown in Fig(2.12) will be used as one of the read-out parts for thepolarimeter data acquisition. ASB IC (JRK-ASB(N)-1) chips were developed by KEK
44

electronics shop and REPIC Co. Since we require to measure an analog output signal
due to the adoption of the charge division method, we cannot use the standard Amp.
Shaper Discriminator (ASD) card. Basically, an analog input signal from an anode wireis integrated for all 16 channels on one board with 25 ns time constant. In addition, theoutput signals pulse height can be changed due to gain controller as shown in Table(2.5).
The ASB has a small input impedance, thus, it is possible to adopt the charge division
method. The main functions are summarized in Table(2.4).

Table 2.4: The main functions of ASB
ASB ICJRK-ASB(N)-001 × 4 pcs
Analog input
negative charge input / 16 ch input
Maximum quantity of charge 1.5 pC with minimum gain
Shaping time constant
about 25 ns
Test input
negative NIM 50 Ω impedance
PP control
nor suppress input impedance
Analog output- 3.75 V ∼ - 1.25 V
Vth control
 + 2.5 V
Digital output
ECL output
Consumption of electricity+ 5 V 500 mA / - 5 V 300 mA

Table 2.5: Gain control set
GC1 = LGC1 = Open GC1 = L
GC1 = OpenGC2 = LGC2 = LGC2 = Open GC2 = Open- 360 mV/pC - 490 mV/pC - 750 mV/pC - 1400 mV/pC

2.9.2

VME discriminator board MODEL RPV-240

The VME discriminator boards have two kinds of output - analog and LVDS signals. The
analog signals are used for the ADC data and the LVDS signals are used for the TDC data.
Although the discriminator modules have a function for adjusting the threshold level, it isnecessary for this module to provide 5 V from another DC power supply. In addition, thismodule has a test output. The test output signal, which is a NIM signal, is generated as
an OR output even if only one channel of the 16 channels has a hit. The main specs are
summarized in Table(2.6).

45

Figure 2.12: Top view of ASB cards.
Table 2.6: The specs of VME discriminator board
INPUT
16 CH Analog INPUT
Vth INPUT
Maximum INPUT 5 V
Analog OUTPUT 16 CH Analog OUTPUT
Digital OUTPUT 16 CH Digital OUTPUT (LVDS 110 Ω)
OR OUTPUT
16 CH OR OUTPUT (Negative NIM 50 Ω impedance)
POWER SUPPLY + 5 V / 1.1 A

2.9.3

De-coupler card

First, the De-coupler card works as an attenuator. Although VME discriminator board
output signals are more than 1 V, the De-coupler cards output signals have 3 times lower
pulse height than the input signals so as to take ADC data. Actually, the quantity of theintegrated charge is limited to the CAEN ADC’s dynamic range. In order to achieve ahigher position resolution along the wire direction, it is necessary to gain a lot of charges
before the pulse shaping by the ASB card. At the same time, the quantity of charge has
to be reduced to be able to take ADC data. In addition, the De-coupler card also works
as a 200 ns delay module. As the trigger timing is always delayed by more than 100 ns ascompared to the time reference, delaying the analog signals is also necessary for ADC datataking. As mentioned above, the De-coupler card plays an important role for the analog
signals.

46

2.9.4

CAEN ADC V792 / CAEN TDC V1190

The CAEN ADC V792 and CAEN TDC V1190 modules were utilized for the data acquisition. One ADC module has 32 channels and provides data for the charge division method.
In addition one TDC module has 64 channels and provides data for making both the muonand the positron tracks. Since it is possible for a wire to be hit two times on one event, a
multi-hit TDC module is required so that one channel can take more than 2 data hits foreach event. This means that both the muon and the positron can pass near the same wire.
This requirement is met by using the CAEN TDC V1190. Although the TDC is multi-hit,
the ADC is not. Thus, we could take just the positron ADC data which was essential tomeasure the position along the wire using the charge division method. Instead a FADC
will be used for the polarimeter data acquisition in the TREK experiment, so it will bepossible to collect both ADC and TDC data for both the muon and the positron.

Figure 2.13: Overview of the modules for DAQ. The silver card on the bottom is oneof the De-coupler cards. The four red modules are the interrupt register (left), the two
ADC modules (center) and the TDC module (right), respectively. All the blue modules
are VME-discriminator modules.

47

Chapter 3
Beam test at TRIUMF

Figure 3.1: Overview of Meson Hall in TRIUMF.
We have performed the beam test at TRIUMF in Vancouver in Nov-Dec 2009. The mostimportant purpose of the beam test was to evaluate the performance of the polarimeteras a drift chamber - i.e. whether the drift chamber could measure both the muon and thepositron tracks clearly. In addition, we wanted to evaluate whether the polarimeter had
some spurious asymmetry due to its structure. At the same time the performance of the
ASB card and the other modules were checked.

3.1

M11 beamline

Fig(3.3) shows the layout of the M11 beam channel.
The primary proton beam strikes the meson production target T1, which is typically 1
cm thick graphite. The momentum of the channel is determined largely by the magnetic
ﬁeld of the two bending magnets B1 and B2. Focusing is achieved by using the 6 quadrupole48

magnets Q1 to Q6. There are also sextupole magnets available for a better focus, but weturned them oﬀ. The two quadrupoles Q1 and Q2 provide a double-focus at the midplane(focused in both horizontal and vertical planes), such that particles of the same momentum
emanating from the object point at various angles, will all intersect at the same point at
this focus.
The midplane of the channel is a plane of momentum focus, such that particles ofdiﬀerent momenta will come to a focus at diﬀerent horizontal locations along this focal
plane. The momentum dispersion is 18 mm/%δp/p. With the horizontal slits open to 90
mm full aperture, the beam channel admits a momentum bite of 5 %δp/p. The horizontal
slits at the midplane can be closed to select a narrower momentum bite if desired. Also
located at the midplane are a set of vertical slits which are considered to be fully open at
30 mm aperture when the septum was in operation, but which may need a larger opening
to increase the ﬂux.
The total length of the M11 channel is 15.3 meters, from production target to nominal
ﬁnal focus. Although the momentum range is from 60 MeV/c to 450 MeV/c, particles witha momentum of 170-180 MeV/c were used for our measurement. The current typical M11
rate is shown in Fig(3.2).

Figure 3.2: M11 beam rate

49

Figure 3.3: Layout of M11 beam channel

50

3.2

Preparation

3.2.1

Beam tuning

Figure 3.4: Experimental setup for beam tuning.
In order to extract and separate both muons and pions with a ﬁxed magnet current, we
tuned the beamline using S0, S1 and RF timing. These signals arrowed a Time-of-Flight(TOF) measurement. The stop timing of TOF was determined by an RF signal. The
experimental setup for this tuning was shown in Fig(3.4). In the beam tuning, the trigger
signal wasselected by triple coincidences, which consisted of S0, S1 and RF timing signals(S0 S1 RF). As shown in the top ﬁgure of Fig(3.5), the trigger timing was determined by
the S1 counter.
 In addition as shown in the bottom ﬁgure of Fig(3.5), a triple coincidence
signal (S0 S1 RF) corresponded to the time of ﬂight between the RF timing and the S1
counter. Here, the three components correspond to the positron (fastest timing), the muonand the pion timing, respectively. In the case of a pion beam, for example, we should haveadded 9 ns delay to the muon signal timing. In fact, the oscilloscope’s signal (S0 S1 RF)
was consistent with the calculations based on the particle velocities (β factor) and the total
beamline length (15.3 + 2 m). We ﬁnally checked the so-called TOF histogram by using a
multichannel analyzer module (MCA) and an oscilloscope. Although the MCA has threefunctions such as integrated charge measurement, peak voltage measurement, and time
diﬀerence measurement between start signal and stop signal event-by-event, the MCA wasused to measure the time diﬀerence. The total TOF spectrum is shown in the top ﬁgure ofFig(3.6). Total pion counts, muon counts, and positron counts corresponded to left peak,central peak, and right peak, respectively. For measuring the spectrum, we adopted thecommon stop method. It was also possible to select just the pions by adding about 10
ns delay as shown in the bottom ﬁgure of Fig(3.6). Although the spectra were measured
for both 170 MeV/c and 180 MeV/c beam momenta, it was a little diﬃcult to adopt 180
MeV/c beam due to its larger muon contamination. Therefore we ﬁnally adopted 170
MeV/c as the beam momentum. In this momentum, the muon contamination at pion peak
was ∼ 105 times lower than pion ﬂux.
At the same time, three counters corresponding to the S3, S4, and S5 counters were51

also prepared. The S3 counter was prepared as a veto counter. In our measurement, ourexperimental goal was to extract the decay positron which was emitted from a stopped
muon in the polarimeter. Therefore the S3 counter was suitable for selecting these events.
In addition to the S3 counter, the S4 and the S5 counters were adopted as a telescope.
The telescope was used in the range curve measurement. The detail of the range curvemeasurement will be explained in a later section.

Figure 3.5: Pictures of oscilloscope. The top one shows the S0 and the S1 counter signal
which correspond to the yellow line and the blue line, respectively. The S1 counter signals
appear 10 ns later than the S0 signals. On the other hand, the bottom one shows the
S0S1 and S0 S1 RF corresponding to the yellow line and the blue line, respectively.
S1 RF coincidence signal has 3 components due to the three kinds of positive charged
particles.

52

Figure 3.6: Pictures of TOF spectrum at 170 MeV/c by using the MCA. The top one
shows the raw TOF spectrum showing three peaks for π, μ, and e. The bottom one shows
the TOF spectrum after the RF cut. In the bottom one, pion peak including a little
contamination of muons has been selected.

53

3.2.2

Experimental setup

Data acquisition system
The data acquisition system consisted of 16 ASB cards, 16 VME-discriminator boards, 8
CAEN ADC modules and 4 CAEN TDC modules. These ampliﬁers and modules havealready been explained in 2.9.
The trigger logic circuit is as shown in Fig(3.10). The trigger system consisted ofseveral trigger counters as already mentioned above.
 Here,
 I will add some explanations.
The delay module which was located before the S0 S1 RF coincidence unit could selectthe kind of particle according to the length of thedelay cable. Therefore, either a muonor a pion trigger could be determined by the S0 S1 RF coincidence unit. The main
trigger coincidence unit at the lower left in Fig(3.8) had 4 channels. Each channel could bechosen according to our purpose. A-channel, for example, was used as test trigger which
was available to tune the PC for data taking in addition to all VME modules. In fact,
the TDC calibration was done by using the test trigger. The B-channel and the C-channel
coincidence was used as the main trigger. This coincidence selected the condition of a
stopped muon and a decay positron in the polarimeter. In addition the D-channel wasused to measure the range curve. The downstream system of the main trigger coincidence
unit consisted of several gate generators and other modules. This system provided theGate for the ADC modules, the TDC modules, and the veto systems. For data acquisitiona clock generator was needed for the TDC operation.

Figure 3.7: Timing chart. The ADC gate was made from the coincidence of both thedelayed trigger and the chamber signals. In addition, the TDC stop has the same timing
as the end of the trigger gate.
The timing chart which was associated with the main trigger is shown in Fig(3.7). The
top one in Fig(3.7) shows both the pion and muon trigger signals that we named π-gateand μ-gate, respectively. Here, I will add some explanations about the trigger in Fig(3.7).
This signal started about 500 ns later than both the μ-gate and the π-gate. As the ADC
modules could not record multi-hit events, we had to choose the particle (incident or decay
54positron) in terms of which particle data were more useful as ADC data. In terms of thecharge division method, determining the decay positron track precisely was more important
than the incident particle track. So the positron ADC was registered. (Of course as the
CAEN TDC could registered multi-hit events, we could reconstruct both the incident π/μand the positron tracks using the TDC data.) Considering the muon mean life time (2.2μs),
it was essential to add about 500 ns delay for ensuring the decay positron event. At thesame time, although less than 500 ns decay time events were discarded, the decay positron
events were taken no less than 70 % as ADC data. The ADC gate was made from thecoincidence of both the chamber signals and the trigger gate. One feature of the CAEN
TDC, which I should especially mention, was its excellent performance of buﬀering. The
TDC common stop was the same timing as the end of the trigger gate as shown Fig(3.7).
Furthermore, it could record all the sense wire hits during the 9 μs before the TDC stop.
The TDC data were not associated with the ADC data.

Figure 3.8: Conﬁguration of the DAQ system.
I also show the typical chamber raw signal in Fig(3.9). As one can see in the picture, thechamber raw signal had a overshoot and some ringings due to the ASB shaping. However,this had no serious eﬀects on the charge division method.

Figure 3.9: Typical chamber raw signal. It had an overshoot and some ringing.

55

56
Figure 3.10: Main ﬂow diagram of the logic circuit.

Gas system
In order to operate the polarimeter, an Ar and ethane gas mixture was adopted. The ratio
was Ar : C2 H6 = 50 : 50. Since the gas ratio is, in general, mainly associated with thedrift velocity of the avalanche ions, keeping a constant gas ratio was very important for its
operation. Because the polarimeter was carried by an airplane, there was the possibility
that the polarimeter might have contained some air at ﬁrst. Therefore, several complete
replacements of the Ar:Et chamber gases were required before its operation.
• Ar gas replacement
Although we ﬁlled in the polarimeter with Ar gas, it could be possible to contain some
air which entered during its ﬂight. In order to pull out air completely, we carried out
the Ar gas replacement 7 times. Since the wires were so fragile, we could not reduce
the pressure below 0.3 atm.
• Ar gas and Ethane gas replacement
After the Ar gas replacement, we have done Ar and Ethan gas replacement bit-by-bit
alternately up to 1.0 atm. We pulled out all gases bit-by-bit down to 0.3 atm again
after ﬁlling up to 1.0 atm. This kind of replacement was done 3 times in total.
• Ar and Ethane mixture gas ﬂow
The Ar and Ethane gases were allowed to ﬂow with the mixture ratio from the gas
house which was located outside of the meson hall with long tube transportation. We
checked the mixture ratio by using a ﬂow meter every 8 hours during the beam test.

Figure 3.11: Conﬁguration of the gas system.

57

3.2.3Degrader tuning

In the beam test, the entire volume of the polarimeter should be tested to determine
whether or not the polarimeter detection eﬃciency depended on position. Hence, we varied
the stopping position of the incident particles. In order to control the stopping position,some 0.5 and 1.0 inch size Al plates were used as degrader. The Al degrader was locatednext to the S1 counter as shown in Fig(3.12).

Figure 3.12: Conﬁguration for degrader tunings.
The stopping range was divided into three regions which we called Upstream, Middle
and Downstream, respectively. At the same time, the thickness of Al degrader had to be
estimated for both muons and pions with 170 MeV/c momentum. Hence, the range curvemeasurement was classiﬁed into 6 groups.
In this measurement, the S4 and the S5 counters as shown in Fig(3.4) and Fig(3.12)
were used. These counters worked as the so-called telescope. Although the telescope wasjust counting decay positrons, the number of counts correlated with the stopping position.
The counters were placed in the transverse direction as shown in Fig(3.4) and Fig(3.12).
The number of telescope counts (S4 S5 RF) was normalized using the number of S0
counts. The results of degrader tuning are shown in Fig(3.13). As shown in Fig(3.13), pions
tended to stop in the polarimeter compared with muons because of their smaller β factor.
From the downstream result, we would prefer to use a higher momentum beam so that
we might not need any degrader. Considering the TOF spectrum, however, the problemof the muon contamination was more serious as compared with this problem. Therefore
0 inch was adopted as the degrader for measuring the downstream position. At the sametime we could assume average stopping power of the polarimeter. Comparing Upstream
data with Middle data, the pion (or muon) peak was shifted from 1.5 (or 3.0) inch to 0.5(or 2.0) inch. In fact, although the Al plate stoppers inside the polarimeter were parallelto the beam axis, the Al stoppers stopped the incident particles due to the spread in the
beam emittance. For measuring the analyzing power, the range curve were measured again
using muons with the same momentum. In this measurement, a vertical stopper alignment
58

Range Curve Measurement (upstream)

×10-3

S4 × S5 × RF/S0

0.09
0.08

Range cureve

0.07

Pion

0.06

Muon

0.05
0.04
0.03
0.02
0.01
0
0

0.5

1

1.5
2
2.5
3
Degrader thickness [inch]

3.5

4Range Curve Measurement (middle)

×10-3

Range cureve
Pion

S4 × S5 × RF / S0

0.05

Muon

0.04

0.03

0.02

0.01

0
0

45

×10

0.5

1
1.5
2
Degrader thickness [inch]

2.5

3Range Curve Measurement (downstream)-6

Range cureve

40

Pion
Muon

S4 × S5 × RF / S0

35
30
25
20
15
10
5
0
0

0.5

1
1.5
2
Degrader thickness [inch]

2.5

3

Figure 3.13: Results of the degrader tuning. Upstream (top), Middle (middle), and Downstream (bottom).

59to incident beam axis was adopted. Thus, the polarimeter was rotated by 90◦ to the wire
axis. The results of the degrader tuning are summarized in Table(3.1).
Table 3.1: Summary of degrader thickness
Upstream Middle Downstream
muon
3.0 inch
2.0 inch 0.0 inchpion
1.5 inch
0.5 inch 0.0 inch
vertical muon 2.0 inch -3.3

Measurement

3.3.1

Null Asymmetry test

Figure 3.14: Conceptual diagram for the null asymmetry test. In this measurement, theπ + beam was used.
The polarization measurement is based on the principle that the muon spin direction isconserved in the muon decay process due to the helicity conservation law. For a precision
measurement of a small asymmetry which is associated with transverse polarization (PT )based on f wd/bwd scheme, it is essential to evaluate any spurious eﬀects generated fromits mechanical structure before the start to the TREK experiment. The principle of thismeasurement is based on the fact that the pion is a pseudo-scalar boson with zero spin.
Hence the decay muon with low momentum (∼ 30 MeV/c) is emitted isotropically. Considering this feature, the resulting decay positron has to be also emitted isotropically. In
terms of the principle above, the stopped pion was adopted as a good probe to search forany spurious eﬀects.
A conceptual diagram of this measurement is shown in Fig(3.14). The conﬁgurationof the inner Al plates was parallel to the beam direction as already mentioned. The
60

experimental setup for the measurement was the same as the experimental setup for the
degrader tunings without both the S4 and the S5 counter. In Fig(3.14), a pion with 170
MeV/c momentum enters into the polarimeter and a decay positron is ﬁnally emitted.
Here, I should add some explanation about the decay muon. Most of the low momentum(∼ 30 MeV/c) muons could not penetrate an Al plate. As a muon could typically travel
only 200 μm in an Al plate, the muon decayed into a positron in the same Al plate inwhich the pion has stopped. In other words, the decay positron vertex corresponded tothe decay muon position in a cell unit. Although the decay chain was π + → μ+ → e+ , thepolarimeter could just measure both pion and positron tracks as shown in Fig(3.14).
The transverse asymmetry is deﬁned as,AT =Ncw − Nccw,
Ncw + Nccw

(3.1)

where Ncw and Nccw correspond to the y direction and the −y direction, respectively.
This deﬁnition is the same as the transverse asymmetry in Kμ3 decay. Although themeasurement was performed for the full volume, changing the position of ASB cards wasneeded since we could not prepare enough number of ASB cards. The analysis results areshown in the next chapter.

3.3.2

Analyzing power measurement

Figure 3.15: Conceptual diagram for analyzing power measurement. In this measurement,μ+ beam was adopted.
If I can show that our polarimeter does not have any spurious eﬀects when measuring themuon transverse polarization, then we can say that the performance of the polarimeter isgood enough to measure transverse polarization in Kμ3 decay.
The ﬁrst purpose of this measurement was, in fact, to evaluate the analyzing power. It
is possible to compare with a Monte Carlo simulation to determine the analyzing power.
61

The purpose of this measurement was, however, not to evaluate the analyzing power but toevaluate the intrinsic beam polarization because there was no way to know the initial beampolarization. Generally speaking, surface muons with very low momentum (∼ 30 MeV/c)
are nearly 100% polarized. In this measurement, however, the muon momentum was muchhigher than the surface muons. The beam could also include cloud muons’. In general,
although cloud muons also have high polarization, their polarization is lower than thesurface muon’s. This time the beam polarization was measured as a f wd/bwd asymmetry
which was observable. The conceptual diagram of this measurement is shown in Fig(3.15).
Before the measurement, the polarimeter was rotated by 90◦ around the x axis as shown inFig(3.15). Then the conﬁguration of the inner plates was replaced with a vertical structure.
Muons with 170 MeV/c momentum enter into the polarimeter perpendicular to the innerplates and the decay positrons were emitted in upstream or downstream direction.
The longitudinal asymmetry is deﬁned as,
AL =Nf wd − Nbwd,
Nf wd + Nbwd

(3.2)

where Nf wd and Nbwd correspond to the z direction and the −z direction, respectively. The
results of the measurement are shown in Appendix C.

62Chapter 4
Analysis of the beam test data
In this chapter the analysis associated with the beam test data is described.

4.1

Veriﬁcation of data quality

Before the measurement, the data quality should be checked carefully. Mistakes suchas cabling mismatch and misalignment of detectors could be overlooked. Thus, it wasnecessary to do the commissioning of the detectors and the data acquisition system. In
fact, some data had to be discarded due to some hardware problems associated with thetrigger.
In order to evaluate the performance of the data, the time reference spectrum (the time
spectrum of the S1 counter) was checked ﬁrst. As shown in Fig(4.1), the time resolution of
S1 counter was obtained as σ = 170 ps. This resolution was good enough to evaluate thechamber signals because the typical sense wire time resolution scale, which was determinedby the drift velocity of the avalanche ions and the cell structure, was much larger than the
S1 counter time resolution scale.

Figure 4.1: Picture of the S1 counter time spectrum. This was used to be the time reference.
A 170 ps in σ time resolution was achieved. This is suﬃciently high in our measurement.
63

Next, the muon decay curve was checked. Using the ADC trigger timing, I found that
all the ADC data mainly consisted of decay positrons as expected. In fact the end of the
ADC trigger gate data corresponded to a muon decay curve as shown in Fig(4.2). Actually,
this data with a little contamination of pion decay could ﬂuctuate due to drift time of theavalanche ions. In addition to the ﬂuctuation, ﬁtting should include the accidental region.
Although the ﬁtting was performed using an exponential function plus a constant term
(exp[−x/τ ] + const.), the muon mean life time was so long that we could not take enoughdata with time ranges over a few 10 μs scales.

Figure 4.2: Picture of the muon decay curve. The parameter (1/τ ) corresponds to ∼ 2μs.
The pictures of single wire ADC and TDC data are also shown in Fig(4.3 - 4.4). Regarding the ADC data, a so-called pedestal suppression was performed. Namely, before
actual data taking, the pedestal was ﬁtted by Gauss function channel-by-channel in orderto suppress all data except for the event of the decay positron. These pedestal data actually
did not correlate with the TDC data of the decay positron.

Figure 4.3: Picture of the TDC data corresponding to a single wire. The TDC spectrum
composed of the decay positron hit with a small fraction of the incident particle.
64Figure 4.4: Picture of the ADC data after a pedestal suppression. The ﬁgure corresponds
to a single wire hit. The ADC spectrum is completely composed of the decay positron due
to the delayed trigger as mentioned in Chapter 3.
Next, a misalignment of the wires with regard to both hardware and software waschecked by looking the incident particle tracks. In fact, the alignment of the wires wasmore complicated. In the beginning of the tracking in a cell unit, although most of theincident particle tracks were made successively, there were no continuous tracks in someevents. After some changes of the analysis code, both pion and muon tracks were mademuch more clearly as shown in Fig(4.5). Here, the ASB cards were attached in the redregion in Fig(4.5).

Figure 4.5: Sample track. In this picture, the pion enters into polarimeter and the decay
positron is ﬁnally emitted.

65After the evaluation of the tracking performance, the incident beam stopping distribution with respect to the result of the range curve measurement was checked. The stopping
distribution also played an important role as a cross check probe of the misalignment ofwires. For analyzing the stopping distribution, two conditions were required.
1) In the beginning of the analysis, only the timing which corresponds to the incident particle was selected in order to avoid the positron contamination.
2) In addition, the stop position was deﬁned as the most downstream position of the incident particle in a cell unit.
The resulting distribution is shown in Fig(4.6).

Figure 4.6: π + stopping distribution. It seems that incident pion stops ASB region withconcentric circles. Its central position tends to concentrate upstream of the full ASB region.
From the picture, the incident particles were spread over the ASB region as concentric
circles. The consistency of the shape with concentric circles means that there was no
misalignment with respect to the wire conﬁguration in my analysis code. The results also
showed that the degrader tuning was roughly successful although the stop position of theincident beam tended to concentrate in the upstream ASB region. The central position ofits distribution, however, did not have a bad inﬂuence on the physics data associated withany spurious asymmetry but it just decreased the number of good events.

66

4.2

Wire eﬃciency

The most important parameter of a tracker is its detection eﬃciency1 . In most cases,a chamber is required to have ≥ 99 % detection eﬃciency. It is diﬃcult to reconstructparticle tracks if the detection eﬃciency is not high enough. Since the wire eﬃciency2
correlates with the detection eﬃciency, an evaluation of the wire eﬃciency is needed. In
our measurement, the eﬃciency of the chamber was evaluated using the muon beam data.
The eﬃciency is deﬁned as follows and as shown in Fig(4.7). In addition, the alignment of
ASB cards are also shown in Fig(4.7).

Figure 4.7: Conﬁguration of the Al plates (left) and the ASB cards (right).
• The 3 wires parallel to the incident beam were selected for the whole volume of thechamber.
• In case that the hits of the pink wires were required, whether the red wire was tagged
or not.
Considering this deﬁnition, it seems that the incident particle should always pass throughthe cell including the red wire. The result of this analysis, however, is not the same as thisassumption as shown in Fig(4.8). From this graph, it was clear that the wire eﬃciency
depended on its position. The tendency of this dependence shows that the eﬃciencies of thewires located downstream region are lower than upstream region. The wires corresponding
to the ID from 0 to 64 are located in the downstream and the wires corresponding to
the ID from 65 to 128 are located in the upstream, respectively. However, since somewires are outside of the ﬁducial volume, it is impossible to determine the eﬃciency forthem. Moreover, since the number of events corresponding to the downstream regions
are lower than in the upstream case, the downstream eﬃciencies often have a large error
bar. The tendency of this graph could be explained as a multiple scattering eﬀect. This
polarimeter was diﬀerent from other trackers in terms of its material density. In general, a
tracker should be made of light material in order to prevent secondary emission or particle
1Here, the word “detection eﬃciency” is deﬁned as whether a particle trajectory can be seen or not.
the word “wire eﬃciency” is deﬁned as whether a wire responses or not in the case that a particle
passes thorough the same cell as the wire.
2

67

scattering. On the contrary, this polarimeter was made of material with some density inorder to stop the incident particles in the volume. A polarimeter with larger density causes
some bad tracks because it was diﬃcult to prevent these eﬀects. Considering the multiple
scattering eﬀects, the eﬃciency should be evaluated not by wire but by layer. Hence, theeﬃciency should be redeﬁned as follows and shown in Fig(4.9).
wire efficiency

Efficiency[%]

95

90

85

80

75
0

20

40

60

80
wire ID

100

120

140

Figure 4.8: The ﬁrst results of the wire eﬃciency measurement. These eﬃciencies reliedon the position of a sense wire due to multiple scattering eﬀect.

Figure 4.9: Schematic view of the Al plates and the new deﬁnition of the wire eﬃciency.
• The 3 wires parallel to the incident beam were selected for the whole volume of thechamber. (the same deﬁnition as above)• In case that the hits of the pink wires were required, whether the red wire was tagged
or not.
• In the case that the red one was not tagged, the green wires are checked whether twoof them (left/right) were tagged or not. Namely, the other two possibilities that theincident beam passes through the left or right cell were allowed.
68

The result of this deﬁnition is shown in Fig(4.10). It shows that the wires had higheﬃciencies.
wire efficiency
99.6
99.4

Efficiency[%]

99.2
99
98.8
98.6
98.4
98.2
98
0

20

40

60

80
wire ID

100

120

140

Figure 4.10: Final result of the detection eﬃciencies in a cell unit. This included thecorrection of the multiple scattering eﬀect.

4.3

Event selection

Before the main analysis, it is essential to extract clean tracks with no-bias. It is not until
some kind of selection for extracting ﬁne tracks is performed correctly that the track reconstruction analysis and the transverse asymmetry analysis can be started. The following
selections were performed in my analysis.
• Time classiﬁcation
Based on the TDC hit timing, the TDC data were classiﬁed into 11 categories as 02500 channels, 2500-10000 channels, ..., 80000-90000 channels, and 90000- channels (1channel = 80 ps). Here, I named the ﬁrst category “BEAM ”. In this case,“BEAM ”
included just the incident particles. There is no positron contamination in this groupdue to the 500 ns delayed trigger gate. In addition, some events have some diﬀerent
timings which belong to more than 3 categories, respectively. These strange eventswere discarded. Finally the events which belong to both “BEAM ” and one of theother groups were selected as a true track.
• Geometrical classiﬁcation
Next a geometrical classiﬁcation was adopted in order to eliminate some noise hits
and to rescue ineﬃcient hits. At ﬁrst, considering ineﬃcient hits, the hit cells were69

connected from upstream towards downstream in a cell unit. Finally, the incident
track was formed as a straight line. Therefore, as some noise hits were not included
in a line, the events which did not form a line were discarded. This method was also
adopted for the positron track. In fact, since the decay positron has a low momentum,
the positron tended to generate secondary particles. Thus, a positron could make twolines. In this case, it was diﬃcult to extract the true positron track, so these eventswere also discarded.
• Vertex selection and classiﬁcation
Finally, the vertex cell was deﬁned as the ﬁnal cell of the incident line. Here, thevertices were classiﬁed into 2 categories whether the positron hit cells overlapped theincident track or not. In case that there were more than 2 cells overlapping, these
events were also discarded because they could include some hits caused by secondary
particles. The events which had zero or one cell overlapping were ultimately chosen.
In order to avoid some kind of bias associated with an incident angle of the beam, thecondition that all incident particles have to pass thorough more than 3 cells parallelto the Al plate, was also required. In other words, all events are satisﬁed with thecondition that incident particles enter into the polarimeter parallel to the Al plate.

4.4

Development of the track reconstruction

Based on these event sections above, the track reconstruction, in particular the positronreconstruction, algorithm was developed. In this algorithm, it is essential to determine theX-T relation ﬁrst, which is corresponding to drift velocity of the avalanche ions. (Here, X
and T are the position and drift time, respectively.) The algorithm of the X-T relation will
be described in detail in the Appendix B.

Figure 4.11: Schematic view of the track reconstruction.
70

In the beginning of the analysis, some parameters below as shown in Fig(4.11) aredeﬁned as,|axk + byk + c|√,
a2 + b2
Ok = X(t − t0 ),σk = σ(t − t0 ),
Ek =

(4.1)

where k is the identiﬁcation number of the wire, Ek is a distance between the sense wire andthe ﬁtting line, Ok is a radius of equi-drift-time line, and σk is a ﬂuctuation of equi-drifttime line. Here, Ok and σk have already been determined as the results of X-T relation.
Furthermore, since σk included a ﬂuctuation of the incident angle, we could regard theequi-drift-time line as a full circle. Then, χ2 was deﬁned using these parameters asχ2 = (Ek − Ok )2
σk 2

k

.

(4.2)

The ﬁtting of the decay positron was performed based on a principle of minimum χ2 .
Here, we should pay attention to the fact that the ﬁtting function has four free parameters
corresponding to a, b, c, and t0 . In my analysis, it was essential to determine t0 because we
could not use a counter for measuring the t0 . Since there was no information for determining
t0 , I had to evaluate t0 as a free parameter. In addition, considering that the ﬁtting was
performed using the four parameters, more than 5 hits in a cell unit were required for the
analysis. Thus, the ﬁducial volume of the polarimeter including the vertex cell was chosen
as a small region. The resulting pictures are shown in Fig(4.12 - 4.13).
Although the ﬁtting was performed based on this simple method, the resulting tracks
were quite clean. Due to the adoption of the X-T relation based not on the simulation but
the experimental data, it was possible to do a simple analysis even if the cell structure is alittle complicated. On the other hand, as shown in Fig(4.14 - 4.15), I will show some otherpictures below as the bad examples.
The bad events included positron scattering due to the large material density in thepolarimeter. As a matter of course, the bad track events have larger χ2 than clean ones.
As mentioned above, the algorithm should be remade with some requirements as follows.
• In order to increase the number of good events after the ﬁtting, the algorithm has
to overcome scattering events. For overcoming the scattering, the Kalman Filter
method [49], which can recover the positron scattering event, should be adopted in
the near future.
• Since the resolution of positrons includes the angular uncertainty, the algorithm has
to be free from this kind of uncertainty. For avoiding this kind of uncertainty, a71

Figure 4.12: Sample picture of the decay positron ﬁtting 1.

Figure 4.13: Sample picture of the decay positron ﬁtting 2.

Figure 4.14: Sample picture of the decay positron ﬁtting 3.
72

Figure 4.15: Sample picture of the decay positron ﬁtting 4.
simpler and more symmetric cell structure should be adopted, namely we should
determine the X-T relation based on the experimental data.

4.5

Spurious asymmetry

The spurious asymmetry associated with the chamber structure is discussed in this section.

4.5.1

Data analysis

Based on the event selections described in 4.3, the good events were extracted. The numberof extracted good events was 5 times lower than the number of total events. Now thetransverse asymmetry analysis could be started. As mentioned in Chapter 3, the transverse
asymmetry was deﬁned as,
Ncw − Nccw
,
(4.3)
AT =
Ncw + Nccw
where Ncw and Nccw correspond to the y direction and the −y direction, respectively. The
conﬁguration of the setup is also shown in Fig(4.16).

Figure 4.16: Schematic view of the null asymmetry measurement and the deﬁnition of axis.

73

For non-bias analysis to be performed correctly, it was essential to keep the conﬁguration of the sense wires symmetric with respect to the beam axis. Assuming that the
conﬁguration of the sense wires is not symmetric with respect to the beam axis, it is natural to generate some spurious asymmetries associated with its conﬁguration even if all
the sense wire eﬃciencies are exactly the same. Hence, the analysis was performed basedon keeping the conﬁguration of “selected sense wires” to the vertex cell symmetric withrespect to both the transverse and the beam axis. Here, “selected sense wires” means
the 14 sense wires around a vertex. At the same time, the analysis was performed using
just “selected sense wires” with respect to a vertex. As the result of these requirements,
it was necessary to narrow the ﬁducial volume down to several cells. The results of thisanalysis are shown in Fig(4.17).

Figure 4.17: Result of null asymmetry measurement. A large spurious asymmetry appears.
It depend on the wire position.
As shown in Fig(4.17), a large spurious asymmetry appears in the data. Consideringthat the conﬁguration of the ASB cards was the same as for the wire eﬃciency measurement,
the graph shows that the positron tended to be emitted in the same direction as the locationof ASB card. In other words, the positron tended to be emitted upward (downward) incase that vertex cell was located upward (downward). Here, upward (or downward) is theperpendicular direction with respect to the inner Al plates. These directions correspondto the cw and the ccw, respectively. This tendency is shown in Fig(4.18). It was diﬃcult
to explain this fact as the wire eﬃciency ﬂuctuation even if there were some 50 % intrinsic
eﬃciency wires. It was clear that this picture had a structure related to the experimental
conditions.

74

Figure 4.18: Schematic view of the decay positron emission. The tendency shows that thepositron tended to be emitted upward (downward) in case of a vertex cell located upward(downward).
Therefore I considered the possibility that the incident pions also contained some muons
generated from π + decay in ﬂight. Can this explain the structure of Fig(4.17) even if theincident pions contained this kind of muon? To explain Fig(4.17), it is essential to meet
two requirements as follows.
• the positive helicity muon was stopped in the volume
Suppose that the muon did not have any polarization, then the positron will beemitted isotropically. One possibility is that only high polarized muons with positive
helicity were coming into the polarimeter and they were stopped in the volume.
Positive helicity muons could make the spurious structure in Fig(4.17).
• this muon was emitted with some incident angle
Suppose that a polarized muon was coming into the polarimeter parallel to the innerplates, the muon could stop both upward and downward of the inner plate. The
probability that the muon was stopped in the upper (lower) plate was 50 %. The
resulting positrons will then be emitted in both upward and downward directions
with the same ratio. Thus, the muon should be coming into the polarimeter withsome incident angle.

Does this possibly satisfy these requirements?
Here, I will summarize the features of muons from pion decay in ﬂight.

75

Figure 4.19: Schematic view of pion decay in rest frame (left) and laboratory frame (right).
In π + → μ+ decay, the muon momentum in the pion rest frame is 29.8 MeV/c and its
direction is isotropic. In the laboratory frame, where the pion moves with momentum pπ ,the muon momentum has a ﬂat distribution between the two limits:pμ F W D = (βπ + βμ ∗ )pπ /[βπ (1 + βμ ∗ )]pμ BW D = |βπ − βμ ∗ |pπ /[βπ (1 + βμ ∗ )](4.4)

where cβμ ∗ is the muon velocity corresponding to its 28.9 MeV/c momentum from pion
decay at rest. These limits correspond to forward and backward decays in the pion rest
frame. Since muons with momenta at both of these limits move along the initial pion
direction, they are easy to transport. Furthermore, they have deﬁned polarizations of+1 and −1, respectively. The muon momentum distribution for a given pion momentum
and the corresponding decay angle in the laboratory frame are shown in Fig(4.20) andFig(4.21) [50].
In our case since the pion momentum was 170 MeV/c, both FWD and BWD muon momenta
were as follows.
pμ F W D = 173M eV /c
pμ BW D = 86M eV /c(4.5)

Therefore considering that the polarimeter has a ﬁnite stopping power, only BWD muons
could be stopped in the ﬁducial volume. In addition, the BWD muons could be emittedwith some incident angle due to the fact that the pions were boosted. Thus, the hypothesis
could meet these requirements.
In order to estimate how many BWD muons could be contained in the pion beam under
our experimental condition, it was essential to consider how to produce the muons in thebeamline. In general, there are three types of muon production according to the spatial
position (with respect to the target) where π + → μ+ decays take place. These are decay
μ, cloud μ and surface μ, respectively. Conceptual views of these three types of muons areshown in Fig(4.22) [50].

76Figure 4.20: Summary of properties of decay muons. Momentum distribution.

Figure 4.21: Summary of properties of decay muons. Decay-cone aperture angle for muons
produced by pion decay in ﬂight.

77

Figure 4.22: Three types of muon source (surface μ+ , cloud μ+ , and decay μ+ ) produced
by energetic protons from accelerators.
Of particular interest to us is the BWD muons because only they could be stopped in
the ﬁducial region. In addition, their momentum (about half of pπ ) is far from the initial
beam momentum and so they can be cleanly separated from other particles such as π ore by bending magnets. Furthermore, muons of lower momentum have a higher stopping
density.
In general, the surface muons are a monochromatic beam with low momentum of 29.8
MeV/c. So the surface muon cannot be a candidate. The cloud muons produced between
the production target and the B1 bending magnet take the form of a cloud around the target
and can be transported together with the pions as shown in Fig(4.22). Since the momentaof the parent pions are unknown, these muons do not satisfy any kinematic condition toassure their polarization, namely they are a mixture of FWD and BWD muons. Therefore,
their polarization was expected to be small. In addition, such cloud muons with 170 MeV/cmomentum can be eliminated using TOF due to the fact that their timing is faster thanthe pion timing. Furthermore the BWD muon produced between the B1 and the B2 do
78

not pass thorough the B2 due to its low momentum. Hence, the only candidate remainingis the BWD muon produced between the B2 and the polarimeter as shown in Fig(4.23).

Figure 4.23: Schematic view of the M11 beamline. BWD muons could be produced after
the B2 magnet.
Considering that the length between the B2 and the polarimeter was nearly 2.5 m,
BWD muons delayed nearly 2.4 ns with respect to the pion timing. This means thatthe contamination of such BWD muon in the pion peak could not be avoided. On theother hand, since the FWD muons were at least 1.0 ns faster than the pion timing, theircontamination in the pion peak was negligible.

Figure 4.24: TOF spectrum. BWD (FWD) muon could be contained in the pion peaktoward the left (right) direction.
However, it is diﬃcult to discuss the quantitative evaluation. Here, in order to solve
the structure in Fig(4.17) completely, it was necessary to introduce a simulation based onMonte Carlo (MC). In the next subsection, an evaluation of spurious asymmetry was doneusing a Geant4 simulation.
794.5.2

Simulation

Before the main discussion, the simulation data quality was conﬁrmed. It goes without
saying that the muon polarimeter must be able to measure the muon spin using the decay
positron. Therefore, whether the muon spin behaves correctly or not was veriﬁed repeatedly
in the simulation. In order to conﬁrm the muon spin behavior, 100 % polarized BWD muons
were generated.
First of all, the conﬁguration of polarimeter was reproduced completely without either
sense or potential wires as shown in Fig(4.25).

Figure 4.25: A polarimeter constructed in Geant4 simulation. In addition, main axes werealso deﬁned. Here, the incident beam was incoming toward the −Z direction.
After the polarimeter and the degrader was reproduced, the muon beam was shot towardthe −Z direction. For keeping with the experimental conditions, the beam was shot fromthe B2 bending magnet. Here, we should pay attention to the conﬁguration of the innerplates. In this muon run, the inner plate conﬁguration was changed to be perpendicular
to the beam, corresponding to the polarization measurement. Of course the degrader was
also changed based on the range curve measurement. The beam proﬁle was spread in boththe x and the y direction keeping a gaussian shape as shown in Fig(4.26). The proﬁles,
however, were not compared with an actual beam proﬁle since we did not scan it. The
beam proﬁles and emittance were not scanned because we did not install any beam tracker
in our experimental setup.
Next the BWD muon status was evaluated. The results are also shown in Fig(4.27). Here,I should add an explanation about the muon decay rate to understand the graph of thepositron emission angle with respect to beam axis. In general, the muon decay rate is afunction of the energy and emission angle of the decay positron. Thus, the diﬀerential

80decay rate integrated energy function is obtained as,dΓ
1 + αe cos θe=,d cos θe2

(4.6)

where αe is determined by the solid angles of the positron. Assuming that the analysis
is done considering a 4π solid angle, then αe is exactly equal to 1/3. Here, I deﬁne theprobability p+ (or p− ) that the decay positron is emitted in the same (or opposite) semisphere as the muon spin polarization as,
 1
7
1 + αe xdx = ,
p+ =
2
12
(4.7)
0 0
1 + αe x5p− =dx = .
212−1Namely, in case that a 100 % polarized BWD muon was shot toward the polarimeter,
the same semi-sphere probability has to correspond to just 7/12. The result of the decay
positron direction (FWD/BWD) was consistent with 7/12 as shown in Fig(4.27). Furthermore, veriﬁcation of the positron energy spectrum was done. It was consistent withwell-known Michel spectrum.

htemp
Entries 30075
Mean
4.681
RMS
40.74

beam profile X

1200

htemp
Entries 30075
Mean
3.398
RMS
35.4

beam profile Y

1000

1000

count/binconut/bin

800
800
600

600

400
400
200

200
0

-150

-100

-50

0

50

100

0
-150

150
200
muon_posX[mm]beam profile X:Y

-100

-50

0

50

100
150
muon_posY[mm]htemp
Entries 30075
Mean
2700
RMS
0

beam profile Z

150

30000
10 2

muon_posY[mm]

100

25000

50

20000
10

0

15000

-50

10000
1

-100

-150

-150

-100

-50
0
50
100
muon_posX[mm]

150

5000

0

200

2699

2699.52700

2700.52701
muon_posZ[mm]Figure 4.26: Incident π + beam proﬁles in Geant4 simulation81

htempEntries 423988
Mean
35.91
RMS
11.23

positron Energy spectrum (Michel spectrum)
24000

positron emission angle with respect to beam axis

22000

htemp
Entries 423988
Mean-0.1081RMS
0.5682

6000

20000
18000

5000
count/bincount/bin

16000
14000
12000
10000
8000

4000
3000
2000

6000
4000

1000

2000
0
0

10

20
30
40
positron kinetic energy [MeV]

50

htemp
Entries 423988
Mean
-1
RMS
0

muon spin direction (BWD)

3

× 10

0

60

-1

-0.5

0
0.5
positron_initDirZ a.u.

1

positron emission angle 2Dimension
103

1

400

positron_initDirY a.u.

350

count/bin

300
250
200
150

0.5
102
0

10

-0.5

100
50
0

-1
-2

-1.5

-1
muon_initPolZ a.u.

-0.5

-1

0

-0.5
0
0.5
positron_initDirZ a.u.

1

1

Figure 4.27: Features of the decay positron in Geant4 simulation
After some veriﬁcations were performed, the spurious asymmetry measurement wasdone in the same manner as our experimental conditions. The result of the simulation isshown in Fig(4.28).

Asymmetry (Geant4)
0.1
Asymmetry Measurement
Pion
Muon

Asymmetry

0.05

Total

0

-0.05

-0.1

8

9

10

11
12
13
14
Al plate number

15

16

17

Figure 4.28: Result of the spurious asymmetry measurement in Geant4 simulation.
In this simulation, since the polarimeter did not have wires, asymmetries were deﬁned
as a layer unit, namely the ”Al plate number” corresponds to the integration of the wires
82

in the same layer. In addition, the particles were completely identiﬁed in the simulation.
It was possible to separate in-ﬂight decay muons from pions. Here, the pink, green, andblue plots correspond to the in-ﬂight muons, pions, and total events(muons + pions),
respectively. The result of the simulation was diﬀerent from the analysis of the beam test
data. Although it is diﬃcult to explain this tendency, at least the in-ﬂight muons can cause
spurious eﬀects. Furthermore, the muons correspond to the FWD muons though beam test
result tended to contain the BWD muons.

4.5.3

Summary of the asymmetry analysis

In my conclusion, this polarimeter could be very sensitive against the beam emittance.
Considering the conﬁguration of Al inner plates, stopping power of this conﬁguration might
be changed event-by-event due to the fact that the conﬁguration was only symmetric withrespect to the beam axis. In our experimental conditions, both FWD muons and BWD
muons are of diﬀerent momentum, 170 MeV and 85 MeV, respectively. Hence, a kind ofmuon (FWD/BWD) can tend to locally generate spurious asymmetry as shown in Fig(4.29).

Figure 4.29: Schematic view of the cause of a spurious asymmetry.
However, we had no way to measure the beam emittance because we could not install
any beam tracker. Of course there might be other reasons except for the beam emittance.
In the TREK experiment, the beam condition is diﬀerent from that during the beam
test. Most muons from Kμ3 decay spread for the full volume of the polarimeter though themuons are longitudinally polarized. Thus, it is expected that this kind of asymmetry will
disappear (or get smaller).
If this kind of spurious asymmetry locally appears, this asymmetry can be canceledout based on the π 0 f wd/bwd scheme because the transverse axis can be determined bythe π 0 direction (f wd/bwd) event-by-event. Hence, the polarimeter is able to measure thetransverse polarization PT precisely.
83

4.5.4

Future plan

We should pay attention to the followings in the next beam test for the polarimeter.
• Beam trackers such as MWPCs
When we try to understand the incident beam emittance, we should add more than
two trackers such as MWPCs between the degrader and the S0 counter in the experimental setup shown in Fig(3.4). (Here, the degrader was placed next to the S1
counter.) Then, we will be able to roughly determine the trajectory of the incident
beam particle. In other words, we can select the incident angles of the beam.
• Conﬁguration of the ASB cards
We should attach a larger number of the ASB cards for the full volume as possible.
If this is impossible due to our budgetary conditions, at least, we should change theconﬁguration of the ASB cards when we take data for the spurious asymmetry test.
Then, we will be able to use a larger ﬁducial volume for the analysis. Furthermore,
we will be able to extract only the selected incident particles, namely only the beam
particles parallel to the inner plates are extracted when we add more than two beam
trackers. Then we can avoid the event of π decay in-ﬂight and we can control theemittance of the incident particles. It is not until the selections above work correctlythat we can start to perform the spurious asymmetry test. Last time, we did nothave an enough number of the ASB cards. Although the number of the ASB cards
correspond to 1/3 for the full volume, we attached the ASB cards to the both end of
the polarimeter in order to take data for the charge division analysis. Suppose that
the ASB cards are taken oﬀ from the one side and all the ASB cards are attachedto the same end, one might worry about how to analyze the charge division analysis.
The selection of the incident particles, however, is more essential than the charge
division analysis when we measure the spurious asymmetry.
• Beam proﬁle scanning
Last time, we could not scan the beam proﬁle at in front of the polarimeter. Thus,
we had no way to determine the center position of the beam along with the wire axis.
As the result, we could not analyze charge division. Therefore, one should perform a
run for the charge division. The charge division run should be performed apart froma run for the spurious asymmetry test in the next beam test for the polarimeter.
Then we should scan the beam proﬁle using a thin counter (or a MWPC) along withthe wire axis in order to determine the center position of the beam. As a matter ofcourse, the ASB cards have to be attached to the both end of the polarimeter when
we can scan the proﬁles.

84Chapter 5
Design of the Muon Tube
PolarimeterIn the previous chapters, the studies of the plate type polarimeter were discussed. We also
prepare a tube type polarimeter as an another possible alternative. Roughly speaking, theinner structure of the polarimeter will change from multi-plates into multi-tubes.
In the positron track reconstruction analysis, there was a diﬃculty caused by a rectangle
cell structure. In a case of the rectangle, the shape of the equi-drift time line is very
complicated. Hence, it is diﬃcult to determine the drift velocity precisely. As a result, wehave to calculate the drift velocity relying on the simulation if we purse higher position
resolution. In addition, the position resolution is limited by an emission angle of the decay
positron. (see Appendix B)
On the contrary, since the tube type polarimeter has a symmetric structure, the equidrift time line corresponds to a circle. In addition, position resolution can be free fromthe emission angle, the accuracy of the position determination is higher than that of theplate type. Moreover, in terms of the track reconstruction analysis, the drift velocity (orthe X-T relation) should be completely determined using the experimental data. This also
allows to decrease some systematics associated with an uncertainty of the calculation of
the electrostatic ﬁeld. This is the ﬁrst reason why the tube polarimeter attracted me.
Furthermore, since the tube type does not have singular axis, we can measure thelongitudinal polarization in Kμ 3 decay based on the f wd/bwd scheme in the case that we
can employ the tube type polarimeter. The longitudinal polarization measurement will beable to suppress some systematics in the TREK experiment. In addition, since the stopping
power of the tube type does not rely on the incident angle of the muon in Kμ3 decay, akind of systematics caused by a misalignment of the polarimeter can also be reduced. The
main parameter comparisons with the plate type are summarized in table(5.1).

85

Table 5.1: Parameter comparisons of the plate type.
Al plate
Al tubeSense wire
SUS304 20 μm
SUS304 20 μm
Number of sense wires∼ 500 channel
371 channel
Number of potential wires
∼ 500
none
The distance between sense wires
16 mm
14.2 mm
Equi-drift-time line
complicatedcircleRead-out AMP
ASB card
ASB card
Solid angle coverage for positron detection ∼ 100 %∼ 100 %
Material density / full volume
24 %
24 %
Inner gas
Ar : Et = 50 : 50 Ar : Et = 50 : 50

5.1

Estimates of Muon Tube parameters

As I optimized the parameters for the muon tube, there were a few constraints and requirements as follows.
• Size of the muon polarimeter magnet
Considering the fact that the muon polarimeter magnet has already been manufactured and the magnetic ﬁeld test has been performed, we should employ the same
muon magnet which has been developed for the plate type polarimeter. This meansthat the full size of the new polarimeter has to be equal to the plate type. Thus, thenumber of tubes and the size of a tube are subject to certain restrictions.
• Higher track eﬃciency
Since the new polarimeter should also have a high track eﬃciency, the ratio of inner/outer diameter is limited. It is quite important to meet the condition that theratio of the inner/outer diameter is over 87 %. Presuming that the speciﬁc condition above is satisﬁed, then both the incident muon and the decay positron can passthrough all the gas volumes as shown in the left picture of Fig(5.1). In addition, thetubes should be aligned as dense as possible to increase the track eﬃciency. The trackeﬃciency is worse in case that the tubes are not densely aligned as shown in the right
picture of Fig(5.1). Furthermore, considering the positron multiple scattering, theinner density should be as low as possible. In the case that a large number of clean
tracks are measured in the polarimeter, the analysis eﬃciency increases even if we do
not employ the correction of positron scatterings. For satisfying the conditions above,
the thickness of the tube should be thin and the tubes should be aligned densely.
• High stopping power86

Figure 5.1: Schematic view of the constraint against the Muon Tube. The tubes are aligned
densely in the left one, while the tubes in the right one are aligned with a lower packing
density.
On the contrary, the incident muons should be stopped as far as possible inside theﬁducial volume. Thus, the thickness of the tube walls should be as thick as possible.
This requirement is in contradiction with the 2nd item.
For the requirements and constraints above, I had to optimize the best parameters of themuon tubes. For optimizing the parameters, I have done a MC simulation using Geant4. In
the simulation, the muon beam generated from the full simulation for the E246 experiment
was adopted, namely the muons from Kμ3 decay. In the beginning of the simulation, theouter diameter (named OD) was ﬁxed from the constraint of the muon polarimeter magnet
and it was equal to 14 mm. On the contrary, the inner diameter (named ID) was treatedas a variable between 9.8 mm and 12.6 mm. Although more than 12.2 mm was requiredas the size of the ID from the requirement of high track eﬃciency, the size of the ID waschanged to extended regions. The resulting pictures are shown in Fig(5.2 - 5.5), where
ΔR corresponds to the thickness of the tube. In Fig(5.2), Many muons are stopped in theend plate of the polarimeter. On the other hand, in Fig(5.4), the muons are stopped in anarrow region though track eﬃciency can be quite low. In Fig(5.3) and Fig(5.5), since mostof the muons are stopped in the comparatively narrow region, ΔR was ﬁnally determined
to be equal to 1.2 mm.

5.2

Current status of MTP

For manufacturing the MTP, we had several meetings with the staﬀs of REPIC Co. Although the MTP has not yet been completed, all the parts of the MTP has been delivered
to REPIC Co. and the assembling has already started.
For checking the process of Al tube manufacturing, I went to Yamakawa Manufacturingindustry Co. For the MTP manufacturing, the Al material-A5052 was adopted. As men87

Figure 5.2: OD : ID = 10 : 9.

Figure 5.3: OD : ID = 10 : 8.

Figure 5.4: OD : ID = 10 : 7.

Figure 5.5: OD : ID = 10 : 8.5.

tioned in Chapter 2.4, A5052 is also good enough as the inner material in terms of the eﬀectof the spin depolarization. It is essential to know the accuracy of the Al tube for optimizing
the alignment of Al tubes. As the result of the tube manufacturing, the accuracy of boththe outer and inner radius corresponds to ≤ 10 μm and we are successfully able to alignthe tubes at the intervals of 14.2 mm. The resulting tubes are shown in Fig(5.6 - 5.7)

Figure 5.6: Side view of Muon tube.

Figure 5.7: End view of Muon tube.

At the same time, the other parts are assembled as shown in Fig(5.8 - 5.13). The
manufacturing process is summarized as follows.
88• Process of the Al tubes washing
When the tubes were delivered to REPIC, the insides of Al tube were very dirty
due to the lubricating oil. Hence all tubes had to be washed using the method ofsteam-washing after manufacturing.
• Connection of the ﬁeld guide to the Al tube
The ﬁeld guide connector, which is made of some kind of insulator, was used toeliminate any electrical contact with the Al tube.
• Process of the Al tubes assembling
The accuracy of the alignment of the Al tubes was determined by one of the template
touching the buﬀer space for the chamber gases. In this process, the Al tubes were
ﬁxed using the connectors and the templates as shown in Fig(5.14).
• Connection of feedthroughs to the end plate
After the Al tubes assembling, the feedthroughs were attached to the end plate of
the polarimeter as shown in Fig(5.16).
• Process of stringing the wires
Finally, the process of stringing the wires were performed. All the sense wires werestrung with the same 30 g tension using a weight as shown in Fig(5.17).

Figure 5.8: Full volume.

Figure 5.9: Buﬀer space.

89

Figure 5.10: Inner template.

Figure 5.11: Tube to template connector.

Figure 5.12: End plate.

Figure 5.13: Feedthrough.

Figure 5.14: The Al tubes assembling.

Figure 5.15: End plate connection.

Figure 5.16: Feedthroughs connection.

Figure 5.17: Process of the wire stringing.
90

Chapter 6
K1.1BR beamline for the TREK
experiment
The TREK experiment will be performed at the Hadron Experimental Hall at J-PARC.
At present there are 4 beam channels, K1.8, K1.8BR, KL, and K1.1BR beamline. The
layout of the Hadron Experimental Hall is shown in Fig(6.1). In the TREK experiment,
we will use a separated K + beam with 0.8 GeV/c momentum from K1.1BR. The K1.1BR
beamline with a total length of 21.5 m was made as a branch beamline of K1.1, namely
the K1.1BR uses the upstream magnets (from D1 to M S) of K1.1.
The beam optics of K1.1BR [51, 52] was designed by J.Doornbos of the TREK collaboration. In the design of the beamline, it is essential to increase the K/π ratio higher than
2 and the kaon yield as much as possible in order to satisfy the TREK requirement. Next
I will describe the detector elements for the beam commissioning of K1.1BR. Finally, I will
describe the current status of the beamline and the result of the beam commissioning of
K1.1BR.

Figure 6.1: Overview of the Hadron Hall at J-PARC
91

6.1

Expected performance of K1.1BR

6.1.1

Design of beamline and optics

The layout of the K1.1BR beamline is given in Fig(6.2). The detector elements and thebeam optics for the K1.1BR beamline are summarized in the following items.

Figure 6.2: The layout of K1.1BR• proton target (T 1) and ﬁrst bending magnet (D1)
The beam is extracted at an angle of 6 degrees to the proton beam from a 5.4 cm
long Nickel production target. A 2.5 mm thick Beryllium window is placed 40 cm
from the production target. The ﬁrst bending magnet D1 which can bend up to 18
degrees is placed 2.0 m from the production target in order to avoid interference withthe ﬁrst bending magnets for the K1.8 and the K1.8BR beamlines.
• quadrupole doublet Q1-Q2 and intermediate vertical focus (IF Y )After D1, the beam passes thorough a set of quadrupole doublets Q1-Q2 that focuses
the beam at the intermediate vertical focus (IF Y ) which is located 1.0 m downstreamof the 26 degree bending magnet D2. A 50 μm stainless steel window is placed 15 cm
downstream of IF Y for vacuum control. In addition, an intermediate horizontal slit
(IF X) is placed as an acceptance slit. In the K1.1BR beamline, the existence of the
IF Y is essential: it has a crucial role for the removal of pions. The existence of the
IF Y will made it possible to perform the TREK experiment in spite of having only92

a single electrostatic separator (ESS). I will summarize the pion contamination as a
background in the next subsection.
• quadrupole doublet Q3-Q4 and the electrostatic separator (ESS)A second doublet Q3-Q4 makes the beam vertically parallel in the ESS and contains
the beam horizontally. The ESS is one of the key elements of the beamline; it
generates a transverse electric ﬁeld along the beam axis and works with a correction
magnet (CM ) to separate particles by their mass diﬀerence. However, an old ESS
from the KEK-PS is being reused due to budgetary constraints. Eventually it will benecessary to increase the length of the ESS to 2.5 m from the current length of the
2.0 m. Then the performance of the K/π ratio will be good enough for the TREK
experiment.
• quadrupole doublet Q5-Q6 and mass slit (M S)
A third quadrupole doublet Q5 and Q6 makes a vertical focus at the position of the
M S. At the M S, a vertical slit can remove most of the background pions which are
spread out vertically and horizontally.
• The ﬁnal bending magnet (D3)
The ﬁnal bending magnet D3 with a bend angle of 40 degrees, is placed after the M S
and the beam is bent toward a ﬁnal doublet Q7-Q8. In the optics design, althougha bend angle of 45 degrees was proposed, the current reused D3 can only bend to 40
degrees.
• quadrupole doublet Q7-Q8 and horizontal focus (HF OC)
A horizontal focus HF OC is produced after the D3 magnet. Before the HF OC, thebeamline still contains pions horizontally. Thus, this slit is crucial for the removal ofpions and muons. A ﬁnal doublet Q7-Q8 focuses the beam at the ﬁnal focus (FF),
3.3 m downstream from the end of Q8.
• sextupole magnets (SX1 and SX2) and octupole magnets (O1)
The beamline contains two sextupoles just before and just after the separator. In
addition, an octupole is placed between Q3 and Q4. Although the corrections of thevertical aberrations at the M S are not perfect, they are suﬃcient to obtain a clean
kaon beam.

The beam envelop of the current K1.1BR together with the various slits are shown inFig(6.3 - 6.6).
93

Figure 6.3: Beam envelop of the current K1.1BR beamline. The top half and the bottom
half corresponds to vertical and horizontal envelop, respectively.

Figure 6.4: Picture of the intermediate focusing slits (IF X + IF Y ) and the mass slit
(M S) before installation. Both slits are located at the vertical focusing point. The IF Y ,in particular, has a crucial role for the removal of pions in spite of the use of a single stage
separator. In addition, IF X is useful to control the overall beam acceptance.

94

Figure 6.5: Picture of the horizontal focusing slit (HF OC) before installation. The HF OC
is placed before the ﬁnal doublet Q7 - Q8 and is also useful for the removal of the pion
contamination in the beam.

Figure 6.6: Picture of the electrostatic separator (ESS) before installation. The ESS is
one of the essential elements for the beamline to extract a clean K + beam.

6.1.2

Pion contamination

There are three sources of pion contamination. The sources and the method of their removal
are summarized below.
• Higher order aberration
The direct pions produced in the production target can pass through the M S due tohigher order aberrations. The direct pion contamination can be corrected by both
SX1 and SX2 which are located just before and after the ESS. In addition, thesinglet O1 located between Q3 and Q4 is also useful.

95• Slit scattering
Suppose that the aperture of the M S is narrow, the K/π ratio will not be goodenough due to the scattering at the M S. Furthermore, in the case that the IF Y is
also a narrow aperture, the K/π ratio will be much worse. Then the horizontal slit
HF OC can help to improve the K/π ratio. The removal of slit scattering pions is
performed by a narrow horizontal aperture condition of the HF OC.
• Cloud pions from Ks (cτ = 2.7 cm)
Cloud pions are generated from the region near the production target. The scattering in a 50 μm stainless steel window, placed 15 cm downstream from the IF Y
for managing the vacuum conditions, can cause a large beam spot (vertically andhorizontally) at the M S. In a single stage of the ESS, the removal of the pions has
to be performed using a vertical focus in the beginning of the beamline before theseparator, thus the IF Y is essential for the beamline. Since a slit is placed at the
IF Y , it can be used to limit the cloud pion contamination. The IF Y slit can bringthe cloud pion fraction down to an acceptable level. However, the pions can be stillcontained at the M S, then the HF OC is also helpful to reduce the contamination in
the beamline by selecting the narrow aperture.

6.1.3

Expected Kaon yield

The beamline and optics were designed for high K/π ratio and high kaon yield. As theresult of trial and error, the best optical conditions were optimized by J.Doornbos for the
TREK experiment.
The expected performance of the kaon yield is evaluated as the comparison with a similar
low momentum beamline LESB3 at BNL-AGS. Its well-established kaon beam intensity at
0.8 GeV/c but with 24 GeV proton energy converts to about 80 k K + /spill for the current
K1.1BR condition assuming a Ni target.
We can also compared the kaon yield for the current K1.1BR with the Sanford-Wang
empirical formula [53]. From the result of this formula, 65 k K + /spill will be expected forthe current K1.1BR. The accuracy of both comparisons, however, is of course limited by
the ambiguity of slit openings and the kind of production target.

96

6.2

Detectors for the beamline commissioning

In the beam commissioning run, the detectors (Beam Hodoscope, MWPCs, Fitch-type
Cherenkov counter, beam deﬁning counter (BDC), TOF counters, and Gas Cherenkov
counter) were all located downstream of the radiation shielding, which had a 2.5 m thickness, as shown in Fig(6.7).

Figure 6.7: Detector components for the beam tuning.

6.2.1

beam detector elements

After the ﬁnal focusing magnet Q8, the beam passes through the Fitch-type diﬀerential
Cherenkov counter ﬁrst. Both pions and kaons can be conﬁrmed by the Cherenkov. Afterthe Cherenkov, the beam passes through the BDC counter, which is one of the trigger
counter, located at the ﬁnal focusing point (FF). The FF is 3.3 m downstream from theexit of Q8. The beam trigger is made of the coincidence of both the BDC and TOF1. In
our conﬁguration of detectors, it is possible to measure the time-of-ﬂight for all kinds ofparticles using a ﬂight length of nearly 4 m. Indeed, the performance of the Fitch Cherenkov
was conﬁrmed by using the TOF system. The TOF spectrum and the performance of thissystem is shown in the next section. We also prepared the MWPCs and Beam Hodoscopecounter. Therefore, the beam proﬁles can be measured at the FF and the end of theshielding by the MWPCs and at the end of Q8 by the Beam Hodoscope. The ﬁnal beam
proﬁles are also shown in the next section. In addition, a Gas Cherenkov counter was also
prepared. Since this counter was ﬁlled with some air at a pressure of 1 atm, the Cherenkov
light can be emitted with some incident angle in the case of the electrons entering into thedetector, therefore the detector can be used as electron veto. The performance of thesedetectors were tested at KEK-PS North Hall at KEK and at Hadron Experimental Hall at
J-PARC. As shown in Fig(6.8), all detectors were ﬁnally installed in our beam channel.
97Figure 6.8: Detector elements for the beamline commissioning.
The Beam Hodoscope, however, cannot be seen in the ﬁgure above due to the fact that
it was located between the shielding and the Q8 magnet. The structure of the Hodoscopeis shown in Fig(6.9). As can be seen in the ﬁgure, the Hodoscope is simply composed of
24 scintillators with a thickness of 12 mm.

Figure 6.9: Picture of the beam Hodoscope. The Hodoscope is composed of 24 scintillatorswith a thickness of 12 mm in a stainless steel frame.

986.2.2Fitch-type diﬀerential Cherenkov counter

In order to trigger on both the kaons and the pions in the beam, a Fitch-type diﬀerential
Cherenkov counter was prepared. In the beginning, this counter was developed for the
E246 experiment [54]. After the stop of E246, several improvements were added to thecounter due to the diﬀerent beam momentum of the E246 experiment [55]. The structureof this counter is as shown in Fig(6.11) and the parameters are also given in Table(6.1). The
kaons and pions enter into an acrylic radiator with a 40 mm thickness and the Cherenkov
light is ﬁnally emitted with a characteristic polar angle according to each velocity. The
light is totally reﬂected at the rear surface of the radiator and detected by an inner photomultiplier(PMT) ring (π ring). The light from the kaons emerging from the radiator is
reﬂected by a backward parabolic mirror and detected by an outer PMT ring (K ring).
Each ring is composed of 14 PMTs with a Winston cone at the entrance. The designed
momentum range is 740-800 MeV/c. The trigger condition is evaluated as the multiplicityof the PMT hit by Monte Carlo simulation as shown in Fig(6.12 - 6.13). From the results ofthe simulation, when a threshold multiplicity of N > 6 is required, more than 99 % trigger
eﬃciency for kaons can be expected with negligible misidentiﬁcation as pions. In addition,
when a threshold multiplicity of N > 4 is required, ∼ 100 % trigger eﬃciency for pions canbe also expected with a negligible kaon misidentiﬁcation.
Table 6.1: Main parameters of the beam Cherenkov counter. The K + momentum is
expected to be 740-800 MeV/c. The K + eﬃciency is obtained to be higher than 99 % bysetting the threshold multiplicity of N > 6.
Parameter
Value+
Accepted K
740-800 MeV/c
Radiator material
acrylic (nD = 1.49)
Eﬀective aperture
12 cm diamiter
Number of PMTs
14 for K + and 14 for π ++K eﬃciency> 99%
π + misidentiﬁcation as K + < 1%

Figure 6.10: Top view of the beam Cherenkov counter.
99

Figure 6.11: Side view and end view of the beam Cherenkov counter. The beam with
740-800 MeV/c momentum emits Cherenkov light with an angle of 38◦ for K + and 47◦ for
π + . The critical angle of the radiator for total reﬂection is 42.2◦ .

Figure 6.12: Distribution of PMT-hit K ring multiplicity @ 770 MeV/c in Monte Carlosimulation.

Figure 6.13: Distribution of PMT-hit π ring multiplicity @ 770 MeV/c in Monte Carlosimulation.

100

6.3

Commissioning of the beamline

The current K1.1BR beamline has been constructed slightly diﬀerent than the original
optics design. The diﬀerent points are the followings:• The length of ESS is not 2.5 m as in the optics design, but 2.0 m, because an old
ESS from KEK-PS has been reused. As a matter of fact, this is disadvantageous for
the K/π separation.
• The bending angle of the last dipole magnet (D3) is not 45 degrees as in the optics
design but only 40 degrees due to performance limit of the reused D3. This might
increase the pion contamination compared with the larger bend angle.
• The ﬁnal focus (FF) is currently 3.3 m distance from the last focusing element Q8,due to the 2.5 m thick Fe shielding as required by the radiation safety group during
the test beam period. This will be shortened to 0.8 m for the TREK experiment.

6.3.1

Result of the beam tuning

The commissioning of the K1.1BR beamline was performed in Oct-Nov 2010. The TREK
collaboration was responsible for the beam commissioning. The 0.8 GeV beam momentum
at an accelerator power of 3 kW on average on a Pt production target was adopted for the
beam tuning.
In the beginning of the beam tuning, we searched for kaons using a TOF system.
Then, we conﬁrmed the time-of-ﬂight for particles corresponding to pions, kaons, andprotons. The ﬁrst observation of kaons from the K1.1BR beamline is shown in Fig(6.16).
For conﬁrming whether the kaon-like peak is consistent with the real kaons or not, theconditions that the π ring and K ring PMT hit multiplicity are zero hit and more than 1
hit, respectively, were required. Finally, we could verify the fact that the TOF spectrum did
not depend on the requirement above. (I have also done the simple calculation using the βfactor and the ﬂight length; the caluculation was also consistent with the TOF spectrum.)
In this step, the pion peak, however, was higher than kaon peak due to the three reasons
below.
• The Fitch Cherenkov detector has not been tuned yet.
• The beamline magnets has not been suﬃciently tuned yet.
• The ESS operation voltage was lower than its maximum voltage (∼ ± 400 kV).
For extracting the maximum performance of the beamline, we tuned the Fitch Cherenkov
detector ﬁrst.

101

Figure 6.14: TOF spectrum. A large number of kaons were observed in the separated
beam. We also see pions and protons in the spectrum. In this ﬁgure, the conditions thatthe π ring and K ring PMT hit multiplicity are equal to zero hit and more than 1 hit, wererequired, respectively.
After the conﬁrmation of the particle timing, the performance of the Fitch Cherenkov
counter was conﬁrmed using the unseparated beam. As shown in Fig(6.15 - 6.17), it is no
exaggeration to say that the performance of the detector is even better than the resultsof the simulation in Fig(6.12 - 6.13); the π + misidentiﬁcation as K + is less than 0.3 %.
Finally, the threshold multiplicity was determined to be equal to N > 6 for K ring and N> 4 for π ring.

Figure 6.15: The performance of the K ring. In this spectrum, the condition of the piontiming conﬁrmed by the TOF spectrum above is required. Thus, the ﬁgure shows the pion
fraction in the K ring.

102

Figure 6.16: The performance of the K ring. In this spectrum, the condition of the kaon
timing conﬁrmed by the TOF spectrum above is required. Thus, the ﬁgure shows the realkaon events.

Figure 6.17: The performance of the π ring. In this spectrum, the condition of the piontiming conﬁrmed by the TOF spectrum above is required. Thus, the ﬁgure shows the realpion events.
The beam survey and the tuning were mostly done using narrow horizontal slit (IF X
and HF OC) conditions to avoid counter performance degradation where the IF X played
the role of an acceptance slit not as a focus point. The full intensity was deduced usinga scaling factor obtained from very narrow vertical slit (M S and IF Y ) conditions. The
ESS was excited to ±150 kV for rough tuning and then raised to ± 250 kV or ±300 kV for
ﬁnal conﬁrmation of the K/π separation. The separation curve was measured by sweeping
the CM current and ﬁnally plotting π + and K + yields triggered by the Fitch Cherenkov
detector. Furthermore the proton yield was also measured as the triggered events above103

the K + peak. The measured kaon yield and the K/π ratio are summarized for various slit
conditions in Table(6.2).

Table 6.2: Results of the K + beam tuning at 0.8 GeV/c at K1.1BR.
–
K + / spill @ 3.6 kW
π/K ratio
Vertical slit
Narrow H.S. Wide H.S. ± 250 kV ± 300 kV
Narrow (IF Y :± 0.5 mm, M S:± 0.75 mm)
1253
3629
1.4
Standard (IF Y :± 1.5 mm, M S:± 2.0 mm)2541≥ 58443
9.8
1.1
Wide (IF Y :± 2.0 mm, M S:± 2.5 mm)
3493≥ 80338
25.2
Widest (IF Y :± 2.5 mm, M S:± 2.5 mm)
3811≥ 87653
26.8
6

The wide horizontal slit (H.S.) settings, which are relevant to the TREK experimental
condition, have some ambiguity due to the uncertainty of the scaling factors. However, thegiven values are lower limits, which should not be very diﬀerent from the real values. In
the standard vertical slit settings, we observed nearly 60 k K + /spill at 3.6 kW power with
6 sec repetition. As shown in the separation curve of Fig(6.18), we achieved considerably
good separation with a π/K ratio of 1.1 on the kaon peak at the ESS operation of ± 300
kV.

Figure 6.18: Mass separation curve obtained with a ESS voltage of ± 300 kV at the beam
momentum of 0.8 GeV/c.

104

From the ﬁgure of Fig(6.18), one can see the kaon fraction in the pion peak. This fraction
shows that the pion misidentiﬁcation as kaons in the K rings and the misidentiﬁcation
corresponds to < 0.03 %.
In the beam tuning, we also tried to ﬁnd optimum focusing condition at the FF (although it will be diﬀerent from the closer FF without the 2.5 m shielding), by varying thelast focusing magnets Q7 and Q8. We ﬁnally succeeded to focus the kaon beam to a roundspot with σx,y = 11 mm as shown in Fig(6.19).

Figure 6.19: Kaon beam spot at the FF for the best tuning setting of Q7 and Q8, and at
the end of Q8 using a beam Hodoscope.

105

Conclusion
In this thesis, the following items regarding the polarimeters for the TREK experiment are
discussed.
1) At present we have two choices as the polarimeter. One is a plate type and theother a tube type. For the plate type, I took part in from the process of the manufacturing
and the beam test at TRIUMF. The analysis based on the beam test was done on myresponsibility.
2) In the track reconstruction analysis, I developed a track reconstruction algorithm
based on my idea. As the result, a simple track algorithm using the X-T relation optimizedby the experimental data was developed though still some kinds of problems I described in
Chapter 4.
3) In the null asymmetry analysis, a spurious asymmetry, which is generated from thepolarimeter mechanical structure, appeared. I think that muons from the pion decay inﬂight can be possible to cause the spurious asymmetry, in other words, the emittance of theincident particle beam can locally make the asymmetry. Further studies for understanding
the spurious eﬀects are essential in order to complete an active polarimeter. I suggested
the new experimental condition for avoiding the eﬀect of decay in-ﬂight in Chapter 4.
4) At present the manufacturing of the tube type polarimeter is in progress under mysupervision. Since the cell of the tube type has a structure of circular symmetry, the equidrift time line completely corresponds to a circle. Hence, the position resolution can befree from the emission angle of the decay positron. As the result, a higher accuracy ofthe position determination will be expected. Furthermore, some systematics in the TREK
experiment will be able to be reduced.
In addition, I described the commissioning of K1.1BR beamline, where 60 k K + /spill
was obtained. In order to start the TREK experiment, it is essential to make some improvements to the beamline. First, we should install a 2.5 m ESS, then the π/K ratio will
be down to 0.5. If we change the current D3 into a new D3 with a bending angle of 45
degrees, we will obtain a π/K ratio smaller than 0.5. Furthermore, we should shorten the
distance to the FF, then the value of the kaon yield will increase up to 90 k K + / spill,which also satisﬁes the TREK requirement.

106

Appendix A
Charge division
Here, the mechanism of the charge division method will be described brieﬂy. As shownin Fig(A.1), the distances between particle hit position and the wire ends are deﬁned as
Z1 and Z2 , and the resistances corresponding to the distances are deﬁned as R1 and R2 ,respectively. In addition to these wire resistances we have to consider the input impedanceof ampliﬁers, which are deﬁned as r1 and r2 , respectively. In this case, the equivalent circuit
can be expressed as shown in Fig(A.2). The collected charge on the virtual capacitance isFigure A.1: The schematic view of charge division system. The distance from avalanche
to wire ends are Z1 and Z2 , and the corresponding resistances of the wire are R1 and R2 ,respectively. The input impedance of ampliﬁers are r1 and r2 .
discharged through the resistances. The experimentally time-integrated I1 and I2 currents
are observed as the charges Q1 and Q2 , respectively. Using the capacitance (C) and voltage(V ), the charge (Q) can be written as,
V = I1 (R1 + r1 ) = I2 (R2 + r2 ),Q=(−I)dt = CV, −I = −(I1 + I2 ) = C

107

(A.1)
dV
,
dt

(A.2)

Figure A.2: Equivalent electric circuit of the charge division system. The collected charge
on capacitor is discharged through resistances. The experimentally time-integrated I1 andI2 are observed as the charges Q1 and Q2 .
thus
dV
V
1
1
V
−
= −(
+
)V,
=−
dt
R1 + r1 R2 + r2
R1 + r 1 R2 + r 2
dV(R1 + r1 )(R2 + r2 ) dV
C
= −τ
V =−
R1 + R2 + r1 + r2 dt
dt
V can be obtained as V (t) = V (0)exp(−t/τ ), and
1
1QQ
exp(−t/τ )andI2 =exp(−t/τ ).
I1 =R1 + r1 C
R2 + r 2 C
The charges from both wire ends are obtained by time-integration of I1 and I2 as
Q
1
R2 + r 2Q,τ=
Q1 = (−I1 )dt =R1 + r 1 C
R1 + R2 + r1 + r2
1
Q
R1 + r 1
Q2 = (−I2 )dt =Q.
τ=R2 + r 2 C
R1 + R2 + r1 + r2
From the relation of
Z1
R1
=
,
Z2
R2
Q1 /Q can be described by using Q = Q1 + Q2 , R = R1 + R2 , and Z = Z1 + Z2 as,C

R2 /R + r2 /R
R2 + r2
Z2 /Z + r2 /R
Q1
=
=
=
.
Q
R1 + R2 + r1 + r2
1 + (r1 + r2 )/R
1 + (r1 + r2 )/R

(A.3)

(A.4)

(A.5)

(A.6)

(A.7)

Therefore, from Eq(A.7) the particle hit positions can be determined by the output charges
from both wire ends as,
r1 + r2 Q1 r2
Z2= (1 +
)
− ,
Z
R
Q
R
Z1
Z2
r1 + r2 Q2 r1=1−= (1 +
)
− ,
(A.8)
Z
Z
R
Q
R
r1 + r2 Q2 − Q1 r1 − r2
Z 1 − Z2
= (1 +
)
−
.
Z
R
Q
R
108

In the coordinates where x is the distance of the particle hit position from the center (x = 0 is center ), x is written as,x
r1 + r2 Q2 − Q1 r1 − r2
= (1 +
)
−
,
Z
R
2Q
2R
where Z1 − Z2 = 2x. The Eq(A.9) is the same as Eq(3.6).

109

(A.9)

Appendix B
An estimate of X-T relation
For determining the X-T relation, ﬁrst of all, an estimate of the typical drift velocity isneeded as an initial parameter. In order to estimate the parameter, the incident beam data
were useful because we have the known start timings (t0 ) determined by the S1 counter.
In addition, the trigger condition in the analysis was as follows,1)in order to extract only the incident particles, less than 200 ns data from the S1 signals
were adopted,
2)the condition that all continuous 5 wires were hit and thus forming a straight line was
required.
As the trigger, any selected 5 wire sets were used. The spectrum, as shown in Fig(B.1),
consisted of the sum of all the central wire hit timings.
Drift time distribution ( 4 mm)
2400

Drift_dis5
Entries
27347
Mean
40.59
RMS
23.1

2200
2000

[count/5nsec]

1800
1600
1400
1200
1000
800
600
400
200
0

0

20

40
time[ns]

60

80

100

Figure B.1: Drift time distribution. The sweep of the drift time distribution corresponded
to a cell size.
In general, the time width was determined by both the cell size and the drift velocity.
In this case, since the cell size has already been ﬁxed as 4 mm, the only parameter was
the drift velocity. From the distribution, the 80 ns time width corresponds to roughly 50
μm/ns. The drift velocity is generally determined by the kind of gas and its pressure. The
110

resulting velocity from the experimental data was roughly consistent with the estimationfrom the gas condition.

B.1

Determination of the X-T relation

Next I will explain the algorithm for determining the X-T relation. Indeed, as the only
data that we could use for analysis were each wire hit timings, the other parameters must
be extracted from them. The 3 wires which meet the same conﬁguration as Fig(B.2) werechosen for the full volume.

Figure B.2: Schematic view of the deﬁnition of wires for analyzing the X-T relation. The
same conﬁguration of wires was adopted in my analysis.
Here, I deﬁne the wires as A, B, and C and the wire hit timing as t1 , t2 , and t3 ,respectively as shown in Fig(B.2). In this analysis, the muon beam was adopted due tothe two reasons given below.
• time zero
As well as the estimate of the drift velocity, we already know the start timing due tothe S1 counter. In this case, the timing just corresponds to t0 .
• stagger structure
For evaluating the X-T relation, the incident particle must have passed between A(or C) and B, then the simple relation given below could be ensured,
X2 = 8 − (X1(t1 ) + X3(t3 ))/2.

(B.1)

Eq(B.1) is essential for my analysis. Here, I must give an account of the explanation above
in detail. Suppose that both X1 and X3 are linear functions of t1 and t3 , respectively
such as X1 = v(t1 − t0 ), then X2 is calculated using Eq(B.1). Here, the fact is essential
111

that the X2 is evaluated without using t2 . In other words, both X2 and t2 are evaluatedindependently. A 2-Dimensional graph of X2 and t2 using the assumed drift velocity as an
initial parameter, namely v = 50 μm/ns, is shown in Fig(B.3).

Figure B.3: 2-Dimensional plot of the X-T relation based on 50 μm/ns drift velocity. The
resulting plot shows that drift velocity was not constant.
From this ﬁgure, the fact is clear that the drift velocity was not constant. This meansthat the drift velocity which has been assumed at ﬁrst is not correct. Indeed, the actual
drift velocity should have been a quadratic function,
X2(t1 − t0 ) = v1 (t1 − t0 )2 + v2 (t1 − t0 )),(B.2)

where X2 is satisﬁed with X(0) = 0. Suppose that the actual velocity has been assumed,
the resulting X-T relation should be the same as the assumed one. Namely, somehow orother I have to look for the actual velocity. For the reason above, the so-called iteration
method was adopted.

B.2

Iteration method

The complete method is as follows,• an estimate of the drift velocity
In the beginning of the iteration, the drift velocity is assumed as an initial parameterbased on the measurement such as the Fig(B.1) (v2 = 50 μm/ns). In my case,although v1 = 0 was adopted as an initial parameter, the value of χ2 ﬁnally diverged.
Thus, for avoiding this kind of situation, a non-zero value was assigned to v1 .

112

• 2-Dimensional X-T relation plot
Next, as already mentioned and shown in Fig(B.3), a 2-Dimensional X-T plot is drawn
based on the trigger condition above. This 2-Dimensional plot must be consistent
with the initial parameters in the case that the correct value has been assumed.
• Projection to X axis
The 2-Dimensional plot was projected onto the X axis by a 10 ns interval. Next, all
the projected histograms are ﬁtted by gaussian function as shown in Fig(B.4).

Figure B.4: Sample of projected histogram. These products were ﬁtted by Gauss function.
Here, one of the ﬁtting parameters, p1, which corresponds to σ, could be roughly
regarded as the position resolution relying on the interval, namely the resolution
corresponds to a drift velocity ﬂuctuation. In fact, the ﬂuctuation is including angle
ﬂuctuation. Supposing a shape of the cell structure corresponds to a circle, the shapeof the equi-drift-time line also corresponds to the circle. On the other hand, since
our polarimeter has the cell structure of a rectangle, the shape of the equi-drift-timeline is more complicated.
• 1-Dimensional X-T relation plot and a ﬁtting using the as-

sumed parameters

All the mean values of the projected products with some deviation are plotted in a
1-Dimensional graph. After all projected products are plotted as a point, the graphwas ﬁtted by a quadratic function with the assumed parameters as shown in Fig(B.5).
113

Although I should use an error of the mean value for the Fig(B.5), the value of sigma
is actually adopted as the error because of the diﬃculty of the iteration method,
namely the error from the mean value causes the value of χ2 to diverge.

Figure B.5: Result of ﬁtting with an assumed parameter. At the same time, the value ofχ2 was recorded every time.
• Recording the value of χ2
After the ﬁtting was performed under the initial condition, the resulting parameters,in particular χ2 , were recorded. In case that the χ2 diverged, the initial drift velocity
was changed.
• An estimate of the new drift velocity
At the same time, the best ﬁtting parameters are also extracted as the new initial
parameters.
It was not until these operations were done repeatedly that the value of χ2 ﬁnally converged. The resulting values of χ2 are plotted every time as shown in Fig(B.6). Furthermore
the results of the ﬁnal parameters are also shown in Fig(B.7). These ﬁnal parameters wereadopted as the actual drift velocity.

114Figure B.6: The variation of χ2 . The value of χ2 converged after several iterations.

Figure B.7: Final result of parameters corresponding to actual drift velocity.

115

x-t 20-30ns

x-t 60-70ns

14000
count/bin

12000
10000
8000

x-t 60-70ns
Entries

60000

1831981

3.739

RMS

0.533835000

p0

6.698e+04

30000

p0

25000

p1

5.35

20000

p2

0.2727

30000

p1

3.64

p2

0.2934

Mean

5.299

RMS

0.55954.719e+04

15000

20000

10000
10000

2000
2

3

4
5
6
position [mm]

7

8

9

0
0

10

x-t 30-40ns

5000
1

2

3

4
5
6
position [mm]

7

8

9

x-t 70-80ns

x-t 30-40ns
Entries

2.17

RMS
p0

0.7953

25000
20000

p1

1.955

p2

0.3515count/bin

Mean

15000

x-t 70-80ns

60000

199149030000

Entries
50000
40000

3.926e+04

30000

35000

2548285

Mean

4.202

RMS

0.508425000

p0

6.432e+04

p1

4.127

p2

0.2864

20000
15000

20000
10000

0
0

0
0

2

3

4
5
6
position [mm]

7

8

9

10

1

2

3

4
5
6
position [mm]

7

8

9

x-t 80-90ns

Mean

2.691

count/binRMS

0.6559p0

5.62e+04

p1

2.548

30000

20000

Entries

50000
40000
count/bin

40000

30000
20000

p2

25000

2328034

Mean

4.62

RMS

0.50553

4
5
6
position [mm]

7

8

9

0
0

10

x-t 50-60ns

40000
30000

Mean

3.229

RMS

0.5813p0

6.493e+04

p1

3.106

p2

20000

40000

30000

20000

0.3046

10

7

8

9

10

7

8

9

10

3.761e+04

p1

5.649

p2

0.2665

1

2

3

4
5
6
position [mm]x-t 120-130ns
11487585.689

p0

2.74e+04

p1

5.883

p2

0.266

5.904e+04
4.579

p2

0.286

10000

15000

5000

1

2

3

4
5
6
position [mm]

7

8

9

0
0

10

1

x-t relation

2

3

4
5
6
position [mm]x-t relation
Entries 2.723666e+07

x-t 90-100ns

9

Entries 2102435

8

Mean

4.985

7

RMS y

RMS

0.52196p0

5.409e+04

p1

4.985

p2

0.279

Mean x85.35

Mean y

4.166

RMS x

44.89
1.495

104

5
10

4

3

102

3
2

10000

10000

p0

0.6897

X[mm]count/bin

50000

50000

2744946

count/bin

Entries0.6149RMS

10x-t 50-60ns

5.535

RMS

Mean

p1

x-t 90-100ns

60000

9

1489716

Mean

20000

p0

10000

2

8

x-t 110-120ns

Entries0.323810000

7x-t 120-130ns

x-t 40-50ns

1

0
0

10

x-t 80-90ns

Entries 2545954

4
5
6
position [mm]

5000

60000
50000

3

10000

count/bin

x-t 40-50ns

2

Entries
30000

10000
5000

1

x-t 110-120ns

count/bin

35000

1

0
0

10

count/bin

1

40000

0
0

Entries

Mean
50000

4000

00

x-t 100-110ns

40000

40000

6000

45000

2715652

count/bin

16000

x-t 100-110ns

70000

x-t 20-30ns
Entries 1093989
Mean
1.837
1.103
RMS
p0
1.739e+04
p1
1.379
p2
0.3681count/bin

18000

10

1
0
0

1

2

3

4
5
6
position [mm]

7

8

9

10

0
0

1

2

3

4
5
6
position [mm]

7

8

9

10

00

1
50 100 150 200 250 300 350 400 450
TDC[ns]Figure B.8: A ﬁnal set of the projected histograms and the 2-Dimensional X-T plot. The
mean value of the histogram is shifted toward the right direction and the value of sigma is
becoming smaller.
In addition, the deviations of the projected products were also plotted with respect toevery time interval as shown in Fig(B.9). The graph was ﬁtted by the function below,p0
σ(t) = √ + p1,
t
116

(B.3)

where both p0 and p1 are free parameters. These parameters are also essential as the
tracking parameters as was explained in Chapter 4.

Figure B.9: The variation of σ. The resulting parameters were adopted as the ﬂuctuationof the equi-drift-time line.

117Appendix C
Beam polarization
In this section, the result of the beam polarization measurement will be described though
the polarimeter has the kind of uncertainty caused by the spurious eﬀects generated fromits mechanical structure. As shown in Fig(4.26), the muon beam enters into the polarimeter
perpendicular to the Al plates in this measurement.

Figure C.1: Conceptual diagram of the longitudinal polarization measurement.
As already mentioned in 4.5.2, the probability p+ (or p− ) that the decay positron isemitted in the same (or opposite) semi-sphere as the muon spin polarization is 1
1 + αe x7p+ =dx = ,
2
12
(C.1)
0 0
5
1 + αe xdx = .
p− =2
12−1
Thus, the probability that the decay positron was emitted into the upstream (or downstream) semi-sphere is5
7+ P− × ,121275
pdown = P+ ×
+ P− × ,1212pup = P+ ×

118

(C.2)

where P+ and P− are positive helicity and negative helicity, respectively. Finally, theasymmetry can be obtained as,A=

Pdown − Pup
1= (P+ − P− ),Pdown + Pup
6

(C.3)

where A is the observable. Therefore, the beam polarization can be replaced with thef wd/bwd asymmetry in this way. The resulting picture is shown in Fig(4.27).

Figure C.2: Asymmetry of the longitudinal polarization measurement.
From the resulting graph, the value of A ∼ 0.16 was observed as the beam asymmetry.
This means that the muon beam has a large polarization corresponding to ∼ 95 % though
there are some uncertainties as mentioned above.
Since the muon beam can mainly include both the cloud muon with low polarizationand the decay muon, the beam polarization should be small enough. However the result is
diﬀerent from the assumption.

119

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