Nuclear-matter modiﬁcation of decay widths
in the φ → e+e− and φ → K +K − channels
studied in 12 GeV p + A reactions

Fuminori Sakuma

Abstract
The experiment KEK-PS E325 has measured the φ meson production via the e+ e− and K + K −decay channels in 12 GeV p + C and p + Cu reactions in order to search for in-medium modiﬁcation of φ mesons, which was theoretically predicted as a consequence of partially-restored
chiral-symmetry at the normal nuclear-matter density. Using the nuclear mass-number dependences of the φ → e+ e− and φ → K + K − yields, we have searched for a possible change ofthe branching ratio Γφ→K + K − /Γφ→e+ e− , since the partial decay width Γφ→K + K − is sensitive
even to a small change in the spectral function of the φ meson and/or kaon because of thesmall Q value in φ → K + K − decays. The observed K + K − spectra are well reproduced by the
relativistic Breit-Wigner function with a combinatorial background shape in three βγ regions
between 1.0 and 3.5. The nuclear mass-number dependence of the yields of the K + K − decay
channel is compared to those of the e+ e− decay channel. We parameterize the production
yields as σ (A) = σ0 × Aα and obtain αφ→K + K − − αφ→e+ e− to be 0.14 ± 0.12. Although wehave concluded that αφ→e+ e− and αφ→K + K − are consistent with each other within an error in
the measured kinematical region, upper limits are obtained for the partial decay widths of φmesons in nuclear matter.

Contents
1 Introduction
1.1 Chiral Symmetry Breaking and its Restoration . . . . . . . . . . . . . . . . . . .
1.2 Theoretical Predictions for Meson Modiﬁcations . . . . . . . . . . . . . . . . . .
1.3 Experimental Searches for Meson Modiﬁcations . . . . . . . . . . . . . . . . . .
1.4 KEK-PS E325 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1
1
2
4
5

2 Experimental procedure
2.1 Overview of Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Accelerator Facility and Beam Line . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Spectrometer Magnet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 Targets and Beam Proﬁle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.1 Targets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.2 Beam Proﬁle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5 Tracking Chambers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5.1 Cylindrical Drift Chamber . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5.2 Barrel-shaped Drift Chambers . . . . . . . . . . . . . . . . . . . . . . . .
2.5.3 Vertex Drift Chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.6 Electron Identiﬁcation Counters . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.6.1 Start Timing Counter . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.6.2 Front Gas-Čerenkov Counter . . . . . . . . . . . . . . . . . . . . . . . . .
2.6.3 Rear Gas-Čerenkov Counter . . . . . . . . . . . . . . . . . . . . . . . . .
2.6.4 Rear Lead-Glass EM Calorimeter . . . . . . . . . . . . . . . . . . . . . .
2.6.5 Side Lead-Glass EM Calorimeter . . . . . . . . . . . . . . . . . . . . . .
2.6.6 Forward Lead-Glass EM Calorimeter . . . . . . . . . . . . . . . . . . . .
2.7 Kaon Identiﬁcation Counters . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.7.1 Hodoscope Counter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.7.2 Forward Time Of Flight Counter . . . . . . . . . . . . . . . . . . . . . .
2.7.3 Aerogel Čerenkov Counter . . . . . . . . . . . . . . . . . . . . . . . . . .
2.8 Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.8.1 Electron Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.8.2 Kaon Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.9 Data Acquisition System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7
7
10
11
18
18
19
20
20
26
28
31
31
32
35
36
37
38
39
39
39
40
41
42
43
44

3 Data Analysis
3.1 Outline of Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Chamber TDC Calibration . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.2 Determination of Drift Length from Drift Time . . . . . . . . . . . . . .
3.2.3 Global Position Alignment . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.4 Gain Calibration of EM Calorimeter . . . . . . . . . . . . . . . . . . . .
3.2.5 Slew Correction and Time Zero Calibration of Scintillation Counters . . .

46
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47
48
49
50
52

i

ii

Contents
3.3

3.4

3.5

3.6

3.7

Event Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.3.1 Track Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.3.2 Chamber Eﬃciency and Resolution . . . . . . . . . . . . . . . . . . . . . 55
3.3.3 Mass Scale and Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.3.4 Vertex Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.3.5 Electron Identiﬁcation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.3.6 Kaon Identiﬁcation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
Reconstructed Invariant Mass Spectra . . . . . . . . . . . . . . . . . . . . . . . . 74
3.4.1 e+ e− Invariant Mass Spectra . . . . . . . . . . . . . . . . . . . . . . . . . 74
3.4.2 K + K − Invariant Mass Spectra . . . . . . . . . . . . . . . . . . . . . . . 78
Detector Simulation for φ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
3.5.1 φ → e+ e− Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
3.5.2 φ → K + K − Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
3.5.3 Momentum Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
Background Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
3.6.1 Background in the φ → e+ e− Channel . . . . . . . . . . . . . . . . . . . 100
3.6.2 Background in the φ → K + K − Channel . . . . . . . . . . . . . . . . . . 102
Mass Scale and Resolution for φ . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
3.7.1 φ → e+ e− Decays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
3.7.2 φ → K + K − Decays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

4 Results and Discussions
109
4.1 Spectral Shape and Yield of φ Meson in the e+ e− Channel . . . . . . . . . . . . 109
4.2 Spectral Shape and Yield of φ Meson in the K + K − Channel . . . . . . . . . . . 114
4.3 Nuclear Mass Number Dependences α in the φ → e+ e− and φ → K + K − Channels119
4.3.1 Determination of α Parameters in the φ → e+ e− and φ → K + K − Channels119
4.3.2 Obtained φ-meson Yields and α Parameters . . . . . . . . . . . . . . . . 123
4.3.3 Comparison of αφ→e+ e− and αφ→K + K − . . . . . . . . . . . . . . . . . . . 128
4.4 Discussion on the Possible Modiﬁcation of Γφ→K + K − and Γφ→e+ e− . . . . . . . . 130
5 Conclusion

136

A Squared-Mass Distribution in Kaon Sample

138

B Double-Arm φ → K + K − Event

140

C Target Thickness

143

D Linear Assumption on α Parameter

145

E Linear Assumption on Width Broadening

147

F Eﬀects of Target Thickness on Invariant Mass Spectrum

149

G Run List used for the Present Analysis

152

H Search for J/ψ Production in 12 GeV p + A Reactions

153

Chapter 1
Introduction
The properties of hadrons, such as mass, decay width, and branching ratio, have been extensively studied and well established in the history of particle physics. Recent interests have been
extended to understand how these properties are modiﬁed in hot or dense matter. This issue
is of fundamental importance since such modiﬁcations can be related to the basic nature of thequantum chromodynamics (QCD), spontaneous chiral symmetry breaking, i.e., the mechanismthat creates most of the hadron masses.

1.1

Chiral Symmetry Breaking and its Restoration

It is well established that most of the masses of leptons, weak bosons, and heavy quarks are
given by the Higgs mechanism, while light quarks obtain their constituent masses mainly due
to spontaneous chiral-symmetry breaking in QCD [1, 2]. The former mechanism has beenstudied by searching for Higgs boson(s) in the LEP at CERN and the Tevatron at Fermilab,
and the searches will continue later at the LHC at CERN. On the other hand, the experimental
approach to the latter mechanism is not well established yet, because the QCD vacuum has a
non-trivial structure which has non-vanishing quark condensate hq̄qi, the order parameter of thesymmetry breaking. Figure 1.1 shows a theoretical calculation of |hq̄qi| as a function of density
ρ and temperature T of a medium [3]. In the ﬁgure, the broken symmetry is expected to berestored as T or ρ increases. In extreme circumstances, the quark gluon plasma (QGP) phaseat very high T or the color superconducting (CSC) phase at very high ρ, the chiral symmetryis expected to be restored completely; therefore, u and d quarks may have only masses from 3
to 10 MeV/c2 resulting from the Higgs mechanism. Further, Fig. 1.1 suggests that the quark
masses at the normal nuclear density may be signiﬁcantly smaller than that at normal vacuum.
|<qq> ,T|    
300

Me V

5 0

)!*,+-/T.10&2.1

!#"%$'&(Figure 1.1: A chiral condensation |hq̄qi| as a function of temperature T and density ρ. The
density is given in units of the nuclear matter density ρ0 ' 0.17fm−3 .

1

2

1.2

Chapter 1. Introduction

Theoretical Predictions for Meson Modiﬁcations

Many theoretical models predict modiﬁcations of meson spectral functions in terms of chiralsymmetry restoration in hot/dense matter.
The present experiment is largely motivated by the following pioneering works. Using aneﬀective chiral Lagrangian, Brown and Rho proposed an in-medium scaling law, “Brown-Rho
scaling”, which predicted a decrease in the meson mass of 20% at the normal nuclear density
ρ0 [4]. Based on a QCD sum rule, Hatsuda and Lee predicted that the vector-meson masses
decrease in a medium as shown in Fig. 1.2; the mass decreases of ρ and ω are about 16% ('130
MeV) and φ in the range of 1 to 4% ('10 to 40 MeV) at the normal nuclear density [5, 6].
They also pointed out that the mass of vector meson (1−− ) has a relatively simple connection
to the constituent quark mass and consequently to the quark condensate.
  

φ     

 

 

ρ, ω   
 

 



 

ρ / ρ0Figure 1.2: Masses of ρ, ω, and φ mesons as functions of density, which is normalized by thenormal nuclear density ρ0 , predicted by Hatsuda and Lee [6]. The hatched regions represent
the theoretical uncertainty which is caused in estimating quark condensates from limited ex¯ N , the u and dperimental information. The uncertainty for ρ and ω mesons is from hūu + ddi
quark contents in the nucleon. For φ meson, there is an extra error from the strange contents¯ N ).
in the nucleon, y = 2hs̄siN /(hūuiN + hddi

Especially, the φ meson, which is a vector meson of an almost pure ss̄ state, has very
attractive features as a probe to detect possible changes in its properties. Its natural width isnarrow (Γφ = 4.26 MeV/c2 ) [7] without any resonance nearby; therefore, we may be able todetect the possible mass modiﬁcation clearly. There are theoretical predictions not only for themass shift of the φ meson as described above, but also for the width broadening. The calculation
taking kaon-nucleon interactions into account predicted the φ-meson spectrum to be modiﬁed
in a nuclear medium, since the spectrum of the φ meson is dominantly characterized by its
decay into K K̄ [8, 9, 10, 11]. Klingl et al. calculated the signiﬁcant broadening of the decay
width as large as 45 MeV/c2 for the φ at rest, 10 times larger than in free space as shown in
Fig 1.3 [8], for example. Table 1.1 lists theoretical predictions for the φ meson modiﬁcation ina medium. According to these predictions, the decrease in mass at the normal nuclear density
is up to 40 MeV/c2 and the width broadening is up to 45 MeV/c2 .

1.2. Theoretical Predictions for Meson Modiﬁcations

3

102

2

-12π ImΠ(ω ,q=0;ρ)/ω

2

ρ=0
ρ=ρ0

101

0

10

-1

10

-2

10

0.70

0.80

0.90

1.00

1.10

1.20

1.30

ω [GeV]

Figure 1.3: The spectrum of the φ meson in vacuum (dashed) and in nuclear matter at ρ = ρ0(solid curve) predicted in Ref. [8]. The data are from the reaction e+ e− → K + K − [12].

authorsmodel

T. Hatsuda andS. H. Lee [5, 6]

QCD sum rule

F. Klingl, T. Waas,
and W. Weise [8]matterpredictions
mass change

total widthcold−10 ∼ −40MeV/c2 @ρ = ρ0–chiral eﬀective Lagrangiancold−10MeV/c2 @ρ = ρ0

45MeV/c2 @ρ = ρ0

E. Oset andA. Ramos [9]kaon mass renormalizationcold

unchanged

22MeV/c2 @ρ = ρ0

D. Cabrera and
M. J. Vicente Vacas [10]chiral SU(3)cold−8MeV/c2 @ρ = ρ0

30MeV/c2 @ρ = ρ0

S. Pal, C. M. Ko,
and Z.-w. Lin [11]AMPT model,chiral eﬀective Lagrangiancold−26MeV/c2 @ρ = ρ0

45MeV/c2 @ρ = 2ρ0

P.-Z. Bi and
J. Rafelski [13]Bag model, chiral invariancehot+5MeV/c2 @T ∼ Tc

10MeV/c2 @T ∼ Tc

J. P. Blaizot and
R. Mendez Galain [14]NJL model

hot−(mφ − 2mK )@T = Tc

0.7MeV/c2 @T = Tc

W. Smith and
K. L. Haglin [15]one-boson-exchange modelhotunchanged

14 ∼ 24MeV/c2 @T = Tc

Table 1.1: Theoretical predictions for the φ meson modiﬁcation in a medium. Where Tc is thecritical temperature (∼ 170 MeV).

Moreover, since mφ is only 32 (24) MeV/c2 greater than 2mK ± (2mK 0 ), the partial decay
width Γφ→K K̄ is sensitive even to a small change in the spectral functions of the φ and/or
K mesons. Several theoretical models pointed out the possible change of the branching ratio
Γφ→K K̄ /Γφ→l+ l− in a nuclear medium [13, 14, 16] like;• the φ-meson mass is unchanged in a nuclear medium but the kaon mass decreases, then
Γφ→K K̄ increases because of an increase in ∆m ≡ mφ − 2mK , or
• the φ-meson mass decreases in a nuclear medium while the kaon mass is unchanged, then
Γφ→K K̄ decreases because of a decrease in ∆m.

4Chapter 1. Introduction

1.3

Experimental Searches for Meson Modiﬁcationscombined 95/96 data

pt>0.2 GeV/cee>35 mrad

dN/dM per 20 MeV/c 2



-6

10



1000





10

0

-7

ee

ee





ee

0

2.1< <2.65

ee

200





10-5

ee

400

/ geo 28%
<dNch/d >=245

0



600

Pb-Au 158 AGeV

2 -1

| p |< 0.5 GeV/c
Nb
LH2<dNee/dmee>/<Nch> (100 MeV/c )

2

800

ee

counts / [ 12 MeV/c ]As for the modiﬁcation of vector mesons in “cold” matter, several experiments including ours
have been performed so far. The TAGX collaboration at the INS-ES studied in-medium
modiﬁcation of the invariant mass distribution of ρ meson in 2 H, 3 He, 12 C(γ, π + π − )X reactions [17, 18, 19, 20]. They have concluded that the observed ρ-meson spectra show a decreaseof its mass by about 100 MeV/c2 [20]. The GSI-SIS S236 collaboration reported changes in thepion-nucleus potential in deeply bound pionic 115 Sn, 119 Sn, 123 Sn nuclei as a possible signatureof chiral symmetry restoration [21]. They argued the 36% reduction of the pion decay constantfπ∗ (ρ)2 /fπ2 , which can be connected with the mass of ρ/ω meson in a nuclear medium by the
Brown-Rho scaling m∗V /mV ' fπ∗ /fπ (V = ρ, ω). The CBELSA/TAPS collaboration at the
ELSA has reported the mass modiﬁcation of the ω meson by measuring the ω → π 0 γ channel
as shown in Fig. 1.4(a) [22]. They concluded that the mass of ω meson decreases by 8% withrespect to the vacuum value at an estimated average nuclear density of 0.6ρ0 , being consistent
with a scaling of the ω mass by m = m0 (1 − 0.14ρ/ρ0 ).
For the modiﬁcation of vector mesons in “hot” matter, there are several measurements at
the CERN-SPS and BNL-RHIC. The experiment CERES/NA45 at the CERN-SPS measured
the low-mass electron-pairs in p + A and A + A collisions as shown in Fig. 1.4(b) [23]. Theyobserved a large enhancement at the lower side of the ρ/ω-meson mass in A+A not in p+A, but
their poor mass resolution is not enough to discuss an origin of the enhancement. The STAR
experiment at BNL-RHIC measured the π + π − spectra in p+p and peripheral Au+Au collisions√
at sN N = 200 GeV [24]. The measured ρ peak in the invariant mass distribution is shifted by
40 MeV/c2 in minimum bias p + p interactions and 70 MeV/c2 in peripheral Au+Au collisions.
The NA60 experiment at the CERN-SPS measured the dimuon spectra in 158 A GeV In+In
collisions as shown in Fig. 1.4(c) [25]. The observed spectrum shows the modiﬁcation of the ρ
meson, not the peak shift but the width broadening.











⁄


700

800 900
2
M [MeV/c ]

ee

600

10-8
0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6
2



mee (GeV/c )(a) ω → π 0 γ @ CBELSA/TAPS(b) e+ e− @ CERESIn-In Central
all pT

500

00

0.2

0.4

0.6

0.8

1

1.2

1.4

M (GeV/c2)(c) ρ → µ+ µ− @ NA60

Figure 1.4: (c) The ω → π 0 γ spectrum at CBELSA/TAPS [22]. (b) The low-mass e+ e−spectrum in Pb+Au at CERES [26]. (c) The ρ → µ+ µ− spectrum at NA60 [25].
Compared to ρ and ω mesons, there are a limited number of experimental reports on the
search for the in-medium modiﬁcation of the φ meson. With regard to the partial decay width
Γφ→K K̄ /Γφ→l+ l− , the experiments NA49 and NA50 in Pb-Pb collisions at 158 A·GeV/c at the
CERN-SPS reported φ-meson yields in the K + K − and µ+ µ− channels, respectively [27, 28, 29].
There are discrepancies by factors ranging from 2 to 4 between these two measurements asshown in Fig. 1.5. These discrepancies have been denied recently by the CERES experimentwith their new results of φ → e+ e− and φ → K + K − measurements [30]. The results in the1.4. KEK-PS E325 Experiment

5

2 -2

1/mtd2N/dmtdy ((GeV/c ) )K + K − channels are in agreement with those of NA49 and with those in the e+ e− channel asshown in Fig. 1.5. However, the φ → e+ e− data of the CERES is not clear enough, so that it
can not conclude evidently the in-medium modiﬁcation of the branching ratio Γφ→K K̄ /Γφ→l+ l−does not exist. For the spectral modiﬁcation of the φ meson, the present experiment E325
recently reported the modiﬁcation in nuclear matter measured in the e+ e− decay channel forthe ﬁrst time [31].

+

CERES
e e+
CERES
K K+ NA49
K K
+
NA50
µ µ



10













1

10

10

-1

-2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2

mt-m (GeV/c )Figure 1.5: Transverse mass distribution of φ mesons measured in K + K − at NA49 (squares),µ+ µ− at NA50 (diamonds), K + K − at CERES (triangles), and e+ e− at CERES (circles) [30].

1.4

KEK-PS E325 Experiment

The experiment KEK-PS E325 has measured the invariant mass spectra of e+ e− and K + K −pairs in 12 GeV p + A reactions at High Energy Accelerator Research Organization (KEK) 12
GeV Proton-Synchrotron. The goal of the experiment is to detect a signature of the partiallyrestored chiral-symmetry at the normal nuclear density appearing by a modiﬁcation of thespectral shape of vector mesons, and a possible change of the branching ratio Γφ→K K̄ /Γφ→e+ e−using the nuclear mass-number dependences of φ → e+ e− and φ → K + K − .
The spectrometer was newly constructed at the high-intensity primary beam-line in KEK
to detect slowly moving vector mesons in ρ → e+ e− , ω → e+ e− , φ → e+ e− , and φ → K + K −modes simultaneously. It should be noted that high quality primary beam on thin targets isneeded to suppress the background from γ-conversions in the e+ e− channel.
The experiment E325 was proposed in the year 1993, and the construction of the spectrometer started on June 1996. The engineering run was performed on November 1996, andthe ﬁrst physics run was executed in June 1997 for the K + K − channel. All the electron-arm
counters were completed on February 1998, and the ﬁrst measurement of the e+ e− channel wasdone in 1998. In July 1999, June 2000, December 2000, and from November to December in
2001, simultaneous data takings both for the e+ e− and K + K − channels were performed. From
February to March in 2002, the data taking dedicated to the e+ e− channel was performed, andthe experiment was completed.
The E325 experiment used 440 shifts of beam time (= 3520 hours) in total, and is the longest
nuclear-physics experiment in the 35 years of the history of KEK 12 GeV PS. From the earlier
data, we reported the signature of ρ/ω modiﬁcation measured in the e+ e− channel in Ref. [32,33]. This discovery was reconﬁrmed later with use of 100 times more statistics in Ref. [34, 35].

6

Chapter 1. Introduction

For the φ meson, we recently reported the evidence of φ meson mass modiﬁcation in Ref.[31, 36].
From these results, we conclude that the modiﬁcation of vector mesons in dense nuclear matteris experimentally conﬁrmed. We also reported the production cross sections and the rapidity
and transverse momentum (pT ) distributions of ω and φ mesons in Ref. [37, 38], where we
conﬁrmed that our measurements on those yields are consistent with other experiments.
In this manuscript, we report the ﬁnal results on the φ → K + K − channel. Based on much
improved analysis procedures, and more importantly with improved statistics compared to ourearlier reports [39, 40], we examine the φ → K + K − invariant mass spectra in terms of thespectral-function modiﬁcation. We also examine the relative yields of φ → K + K − decays andφ → e+ e− decays for carbon and copper targets, in order to ﬁnd a modiﬁcation on the partial
decay widths. Finally, we set upper limits on those decay widths in nuclear media with use ofa simple theoretical model.
The e+ e− data presented in this manuscript was taken from the run in 2001 and 2002,
and the K + K − data was from the run in 2001. In Chap. 2, the experimental procedure ispresented. The detail of the analysis is described in Chap. 3. The invariant mass spectra of φmeson both in the e+ e− and K + K − decay channels and the nuclear mass-number dependenceof the φ-meson production cross section are presented and discussed in Chap. 4. Finally, theconclusion is given in Chap. 5.

Chapter 2
Experimental procedure
2.1

Overview of Apparatus

The spectrometer for studying vector mesons produced in nuclei was constructed at the primarybeam-line EP1-B in 12 GeV Proton Synchrotron (PS) at KEK. The beam line EP1-B was newly
constructed for experiments requiring a high-intensity primary beam [41]. The spectrometer
was designed to measure the invariant mass spectra both in the e+ e− channel for the ρ/ω/φmeson decays and in the K + K − channel for the φ meson decays within the same apparatus.
There are two key points in this spectrometer. First is to optimize the acceptance for slowly
moving vector mesons, which have a larger probability to decay inside a nucleus. The typicalacceptance for φ → e+ e− is 0 < pT < 1 GeV/c and 0.5 < y < 2.0 where the beam rapidity
is ybeam = 3.3 (yc.m. = 1.66). This coverage corresponds to 0.5 < βγφ < 4. Second is to usehigh quality primary beam on thin targets. The combination of the high intensity beam withthin targets was essential to keep the γ-conversion rate in the target material below the Dalitz
decay rate. The typical interaction rate was as high as 1.2 MHz in the year 2002. Detailed
descriptions of the E325 spectrometer can be found in [42]. The detector elements relevant tothis manuscript are discussed below.
The layout of the detectors is shown in Fig. 2.1 and 2.2 1 , and photographs of the spectrometer are shown in Fig. 2.3. The spectrometer had two electron arms and two kaon arms,
which shared the dipole magnet and the tracking devices. The electron arms covered from
±12 degrees to ±90 degrees horizontally and ±22 degrees vertically. The kaon arms coveredfrom ±12 degrees to ±54 degrees horizontally and ±6 degrees vertically.
In this manuscript, results of the analysis with the e+ e− -triggered data collected in 2001
and 2002, and the K + K − -triggered data collected in 2001 are presented. Primary protons
with a typical intensity of 8.7×108 protons per spill in 2001 and 6.4×108 protons in 2002 weredelivered to the targets at the center of the dipole magnet. In 2001, one carbon and two copper
targets were used simultaneously, while in 2002 one carbon and four copper targets were usedsimultaneously. The interaction length of each copper target was 0.054% and that of the carbon
target was 0.11% in 2001 and 0.21% in 2002.
Tracking was performed with the cylindrical drift chamber (CDC) and the barrel-shaped
drift chambers (BDC’s). The vertex drift chamber (VTC) was installed at the center of CDC to
improve the vertex reconstruction resolution. However, we do not use the VTC information in
the present analysis because the mass acceptances of VTC are signiﬁcantly diﬀerent between theﬁve targets. The dipole magnet which had circular pole pieces of 880 mm in radius, provided
the ﬁeld integral of 0.81 T·m from the center to 1680 mm in radius where the BDC’s werelocated.
1

In this manuscript, we adopt the right-handed coordinate system of which the origin is at the center of thespectrometer magnet, the x-axis is parallel to the beam direction, and the z-axis is vertical pointing upward.

7

8

Chapter 2. Experimental procedure

FTOF Counter
Aerogel Cherenkov
KDC
HodoscopeCounter

Forward LeadGlass

Start Timing
Counter

Rear GC
Rear LG
Side LG
Barrel DC

B

Front
Gas Cherenkov

1000mmCylindrical DC

targetVertex DC

X
beam

.Z

Y

Figure 2.1: Schematic view of the E325 spectrometer, the top view.

Front GC
magnet return yoke

Rear GC
Aerogel Cherenkov

3980 mm

Rear LG
Start
TimingCounter

Forward LeadGlassX
FTOFCounter

Vertex DC

KDC
Hodoscope Counter
Barrel DC
Cylindrical DC

Figure 2.2: Schematic view of the E325 spectrometer, the cross section along the center of thekaon arm, 33 degrees from the beam line, is shown.

2.1. Overview of Apparatus

9(a) the top view(b) the front view

Figure 2.3: Photographs of the E325 spectrometer for (a) the top view and (b) the front view.

10

Chapter 2. Experimental procedure

For the electron identiﬁcation the whole region of the electron arm was covered by two or
three stages of electron identiﬁcation counters. The ﬁrst stage of the electron identiﬁcation was
done by the front gas-Čerenkov counters (FGC’s) which covered from ±12 degrees to ±90 degrees horizontally and ±23 degrees vertically. The second stage consisted of three types ofelectron-identiﬁcation counters. The rear gas-Čerenkov counters (RGC’s) covered from ±12 degrees to ±54 degrees horizontally and ±6 degrees vertically. These regions corresponded to thekaon-arm acceptance. The rear lead-glass EM calorimeters (RLG’s) covered the same horizontal angle as RGC’s, but vertically covered outside the kaon-arm acceptance, from ±9 degrees to±23 degrees. In the backward region where the horizontal angle was larger than 57 degrees, thesecond-stage electron identiﬁcation was done by the side lead-glass EM calorimeters (SLG’s)
which covered from ±57 degrees to ±90 degrees horizontally and ±23 degrees vertically. As thethird-stage electron identiﬁcation counter in the kaon-arm acceptance, the forward lead-glass
EM calorimeters (FLG’s) vertically covered ± 7 degrees, and horizontally from 12 to 54 degrees
in the left arm, from –40 to –12 degrees in the right arm.
For the kaon identiﬁcation, the segmented aerogel Čerenkov counters and time of ﬂight
counters were used. The aerogel Čerenkov counters (AC’s) were threshold-type Čerenkov detectors using aerogel whose refractive index was 1.034, to separate kaons from pions in the
momentum region of 0.53 to 1.88 GeV/c [43, 44]. Since we could not count beam protons
particle by particle due to the high intensity, the event time-zero was given by the start timing counters (STC’s) placed at 380 mm from the targets. The forward time of ﬂight counters(FTOF’s) were used to measure the time of ﬂight of particles in the kaon acceptance. They
were also used in combination with the hodoscope counters (HC’s) to determine the charge
and the crude momentum of the particles, and to make the kaon selection possible with the β(=v/c) measurements in the trigger.
In the following section, details of the experimental components are described.

2.2

Accelerator Facility and Beam LineThe proton synchrotron facility at KEK consists of four stages of accelerators, the 750 kV
Cockroft-Walton, the 40 MeV LINAC, the 500 MeV Booster Synchrotron and the 12 GeV
Proton Synchrotron (PS).
The typical beam intensity was 3×1012 in PS. During our experiment these protons weredelivered to two primary beam lines simultaneously, about 1% to the EP1 beam line and 99%
to EP2. The beam in EP1 can be switched either to EP1-A or to EP1-B. The beam line EP1-A
is used for experiment using low energy kaons in the slow extraction mode and for the neutrino
oscillation experiment in the fast extraction mode. The present experiment is performed at
EP1-B which is a special beam line for primary proton usage. The schematic view of the beamline EP1-B is shown in Fig. 2.4.

Figure 2.4: Schematic view of Beam Line (EP1B).

2.3. Spectrometer Magnet

11

When EP1-B is in operation, protons extracted to the EP1 beam line were focused with aset of quadrupole magnets, Q01 and Q02 to the ﬁrst vertical collimator 1V where the intensity
was typically reduced to one-ﬁfteenth. Here the initial image of the beam was deﬁned by 1V
together with the horizontal collimator 2H. At this point, the beam spot from PS is verticallylong so that the beam intensity was controlled by changing the aperture of the collimator 1V.
Typical aperture of the collimators 1V and 2H were set as 8.0 mm and 2.2 mm respectively.
Then the beam was bent by six degrees with the steering magnets SM1 and SM2, and wasvertically focused with a set of quadrupole magnets (Q03, Q04, Q05, Q21) to the point wherethe vertical collimator 3V was placed. The vertical collimator 3V was used to remove beam
halo. Then the beam was transferred by the ’DQQ’ (B21, Q22, Q23) complex to the ﬁrst
focusing point where the collimators 4V and 5H were located and again the rejection of beam
halo was performed. After passing through the other beam-focusing complex ’QQDQQ’ ( Q24,
Q25, B22, Q26, Q27), the beam was delivered to the ﬁnal focusing point at the center of thespectrometer. At the target, we obtained the size of the beam spot of 1∼2 mm in FWHM.
At the end of the EP1-B beam line, the intensity of beam protons was monitored with 10%
accuracy using an ionization chamber [45]. The repetition period was four seconds, and theﬂat top of the spill was about 1.8 seconds.
In prior to the experimental data accumulation, the aperture of the collimators were tuned
to reduce the beam halo. It was turned out that the adjustment of the collimators was eﬀective
to reduce the random trigger rate, so that the adjustment was done to minimize the interaction
trigger rate of the spectrometer with keeping the transmission of beam particles constant. The
scanning of the magnetic ﬁeld strengths of B21 and B22 was also eﬀective to reduce the beamhalo, by controlling the beam trajectory and minimize the interference of the beam halo withthe beam pipe. We chose the setting where the least trigger rate was realized. The collimatorsettings in the present data-taking period are listed in Table 2.1. The collimator 4V (and 3V
in 2002) was full opened, because these were not eﬀective to reduce the halo.
year
1V
2H
3V
4V
4.0mm 50mm
2001
8.0mm
full
2002
2.7mm
full

5H
15.0mmTable 2.1: The collimator width setting.

2.3

Spectrometer Magnet

The spectrometer magnet was a dipole type with the overall weight of 300 ton. The dimension
was 5655 mm in width, 3980 mm in height and 2120 mm in depth. To ensure the maximum
vertical acceptance for electrons (±23 degrees), the pole piece was made of two layers of cylinder
with the diameters of 1760 mm and 2120 mm as shown in Fig. 2.5. The gap between the poles
was 907 mm. Other dimensions can be seen in Fig. 2.5.
The magnetic ﬁeld at∫ the center of the pole piece was adjusted at 0.71 T to supply the
integrated magnetic-ﬁeld B · dl of 0.81 T·m from the targets to the radius of 1680 mm where
the barrel drift chambers (BDC’s) were located. The materials through the ﬂight path ofparticles from the target to BDC are summarized in Table 2.2. As described later in Sec. 3.5,
by taking into account Coulomb scattering and energy losses in the materials and the chamber
resolutions, we estimated the mass resolution for φ → e+ e− (φ → K + K − ) decays to be 10.7(2.3)
MeV/c2 using a detailed detector
simulation.
∫
Since the amplitude of the B · dl is proportional to the rigidity of tracks, it is important
to know the precise magnetic ﬁeld-strength everywhere in the acceptance. The magnetic ﬁeld

12

Chapter 2. Experimental procedure

12 degrees

2590

coil

2120

2120

1760

90 degrees

Beam

130

830

130

22 degrees

844
911
3980

2320

907

1522

1720

Beam

-22 degrees

1950

1950
830

2731

2664
5395
5655

Figure 2.5: Schematic view of spectrometer magnet. The dashed lines indicate the electron
acceptance.

2.3. Spectrometer Magnet
Countermaterial

VTC

Ar-C2 H6 (50:50)
Wire(Cu-Be)
Wire(W)
Mylar
air
scintillator
lappingair
Mylar
Ar-C2 H6 (50:50)
Wire (Cu-Be)
Wire (W)
Mylar
air
Mylar
isobutane
acrylic mirror
aluminum cover
air
Mylar
Ar-C2 H6 (50:50)
Wire (Cu-Be)
Wire (W)

STC

CDC

FGC

BDC

SUM

13
radius[mm]
0.00
245.00245.05380.00385.00385.20400.00400.05880.00880.05899.95900.001560.00
1563.00
1564.00
1569.95
1570.00-

thickness
X [mm]
245.000.01730.00040.05
134.95
5.00
0.20
14.80
0.05
479.950.031
0.0005
0.05
19.90
0.05
660.00
3.00
1.00
5.95
0.05
110.000.010
0.0001λrad[mm]340350.0
14.3
3.5
287.0
304200.0
425.0
287.0
304200.0287.0340350.0
14.3
3.5
287.0
304200.0287.0169300.0344.0
89.0304200.0287.0340350.0
14.3
3.5

X/λrad
[%]
0.072
0.121
0.011
0.017
0.044
1.176
0.070
0.005
0.017
0.141
0.217
0.014
0.017
0.007
0.017
0.390
0.872
1.124
0.002
0.017
0.032
0.070
0.003
4.458

Table 2.2: List of the materials and their radiation lengths from the center of CDC to theradius of 1680 mm where BDC’s were located.
map were obtained by the calculation and compared to the hall-probe measurements. The
magnet itself is symmetrically build from left to right and upstream to downstream, and top
to down. The actual ﬁeld, however, was distorted due to other magnetic materials which were
the iron plate on the ﬂoor to support the magnet weight and the magnetic shield placed justfront of the photomultiplier tubes of the aerogel Čerenkov counter. We calculated the magnetic
ﬁeld map using TOSCA [46], which performs ﬁnite-element-method analysis. All the magnetic
materials were taken into account in the calculation. Since the preliminary calculations andthe measurements proved the left-right symmetry of the ﬁeld, we performed a full calculation
assuming the left-right symmetry to reduce the calculation time. The strength of magnetic
ﬁeld on the x-y plane (the horizontal plane 400 mm below the beam line) is shown in Fig. 2.6.
We measured the magnetic ﬁeld (Bx , By , Bz ) with a set of hall probes which were placedorthogonal to each other. The measured region was limited within the reach of the measurement
device. We covered the region shown in Fig. 2.7 with 3-dimensional lattice points of 50 mm
pitch. The three components of the magnetic ﬁeld on the horizontal plane 363 mm below thenominal beam height is shown in Fig. 2.8.

14Chapter 2. Experimental procedure[Gauss]

10000.0
10000.0

9000.09000.08000.08000.07000.07000.06000.06000.05000.04000.05000.03000.04000.01=150.0
150.0
40.0
2=0.0
150.0
40.0
3=0.0
-150.040.0
4=150.0-150.040.0
Cartesian

2000.03000.01

1000.02000.01000.042Component: BMOD
Minimum = 341.908, Maximum = 10038.1
Integral = 2.07143E+08

3Figure 2.6: The calculated magnetic ﬁeld map (z = -400 mm).

coil

2590

2120

C

2120

1760

A
B

Beam

y

B

130

911

z
830

130

x

844

3980

2320

1720

910

1950

1522

Beam

1950

C
2731

830

A
2664
5395

Figure 2.7: The region of the magnetic ﬁeld measurements. The three areas, A, B, and C arewith diﬀerent settings of the measuring device.

2.3. Spectrometer Magnet









15





































































































































Figure 2.8: The measured magnetic ﬁeld map (z = -363 mm).

The measured map was compared to the calculated one, and we observed a good agreement∫
on B · dl. However the magnitude in average was 0.2% larger than the TOSCA calculation;
it probably comes from the incomplete knowledges for the magnetic permeability of the iron of
the spectrometer around 0.71T, which was an input parameter of TOSCA. We increased theﬁeld strength of the calculated map by 0.2% and used it for the track ﬁtting.
We evaluated the systematic uncertainty of the momentum determination caused from theinaccuracy of the magnetic ﬁeld map as follows. We generated the drift chamber hits points
for the charged particle trajectories which were generated with the measurement map, andwe ﬁtted them using the Runge-Kutta method with the calculated map. By comparing theoriginal momenta with the ﬁtted results, we found that the discrepancy was within 0.3% in the
momentum region from 0.5 to 2.0 GeV/c, as shown in Fig. 2.9. The systematics is small enoughcompared with the present momentum resolution. Since the measured region was limited, thecalculated magnetic ﬁeld was used to ﬁnd a track of particles.

16

Chapter 2. Experimental procedure

momentum error [%]momentum error [%]

(A)

(B)

vertical angle [ radian ]horizontal angle[ radian ](C)momentum error [%]Figure 2.9: Possible uncertainty of the momentum determination due to the magnetic ﬁeld map.
Test tracks were generated with the measured map and reconstructed with the calculated map.
The diﬀerences of the reconstructed momenta from the generated momenta were plotted as afunction of the vertical angle in (A), and the horizontal angle in (B). The histogram (C) gives
the projection of all the diﬀerences.

In 2001, we had a trouble in isolation in the coils of the dipole magnet. We had 14 independent coils for the magnet, seven coils for each pole piece. Because of the trouble, we had togive up the three coils for the upper pole piece. To keep the ﬁeld integral as before, we had tooperate the magnet with 14/11 times larger current than before. Since the available 11 coils are
four in the upper side and seven in the lower side, the magnetic ﬁeld became asymmetric from
top to down. Under this condition, the magnetic ﬁeld map was calculated again with TOSCA.
The systematic uncertainty was estimated through the measurement of the magnetic ﬁeld witha NMR probe for several sample heights at the center of the magnet. The measured values arelisted in Table 2.3. The absolute values of the calculated magnetic ﬁeld were 0.48±0.03% larger
than the measured values, as shown in Fig. 2.10. We scaled the absolute value of the calculated
magnetic ﬁeld to the measured value. A systematic error on the momentum determination due
to this discrepancy is then expected to be within 0.03% and is negligible.

z[mm]
446.5
225.5
1.5
-222.5-446.5

measured[mT]
698.367699.225706.540
721.317730.180

calculated[mT]
701.910702.792710.069
724.732733.540

Table 2.3: The measured and calculated magnetic ﬁelds for ﬁve values of z. The voltage was
set to 1985.45A.

17

Diff[%]

2.3. Spectrometer Magnet

measured-point-Z[mm]Figure 2.10: Diﬀerences between the measured magnetic ﬁeld strength and the calculation withTOSCA. Deﬁnition of the vertical axis is the ratio of the diﬀerences to the measured values.
The horizontal axis is the z position of the measured points.

The magnetic ﬁeld strength was monitored with a MNR probe placed at the center of thebottom pole peace, at the beginning and the end of each run of about 2 hour long, and theaveraged value for each run was used for a run-by-run correction for the scale of the ﬁeld map
strength. An actual drift was as small as 0.07%, as shown in Fig. 2.11.

2001

2002

magnettroubleFigure 2.11: The magnetic ﬁeld strength for each run measured with a NMR probe. The jumps
were caused by switching on and oﬀ the power supply.

18

Chapter 2. Experimental procedure

2.4

Targets and Beam Proﬁle2.4.1

Targets

We used two copper targets and one carbon target in 2001, and four copper targets and one
carbon target in 2002, which were aligned in-line along the beam axis. We call them Cu-1, C,
and Cu-2 in 2001, and Cu-1, Cu-2, C, Cu-4, and Cu-5 in 2002, from upstream to downstream
target. The interaction length and radiation length of the targets are summarized in Table 2.4.

year
2001
2002

material
carboncoppercarboncopper

C
Cu
C
Cu

mass
number
12.01163.54612.01163.546

number oftargets
1
2
1
4

width
[mm]
25
25
10
10

hight
[mm]
25
25
25
25

thickness[g/cm2 ]
0.092
0.073
0.184
0.073

interaction
length [%]
0.106
0.054
0.213
0.054

radiation
length [%]
0.215
0.564
0.431
0.565

Table 2.4: The target dimensions, interaction lengths, and radiation lengths used in the experiment.
These targets were placed at the center of CDC by 46 mm apart from each other in 2001,
and 23 mm in 2002. The schematic view of the target holder in 2002 is shown in Fig. 2.12. The
targets were attached on the polyethylene stays with a thickness of 1 mm. In 2001, the target
x-positions with respect to the center of CDC were –47 mm, 0 mm and 45 mm for the Cu-1,
C and Cu-2 targets, respectively. In 2002, those were –43 mm, –23 mm, 0 mm, 24 mm and
48 mm for the Cu-1, Cu-2, C, Cu-4 and Cu-5 targets, respectively. The width of each target
was determined that no target was in the acceptance of any other targets.

Figure 2.12: Schematic view of Target in 2002.

To reduce the interaction of beam protons with air, the entire beam line was kept as vacuum
from the extraction point to a front of VTC. The region of vacuum was terminated with a 200µm-thick Mylar sheet at the front of VTC. Behind the exit of VTC, the beam line was followed
by a helium-ﬁlled beam pipe, as shown as “He Bag” in Fig. 2.13. A helium gas was ﬂowed at

2.4. Targets and Beam Proﬁle19

a rate of 1000 cc per minute. The ion chambers (IC’s) were located at the end of the He Bag
to measure the beam intensity. Between the IC and the beam dump, a vacuum beam pipe of
2.5 m long was placed.

      )          , .  *  "  + , -               '   ,            .     !" #   " $   %  &    ' (Figure 2.13: Schematic view of Target and Beam Pipe.

2.4.2

Beam ProﬁleFigure 2.14 shows the beam proﬁle at the target position which was measured as follows. The
center target, which was carbon of 0.5(1) mm thick in 2001(2002), worked as the 0.5(1) mmwide probe for the beam proﬁle measurement when the target holder was rotated by 90 degrees
around the z axis.
The horizontal beam position was moved with the bending magnet B22 located most downstream of EP1-B beam line (see Fig. 2.4). The beam proﬁle in the horizontal direction can bemeasured by counting the interaction rate by changing the beam position. The interaction rate
as a function of the beam position is plotted in Fig. 2.14. Here, the beam position y [mm] is
obtained as
y = 0.109 × (V − V0 ) ,(2.1)
where V [V] is the reference voltage of the B22 power supply, and V0 is the nominal value toshoot the target center. The one standard deviation of the beam spot size in the horizontal
direction was estimated to be 1.59 mm in 2001 and 0.83 mm in 2002 by subtracting the eﬀective
thickness of the carbon target.

Chapter 2. Experimental procedure

E1stRequest

yield

20

6000

5000

4000

3000

2000

1000

0

beam center in y-axis [mm](a) 2001

-4

-3

-2

-1

0

1

2

3

4

beam center in y-axis [mm](b) 2002

Figure 2.14: Interaction rate as a function of the beam position.

2.5

Tracking Chambers

2.5.1

Cylindrical Drift Chamber

The schematic view of Cylindrical Drift Chamber (CDC) is shown in Fig. 2.15. The outer
diameter of CDC is 1760 mm, the inner diameter is 800 mm and the height is 840 mm. We
located CDC on the pole piece of the spectrometer magnet. The acceptance of CDC was from
±12 degrees to ±132 degrees horizontally and ±22 degrees vertically.
The CDC consists of ten radial layers of the drift cells, and they were grouped into three
super-layers. The ﬁrst super-layer was in the radial region from 445.0 to 475.0 mm having threelayers of drift cells (X, X0 , U), the next was from 602.5 to 642.5 mm having four layers (V, V0 ,X, X0 ), and the last was from 800.0 to 830.0 mm having three layers (U, X, X0 ). In the X and
X0 layers the direction of wires was vertical and in the U and V layers the wires were tilted byabout ± 0.1 radian. Argon-ethane mixed gas of 50% and 50% was used at 1 atm.
The structures of the drift cells are shown in Fig. 2.16. The sense wires were gold-plated
tungsten of 30 µmφ and the potential wires were Be-Cu of 100 µmφ. The position of the wire
was determined by the bush inserted at the end of the feed through pipes. We used the bushwith an 80 µmφ hole for the sense wires, so that the precision of the wire positioning was about
25 µm. All the drift cells of CDC had the same horizontal angular coverage of 1.5 degrees withrespect to the center. Details of the wire arrangements were shown in Table 2.5.

2.5. Tracking Chambers

TOP View

21

CeramicParts

wire
regiontargetbeam

to AmpDiscri.

SIDE View

gas

840mm

High Voltage

mm

Figure 2.15: Schematic view of CDC.

22

Chapter 2. Experimental procedure

Guard Wire

Sense Wire

Potential Wire

10.47 mmX’-layer
X- layer

R=800
U- layer

7.89 mmX’-layer
X- layerV’- layer

R=602.5

V- layer

5.8mm

U- layer

R=445

X’-layer
X- layer

Figure 2.16: The cell structures of CDC.

layer number
1
2
3
4
5
6
7
8
9
10
wire direction
X
X0
U
V
V0
X
X0
U
X
X0
radial location of 445 455 475 602.5 612.5 632.5 642.5 800 820 830
sense wire [mm]cell width [degree] 1.5 1.5
1.5
1.5
1.5
1.5 1.5
1.5
1.5 1.5
cell width [mm] 11.65 11.91 12.43 15.77 16.04 16.55 16.82 20.94 21.47 21.73
tilt angle [radian]0
0 0.1127 0.1116 0.1135 0
0 0.1174 00wire length [mm] 441 441 443.8 568.5 568.7 565 565 717.9 713 713
number of
81
81
77 76/77 77/76 81
81
77
82
82
sense wires(*)(*)(*) left-arm and right-arm

Table 2.5: CDC wire conﬁguration.

2.5. Tracking Chambers

23

We calculated the electrical ﬁeld shape in the chamber cell and the relation between thedrift length and the drift time with use of the drift chamber simulation code Garﬁeld [47]. The
simulated drift line in the outer super-layer is shown in Fig. 2.17(a), and the relation between
the drift length and the drift time (x-t relation) is shown in Fig. 2.17(b). The obtained x-t
relation was used to determine hit positions after the adjusting the drift velocity and the time
zero to the real data.

[ µ sec]




0.5
0.4
0.3
0.2
0.1
0
−1

(a) simulated drift line

0

1

[cm]

(b) calculated x-t relation

Figure 2.17: (a)The simulated drift line in the outer super-layer (3 layers) in the magnetic ﬁeldof 0.61T, which is the magnetic ﬁeld strength at this location when the spectrometer magnet
is fully excited. (b)The calculated relation between the drift time and the drift length of the X
layer.

The structure of CDC was designed to restrict its active region only to the spectrometer
acceptance. The top and bottom end plates were semi-curved with 3 stages as shown in
Fig. 2.15. This structure was eﬀective to gain the mechanical strength of the chamber frameand consequently to minimize the support structure within the spectrometer acceptance.
The end plates and the support structure of CDC were made of aluminum. Thirty ceramic plates were mounted on each aluminum end plate as shown in Fig. 2.15 and Fig. 2.18.
The ceramic plates had a print-circuit pattern which provided electrical connections to thefeedthrough pins as shown in Fig. 2.19(a). The feedthroughs were made of gold plated brass of
a 1.6 mm diameter pipe. To secure the electrical connection, a cut-ring spring was inserted between the feedthrough and the through hole. The ceramic board on the top provided the signal
connections to the sense wires and these on the bottom provided the high voltage connections.
The ceramic boards were 100 mm in width, 200 mm in length and 20 mm in thickness andlocated precisely on the end plates by the knock pins with the machining precision of about 10µm. In-between the ceramic boards, there were the ribs of the aluminum end plate, where thefeedthroughs made of Delrin as shown in Fig. 2.19(b) were used.

24

Chapter 2. Experimental procedure

Alminum
Ceramic

196 mm

480 mmFigure 2.18: The cross section of the aluminum end plate and the ceramic plate.

to PreAmp

potential wire sense wire
1.6

print-circuit
feedthroughfeedthroughdelrin part

ceramic plate

aluminum frame

unit: mm
20

25

5

1.6

1.8
2.0

unit: mm

3.2
(a)

(b)

Figure 2.19: (a) Schematic view of the feedthrough structure for the ceramic plate of CDC. (b)Schematic view (not to the scale) of the feedthrough structure for the one on the aluminumribs of CDC.
The read-out electronics of CDC consisted of Ampliﬁer-Shaper-Discriminator (ASD) IC’son a print circuit board mounted on CDC (ASD board, Fig. 2.20(a)), a LVDS-ECL converter(Fig. 2.20(b)) and a time to digital converter (TDC). The ASD IC was developed for the Thin
Gap Chambers in the forward muon trigger system of the LHC ATLAS experiment [48]. The
block diagram of the ASD chip and the pin assignment of the ASD IC are shown in Fig. 2.21.
The observed gain of the pre-ampliﬁer of the ASD is 360 mV/pC, and the observed gain of themain-ampliﬁer is 4, while the speciﬁcation values are 800 mV/pC and 7 for the pre-ampliﬁer
and the main-ampliﬁer, respectively. The output signal of the ASD board was sent to LVDSECL converter board via 10 m-long twisted-pair cables. From the LVDS-ECL converter, thesignal was transferred to the counting house with 35 m-long twisted-pair cables.
When a minimum ionizing particle passed through one drift cell of CDC, it generated
about a hundred ionizing electrons. The electric ﬁeld around the wire ampliﬁed these electrons
by 1.6×104 . Through the ASD, the pulse height of the signals before the discriminator was
typically 240 mV for minimum ionizing particles (observed value). The threshold voltage ofthe discriminator was set at from 5 to 18 mV 2 .
2
The threshold voltage is magniﬁed by 20 times compared to the pulse height before the discriminator. The
actual set up values were from 100 to 350 mV.

2.5. Tracking Chambers

25(a) ASD board(b) LVDS-ECL converter

Figure 2.20: Photographs of (a) ASD board and (b) LVDS-ECL converter.

26

Chapter 2. Experimental procedure

SW
A

B

offsetsetting

Cb

IN 4

AGND

29

28

27

26

AGND

IN 3

30

AGND

NC

IN 2

AGND

IN 1

31

25

24

NC

AOUT 1

38

23

AOUT 4AVCC 1

P

P

P

39

22

40

21

AOUT 3AVEE 2

41

20

AVEE 1

NC

42

19

NC

NC

43

18

NC

DVCC 244

17

DVCC 1

M

M

C

M

C

M

C

C

DGND

45

16

DGND

DVEE 2

46

15

DVEE 1

DGND

47

14

DGND

NC

48

13

NC

comparator

Vth(a) Block diagram

8

9

10

11

12

DOUT 4_

DOUT 4

7

DOUT 3charged-up by i

6

DGND

A

5

DOUT 3_

NON-INV < INV

4

VTH

discharged by i

3

NC

C b

B

2

DGND

SW-position
NON-INV > INV

preamplifier

DOUT 1_

1

DOUT 2i

DOUT 2_

Rf

32

P

AVCC 2

NON-INV



33

37

DOUT 1

Cf

34

NC

AOUT 2C f = 1 pF
Rf = 16 k
INV

35

AGND

36

2i

AGND

AGND

CXA3183Q TGCASD(b) Pin assignment

Figure 2.21: (a)Block diagram of the ASD chip. (b)Pin assignment of the ASD IC.

2.5.2

Barrel-shaped Drift Chambers

The mechanical structure of Barrel-shaped Drift Chambers (BDC’s) consisted of 90-degrees arcshaped end plates at the top and the bottom which were supported by three aluminum bars
as shown in Fig. 2.22. The inner radius was 1570 mm, the outer radius was 1680 mm and theheight was 1420 mm. The acceptance of BDC’s was the same as CDC in the vertical coverage,
but with a smaller horizontal coverage from ±7.5 degrees to ±94.5 degrees. The BDC’s have
4 layers of drift cells with an X-X0 -U-V conﬁguration, located at r=1600 to 1650 mm. In the X
and X0 layers the direction of wires was vertical and in the U and V layers the wires were tilted
by about ± 0.1 radian. As CDC argon-ethane mixed gas of 50% and 50% was used at 1 atm.
The structure of the drift cells is shown in Fig. 2.23. All the drift cells of BDC had thesame horizontal angular coverage of 0.75 degrees with respect to the target position. The sizeof the drift cells of BDC was the same as that of the outer super layer of CDC. Details of thewire arrangements are shown in Table 2.6.
The read-out electronics of BDC were the same as that of CDC and the threshold voltageof the discriminator was set at from 13 to 15 mV.
layer number
wire direction
location of sense wirefrom the center of the arc [mm]cell width [degree]
cell width [mm]tilt angle [radian]wire length [mm]number of sense wires

1
X
1600

2
X0
1610

3
U
1630

4
V
1650

0.75
20.81
0
1403
116

0.75
20.94
0
1403
116

0.75
21.21
0.10581410.9
109

0.75
21.47
0.10711411.1
109

Table 2.6: BDC wire conﬁguration.

2.5. Tracking Chambers

27

wire region
110

Top
View
90 degree1570

6 degreeBeam axis

Side
View

1420

Figure 2.22: Schematic view of BDC.

Guard Wire

Potential Wire

Sense Wire

10.41 mm

V- layer

U- layer

R=1600X’-layer
X- layer

Figure 2.23: The cell structure of BDC

28

Chapter 2. Experimental procedure

2.5.3

Vertex Drift Chamber

The Vertex Drift Chamber (VTC) was newly installed in 2000 to give tracking informationin the vicinity of the beam and the targets. A signiﬁcant beam halo of about 100 kHz was
observed at 20 mm away from the beam with a 120 mm long and 1 mm wide scintillator. To
make the chamber operational under such a circumstance, special cell arrangements as shownin Fig. 2.24, were chosen. The VTC was located in the center of CDC, and the frame of
VTC was made of aluminum with dimension of 445 mm long, 320 mm wide and 220 mm
high. To minimize the material in the spectrometer acceptance, the top and bottom end-plates
were supported only at the upstream side. The acceptance of VTC was from ±6 degrees to±141 degrees horizontally, and the same as CDC vertically.
The VTC consisted of six radial layers of the drift cells, and they were grouped into two;the backward and the forward layers. The backward 3 layers covered from ±18 to ±141 degrees
at r = 100 mm, and the forward three layers covered the horizontal region from ±6 to ±24
degrees at r = 200 mm. All of the layers had a hexagonal cell structure, as shown in Fig. 2.25.
In the backward layers, the drift length was 2.62 mm, and in the forward layer it was 1.75 mm.

220mm

Be
am

44

5m

m

m
0m
2
3

Figure 2.24: Schematic view of VTC. The target arrangement in 2001 is also shown.

layer number
wire direction
radial location ofsense wire [mm]cell width [degree]
cell width [mm]wire length [mm]number of sense wires
global angle ofwire ID=1 [degree]

1
X
100.002
X0104.533
X
109.06

4
X
200.005
X0
203.03

6
X
206.06

3.0
5.24
184
41
19.5

3.0
5.47
184
42
18.0

3.0
5.71
184
41
19.5

1.0
3.49
184
18
6.5

1.0
3.54
184
19
6.0

1.0
3.60
184
18
6.5

Table 2.7: VTC wire conﬁguration.

2.5. Tracking Chambers

29

0 ./  !1"  (  !#" $&%' ( $) ( % '* " $+ ,% - ./  %  

3 " $+  !#"  (    ! !
"   # $
 %'&$((. %'&   

1   #  0  

2 $) (  !#"  (      /    0   

 
 

     

(a) backward cells)+*  

)+*  )+* ! , -$    (b) forward cells

Figure 2.25: The cell structures of VTC (a) for the backward cells and (b) for the forward cells.

The sense wires were gold-plated tungsten of 30 µmφ and the potential wires were Be-Cu
of 100 µmφ as same as CDC. In the backward cells, 2.9 mmφ NORYL (degeneration PPE
resin) feedthroughs are used with a pitch of 3.02 mm (Fig. 2.26(a)). The sense wires were kept
at the ground level, and the signals are read out through DC coupling (Fig. 2.27(a)). In theforward cells, all of the cathode wires are grounded through metallic feedthroughs which are
directly mounted on the end-plate (Fig. 2.26(b)). For the anodes, NORYL feedthroughs as the
backward cells are used. A positive high voltage is applied on the sense wires, and the signals
are read out through AC coupling (Fig. 2.27(b)). Details of the wire arrangements were shownin Table 2.7. Figure. 2.28 shows a photograph of the VTC with the targets in 2000 3 , andconcentration of the wires can be seen.
In the typical data-taking condition, the maximum hit rates per wire were 100 kHz in
the backward cells and 300 kHz in the forward cells. As the chamber gas, an argon(50%)ethane(50%) mixture was used through an ethanol bubbler at room temperature and 1 atm.
Without ethanol, the chamber could not work at such high rates. H2 O and ethanol are known
to be eﬀective in a wire ageing [49].
As CDC and BDC we calculated the electrical ﬁeld shape in the chamber cell and therelation between the drift length and the drift time with the drift chamber simulation code
Garﬁeld. The simulated drift line in the forward layer is shown in Fig. 2.29(a), and the relation
between the drift length and the drift time (x-t relation) is shown in Fig. 2.29(b).
The read-out electronics of VTC were the same as that of CDC, and the threshold voltageof the discriminator was typically set at 5 mV in the forward layers and 30 mV in the backward.
3

in 2000, polyethylene, copper, and carbon targets were used

30

Chapter 2. Experimental procedure   

3.02       !
2.02

Endplate

Positioning
Bush

Figure 2.26: Feedthrough structures (a) for the backward cells and (b) for the forward cells.
Figure 2.27: The read-out and highvoltage circuit (a) for the backward
cells and (b) for the froward cells.

Figure 2.28: Photograph of the VTC and the targets in 2000.

31(µsec)

2.6. Electron Identiﬁcation Counterslayer4(cm)(a) simulated drift line(b) calculated x-t relation

Figure 2.29: (a) The simulated drift line in the forward layer in the magnetic ﬁeld of 0.71T,
which is the magnetic ﬁeld strength at this location when the spectrometer magnet is fully
excited. (b) The calculated relation between the drift time and the drift length of the layer-4
under the magnetic ﬁeld of 0.71T.

2.6

Electron Identiﬁcation Counters

2.6.1

Start Timing Counter

The time zero of an event was deﬁned by the start timing counters (STC’s), since we could notcount the beam protons one by one because of their high rate (∼ 9 × 108 protons per spill). We
located STC at 380 mm from the center of the spectrometer, covering from ±12 to ±60 degrees
in the horizontal angle and ±23 degrees in the vertical angle. In each arm STC was segmented
into 8 units horizontally.
The scintillators of STC were made of Bicron BC404. The dimension of the scintillator
segment was 400 mm in height, 40 mm in width and 5 mm in thickness. The scintillation
light was transferred through light guides to a pair of photomultipliers attached at the top andbottom ends. The photomultipliers were H6154 of Hamamatsu Photonics, whose diameter ofthe photo-cathode was 2 inches and the dynode structure was a ﬁne-mesh type. They could be
operated under the magnetic ﬁeld of 0.71 T. The number of dynodes was 19 with the typicalgain of 1×106 at the present ﬁeld strength. Since the coincidence rate of the top and bottom
photomultipliers reached 1M counts per spill in the forward segments close to the beam, the highvoltage breeder was modiﬁed to supply enough current to the last three dynodes. The breeder
circuit is shown in Fig. 2.30. Typical breeder current was 0.4 mA which was increased to 4 mAat the last three dynodes. Discriminated signals from the top and bottom photomultipliers
were fed into the mean timers and provided the timing of each segment. The timings of all the
STC segments were adjusted within 1 nsec. These signals were OR-ed and used as the event
time-zero signal.

32

Chapter 2. Experimental procedure

photocathode

DY1

DY2

Anode

DY3

DY4

DY5

DY6

DY7

DY9

DY8

DY10 DY11 DY12 DY13 DY14 DY15 DY16 DY17 DY18 DY19

R26
R22

R1

R5

R3

R2

R4

R7

R6

R11

R9

R8

R10

R13

R12

R15

R14

R16

R23

R24

R25

R17

R19

R20

R21

C1

C3

C4

C5

330k

330k

330k

R18
C2

R27

C6

coaxial
cable

  
   

- HighVoltagecoaxialcable
R1, R3 - R17 1.3M
R2
2.0M
R18
660k
R19 - R21330k
R25 - R25
55
R26
1.0M
R27
10k

C1
C2 - C5C6

0.01 µ F / 500V
0.01 µ F / 200V
4700 pF / 3kV

additional
circuit

Booster
Voltage

Booster
GroundSignaloutputFigure 2.30: The breeder circuit of the photomultiplier used for STC (Hamamatsu H6154).

2.6.2

Front Gas-Čerenkov Counter

The front gas-Čerenkov counters (FGC’s) covered from ±12 degrees to ±90 degrees horizontallyand ±23 degrees vertically. They were horizontally segmented into 13 units in each arm so thatone segment covered 6 degrees. The cross section of FGC is schematically shown in Fig. 2.31,
together with the light collection scheme. Iso-butane gas with the refractive index of 1.00127 atroom temperature (1.0019 at STP) was used as the Čerenkov photon radiator . The threshold
momentum for pions is 2.7 GeV/c. Since the path length of particles in the counter was
rather short, we used the gas having high refractive index. Another merit of iso-butane wasits transparency for ultra-violet lights down to the wave length of 220 nm. It is important forthe detection of the Čerenkov light because the intensity of Čerenkov light is higher at a shortwavelength with a 1/λ2 dependence.
A radiated Čerenkov photons were reﬂected twice on the ﬂat and the arc mirrors. To
suppress multiple scattering, it was required to use thin mirrors. For the ﬂat mirror we used
0.05 mm-thick aluminized Mylar supported with a honeycomb backplane made of paper. The
arc mirrors were made by a 3 mm-thick Acrylic plastic on which aluminum and SiO weresuccessively evaporated. Čerenkov photons were reﬂected also at the side walls which separated
the 13 segments. We used MgF2 -coated aluminized Mylar which has 88% reﬂectance for thewave length down to 200 nm.
The Čerenkov photons were focused with a Winston funnel [50] attached on the photomultipliers. Since the photomultipliers of FGC’s were operated under the magnetic ﬁeld of about
0.2 T, we used R5542 of Hamamatsu Photonics which had 19 stages of ﬁne-mesh dynodes. For
the detection of Čerenkov photons, their window was made of UV-transparent glass with adiameter of 3 inches.

2.6. Electron Identiﬁcation Counters

33

RLG
FGC

3" FineMesh PMT
Winston funnel

Winstonfunnel

2nd reflection
mirrorreflection
mirror

1st reflection
mirror

700mm

RGC

Figure 2.31: Schematic view of FGC,RGC and RLG.

We tested a 1/2 sector model with no magnetic ﬁeld. The vertical and horizontal incidentangle dependence of the eﬃciency and the number of mean photo-electron were obtained using
500 MeV/c electrons. The results are summarized in Fig. 2.32 and 2.33. We obtained more thanﬁve photo-electrons in all the angular region required for the spectrometer. With the horizontal
angle more than 0.15 radians electrons pass more than one segment so that the pulse from theneighbor segment must be added. The horizontal incident angle of 0.2 radian corresponds tothe momentum of 400 MeV/c. Figure 2.34 shows the ADC spectrum for 1 GeV/c pions. The
pion rejection is 0.8×10−2 when the threshold is set to one photo-electron.

34

Chapter 2. Experimental procedure

F

101

DE
C
7B

100.5
100

A;

99.5

;

98.5

99

>>A B

98
97.5

   97   

96.5
96

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

 "!# $&%('*)+$&,+%$.-",+#' ,0/1)32 !'-*4

8

; @
> ?.@
=

7.5

: ;<

7

78

6.5

9

0

6
5.5
5

!# $&%('*)+$&,5%$.-",+#6',0/1)32 !' -*4

Figure 2.32: The eﬃciencies (upper ﬁgure) and the averaged number of photo-electrons (lower
ﬁgure) of the FGC test module for 0.5 GeV/c electrons as a function of the vertical incident
angle. The circles and the squares show eﬃciencies with threshold at one and two photo-electronlevels, respectively.

+

)*

( 104

' 102&,-. / 0 1230 410 5-4 /62473 8:9; < . 25+)*

' 102&#&# ' 100

( 104#&# ' 100

98

98

96

96

94

94

92

92

90

90

88

88

86

86

  1
%# $" %
 !

10
9 1 0  0.1  0.2

,-. / 0 1230 410 5-4 /62473 8:9; < . 25%# $" %
 !

8



7

10
9

6
5

4

4

3

3

2

2

1

1

 0  0.1  0.2

,-. / 0 1230 410 5-4 /62473 8:9; = . 2575 1 0 0.1  0.2

8



6

0

,-. / 0 1230 410 5-4 /62473 8:9; = . 250 1 0  0.1  0.2

Figure 2.33: The eﬃciencies (upper ﬁgures) and the averaged number of photo-electrons (lower
ﬁgures) of the FGC test module for 0.5 GeV/c electrons as functions of the horizontal incident
angle. The left ﬁgures were measured when the vertical incident angle was 0.1 rad, and theright ﬁgures were when that was 0.3 rad. The open marks are mirror image of the closed marks.

2.6. Electron Identiﬁcation Counters

35

ID

10

10

10

77

Entries

49396

Mean

-0.5366E-02

RMS

0.2558

4

3

2

10

1

0

2.5

5

7.5

10

12.5

15

17.5

20

22.5

MGC

Figure 2.34: FGC response for 1 GeV/c pions. The horizontal axis is normalized to the numberof photo-electrons.

2.6.3

Rear Gas-Čerenkov Counter

The rear gas-Čerenkov counters (RGC’s) covered from ±12 degrees to ±54 degrees horizontallyand ±6 degrees vertically with 7 horizontal segments in each arm. These regions corresponded
to the kaon-arm acceptance. The cross section of RGC is schematically shown also in Fig. 2.31,
together with the light collection scheme.
Iso-butane gas was used for the radiator as FGC. A radiated Čerenkov photons were reﬂected once on the arc mirror which was made by the 3 mm thick Acrylic plastic on which
aluminum and SiO were evaporated. Čerenkov photons were reﬂected also at the side walls
for the segmentation. The photons were focused with a Winston funnel [50] attached on thephotomultipliers. We used R1652 of Hamamatsu Photonics with a diameter of 3 inches.
The test results for a 1/2 sector model with no magnetic ﬁeld are shown in Fig. 2.35(a) and(b). The vertical and horizontal incident-angle dependence of the eﬃciency and the numberof mean photo-electron were obtained using 1.0 GeV/c electron. We obtained the number ofphoto-electrons of more than three in the acceptance required for the spectrometer. The lower
number of photo-electrons at 0.0125 radian (Fig. 2.35(a)) is due to the acceptance of the test
module. The pion rejection is also demonstrated in Fig. 2.36, which shows the ADC spectrumof 1 GeV/c pions. When the threshold is set to 10 ADC channel above the pedestal, which
realize the 99% eﬃciency for electrons, the pion rejection power is estimated to be 3 × 10−3 .

Chapter 2. Experimental procedure

100

%

%

36

98

98

96

96

94

94

92

92

90

90

88

88
86

86
0

0.02

0.04

0.06

0.08

0.1

−0.25

0.12

7

6

6

5

5

4

4

3

3

2

2

1

1
0.02

0.04

0.06

0.08

0.1

tan

0.12

−0.1

−0.05

0

0.05

0.1

0.15

0.2

0.25

tan

8

7

0

−0.15

efficiency vs horizontal incident angle
p.e.

8

0

−0.2

tan

efficiency vs azimuthal incident angle
p.e.

100

0
−0.25

−0.2

−0.15

−0.1

−0.05

0

0.05

0.1

0.15

number of photo−electron vs horizontal incident angle

number of photo−electrons vs azimuthal incident angle(a) vertical angle

0.2

0.25

tan

(b) horizontal angle

Figure 2.35: The eﬃciency (top panels) and the number of photo electron (bottom panels) of
the RGC test module as functions of (a) the vertical angle of incident electrons and (b) the
horizontal angle of incident electrons.

10 4

10 3

Radiation length
Refractive index
Critical energy
Moliere radius
Density

10 2

10

1.69cm
1.805
12.6MeV
2.8cm
5.20g/cm3

1

Table 2.8: Characteristics of SF6W [51].
-1

10

0

100

200

300

400

500

Figure 2.36: RGC response for 1 GeV/c pions.

2.6.4

Rear Lead-Glass EM Calorimeter

The rear lead-glass EM calorimeters (RLG’s) covered the same horizontal angle as RGC’s
with 12 segments in each arm, but vertically covered outside the kaon-arm acceptance, from
±9 degrees to ±23 degrees.
The one unit of RLG consisted of SF6W lead-glass block, which had the size of 340 mm
height, 124 mm width and 114 mm thickness, and a PMT 1652 of Hamamatsu Photonics witha diameter of 3 inches was attached. The characteristics of SF6W are listed in Table 2.8. These
units were recycled from the EM calorimeter of the TOPAZ experiment at KEK TRISTAN.
These units were arranged as particles come into the side of each block, as shown in Fig. 2.31.
So that typical eﬀective thickness as a Čerenkov radiator was 6.7 radiation lengths. To cover2.6. Electron Identiﬁcation Counters

37

a large region with the small number of segments, such unusual arrangements were adapted.
Čerenkov photons from an EM shower were transported vertically by the total reﬂection to thephotomultipliers at the end of the block.

2.6.5

Side Lead-Glass EM CalorimeterIn the backward region where the horizontal angle was larger than 57 degrees, the second-stage
electron identiﬁcation was done by the side lead-glass EM calorimeters (SLG’s) which coveredfrom ±57 degrees to ±90 degrees horizontally and ±23 degrees vertically with 9 horizontal
segments in each arm. The cross section of SLG is schematically shown in Fig. 2.37 with FGC.
We reuse the TRISTAN/TOPAZ lead glass calorimeter blocks same as RLG. For SLG, wereshaped and re-polished the blocks in Tochigi Nikon Corporation into a rectangular shapefrom the original tapered shape, and 5 units of the lead-glass blocks were stacked verticallyand glued epoxy resin to form one segment of the calorimeter. The one segment of SLG had
the size of 165 cm height, 12 cm width and 11 cm thickness. We placed SLG along the returnyoke of the magnet like a hodoscope behind BDC. Čerenkov photons from an EM shower weretransported vertically by the total reﬂection to the photomultipliers at the top and bottom
ends. We used R1911 of Hamamatsu Photonics with a diameter of 3 inches.
We tested a one-segment model. The light yield was measured as a function of the vertical
position using a 500 MeV/c electron beam. Although the light yield decreased by 75% at eachblock, the sum of the both end was almost ﬂat as shown in Fig. 2.38(a). Typical response forpions and electrons was obtained as shown in Fig. 2.38(b). Although the eﬀective thickness forthe electron
shower-development was only 6.5 radiation lengths, typical energy resolution of√
15%/ E was obtained. By keeping 95% eﬃciency for electrons, the pion rejection of 2×10−2
was achieved.

Winstonfunnel3" FineMesh
PMT

FGC

EM shower

2nd reflection
mirror

1st reflection
mirror

700mm

SLG

Figure 2.37: Schematic view of FGC and SLG.

Chapter 2. Experimental procedure

(%)

38

25





60

80

20
15
10
0.5GeV/c
1.0GeV/c
1.5GeV/c

5

2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

(%)

(arbitrary)

0

sum
A1
A2

0

20

40

100



4

3

0.5GeV/c
1.0GeV/c
1.5GeV/c

20

40

120

140

(cm: from PMT A1)

 $#
!" 
%! & '

2

1

0

20

40

60

140
  100 (cm :120
from TOP PMT)

80

0

0

(a)

60

80

100

120
140
(cm: from PMT A1)(b)

Figure 2.38: (a)Vertical position dependence of the light yield for SLG. The open rectangles andclosed circles are the light yields from the top and the bottom PMT’s. The closed rectangles
are for the sum. (b)The vertical position dependence of the energy resolution for electrons(top) and the pion rejection power (bottom) of SLG, measured with 0.5, 1.0, and 1.5 GeV/celectrons and pions.

2.6.6

Forward Lead-Glass EM Calorimeter

The forward lead-glass EM calorimeters (FLG’s) were installed in 2000 to improve the electron
identiﬁcation capability in the kaon arm acceptance. The FLG’s were located at just behind
the FTOF wall covering the same acceptance as RGC’s. The FLG’s had 24 segments in theleft arm and 16 segments in the right arm. The 8 segments to cover the most right end of theright arm were omitted due to the space limitation of the experimental area.
We reused the TRISTAN/TOPAZ lead-glass calorimeter blocks also for FLG. One segmentof FLG consisted of three lead-glass blocks. Only the center block was reshaped and re-polishedat Tochigi Nikon Corporation into a rectangular shape from the original tapered shape. Top
and bottom blocks just reused the TOPAZ modules as they were. The three blocks of thelead-glass blocks were stacked vertically and glued with epoxy resin, as shown in Fig. 2.39. The
one segment of FLG had the size of 950 mm height, 124 mm width and 110 mm thickness.
Čerenkov photons from an EM shower were transported vertically by the total reﬂection to thephotomultipliers at the top and bottom ends. We used R1652 of Hamamatsu Photonics witha diameter of 3 inches.

2.7. Kaon Identiﬁcation Counters

39

Figure 2.39: Schematic view of FLG. The hatched areas are lead-glass radiators.

2.7

Kaon Identiﬁcation Counters

2.7.1

Hodoscope Counter

Hodoscope Counters (HC’s) were used to determine the sign of a charged particle and its roughmomentum in the trigger in combination with the FTOF counters. Signals from HC were usedin the on-line ﬁrst-level and the second-level kaon-triggers, as described in Sec. 2.8.2.
The HC’s covered from ±12 degrees to ±54 degrees in the horizontal angle, and ±6 degrees
in the vertical angle, and were placed 2632.5 mm from the center of the magnet. They consistedof 28 segments in each arm. The dimension of the scintillator was 660 mm in height, 70 mm
in width, and 5 mm in thickness. The two segments located most backward had a diﬀerent
width of 200 mm. They were arrayed with an horizontal overlap of 5 mm. Each segment wasread by a pair of photomultipliers from the top and bottom ends through light guides. The
photomultipliers were H1161 of Hamamatsu Photonics with the photocathode diameter of 2
inches. The number of dynodes was 12 of linear focusing type with the typical operation gainof 1.1×106 .

2.7.2

Forward Time Of Flight Counter

Forward Time Of Flight Counters (FTOF’s) were used to measure the ﬂight time of charged
particles together with STC’s. Particle identiﬁcation was performed with the ﬂight time information together with a ﬂight length and a momentum given by the track ﬁtting.
The FTOF’s were located behind the Aerogel Čerenkov counters (AC’s), and they coveredfrom ±12 degrees to ±54 degrees in the horizontal angle, and ±6 degrees in the vertical angle.
The distance from the center of the spectrometer to the center of the FTOF array was 3951 mm.
The FTOF’s consisted of 16 segments in each arm. Two types of scintillator slabs were used,
one was 800 mm in height, 200 mm in width and 30 mm in thickness, and the other was 800 mm
in height, 170 mm in width and 20 mm in thickness. They were arrayed alternatively with anhorizontal overlap of 2 mm. The scintillation light was read out with a pair of photomultipliers
through light guides mounted on the both ends of the slabs. The photomultipliers were H1949
of Hamamatsu Photonics with a photocathode diameter of 2 inches. This photomultiplier was

40

Chapter 2. Experimental procedure

specialized for the time of ﬂight measurements with a high gain of 2.0×107 and the typicalsignal rise-time of 1.3 nsec.

2.7.3

Aerogel Čerenkov CounterTo trigger kaons, we used the threshold-type Aerogel Čerenkov counters (AC’s). Since therefractive index of the Čerenkov radiator was 1.034, we can separate kaons from pions in the
momentum region from 0.53GeV/c to 1.88GeV/c . The AC’s were located just in front of the
FTOF counters, and both of them had geometrically-matched 16 segments in each arm. The
cross section of the AC is schematically shown in Fig. 2.40 together with the light collection
scheme. When a hit in a FTOF segment was associated with a hit in either of 3 AC segmentsin the front, it was considered as a pion having a momentum above 0.53GeV/c, and the FTOF
hit was vetoed in the ﬁrst-level kaon trigger as described in Sec. 2.8.2.
The AC’s covered from ±12 to ±54 degrees in the horizontal angle and ±6 degrees in thevertical angle. The AC’s had an eﬀective area of 2640 mm in width, 706 mm in height, and
125 mm in thickness. The dimension of each AC segment was 160 mm in width and 706 mm
in height. Radiated Čerenkov photons were read out by a pair of photomultipliers throughthe optical system made with cylindrical concave mirrors and Winston funnels [50] attachedon each photomultiplier. The equipped photomultipliers were single-photoelectron sensitive
H6527 of Hamamatsu Photonics with a photocathode diameter of 5 inches. It had 14 dynodesof linear-focusing type. They were operated with a typical gain of 1.4×107 .
In Fig. 2.41, the pulse height distributions of AC are shown for 1.4 GeV/c positive pions
and protons delivered at the center of the segment. We obtained 5.4 photoelectrons for pions.
The photoelectrons observed for protons are attributed to δ rays or scintillation lights. Setting
the threshold level at 1.1 photoelectron, we have achieved the pion rejection eﬃciency of 99.0%
and an over-killing rate for protons of 0.3%.
Winston funnel  "!#%$&#('*),+-/.102#434!65-7989897,':%;

particle <"7,#('*),==>02%?,?@767,('AB;

Reflection Mirror

Aerogeln=1.034CD
EF(GIHJKFL%M<NM<H O1H M

1000 mmFigure 2.40: Schematic view of AC and the lightcollection scheme.

 

Figure 2.41: Pulse height distributions of
AC for 1.4 GeV/c positive pions and protons.

2.8. Trigger

2.8

41

Trigger

The schematic diagram of the trigger control system is shown in Fig. 2.42. We applied thethree-level trigger logic for e+ e− events and the two-level for K+ K− events. The both modes
worked simultaneously. If the condition of the electron or the kaon ﬁrst-level trigger logic wassatisﬁed, the event latch was set as “busy”, the gates for ADC’s were opened and the common
start (or stop) timing signals for TDC were generated. The “busy” state of the event latch was
kept until the clear signal was generated by the higher-level triggers.
If the latched events satisﬁed all the levels of the electron or kaon trigger requirements, the“event accept” signal was issued and the digitized data in the ADC and the TDC modules weretransferred to the memory modules. When the data transfer was completed, the event latch
was cleared and the trigger logic became ready for a next event. If the latched event did notsatisfy the higher-level trigger logic, the clear signal was sent to the ADC’s and TDC’s and theevent latch was also cleared. Typically the duration of the “busy” state was 600 µsec for therecorded events and 50 µsec for the cleared events.
In order to estimate the trigger eﬃciencies and to monitor the trigger logic operation, werecorded events which satisﬁed the lower-level trigger logics regardless of the result of thehigher-level triggers. Such sampled events were about 5% of all the recorded events.
We required the second and third level trigger for e+ e− events until the year 2000. After theyear 2000, we decided to collect only “double-arm events” which mean either positron in theleft arm and electron in the right arm (“LR event”) or vice versa (“RL event”), to suppress the
background trigger from Dalitz decays and conversions. This change reduced the rate of theelectron ﬁrst-level trigger signiﬁcantly so that higher-level triggers were not used. The typicaltrigger rates in 2001 and 2002 are shown in Table 2.8.
Below we explain the electron ﬁrst-level trigger and the kaon ﬁrst and second-level triggers.

Not Go

E1st

Go

E2nd

E3rd
Go

Fast
Clear

open

Event Latch
reset

Event Trig

Sampling

ADC Gate
TDC Start(Stop) Timing

Sampling

K1st

Go

K2nd

ACCEPTGo

SMP
SMP BUSY

Data
Transfer

Not GoFigure 2.42: A diagram of the trigger control system.

data scanrequestADC TDC

42

Chapter 2. Experimental procedure

Level

Kaon trigger
57.8k
1/50
0.8k
0.5k

RequestPreset Scale
AcceptAccept

1st
2nd

2001
Electron trigger
1.2k
1/1
0.7k
–

2002
Electron trigger
1.6k
1/1
1.0k
–

Table 2.9: Trigger rates in a typical spill of 1.8 sec-long in the year 2001 and 2002.

2.8.1

Electron Trigger

The electron ﬁrst-level trigger worked as follows. We selected electron-pair candidates using thecoincidence signal of the front-stage (FGC) and the rear-stage detectors (RGC, RLG, SLG),
by requiring the horizontal position matching as shown in Table 2.10. The hit signals of eachsegment were deﬁned as an ORed signal of the top and the bottom PMT’s and strobed by
the STC or-signal in the corresponding arm. The size of the matching windows corresponds tothe momentum range greater than 400 MeV. To suppress electron pairs with a small opening
angle, such as from Dalitz decays and γ-conversions, we required the electron candidates to bepresent in both arms during the data taking periods used in the present analysis.

SLG IDRLG IDRGC ID

1
1
2
3
4
5
6
7
1
2
3
4
5
6
7
8
9
10
11
12
1
2
3
4
5
6
7
8
9

2
°
°
°

°
°
°
°
°
°

3
°
°
°

°
°
°
°
°
°

4
°
°
°

°
°
°
°
°
°

5

°
°
°

°
°
°
°
°
°

6

FGC ID
7
8

°
°
°

°
°

°
°
°
°
°
°
°

°
°
°
°
°
°
°

9

10

°
°
°
°
°
°

°
°
°
°
°
°
°

11

12

13

°
°
°
°
°
°
°
°

°
°
°
°
°
°

°
°
°
°

°

°
°
°
°
°
°

Table 2.10: The pattern of the matrix coincidence for the FGC segments and the RGC, RLG,
and SLG segments in the electron ﬁrst-level logic. The counters were numbered from forward
to backward in each arm.

2.8. Trigger

2.8.2

43

Kaon Trigger

Hodoscope ID

The kaon ﬁrst-level trigger selected events with two kaon candidates by using the informationfrom the kaon-arm counters. To eliminate pions whose momentum was larger than 0.53 GeV/c,
at least two FTOF hits which were not associated with geometrically-matched AC hits wererequired. To select tracks whose momentum was larger than 0.4 GeV/c, these AC-vetoed FTOF
signals were fed into matrix-coincidence logic together with the HC signals. The matrix pattern
was set as shown in Table 2.11. To invoke an event trigger, at least one STC hit both in the left
and right arms was also required. The rate of the kaon ﬁrst-level trigger requests was typically
58k per spill and it was down-scaled to 1/50 to keep the live time at the level of 60% for theelectron trigger.

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28

1
°
°
°
°

2
°
°
°
°
°
°

3
°
°
°
°
°
°
°
°

4
°
°
°
°
°
°
°
°

5

°
°
°
°
°
°
°
°

6

°
°
°
°
°
°
°
°

7

FTOF ID
8
9

°
°
°
°
°
°
°
°

°
°
°
°
°
°
°
°

°
°
°
°
°
°
°
°

10

°
°
°
°
°
°
°
°

11

°
°
°
°
°
°
°
°

12

13

°
°
°
°
°
°
°
°

°
°
°
°
°
°

14

15

16

°
°
°
°
°
°

°
°
°
°

°
°

Table 2.11: The pattern of the matrix coincidence for the FTOF segments and the HC segmentsin the kaon ﬁrst-level trigger logic. The counters were numbered from forward to backward ineach arm.
The kaon second-level trigger used the ﬂight time information from the FTOF counters andthe hit information of HC counters. Since average momentum of charged particles is diﬀerent
in each hit combination of FTOF and HC, a timing window for kaons was determined for each
FTOF-HC pair. Before starting the every run of about 90 minutes long, the peak positions of
TDC counts for pions in all the FTOF segments were monitored, and the timing windows forkaons with a momentum larger than 0.5 GeV/c were determined for each FTOF-HC hit pair.
We required at least two FTOF-HC hit pairs whose ﬂight time was inside the kaon window andthe charges were at least one positive and one negative. The kaon second-level logic reduced thetrigger rate to about 60% and the decision time was less than 100 µsec including the conversion
time of the fast encoding TDC’s.

44

2.9

Chapter 2. Experimental procedure

Data Acquisition System

K3922 CAMAC
Crate Controller

The on-line data-acquisition system (DAQ) was constructed with the VME [52], TKO [53] andCAMAC [54] based front-end electronics. Schematic diagram of the DAQ is shown in Fig. 2.43.

VME SMP #13

VME SMP #02

VME SMP #01

K2917 CAMAC interface

SCSI

Interupt register

DAT

HP-743 front end CPU

VME crate

CAMAC scaler

SCH TKO #01 ADC
SCH TKO #02 TDC

TRG ACCEPTSCH TKO #13 Dr.T

Spill OFF Trigger

Event Trigger

Ethernet

ADC 3 crates
TDC 2 crates
Dr.T 8 crates

monitoring PC( online monitoringand human interface of DAQ)

Figure 2.43: The schematic view of Data Acquisition System.

The Hewlett-Packard Model 743 (HP-743), VME on-board workstation, played a main rolein the front-end data-acquisition system. There were 13 Super Memory Partner (SMP) modules
and a Kinetic K2917 VME-CAMAC interface-board in the VME crate. There were also 13 TKO
crates, 2 of them contain high resolution TDC’s, 3 of them ADCs, and 8 of them TDC’s fordrift chambers (Dr.T). The SMP’s work as an interface module between the VME bus and the
TKO bus via the Super Controller Head (SCH) module which was installed in each TKO crate.
Once the trigger signal was supplied to the ACCEPT input in the front panel of SMP, data
scanning for all the channels of ADC’s and TDC’s in the TKO boxes was performed by SCH’s,
and the scanned data were stored in the local memories in SMP’s. A busy signal was issued
by SMP’s during the scanning of the data, and further triggers were prohibited by the trigger
control system. The process was repeated during the spill on, and at the spill end, these stored
data were read out by HP-743 via VME bus and written in the digital data storage (DDS-4)
tape, as well as the scaler data via the VME-CAMAC interface boards connected to the Kinetic
K3922 CAMAC crate controller.
Software for the data collection, recording, transfer and monitoring was written in programming language C/C++. The data collection process (collector), the recording process(recorder) and transfer process (sender) were also running on HP-743, on which HP-RT v2.0
was operated.
The “collector” read the accumulated data on SMP’s and CAMAC scalers through the
VME bus at the timing of the spill-end notiﬁed by the VME interrupt register. Device drivers
for TKO and CAMAC on HP-RT, used in “collector”, were developed by KEK on-line group.
The data were written to the buﬀer area on the UNIX shared memory region in the format
which has some additional informations like as run number, date and time, event-number and2.9. Data Acquisition System45

headers/footers for decoding. The data buﬀering system is NOVA [55], which is implemented
using UNIX shared memory for a local host environment, and TCP/IP (socket) for the network
distributed machines. The buﬀer size for one event was 4 Mbyte and six buﬀers were kept.
The “recorder” read the data from NOVA and wrote to the DDS-4 drive connected to HP743 via SCSI. The “sender” also read the data from NOVA and sent them to a PC for data
monitoring via Ethernet by the subroutine in the NOVA system, which was implemented using
UNIX socket.
For the data monitoring, IBM PC was used, on which Linux (kernel 2.2) was operated. All
the data monitoring processes, “analyzer”, “scaleranalyzer” and “visualscaler” are read the datafrom NOVA operated in the PC. The “visualscaler” displayed the scaler data tabularly spillby spill. The “analyzer” and “scaleranalyzer” read the event and the scaler data respectively,
analyzed them and ﬁlled the HBOOK histograms, which were displayed by PAW [56] via “global
memory” function in HBOOK [57] which is also implemented using UNIX shared memory.
The Graphical User Interface process to control and to monitor these many processes named“Z2” was written in the script language ruby/Tk. Typical view of the GUI environment on X
window system [58] running on Linux on the monitoring PC is shown in Fig. 2.44.

Figure 2.44: Screen shot of the GUI environment on X window system.

The typical data taking rate was 3 Mbyte/spill in a 1.8 sec-long spill, corresponding toabout 1k event per spill, and the live time of the data acquisition system was about 56%.
The data are also transferred to Mass Storage system in a semi-realtime way. The recorded
data on the DDS-4 tape are read out by another IBM PC (Linux) in the counting house,transferred to RIKEN-CCJ [59] via Internet using the command bbcp [60] and archived in
HPSS [61] in CCJ. The typical transfer rate between KEK and RIKEN was about 2 Mbyte/sec.
The amount of the data taken in 2001 was about 1.2 Tbyte, and in 2002 was about 1.1 Tbyte.

Chapter 3
Data Analysis
3.1

Outline of Data Analysis

The data described in this manuscript were taken for 34 days from November to December in2001 and 32 days from February to March in 2002. The electron events were acquired in theyear 2001 and 2002, and the kaon events were acquired in 2001. The number of beam protons
on target and the number of triggered events in this period are summarized in Table 3.1.

year
2001
2002

number of

number of

averagednumber of electron

number of kaon

beam protons

spillsproton intensity

triggered events

triggered events

3.8×1014
3.2×1014

435k
508k

8.7×108
6.4×108

3.1×108
5.1×1082.1×108-

Table 3.1: The number of beam protons and triggered events.

The calibration of the detectors is described in Sec. 3.2. We explain the calibration of thechambers, i.e., the iterative determination of the x-t relation, the position alignment of the
tracking chambers, the energy gain calibration of the EM calorimeters, and the calibration of
the kaon identiﬁcation counters.
The track reconstruction using hits in CDC and BDC is described in Sec. 3.3.1. In the ﬁrst
step of the track ﬁnding, a track was approximated by a quadratic function in the horizontal
plane which was perpendicular to the magnetic ﬁeld and a straight line in the vertical plane.
For the electron-triggered events, the events were required to have oppositely-charged tracks in
diﬀerent arm. For the kaon triggered events, the events were required to have more than two
tracks in the kaon acceptance. In the next step, track candidates were ﬁtted by the Runge-Kutta
method over the magnetic-ﬁeld map to determine the precise momenta and the trajectories of
the charged particles. And then vertex position for each event was determined as described inSec. 3.3.4.
Particle identiﬁcation was performed as follows. For electrons, tracks were required to haveposition-matched hits in both the ﬁrst and the second stage electron counters, certain pulse
heights in associated FGC and RGC, and energy/momentum matching in the EM calorimeters as described in Sec. 3.3.5. We required at least one positron candidate and one electron
candidate in each arm. For kaons, tracks were required to have position-matched hits in the
scintillation counters without associated hits in AC. With the Time-of-Flight measurements,
we identiﬁed kaons as described in Sec. 3.3.6, and a pair of positive and negative kaon was
required. Because of small Q value in φ → K + K − decay, such pairs were normally in a samearm. For the ﬁnal electron or kaon pair tracks, we repeated the Runge-Kutta ﬁt by requiringthat both tracks from the pairs were originated from the same point on the target disks.
46

3.2. Calibration

47

As described in Sec. 3.5, the event simulation was performed using Geant4.5.1.p01 [62]to evaluate all the detector eﬀects, such as energy loss of particles, multiple scattering, andthe tracking performance with the chamber resolution. An event generator is made by hand.
The nuclear cascade code JAM (1.011.00) [63] was used mainly to generate the momentum
distribution of mesons in the event generator. The mass shapes of the mesons used in thegenerator are discussed in the Sec. 3.5.

3.2

Calibration

3.2.1

Chamber TDC Calibration

For the drift time measurement, we used TKO 32CH DRIFT CHAMBER TDC(Dr.TII) modules produced by REPIC (RinEi Precision Instruments Corporation [64]). The full scale ofthis module is 1000 ns and typical time resolution is 350 ps. The time gain was calibratedusing CAMAC TDC TESTER which is also produced by REPIC. The obtained time gain was
typically 0.7 ns/channel.
We determined the relative time oﬀset of all the CDC, BDC and VTC signals using drift
time spectra. The time spectrum of each wire had an edge structure close to the wire as shownin the upper panel of Fig. 3.1. The peak position of the diﬀerentiated time spectrum (the lower
panel of Fig. 3.1) provided the relative time oﬀset in each signal.
This calibration was done run by run to cope with the temperature-dependent drift of delayin the signal cables and the common stop logic. The run dependence of time oﬀset was shownin Fig. 3.2. The typical drift was within 3 ns.

time spectrum[channel]differencial[channel]Figure 3.1: Typical TDC spectrum and its diﬀerential.

 

T0(ch)

Chapter 3. Data Analysis

T0(ch)

48

  run(a) the year 2001

run(b) the year 2002

Figure 3.2: Run dependence of typical time-oﬀset adjustment, (a) in the year 2001 and (b) inthe year 2002.

3.2.2

Determination of Drift Length from Drift Time

To convert the measured drift time to the hit position in the cell, the relation of drift length(X) and drift time (T) was determined by the procedure described below. The initial parameterization of this relation was obtained with the drift chamber simulation code Garﬁeld [47].
We iteratively adjusted the common time-zero oﬀset and the scaling factors of drift velocity,by minimizing systematic shifts in the residuals as a function of the drift length between thehit points and the track positions obtained by the Runge-Kutta ﬁtting. The incident angle
dependence was small and neglected. After the calibration, we obtained the position resolutionof 350 µm typically as shown in Fig. 3.3. Noted that the resolution in the Fig. 3.3(c) includes
the precision of the Runge-Kutta ﬁt and their intrinsic resolution.

  

    
     
 
 

 


 
       

Figure 3.3: The correlations between the CDC residual as a function of the drift length (a) andof the incident angle of tracks (b). (c) shows the over all resolution.

3.2. Calibration

3.2.3

49

Global Position Alignment

In the present analysis, the origin of the coordinate was set at the center of CDC. All the otherchambers and counters were aligned to the CDC coordinate. The magnet position with respect
to CDC was obtained by the survey performed before and after the beam time. The alignmentof the BDC position with respect to CDC was also surveyed and reﬁned using the data taken
without the magnetic ﬁeld. Since the trajectories of all the particles were straight, a linear
equation was adopted as a track-ﬁtting function.
In the alignment procedure, the residuals in BDC with respect to the straight track obtainedwith the CDC hits were systematically analyzed to determine 6 parameters which determines
the three dimensional positions and rotations of BDC (see Appendix A in Ref. [35]). Hit
associations to the tracks were required to be at least 5 out of 6 X-X0 layers and 3 out of 4
stereo layers in CDC and all the layers in BDC. The active area in BDC was divided into 30, 6
in horizontal and 5 in vertical. We obtained 6 parameters of the transfer matrix by minimizing
the systematic shifts appeared in the horizontal matchings between CDC track and BDC hit
in the 30 BDC regions. The residual distributions of the BDC hits to the CDC tracks after
the alignment are shown in Fig. 3.4. The values of the shifts (dx, dy, dz) and the rotations(τx , τy , τz ) for the run 2001 and 2002 are summarized in Table 3.2. Here rotation angles aredeﬁned around the 3 axes which cross the origin of the global coordinate (the center of CDC).
period

dx
arm
[mm]
I
L +2.40 ± 0.90
R +2.35 ± 0.99
II
L +2.30 ± 0.92
R +1.94 ± 0.79
III L +2.44 ± 0.54
R +2.20 ± 0.73

dy
dz
[mm]
[mm]
−0.85 ± 0.65 +2.54 ± 0.33
+0.47 ± 0.70 −0.35 ± 0.44
−0.62 ± 0.67 +2.15 ± 0.14
+0.47 ± 0.58 −1.06 ± 0.13
−1.11 ± 0.42 +2.60 ± 0.15
−0.05 ± 0.52 −0.39 ± 0.21

τx−3[×10 rad]τy−3[×10 rad]τz−3[×10 rad]−0.33 ± 0.55
−0.19 ± 0.58
−0.13 ± 0.37
−0.24 ± 0.16
−0.20 ± 0.43
−0.38 ± 0.46

+1.59 ± 0.59
+0.02 ± 0.61
+1.33 ± 0.35
−0.22 ± 0.17
+1.42 ± 0.37
−0.24 ± 0.45

+2.30 ± 0.39
−1.69 ± 0.37
+2.12 ± 0.29
−1.49 ± 0.25
+1.08 ± 0.20
−2.79 ± 0.24

Table 3.2: The shifts and rotations parameters of BDC with respect to the nominal position.
The unit of dx, dy and dz are [mm], and τx , τy and τz are [×10−3 radian]. The period I
corresponds to from run 6000 to 6292 in 2001, the period II from run 6293 to 6999 in 2001,
and the period III from run 7000 to 7999 in 2002.

50

Chapter 3. Data Analysis

Figure 3.4: The residual distributions between BDC hit positions and the CDC extrapolated
tracks. The upper ﬁgures show the residuals in the horizontal position at the BDC location,
the lower are in the vertical position.

3.2.4

Gain Calibration of EM Calorimeter

The energy gain of each EM calorimeter was calibrated using the electron data sample. Since
the energy deposit in calorimeters is linear to the momentum of the reconstructed track forelectrons, we adjusted the gain of each segments so that the energy deposit divided by the track
momentum (E/p) became unity. After the track reconstruction, segments of the calorimeters
were associated to the track. Since a distribution of the energy deposit on the calorimeterspreads over a few segments, the pulse heights of the associated segments were summed up if
the diﬀerence between the segment ID and a cross point of the associated track at the segment
location was within ± 2.2, 2.0 and 2.5 segments for RLG, SLG and FLG, respectively. We
calibrated the E/p ratio for the energy sums to be unity iteratively, thus the gain of any single
segment should also be unity. Figure 3.5 shows the scatter plot of the energy deposit versus
the track momentum. The peak positions of the Gaussian ﬁt on the E/p distributions were
adjusted to unity within 4% as shown in the Fig. 3.6.

3.2. Calibration

51










Figure 3.5: The correlation between RLG energy and momentum. The region E/p > 0.5 ischosen for the electron selection.

E/p

E/p

E/p

Figure 3.6: The E/p ratios in all the segments of RLG/SLG/FLG. The segment id is numberedfrom top to bottom PMT, from forward to backward, and from left to right arm. The error
bars only show the statistical errors.

52

3.2.5

Chapter 3. Data Analysis

Slew Correction and Time Zero Calibration of Scintillation
Counters

Since the transmission delays of the signals from the photomultipliers were diﬀerent channels
by channels and they could have some drift during the data taking period, we have chased thestability of the time zeros of all the TDC channels over the runs. We used negative pion toadjust the time zero of all the STC, FTOF and HC counters.
The negative tracks which had geometrically-matched hits in all the scintillation counterswere selected to obtain negative pion tracks. We calculated the hit time of the FTOF counter(TFTOF ) from the measured time (Tmeasure ) by
TFTOF = (Tmeasure − T 0) × Gtime(3.1)

where time zero (T 0) was given temporarily and the time gain (Gtime ) of TDC was measured
for all the channels in advance. We also evaluated the hit time of STC and HC similarly, andwe got the measured ﬂight time between STC and FTOF as TFTOF − TSTC .
We calculated the expected ﬂight time Texp from the momentum p and the ﬂight length L
assuming all the tracks were pion;
Texp =

L,(c × β)√β = p2 /(p2 + Mπ2 ) ,(3.2)

where p and L were obtained by the Runge-Kutta ﬁtting. We adjusted the center of the
distribution of Texp − (TFTOF − TSTC ) within ±50 psec for all the possible hit combinations by
iteratively changing the time zeros (T0 ) of STC and FTOF.
Another important correction for the ﬂight-time measurements was time slewing which wascaused because the timing of crossing the discriminator level√is pulse-height dependent due tothe signal rise-time. We corrected the time slewing with 1/ A, where A is the ADC counts.
The hit time of the STC counter TSTC , for example, were thus obtained by√

TSTC = (Tmeasure − T 0) × Gtime + α/ ASTC ,(3.3)

where α is the slewing-correction parameter. The correlation plot between Texp −(TFTOF −TSTC )and ASTC before the slewing correction on STC is shown in Fig. 3.7(a) (the slewing correction
on FTOF was already done.). The bottom ﬁgure shows
averaged Texp − (TFTOF − TSTC ) as√a function of ASTC with the best ﬁt function of α/ ASTC + T 0. We can see the correlation
is well described with this function. After the slewing correction on STC, the distribution of
Texp − (TFTOF − TSTC ) was improved as shown in Fig. 3.7(b). The pulse height dependenceof the timing was diminished. The slewing correction was done for all the STC and FTOF
segments, and we have achieved the time resolution of 400 psec as shown in Fig. 3.8 for any
combination of the STC and FTOF counters. This value was used in the detector simulation
as the resolution of time of the ﬂight measurements.

3.2. Calibration53[ nsec ]

T exp

(T

FTOF

TSTC )STC ADC counts

T exp[ ADC counts ]

(T

FTOF

TSTC )STC ADC counts[ nsec ][ ADC counts ][ nsec ][nsec]

T exp

(T

FTOF

TSTC ) vs STC ADC counts[ ADC counts ](a) before slewing correction

T exp

(T

FTOF

TSTC ) vs STC ADC counts[ ADC counts ](b) after slewing correction

Figure 3.7: (a)Before the STC slewing correction, the distribution of the time diﬀerence between
the measured time and the expected time is shown at top. The ADC distributions at middle,
and the slewing eﬀect at bottom. (b)As same as (a) but after the STC slewing correction.

        

Figure 3.8: The resolution of the ﬂight time measurements of any combinations between the
STC and FTOF counters after the slewing correction.

54

Chapter 3. Data Analysis

3.3

Event Reconstruction

3.3.1

Track Reconstruction

As described in Chap. 2, CDC had 10 layers of drift cells which were grouped into 3 superlayers. Track candidates were searched using the X and X0 layers in each super-layer. Since wecannot determine whether the drift direction is left or right without track ﬁtting, each hit was
treated as 2 independent hits in both sides of the sense wire. To reduce CPU time for the track
ﬁnding, a hit combination in the X and X0 layers was regarded as a hit pair with the positionat the center of the 2 hits. A hit without an associated hit in the adjacent layer was also kept
as a hit-pair candidate.
All the possible combination of 3 hit-pair candidates over the 3 super-layers was regarded
as a track candidate if the following conditions were satisﬁed:(a) The track candidate included 5 or more hits in the X-X0 layers.
(b) Since the magnetic ﬁeld was almost constant at the location of CDC, a trajectory of acharged particle was approximately a circle in the x-y plane and a straight line in the r-z
plane. The circle which passes over the 3 hit-pair combinations gives the simple track
momentum on the x-y plain. This momentum should be greater than 0.35 GeV/c.
(c) The circle should cross the target region within a distance of 50 mm from either of thecenter, the most upstream or the most downstream target.
(d) The local vector which is determined by the 2 hits in a pair should be consistent with thetangent of this circle within 0.4 radians.
Next, associated hits in the tilt layers were searched for each track candidate. Since there
was a pair of the V-V0 layers in the middle super-layer, hit pairs were made similarly to the
X-X0 layers. The search region of hit points in the tilt layers was limited within the neighboring
5 cells which were determined by the tilt angle of 0.11 radian. The three-dimensional track
candidate required 3 or more hits from the 4 tilt layers. In the X-X0 layers, 5 hits were requiredout of 6 layers. Now the track candidates were ﬁt with a quadratic function in the horizontal
plane and a straight line in the vertical plane.
Track candidates in BDC were searched independently. As least 3 hits out of 4 in the BDC
layers (X, X0 , U, V) were required to form a track segment in BDC. The combination of X and
X0 was only made if they were apart less than a quarter of a cell, otherwise they were treatedas 2 independent hits. Associated U and V hits were required to be in the neighboring 9 cells
from the hit position in the X-X0 plains, which was determined by the tilt angle of 0.11 radian.
If a track segment in BDC has both U and V hits, the vertical heights determined from X-X0 -U
and X-X0 -V combinations were required to be within ± 290 mm.
Then the CDC track was extrapolated to BDC, where we required the horizontal position
matching of ± 1.2 BDC cells and the height (z) matching of 100 mm. The track segments in
BDC were ﬁtted with a linear function with the constraint of the vertical angle given by the
CDC track, and we required the residual of each hit of BDC did not exceed 0.2 BDC cells.
At this point, there were so many track candidates which could not be ﬁtted with the RungeKutta method in limited CPU time. So we selected tracks with the best χ2 of the ﬁtting among
those who shared the same combinations of hits in CDC and BDC cells but with diﬀerent drift
directions.
All the track candidates obtained in CDC with a connection to a BDC track segment were ﬁt
with the Runge-Kutta method to determine the reﬁned momentum and the precise trajectory.
The particle trajectories were traced in a 50 mm step through the magnetic ﬁeld map describedin Sec. 2.3. The Runge-Kutta track tracing started from the surface of a virtual cylinder with

3.3. Event Reconstruction

55

a diameter of 100 mm located at the center of the magnet. The initial starting point and theinitial momentum vector for the minimization were given by the track ﬁnding process. In eachtrace by the Runge-Kutta method, a reduced χ2 was calculated for all the hit along the track.
The χ2 value was minimized with a help of the minimization code MINUIT [65].
Finally, if there were 2 or more track candidates sharing more than 2 common hits in CDC
and BDC, we selected the track candidate with the best χ2 in the Runge-Kutta ﬁtting anddiscarded others. The reduced χ2 distribution of the ﬁnal sample is plotted in Fig. 3.9. We
used the tracks whose reduced χ2 was less than 5 for the later analysis.

Figure 3.9: Reduced χ2 distribution in the Runge-Kutta ﬁtting.

3.3.2

Chamber Eﬃciency and Resolution

Chamber Eﬃciency
We evaluated the each layer eﬃciency, E(layer), deﬁned asE(layer) = Nall /(Nall + Noﬀ (layer)).

(3.4)

Here, Nall denotes the number of tracks having hits in all the layers of the chambers (VTCforward+CDC+BDC or VTC-backward+CDC+BDC) 1 . And Noﬀ (layer) denotes the numberof track missing only one hit in the relevant layer. The results are summarized in Table 3.3.
Chamber Resolution
We evaluated the resolution of each chamber layer as follows.
1. We obtained the chamber residual and the track χ2 /N distribution in the ﬁnal e+ e−sample (shown as DATA in Fig. 3.10).
2. The e+ e− pairs from the φ mesons which were generated by JAM were traced in thedetector simulation using Geant4 as described in Sec. 3.5.
1

The VTC hit candidates were searched from the CDC-BDC tracks, which were obtained from the RungeKutta ﬁt using the CDC and BDC hits as described above. The tracks were extrapolated to VTC, and we
required the horizontal position matching in VTC within ± 1.5 VTC cells. The associated hits, which wererequired 1 or more hits from the 3 layers either in the forward layers or the backward layers, were ﬁtted with
the Runge-Kutta method together with the CDC and BDC hits.

56

Chapter 3. Data Analysis
super layer
VTC backward
VTC forward
CDC inner
CDC middle
CDC outer
BDC

layer
(X,X0 ,X)
(X,X0 ,X)
(X,X0 ,U)(X,X0 ,V,V0 )(U,X,X0 )(X,X0 ,U,V)eﬃciency [%](73.5, 64.7, 52.4)(92.4, 100.0, 93.3)(96.1, 96.8, 90.2)(94.6, 95.7, 94.6, 93.1)(97.2, 95.7, 94.2)(99.0, 99.1, 99.0, 96.8)

Table 3.3: Estimated eﬃciency of each chamber layer.
3. The chamber hits obtained from the simulation were smeared with a double Gaussian
distribution to reproduce the chamber residual and the track χ2 /N distribution in thedata. For the main component of the double Gaussian, we applied an independent width(σ1 ) to each layer. For the second component, which was wider than the main component,
we applied a common width (σ2 ) and a common second/main ratio within a super layer.
4. The simulated hits were reconstructed as same as the real-data analysis, and the hit
residual and the track χ2 /N distribution were obtained (shown as MC in Fig. 3.10).
5. The chamber residual and the track χ2 /N distribution were compared between DATA andMC, and we iteratively adjusted the chamber resolution until MC reproduced DATA.
The typical chamber residual and track χ2 /N distribution for DATA and MC are shown in
Fig. 3.10, and the results are summarized in Table 3.4. Similar procedure was repeated for the
K + K − pairs using Table 3.4, and the results are shown in Fig. 3.11.



[mm](a) chamber residual(b) track χ2 /N

Figure 3.10: The typical chamber residual and track χ2 /N distribution for the data (DATA)
and the tuned detector simulation (MC) in the ﬁnal e+ e− sample.

3.3. Event Reconstruction
super layer
VTC backward
VTC forward
CDC inner
CDC middle
CDC outer
BDC

57
layer
(X,X0 ,X)
(X,X0 ,X)
(X,X0 ,U)(X,X0 ,V,V0 )(U,X,X0 )(X,X0 ,U,V)

σ1 [mm](0.389, 0.394, 0.429)(0.174, 0.212, 0.183)(0.197, 0.203, 0.286)(0.238, 0.217, 0.183, 0.181)(0.285, 0.212, 0.261)(0.292, 0.289, 0.340, 0.261)

σ2 [mm]
0.75
0.75
0.595
0.644
0.718
0.661

ratio
0.37
0.37
0.436
0.367
0.395
0.488

Table 3.4: Estimated resolution of the chamber layers. The values σ1 are the widths for themain component of the double Gaussian distribution, σ2 are those for the second component,and “ratio” are the second/main ratios.



[mm](a) chamber residual(b) track χ2 /N

Figure 3.11: The typical chamber residual and track χ2 /N distribution for the data (DATA)
and the tuned detector simulation (MC) in the ﬁnal K + K − sample.

3.3.3

Mass Scale and Resolution

To evaluate the performance of the spectrometer, the mass resolution was examined for theobserved peaks of Λ → pπ − and K0s → π + π − decays as shown in Fig. 3.12. The observed peakwidths and centroids of the mass spectra were compared with the expectations from a detailed
detector simulation described in Sec. 3.5. In the simulation, the three-momentum distributionsof daughter particles were tuned to reproduce the data. The eﬀects on the invariant mass spectrum caused by multiple scattering and energy loss of particles, the tracking performance withthe chamber resolution, and a miss-alignment of the tracking devices were minutely inspected.
The expected peak position and resolution of Ks0 are 496.9 MeV/c2 and 3.5 MeV/c2 , whereas
the measured peak position was 496.8 ± 0.2 MeV/c2 , with the Gaussian σ of 3.9 ± 0.4 MeV/c2 .
The simulated spectrum reproduces the data almost perfectly as shown in Fig. 3.12. Note thatthe non-Gaussian shape of the Λ peak is well reproduced with the simulated shape 2 .
2When we ﬁt the shape by a Gaussian only around the peak, the expected peak position and Gaussian σ
are 1115.52 MeV/c2 and 1.63 MeV/c2 , whereas the obtained values were 1115.62 ± 0.02 MeV/c2 and 1.78 ±0.04 MeV/c2 .

58

Chapter 3. Data Analysis[GeV/c2][GeV/c ]2(a) Λ → pπ −(b) K0s → π + π −Figure 3.12: (a) Invariant Mass spectrum of p π − showing the Λ peak. The curve is the ﬁt
result with the simulated mass shape over a linear background. (b) Invariant Mass spectrumof π + π − showing the K0s peak. The curve is the ﬁt result with the simulated shape over aquadratic background.

3.3.4

Vertex Reconstruction

The vertex point of the interaction in each event was determined by minimizing S, the weighted
quadratic sum of the distances from the vertex to each track, which was deﬁned as;
S=(

Nt
∑

[(djx /σx )2 + (djy /σy )2 + (djz /σz )2 ])/(3Nt − 4),

(3.5)

j=1

where Nt is the number of the tracks, dij (i=x, y, z) is the distance between the vertex point andthe nearest point of the j-th track in each axis, and the weight σi represents the error in the
track-vertex determination in each axis. The weights σi were determined as σx = 1.14 mm,
σy = 1.80 mm, and σz = 7.15 mm. We examined the quality of the determined vertex byrequiring the equation below to be satisﬁed to each track-j.
(djx /3σx )2 + (djy /3σy )2 + (djz /3σz )2 < 1.0.

(3.6)

We discarded tracks which did not satisfy this requirement, and re-determined the vertex fromthe remained tracks by repeating the same procedure. We determined the spatial points withthe minimum S with use of MINUIT [65].
The reconstructed vertex distributions for double-arm e+ e− events are shown in Fig. 3.13.
The obtained target positions and the vertex resolution are listed in Table 3.5. We required
the vertex to be inside the rectangles shown in Fig. 3.13 in the x-y plane which corresponded
to 3 σ cuts, and in the vertical (z) axis within 3 σz . The reconstructed vertex distributions for
single-arm K + K − events are also shown in Fig. 3.14. When the two tracks were in the samearm, the accuracy of the vertex point determinations got worse due to a narrow opening angle
between the two tracks. So we used the target-image distribution viewed from the directionof the kaon arm as shown in Fig. 3.14(b). We required the vertex to be inside the rectangles
shown in Fig. 3.14(b) in the x-y plane, and in the vertical (z) axis within ± 10 mm.

59

y[mm]

y[mm]

3.3. Event Reconstruction

2001_vertex_xy

x[mm]2002_vertex_xy

x[mm]2001_vertex_x[mm]

2002_vertex_x[mm]Figure 3.13: Vertex distribution for double-arm e+ e− events in 2001 (left) and 2002 (right).
Vertex distribution in the xy-plane (upper) and the projection in the x-axis (lower). The
indicated rectangles in the upper ﬁgure are the cut regions for the vertex position in the x-yplane.

year
targetx [mm]y [mm]z [mm]
σ x [mm]
σ y [mm]σ z [mm]

2001
Cu1
C
−47.04 −0.14
3.18 4.03
0.61 0.62
3.73 3.48
3.24 3.74
3.68 3.70

Cu2
45.46
4.91
0.67
2.71
2.41
3.14

2002
Cu1
Cu2
C
−48.03 −23.41 0.17
0.89
1.31 1.72
0.55
0.54 0.52
3.21
3.35 3.20
1.93
2.27 1.97
4.33
4.54 3.85

Cu3
24.6
2.22
0.54
1.98
2.94
3.98

Cu4
44.21
2.57
0.57
2.01
2.61
3.74

Table 3.5: The mean values (target position) and precisions of the vertex determination for
double-arm e+ e− events.

x [mm]vertex xy(a)x [mm]

vertex xy (L-arm)

x [mm]

vertex x

y [mm]y [mm]

Chapter 3. Data Analysis

y [mm]

60x [mm]

vertex xy (R-arm)

[mm]

[mm]

vertex projection xy (L-arm) vertex projection xy (R-arm)(b)

Figure 3.14: Vertex distribution for single-arm K + K − events in 2001. (a)Vertex distribution
in the xy-plane (upper) and the projection in the x-axis (lower). (b)Vertex distribution in thexy-plane (upper) and the projection in the direction of the corresponding arm (lower). The left
ﬁgure is for left arm events, the right ﬁgure is for right arm events. The indicated rectangles
in the upper ﬁgure are the cut regions for the vertex position in the x-y plane.
For the ﬁnal e+ e− and K + K − pair tracks, we repeated the Runge-Kutta ﬁt procedure, which
was named as “Common Vertex Track Fitting”, by requiring that both tracks were originatedfrom the same point of particular target plate determined as described above. The x positions(beam direction) of the targets were ﬁxed to the measured values on Table 3.5. In this ﬁt, we
minimized the quadratic sum of residuals at all the hit layers of the chambers and residuals at
the vertex point from the nominal beam position in the y and z directions. The weights forthe vertex position in the y and z directions were set to be the one standard deviation of thebeam size, 1.59 mm in 2001 and 0.83 mm in 2002, which was described in Sec. 2.4.2. Since thebeam size was measured only in the y direction, we assumed that the size in the z direction wassame as that in the y direction. This procedure improved the mass resolution for e+ e− events
1.5 times, and for K + K − events 1.2 times.

3.3. Event Reconstruction

3.3.5

61

Electron Identiﬁcation

The electron identiﬁcation was performed with 2 or 3 stages of the iso-butane-ﬁlled gasČerenkov counters and the lead-glass EM calorimeters in the momentum range from 0.4 to
2.7 GeV/c. The lower limit is determined by the trigger condition in which a geometricalmatching of 2 stages of the electron ID counters was required. The upper limit is the momentum where pions started to produce Čerenkov light in iso-butane. The observed momentum
distributions of electrons and positrons are shown in Fig. 3.15.
The horizontal position matching between the Runge-Kutta tracks and the electron identiﬁcation counters is shown in Fig. 3.16. We deﬁned the matching window to be within±1.0 counter size for all the counters.

+ 

(GeV/c)(GeV/c)+  (GeV/c) (GeV/c)Figure 3.15: The momentum distributions of electrons in the ﬁnal sample. The upper ﬁgures
are for e+ and the lower ﬁgures are for e− . The left ﬁgure is for the C targets and the rightﬁgure is for the Cu targets.

62

Chapter 3. Data Analysis

FGC

RGC

[segment][segment]

RLG

SLG

[segment][segment]

FLG[segment]

Figure 3.16: Horizontal matching between electron tracks and electron-counter hits in the ﬁnal
e+ e− sample. The arrows indicate the region for the electron selection, and the x coordinate isin a unit of the counter size.

Electron Identiﬁcation with Gas Čerenkov Counters
For FGC, the horizontal matching was examined at r = 1200 mm. We required that ADC sums
from the top and the bottom photomultipliers to exceed 200 channels. The gain of FGC wascalibrated using the ADC distribution. We required the time diﬀerence between the measured
TOF value (TFGC − TSTC ) and the expected TOF value (Texp ) to be within ± 10 ns, as shownin Fig. 3.17. Since the vertical acceptance of FGC is ±0.4 radian, we required the dip angle ofthe track to be within ±0.45 radian.
For RGC, the horizontal position matching was examined at r = 2105 mm as shown in
Fig. 3.16. The RGC hit was deﬁned when the ADC sum from the top and the bottom photomultipliers of the associated segments exceeded 50 channels, which corresponds to about one
photo-electron. The time diﬀerence was required to be within ± 10 ns, as FGC. Since thevertical acceptance of RGC is ±0.1 radian, we required the dip angle of the track to be within±0.15 radian.

3.3. Event Reconstruction

63

FGC

[nsec]

RLG[nsec]

RGC[nsec]

SLG[nsec]

Figure 3.17: The time diﬀerence between the measured TOF value (Tcounter − TSTC ) and the
expected TOF value (Texp ). The arrows indicate the region for the electron selection.

Electron Identiﬁcation with Lead Glass Calorimeters
The tracks were selected as an electron in RLG, SLG or FLG when the sum of the energies
from the horizontally-associated three segments exceeded 0.3 GeV and the energy over the
momentum (E/p) was greater than 0.5, as shown Fig. 3.18.
The time diﬀerence between the measured TOF value (TRLG − TSTC ) and the expected TOF
value (Texp ) to be within ± 10 ns. For SLG, the time diﬀerence was required to be within ±20 ns. Since the vertical acceptance of RLG is 270 mm < z < 880 mm and –880 mm < z <–270 mm from the beam line as shown in Fig. 2.2, we required the vertical position of the trackat RLG, at r = 1730 mm, to be in the range from ±170 mm to ±980 mm, including 100 mm
as a margin. Similarly, the vertical position of the track was required to be in the range from–575 mm to +575 mm for FLG, since the vertical acceptance of FLG is from –475 mm to+475 mm. The dip angle of the track which was associated to SLG was required to be within± 0.45 radian.

64

Chapter 3. Data Analysis










Figure 3.18: The correlation between RLG energy and momentum. The region E/p > 0.5 ischosen for the electron selection.

Eﬃciency of Electron Identiﬁcation
To evaluate the eﬃciency of the electron identiﬁcation, we used a pure electron sample extracted
γ-conversion and Dalitz decay electrons in the data. To eliminate the trigger-bias, the following
procedure was taken. At ﬁrst, one e+ track and one e− track which satisﬁed the triggeredcondition were excluded. If there were two or more e+ or e− tracks which satisﬁed the trigger
condition in the same event, one of them was randomly selected and excluded as the trigger
particle. For the remaining tracks, we required that they had a partner track with which the
opening angle was less than 0.01 radian and the invariant mass was less than 0.01 GeV/c2 ,to ensure that they were originated from Dalitz decays or γ-conversions. The opening angle
and the invariant mass distributions of those no-bias electrons are shown in Fig. 3.19(a) and(b), respectively. Electrons from γ-conversions and Dalitz decays appear as a clear peak at azero mass. Using these no-bias electrons, the electron identiﬁcation eﬃciencies were obtained.
Figure 3.20 shows energy-momentum correlation of the pure electron sample.
The electron identiﬁcation eﬃciency as a function of the momentum of pure electrons isshown in Fig. 3.21. The eﬃciency curves were ﬁtted with a phenomenological function;f = a − b/pc ,(3.7)

where a, b, c are the ﬁt parameters, and p is the momentum of electrons. The obtained parameters are listed in Table 3.6(a) and the curves are plotted in Fig. 3.21. These eﬃciency functions
were used in the detector simulation to take into account an eﬀect of the electron identiﬁcationeﬃciency. For single electron tracks in the ﬁnal e+ e− sample, the averaged eﬃciencies including
the oﬀ-line cuts were summarized in Table 3.6(b). Using the detector simulation (see Sec. 3.5),
the eﬃciency for φ → e+ e− decays was estimated to be 33%.

65

2

counts/[2.5MeV/c ]counts/[0.0025rad]3.3. Event Reconstruction

4000
3500
3000

9000
8000
7000
6000

2500

5000
2000
4000
1500

3000

1000

2000

500
0

1000
0

0.02

0.04

0.06
0.08
0.1
e e- opening angle [rad]0+(a) opening angle distribution

0

0.02

0.04
0.06
0.08
0.1
e+ e- Invariant Mass [GeV/c2](b) invariant mass distribution

Energy [GeV/c2]

Figure 3.19: (a)The opening angle distribution of the pure electron candidates. The region lower
than the arrow was used to select pure electrons. (b)Invariant mass distribution of electron
pair in the low mass region. The region lower than the arrow was used to select pure electrons.

1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

0

0.5

1

1.5
Momentum [GeV/c]

Figure 3.20: The correlation between RLG energy and momentum for the pure electron sample.
The solid lines show the region for the electron identiﬁcation.

66

Chapter 3. Data Analysis

FGC

RGC

momentum [GeV/c]momentum [GeV/c]

RLG

SLG

momentum [GeV/c]momentum [GeV/c]

FLG

momentum [GeV/c]

Figure 3.21: The electron identiﬁcation eﬃciency as a function of track momentum.

(a) Parameters of the eﬃciency curve(b) Averaged eﬃciencies

counter
FGC
RGC
RLG
SLG
FLG

counter
FGC
RGC
RLG
SLG
FLG

a
b
c
0.782 0.078 1.129
0.752
0
0
0.933 0.006 3.770
0.982 0.041 2.527
0.922
0
0

eﬃciency(%)
66±1
75±1
88±1
74±2
92±1

Table 3.6: (a)The parameters of the eﬃciency curves for the electron identiﬁcation counters.
The parameter b and c were ﬁxed to zero for RGC and FLG. (b)The averaged eﬃciencies
including the oﬀ-line cuts for single electron tracks in the ﬁnal e+ e− sample.

3.3. Event Reconstruction

67

Other Cut for e+ e− Pairs
If there were three or more electron tracks in an event, such an event was excluded from theﬁnal e+ e− sample. This selection eﬀectively works as Dalitz decay and γ-conversion rejection.
The amount of the eliminated events was 7% of the ﬁnal e+ e− sample.

3.3.6

Kaon Identiﬁcation

Kaon identiﬁcation was performed using the particle mass calculated from the ﬂight time measurements and the momentum analysis, helped by the pion veto with the aerogel Čerenkov
counters. To determine the ﬂight time, tracks were required to have an associated hit in STC,
HC and FTOF. The horizontal and vertical position matching of counter hits to the RungeKutta tracks were shown in Fig. 3.22 and 3.23, respectively. The vertical position of the counter
hit was obtained by the timing diﬀerence between the top and bottom TDC’s. Since the refractive index of the aerogel was 1.034, the threshold for pions was 0.53GeV/c and for kaons was
1.88GeV/c. In the following analysis, a cut for the highest momentum was set at 1.9 GeV/c.
The observed momentum distributions of kaon are shown in Fig. 3.24.

STC[segment]HC[segment]

FTOF[segment]

Figure 3.22: Horizontal matching between kaon tracks and the kaon identiﬁcation countersin the ﬁnal K + K − sample. The arrows indicate the region for the kaon selection, and the xcoordinate is in a unit of the counter size. (The ﬁgures are shown after the matching cuts wereapplied.)68

Chapter 3. Data Analysis

track-z(mm)HC

HC

HC-z(nsec)

(mm)

FTOF

FTOF

track-z(mm)FTOF-z(nsec)(mm)

Figure 3.23: Vertical matching between kaon tracks and diﬀerential timings of two PMT’s in
the kaon identiﬁcation counters in the ﬁnal K + K − sample. The right ﬁgures show projection
along the correlation line of the left ﬁgures. The indicated rectangles in the left ﬁgures and thearrows in the right ﬁgures are the cut regions for the matching.

+ 

+ 


(GeV/c)







(GeV/c)(GeV/c)

(GeV/c)Figure 3.24: The momentum distributions of kaons in the ﬁnal sample. The upper ﬁgures arefor K+ and the lower ﬁgures are for K− . The left ﬁgures are for the C target and the rightﬁgures are for the Cu targets.

3.3. Event Reconstruction

69

Particle Identiﬁcation with Particle Mass
The mass square (M2 ) of a particle is obtained as
M 2 = p2 ×

(1 − β 2 )
,
β2

(3.8)

with

L
,
(3.9)
T ×c
where p is a momentum of the particle, T and L are the ﬂight time and the ﬂight length between
STC and FTOF respectively, and c is the light velocity. The resolution of the squared mass(σM 2 ) is represented as
β=

4
2
σM
2 = 4M (σp 2
σTOF 2) + 4c2 p2 (p2 + M 2 )(),
p
L

(3.10)

momentum [GeV/c]momentum [GeV/c]

where σp is the resolution of the momentum, and σTOF is the resolution of the time of the ﬂight
measurements. For kaons with 1GeV/c of momentum, the error contribution from the second
term is ﬁfty times larger than that from the ﬁrst term, so the error for the mass measurements
is almost described with σTOF . The distributions of the momentum versus squared-mass areshown in Fig. 3.25.

squared-mass [(GeV/c ) ]2 2(a) + chargesquared-mass [(GeV/c ) ]2 2(b) – charge

Figure 3.25: The distributions of the momentum versus squared-mass for (a) positive and (b)negative particles, after the AC veto is applied. The indicated regions are the selected regions
for the kaon identiﬁcation.
To select kaons we assumed that all the particles had the kaon mass, and the expected ﬂight
time was calculated from the momentum and the ﬂight length between STC and FTOF. We
required the time diﬀerence between the expected time and the measured time to be less than
1.2 nsec which corresponds to ±3σTOF . Additionally, the cut was set on the squared mass from0.04 to 0.49 (GeV/c2 )2 , and the momentum was required to be less than 1.9 GeV/c. The kaon
identiﬁcation regions are shown in Fig. 3.25.
The purity of the kaon candidates in the ﬁnal sample was obtained as described below.
Since σM 2 is a function of momentum, we obtained the momentum-sliced M2 distributions from
Fig. 3.25, and each M2 distribution was ﬁtted by three peaks, pion, kaon and proton using a

70

Chapter 3. Data Analysis

double Gaussian distribution. We ﬁxed the centroid of pion mass to the value which determinedin counter calibration, and ﬁxed the main component of σM 2 of kaon to the evaluated values
from Eq. 3.10 using the obtained σTOF and the simulated σp as described in Sec. 3.5.3 for each
M2 distribution. Thus for the ﬁt, free parameters were the centroids of kaon and proton, andthe two widths of double Gaussian for pion and proton, and the second component width forkaon. Examples of the sliced M2 distributions and the ﬁt results are shown in Fig. 3.26 (theothers are shown in Appendix A). By summing the background over the sliced M2 distributions,the purity of the kaon candidates is obtained as Table 3.7.
In the detector simulation for φ → K + K − (see Sec. 3.5), the ﬂight time is smeared withσTOF and the above cuts were applied. We found that the eﬃciency for the squared-mass cut
was estimated to be 87% for φ → K + K − decays.
0.8<p<1.0

0.8<p<1.0

squared-mass [(GeV/c ) ]squared-mass [(GeV/c ) ]2 2(a) + charge

2 2(b) – charge

Figure 3.26: The distributions of the squared-mass, when the momentum from 0.8 to 1.0 GeV/c
is selected. The distributions were ﬁtted with a sum of double-Gaussian distributions. Thelines indicate the approximate region for the kaon selection.

+

KK−
K +K −

purity(%)
93.4 ± 3.4(stat) ± 0.6(syst)
91.7 ± 3.7(stat) ± 0.5(syst)
85.6 ± 4.7(stat) ± 0.7(syst)

Table 3.7: The kaon purity of the ﬁnal sample.

Particle Identiﬁcation with Aerogel Čerenkov Counters
We have examined the performance of the aerogel Čerenkov counters (AC) using the data
triggered by requiring any two charged particles.
The horizontal position matching of AC to the Runge-Kutta tracks is shown in Fig. 3.27(a).
Since a cross talk over the aerogel segments occurred due to the segmentation, the cut region forthe matching became broader than the scintillation counters. The AC was considered to havea hit when the ADC sum from the top and bottom photomultipliers of the track-associatedsegments exceeded 0.5-photoelectron level and the discriminator signal gave a good timing as

3.3. Event Reconstruction

71[segment](a) Horizontal matching[nsec](b) Hit-timing diﬀerence

Figure 3.27: (a) Horizontal matching between pion tracks and AC hits in the pion sample. (Theﬁgures are shown after the matching cuts were applied.) (b) Hit-timing diﬀerence between AC
and associated FTOF counters. The arrows indicate the cut regions for the AC hit.

shown in Fig. 3.27(b). It should be noted that the input signals to the discriminators forthe on-line trigger was also a linear sum of the top and bottom photomultiplier-outputs. The
summed signal was discriminated at also 0.5-photoelectron level.
The correlations between the vertical positions of the Runge-Kutta tracks and the asymmetries of the ADC counts of the top and bottom photomultipliers are shown in Fig. 3.28. The
asymmetry A was deﬁned asΣAtop − ΣAbottomA=,(3.11)
ΣAtop + ΣAbottom
where Atop (Abottom ) is the ADC counts of the top (bottom) photomultiplier and the summation
was made over the phototubes which satisﬁed the position matching criteria and the timing requirement. The region indicated in Fig. 3.28(a) corresponds to particles which radiate Čerenkov
photons. Since Čerenkov angle for β=1 particles is 0.257 radian, the tracks whose vertical position was within ±120 mm from the center made hits in both top and bottom photomultipliers.
The same plot for protons does not show such correlation as can be seen in Fig. 3.28(b).
When we apply the regions in Fig 3.28 as the deﬁnition of track associated AC hits, theAC eﬃciency for pions and protons as a function of the momentum can be obtained as shownin Fig. 3.29. For particles with a momentum greater than 1.0 GeV/c, the vertical position
dependence of the AC eﬃciency is plotted in Fig. 3.30, (a) for pions and (b) for protons.

AC ADC Top/Bottom Asymmetry

Chapter 3. Data Analysis

AC ADC Top/Bottom Asymmetry72

track vertical position at AC [mm]track vertical position at AC [mm](a) pion(b) proton

efficiency

efficiency

Figure 3.28: Correlation between the track vertical position and the asymmetry of the top andbottom photomultipliers of AC.

pion momentum [GeV/c](a) pion

proton momentum [GeV/c](b) proton

Figure 3.29: The momentum dependence of the AC eﬃciencies, (a) for pions and (b) for protons.

73

efficiency

efficiency

3.3. Event Reconstruction

track vertical position [mm](a) piontrack vertical position [mm](b) proton

Figure 3.30: The vertical position dependence of the AC eﬃciencies, (a) for pions whose momentum was larger than 1.0 GeV/c and (b) for protons

Other Cut for K + K − Pairs
We required the K + K − track pairs not to share the common hit in a FTOF segment and inHC, because these tracks possibly had a wrong hit timing and a wrong vertical position. We
also eliminated events which contained three or more kaon tracks in a same event, and theamount of the eliminated events was 5%.

74

Chapter 3. Data Analysis

3.4

Reconstructed Invariant Mass Spectra

3.4.1

e+ e− Invariant Mass Spectra

We deﬁned e+ e− pairs with a positron coming into the left arm and a electron coming into theright arm as LR events, and pairs with the opposite pattern as RL events, as shown in Fig. 3.31.
 








X



Y

.Z

Figure 3.31: The deﬁnition of LR (blue) and RL (red) event.
The invariant mass spectra of the ﬁnal e+ e− sample are shown in Fig. 3.32. The ﬁgure
contains the LR and RL events and the 2001 and 2002 data. The invariant mass spectra
divided into the LR and RL events are shown in Fig. 3.33, and the spectra in the mass region
from 0.85 to 1.2 GeV/c2 are shown in Fig. 3.34. For reference, Fig. 3.35 shows the invariant
mass spectra divided into each target disk, and Fig. 3.36 shows their close up views for the φmeson peak. Because e+ e− events were requested to be a double-arm event by the trigger logic,
the low-mass regions of the spectra are largely suppressed. The suppressions of the low-mass
regions in the RL events are larger than those in the LR events, whereas diﬀerences in mass
spectra are small in each target.

3.4. Reconstructed Invariant Mass Spectra

75

events [/10MeV/c2]

events [/10MeV/c2]C

Cue e Invariant Mass [GeV/c ]+ -2e e Invariant Mass [GeV/c ]+ -2Figure 3.32: The e+ e− invariant mass spectra of the ﬁnal data sample for the carbon targets(left) and for the copper targets (right).

76

Chapter 3. Data Analysis

events [/10MeV/c2]

events [/10MeV/c2]C

Cue e Invariant Mass [GeV/c ]+ -e e Invariant Mass [GeV/c ]

2

+ -

2

Figure 3.33: The e+ e− invariant mass spectra. The spectra of the LR events and the RL events
are shown separately.

events [/10MeV/c2]

events [/10MeV/c2]C

Cue e Invariant Mass [GeV/c ]+ -2e e Invariant Mass [GeV/c ]+ -2Figure 3.34: The e+ e− invariant mass spectra, close up views of Fig. 3.32 and 3.33 to the φmeson peak.

3.4. Reconstructed Invariant Mass Spectra

events [/10MeV/c2]

77

events [/10MeV/c2]

events [/10MeV/c2]

2001
Cu1

e e Invariant Mass [GeV/c ]
+ -

2001
Cu2

e e Invariant Mass [GeV/c ]2events [/10MeV/c2]

+ -

+ -

2002
C

e e Invariant Mass [GeV/c ]
+ -

+ -

2002
Cu3

e e Invariant Mass [GeV/c ]2events [/10MeV/c2]

2

events [/10MeV/c2]

2002
Cu2

2

e e Invariant Mass [GeV/c ]2events [/10MeV/c2]

2002
Cu1

e e Invariant Mass [GeV/c ]2001
Cu_alle e Invariant Mass [GeV/c ]2events [/10MeV/c2]+ -events [/10MeV/c2]

2001
C

+ -

e e Invariant Mass [GeV/c ]

2

+ -

2

events [/10MeV/c2]

2002
Cu4

2002
Cu_alle e Invariant Mass [GeV/c ]+ -e e Invariant Mass [GeV/c ]

2

+ -

2

Figure 3.35: The e+ e− invariant mass spectra divided into each target disk.

events [/10MeV/c2]

events [/10MeV/c2]

events [/10MeV/c2]

2001
Cu1

e e Invariant Mass [GeV/c ]
+ -

2001
Cu2

e e Invariant Mass [GeV/c ]2events [/10MeV/c2]

+ -

+ -

2002
C

e e Invariant Mass [GeV/c ]
+ -

+ -

2002
Cu3

e e Invariant Mass [GeV/c ]2events [/10MeV/c2]

2

events [/10MeV/c2]

2002
Cu2

2

e e Invariant Mass [GeV/c ]2events [/10MeV/c2]

2002
Cu1

e e Invariant Mass [GeV/c ]2001
Cu_alle e Invariant Mass [GeV/c ]2events [/10MeV/c2]+ -events [/10MeV/c2]

2001
C

+ -

2

e e Invariant Mass [GeV/c ]+ -2events [/10MeV/c2]

2002
Cu4

2002
Cu_alle e Invariant Mass [GeV/c ]+ -2e e Invariant Mass [GeV/c ]+ -2Figure 3.36: The e+ e− invariant mass spectra, close up views of Fig. 3.35 to the φ meson peak.

78

Chapter 3. Data Analysis

3.4.2

K + K − Invariant Mass Spectra

In the K + K − channel, the events were required to have K + and K − tracks in a same arm
because of the small Q value in the φ → K + K − decays. The invariant mass spectra of the ﬁnal
K + K − sample are shown in Fig. 3.37 for the carbon and copper targets. The spectra divided
into each target disk are shown in Fig. 3.38, and Fig. 3.39 shows the spectra divided into the
L and R arm events. Diﬀerences in mass spectra are small in each target and arm.
events [/4MeV/c2]

events [/4MeV/c2]

CCu

K K Invariant Mass [GeV/c ]+-2

K K Invariant Mass [GeV/c ]+-Figure 3.37: The K + K − invariant mass spectra for C (left) and Cu (right) targets.

2

3.4. Reconstructed Invariant Mass Spectra

79

events [/4MeV/c2]

events [/4MeV/c2]

Cu1

C

K K Invariant Mass [GeV/c ]+-K K Invariant Mass [GeV/c ]2events [/4MeV/c2]

+

-

2

events [/4MeV/c2]

Cu2

Cu_allK K Invariant Mass [GeV/c ]+-K K Invariant Mass [GeV/c ]

2

+

-

2

Figure 3.38: The K + K − invariant mass spectra divided into each target disk.

events [/4MeV/c2]

events [/4MeV/c2]

events [/4MeV/c2]

Cu1
L arm

K K Invariant Mass [GeV/c ]
+

-

Cu2
L arm

K K Invariant Mass [GeV/c ]2events [/4MeV/c2]

+

-

-

+

-

-

-

Cu2
R arm

K K Invariant Mass [GeV/c ]
+

+

2

2

events [/4MeV/c2]

C
R arm

2

K K Invariant Mass [GeV/c ]2events [/4MeV/c2]

Cu1
R arm

K K Invariant Mass [GeV/c ]Cu_allL arm

K K Invariant Mass [GeV/c ]2events [/4MeV/c2]+

events [/4MeV/c2]

C
L arm

Cu_allR arm

K K Invariant Mass [GeV/c ]+-2

K K Invariant Mass [GeV/c ]+-Figure 3.39: The K + K − invariant mass spectra divided into the L and R arm events.

2

80

3.5

Chapter 3. Data Analysis

Detector Simulation for φ

The detailed detector simulation was performed using Geant4.5.1.p01 toolkit [62] to evaluate all
the detector eﬀects, such as energy loss of particles, external bremsstrahlung, multiple scattering, detector acceptance, and the tracking performance with the chamber position resolution.
To reproduce precisely those eﬀects on a passage of particles through the detector materials,
we implemented the all detector components from the targets to BDC’s with the materials
listed in Table 2.2. It should be noted that all chamber wires, which included sense, potential,
and guard wires, were implemented as they were in the simulation. However, materials behind
BDC’s were neglected in the simulation, since the determination of the track momentum was
performed with CDC and BDC’s.

Figure 3.40: The E325 spectrometer implemented in the detector simulation using Geant4
toolkit.
Charged particles were traced in the magnetic ﬁeld, and chamber and counter hits were generated according to the measured eﬃciencies. The chamber hits were smeared with the position
resolution as described in Sec. 3.3.2. For e+ e− pairs, the functions of counter eﬃciency wereapplied to each track as described in Sec. 3.3.5. For K + K − pairs, (TFTOF − TSTC ) were smearedwith the overall TOF resolution as described in Sec. 3.2.5. The tracks were reconstructed andthe cuts were applied to the reconstructed tracks as same as the real-data analysis.

3.5.1

φ → e+ e− Simulation

Spectral Shape of φ → e+ e−
The spectral shape of φ → e+ e− was generated using the non-relativistic Breit-Wigner distribution
Γ2tot /4
BW (m) =,(3.12)(m − m0 )2 + Γ2tot /4
with the pole mass m0 of 1019.456 MeV/c2 and the total decay width Γtot of 4.26 MeV/c2 [7].
We compared the non-relativistic Breit-Wigner distribution with the relativistic BreitWigner distribution which is given bymm0 Γee (m)
dσ
=
,
2
2
dm
(m − m20 ) + (m0 Γtot (m))2(3.13)

3.5. Detector Simulation for φ

81

where

(

/

√

/

Γtot (m) = Γtot q tot q0tot
q tot =

(m0 /m) ,(3.14)

m2 4 − m2K ,√q0tot =

)3

(3.15)/

m20 4 − m2K ,(3.16)

Γee (m) = Γee (q ee /q0ee )3 (m0 /m) ,√q ee =/

m2 4 − m2e ,√q0ee =(3.17)(3.18)/

m20 4 − m2e ,(3.19)

with the partial decay width of φ → e+ e− , Γee [66]. Since a diﬀerence between the nonrelativistic and the relativistic Breit-Wigner distribution in φ → e+ e− is negligible as shown in
Fig. 3.41, we used the non-relativistic Breit-Wigner distribution in the φ → e+ e− simulation.



e+e-

mass [MeV/c2]

mass [MeV/c ]2

Figure 3.41: The non-relativistic (red) and the relativistic (blue) Breit-Wigner distributions forthe φ → e+ e− decays. The distributions are normalized by their peak count to unity.

Kinematical Distribution
In the simulation, φ mesons were generated using the nuclear cascade code JAM 1.011.00 [63].
Only three momenta of generated mesons were obtained by JAM and the mass distribution
was forced to have the Breit-Wigner. The kinematical distributions of the generated φ’s areshown in Fig. 3.42 together with those in detector acceptance, and the diﬀerences between the
C and Cu target are compared in Fig. 3.43.
The generated φ mesons were forced to decay into e+ e− , and the daughter particles weretraced in the detector simulation using Geant4. The angular distribution of vector-meson decay
into e+ e− was considered to be isotropic, i.e. no alignment exists in produced mesons. This
assumption was supported by the fact that the observed decay angular distribution was well
reproduced with the simulation as shown in Fig. 3.44. The momentum distributions of electronsand positrons are also shown in Fig. 3.45.

82

Chapter 3. Data Analysis

The observed and simulated distributions of φ mesons are compared in Fig. 3.46 and 3.47.
The observed distributions were obtained by subtracting the background distribution fromthat of the signal region from 0.99 to 1.04 GeV/c2 as shown in Fig. 3.48. The background
distributions were obtained as an average of the region from 0.94 to 0.99 GeV/c2 (left side) andthe region from 1.04 to 1.09 GeV/c2 (right side). The observed kinematical distributions areagain well reproduced with the simulated ones.



rapidity
pT

pT

rapidity

rapiditypT

pT vs. rapidity

rapidity

pT

(a) C

pT vs. rapidity(b) CuFigure 3.42: The kinematical distributions of the generated φ mesons using JAM (black lines)
and for the accepted φ → e+ e− in the detector (red lines).



rapiditypT

Figure 3.43: The kinematical distributions of the generated φ mesons for C (black lines) andCu (red lines), normalized with the number of entries.

3.5. Detector Simulation for φ

83

Cu

C

cos

Cu

C

cos

cos

Cu

C

Cu

C

angle [rad]angle [rad]cosangle [rad]angle [rad](a) the Gottfried-Jackson frame(b) the helicity frame 

 

−# "$ % #  "!

+(c) the Gottfried-Jackson frame−

# "$ % #  "!
θ

&&'

φ&'(




θ



φ



+

(d) the helicity frame

Figure 3.44: The decay angular distributions for the data (closed circles) and the simulation(lines), (a) in the Gottfried-Jackson frame and (b) in the helicity frame. The LR and RL events
are summed. The scaling is determined arbitrarily. (c) In the Gottfried-Jackson frame, z-axis
parallel to the beam direction in the φ rest frame. (d) In the helicity frame, z-axis parallel tothe φ direction in the center-of-mass frame.

84

Chapter 3. Data Analysis

momentum [GeV/c]px

momentum [GeV/c]pz

momentum [GeV/c]py

momentum [GeV/c]p(a) e+ in φ → e+ e− for C

momentum [GeV/c]px

momentum [GeV/c]pz(c) e− in φ → e+ e− for C

momentum [GeV/c]px

momentum [GeV/c]pz

momentum [GeV/c]py

momentum [GeV/c]p(b) e+ in φ → e+ e− for Cu

momentum [GeV/c]py

momentum [GeV/c]pmomentum [GeV/c]px

momentum [GeV/c]pz

momentum [GeV/c]py

momentum [GeV/c]p(d) e− in φ → e+ e− for Cu

Figure 3.45: The momentum distributions of the observed (closed circles) and simulated (lines)
daughter e+ (upper panels) and e− (bottom panels) in the φ → e+ e− decays, for C (left panels)
and for Cu (right panels). The LR and RL events are summed. The scaling is determined
arbitrarily.

3.5. Detector Simulation for φ

85





rapidity
pT

pT

rapidity

rapiditypT

pT vs. rapidity

rapiditypT(a) φ → e+ e− for C

pT vs. rapidity(b) φ → e+ e− for Cu

Figure 3.46: The kinematical distributions of the observed (closed circles) and simulated (lines)
φ → e+ e− pairs, for C (left four panels) and for Cu (right four panels). In the scatter plots ofpT versus rapidity, only the observed events are shown. The LR and RL events are summed.
The scaling is determined arbitrarily.



rapidity
pT

pT

rapidity

rapiditypT

pT vs. rapidity(a) φ → e+ e− for C

rapiditypT

pT vs. rapidity(b) φ → e+ e− for Cu

Figure 3.47: The kinematical distributions of the observed (closed circles) and simulated (lines)
φ → e+ e− as Fig. 3.46. Here the LR and RL events are represented in red and blue, respectively.
The scaling is determined arbitrarily, but the ratio of the number of LR events to RL events is
not changed in the data and the simulation.

86

Chapter 3. Data Analysis

C

+ -

2

e e Invariant Mass [GeV/c ]Figure 3.48: The separation of the signal region and the side-band (background) regions.

Internal Radiative Eﬀects and Expected Mass ShapeThe mass spectrum of φ → e+ e− is deformed by the internal radiative eﬀects like internalbremsstrahlung, vertex correction, vacuum polarization, etc. As a result, only the eﬀect of the“internal bremsstrahlung” is only signiﬁcant and other eﬀects discussed as follows are neglected
to evaluate the mass shape of φ → e+ e− . Here, the “internal bremsstrahlung“ is including thecancellation by the vertex correction, of course.
• Internal Bremsstrahlung
The internal bremsstrahlung is expressed by the Feynman diagram in Fig. 3.49, which is aprocess in next to the leading order. It has an infrared divergence, but the divergence cancels
with the vertex correction term as described later.
e



V

e
Final State Radiation

Figure 3.49: Internal bremsstrahlung in V → e+ e− decays.
According to Ref. [67], the invariant mass shape of V → e+ e− are deformed as shown in
Fig. 3.50, which was calculated by using the Eq. (14) in Ref. [67];(αm4
1 dΓ (V → l+ l− γ)
2m
=
1
+
Γ0
dm
π (M 2 − m2 )
M4

)(

)

1+τ
ln
−τ ,
1−τ

(3.20)

3.5. Detector Simulation for φ87

where V is the vector meson, Γ0 is the partial decay width of V → l+ l− , m is the invariant
mass
√
+ −
2
of lepton pair l l , α is the ﬁne structure constant, M is the mass of V , and τ = 1 − 4ml /m2
with the lepton mass ml . The eﬀect is small but visible as shown in Fig. 3.50(a). In Fig. 3.50(b),we include all the material eﬀects in the detectors and the chamber resolution, and the blue
curve was used to reproduce the measured spectra.

22[GeV/c ](a) w/o exp. eﬀ.

[GeV/c ](b) w/ exp. eﬀ.

Figure 3.50: The internal radiative eﬀects in φ → e+ e− decays. The red spectra are withinternal radiative eﬀects, and the blue are without. (a)The detector eﬀects are not considered.
(b)The detector eﬀects are considered. The green line is the ﬁt result to the blue spectrumwith the Breit-Wigner function folded with a Gaussian.

• Other Internal Radiative Corrections
Possible other smearing eﬀects in the decay V → e+ e− are vertex correction, vacuum polarization, and box diagrams of propagating gauge bosons. Although those are all negligible in thepresent experiment, we describe them brieﬂy below.
According() to Ref. [68], the magnitude of quantum electrodynamics (QED) radiative correcdσtion δ
up to order α3 can be written asdΩδ() dσ Qdσ
0
Q= δVC + δVP + δγγ,dΩdΩ(3.21)

Q
is two photon
where δVC is the vertex correction term, δVP is the vacuum polarization term, δγγQdσ0box diagram correction term, andis the pure QED cross section in tree level. From thedΩparity conservation, a vector meson does not decay into two photons, thus the contribution ofQis zero.
the box diagram δγγ

88

Chapter 3. Data Analysis

e

V

e
V

e

e

Figure 3.51: Feynman diagrams of the vertex correction term (left) and the vacuum polarization
term (right).

The left panel of Fig. 3.51 shows the Feynman diagram of the vertex correction term δVC ,which is expressed as Eq. (2.11) in Ref. [68],
δVC

(

m2e

)

[

(

)

]

2α
1
3
s
1
s
s
me
=
−1 + π 2 + ln 2 − ln2 2 + 1 − ln 2 ln,π
3
4 me 4meme
λ(3.22)

where me is the electron mass, s is the meson mass square, and λ is a ﬁctitious photon mass
regularizing the infrared divergence. This infrared divergence cancels an infrared divergence in
the internal bremsstrahlung. The Feynman diagram of the vacuum polarization term δVP isshown in the right panel of Fig. 3.51. This term is expressed as Eq. (2.12) in Ref. [68],
(

)

(

)

(

)

δVP = δVP m2e + δVP m2µ + δVP m2τ + δhad ,(3.23)

with the various contributions originating from lepton loops and hadron loops. Both diagrams
change the partial decay width of φ → e+ e− . The former√diagram changes Γee by factor of
about 15% and the latter diagram by factor of about 2% at s = 1.2 GeV. These are negligible
in the observed line shapes since Γee ¿ Γtotal .
Coulomb Potential of Target Nucleus
The eﬀect of the Coulomb potential of target nuclei was small enough to be ignored in thesimulation. The magnitude of this eﬀect was estimated with a toy model, in which only Coulomb
ﬁeld of the target nucleus was considered. The potential V (r) is given as
(

(
)2 )
2
Ze
r



3−
r ≤ RC

V (r) =

2RC


Ze2




r

RC

(3.24)RC ≤ rwhere Ze is the charge of a target nucleus, e is the charge of an electron, RC is the radius of atarget nucleus, and r is the radial distance from the centre of a target nucleus. We checked twocases, one is that vector mesons are generated uniformly on the incident surface of a nucleus
and the other is that they are generated uniformly in a nucleus. We considered 12 C and 63 Cu as
target nuclei, whose radii (RC in Eq. (3.24)) are 2.4 fm and 4.2 fm, respectively. The momentaof vector mesons were distributed as those produced by JAM. The mesons were considered toﬂy without any interaction and decay into e+ e− with their natural total width. We have chasede+ e− and bent them with the Coulomb potential V (r) until they reached 10 nm away from thetarget nucleus. The results of ω → e+ e− decays are shown in Fig. 3.52. The changes of invariant
mass shapes are found to be negligible (below a half MeV/c2 ) in the present experiment.

3.5. Detector Simulation for φ  

89




 

Figure 3.52: The eﬀect of electromagnetic ﬁeld of target nuclei, for carbon (left) and copper(right). In the upper two panels, mesons were generated uniformly in a nucleus. In the lowers,
mesons were generated uniformly on a nuclear surface of the half hemisphere where the beam
protons enter.

Mass Acceptance for e+ e− Decays
The eﬀect of the acceptance on the invariant mass spectrum was examined in the same detector
simulation. In the 2001(2002) run, we used the 3(5) targets simultaneously and they wereplaced 46(23) mm apart from each other, so the acceptance of the spectrometer for each target
is diﬀerent from each other. The arrangement of the target disks (Cu-C-Cu or Cu-Cu-C-Cu-Cu)
assumed that the average of the Cu-target acceptances is equivalent to the C-target acceptance.
We examined this assumption as follows.
We evaluated the mass acceptance for each target using artiﬁcial mesons with the ﬂat mass
distribution from 0.85 to 1.2 GeV/c2 , with the momentum distribution of φ-mesons obtained by
JAM. We used the same momentum distribution for the C and Cu targets to compare directly
the experimental acceptance among the targets. We estimated the mass acceptance as theratio of the accepted mesons to the generated mesons. It should be noted that the acceptanceincluded not only the geometrical acceptance but the detector eﬃciencies and all other cut
conditions which were used in the present analysis.
The obtained mass acceptances for each target in the 2001 run are shown in Fig. 3.53. The
averaged acceptance for the two Cu targets is compared with the C target in Fig. 3.54 showing
good agreements. In the future discussions in Sec. 4.1, we divide the data into four bins in βγ,
rapidity, and pT . With these divisions, we obtained the mass acceptances as shown in Fig. 3.55.
The acceptance at the φ-meson peak (1.02 GeV/c2 ) was about 1.5%, 1.2%, and 0.3% for theall, LR, and RL event respectively.

90

Chapter 3. Data Analysis+ -2

AcceptanceRL event

AcceptanceLR event

Acceptanceall event+ -e e Invariant Mass (GeV/c )2+ -e e Invariant Mass (GeV/c )2

e e Invariant Mass (GeV/c )Figure 3.53: The mass acceptances for e+ e− decays in the 2001 run. The acceptances of eachtarget disk for the all events (left), LR events (center), and RL events (right) are shown.

e+e- Invariant Mass (GeV/c2)

RL event
AcceptanceLR event
AcceptanceAcceptanceall evente+e- Invariant Mass (GeV/c2)

e+e- Invariant Mass (GeV/c2)

Figure 3.54: The mass acceptances for e+ e− decays for the C and the averaged Cu targets, forthe all events (left), LR events (center), and RL events (right).

1.25<rapidity<1.5e+e- Invariant Mass (GeV/c2)

0.4<pT<0.6

e+e- Invariant Mass (GeV/c2)

e+e- Invariant Mass (GeV/c2)

1.5<rapidity

e+e- Invariant Mass (GeV/c2)

Acceptancee+e- Invariant Mass (GeV/c2)

0.25<pT<0.4

2.5<

e+e- Invariant Mass (GeV/c2)

Acceptance

1<rapidity<1.25

e+e- Invariant Mass (GeV/c2)

AcceptanceAcceptancee+e- Invariant Mass (GeV/c2)

AcceptanceAcceptanceAcceptancee+e- Invariant Mass (GeV/c2)

e+e- Invariant Mass (GeV/c2)

pT<0.25

1.75< <2.5

Acceptance

1.25< <1.75

e+e- Invariant Mass (GeV/c2)

rapidity<1

Acceptance91

Acceptance<1.25

AcceptanceAcceptance3.5. Detector Simulation for φ

0.6<pTe+e- Invariant Mass (GeV/c2)

Figure 3.55: The mass acceptances for e+ e− decays divided into four bins in βγ (top), rapidity(middle), and pT (bottom). The acceptances for the averaged Cu targets for the all events, LR
events, and RL events are shown.

3.5.2

φ → K + K − Simulation

Spectral Shape of φ → K + K −The spectral shape of φ → K + K − was generated using the relativistic Breit-Wigner distribution
which is given by Ref. [66];mm0 Γ (m)
dσ
,
=
2
2
dm
(m − m20 ) + (m0 Γ (m))2(3.25)

Γ (m) = Γ0 (q/q0 )3 (m0 /m) ,(3.26)

where
√

q=

√

q0 =

/

m2 4 − m2K ,/m20 4 − m2K ,(3.27)(3.28)

with K + K − invariant mass (m), the pole mass of the φ (m0 ), and kaon mass (mK ). The
distribution is compared with the non-relativistic one in Fig. 3.56, in which visible changes
exist. In addition, the K + K − threshold should be included in the mass shape. Thus we used
relativistic Breit-Wigner form unlike the the φ → e+ e− case.

92

Chapter 3. Data Analysis

K+K-

mass [MeV/c2]

mass [MeV/c ]2

Figure 3.56: The non-relativistic (red) and the relativistic (blue) Breit-Wigner distribution for
φ → K + K − decays. The distributions are normalized by their peak count to unity.

Kinematical Distribution
The kinematical distribution of φ → K + K − decays was obtained as same as e+ e− decays
as described before, and the results are shown in Fig. 3.57. The observed and simulated
distributions are compared in Fig. 3.58, 3.59, and 3.60. The agreements are quite good again.
The observed distributions were obtained again with the side-band subtracting method, as
φ → e+ e− decays. The signal region was chosen from 1.01 to 1.03 GeV/c2 and the side-bands
were from 1.00 to 1.01 and from 1.03 to 1.04 GeV/c2 , as shown in Fig. 3.61.

3.5. Detector Simulation for φ

93




pT

rapidity

pT

rapidity

rapidity

pT

rapiditypT vs. rapidity

pT

(a) C

pT vs. rapidity(b) CuFigure 3.57: The kinematical distributions of the generated φ mesons using JAM (black lines)
and of the accepted φ → K + K − in the detector (red lines). The accepted φ → K + K − arescaled up by a factor of 50.

Cu

C

cos

cos

cos

Cu

C

cos

Cu

C

angle [rad]


Cu

C

angle [rad](a) the Gottfried-Jackson frame

angle [rad]angle [rad](b) the helicity frame

Figure 3.58: The decay angular distributions for the data (closed circles) and the simulation(lines), (a) in the Gottfried-Jackson frame and (b) in the helicity frame. The scaling is determined arbitrarily.

94

Chapter 3. Data Analysis

momentum [GeV/c]px

momentum [GeV/c]py

momentum [GeV/c]momentum [GeV/c]

pzp(a) K + in φ → K + K − for C

momentum [GeV/c]px

momentum [GeV/c](c) K − in φ → K + K − for C

momentum [GeV/c]pz

momentum [GeV/c]py

momentum [GeV/c]p(b) K + in φ → K + K − for Cu

momentum [GeV/c]pypz

momentum [GeV/c]px

momentum [GeV/c]pmomentum [GeV/c]px

momentum [GeV/c]pz

momentum [GeV/c]py

momentum [GeV/c]p(d) K − in φ → K + K − for Cu

Figure 3.59: The momentum distributions of the observed (closed circles) and simulated (lines)
daughter K + (top panels) and K − (bottom panels) in the φ → K + K − decays, for C (leftpanels) and for Cu (right panels). The scaling is determined arbitrarily.

3.5. Detector Simulation for φ

95




pT

rapidity

pT

rapidity

rapidity

pT

rapiditypT vs. rapiditypT(a) φ → K + K − for C

pT vs. rapidity(b) φ → K + K − for Cu

Figure 3.60: The kinematical distributions of the observed (closed circles) and simulated (lines)
φ → K + K − pairs, for C (left four panels) and for Cu (right four panels). In the scatter plots ofpT versus rapidity, only the observed events are shown. The scaling is determined arbitrarily.

C

+ -

2

K K Invariant Mass[GeV/c ]Figure 3.61: The separation of the signal region and the side-band (background) regions.

96

Chapter 3. Data Analysis

Rescattering of Kaons in Nucleus
When a φ meson decays inside a nucleus, daughter K and K̄ are considered to be absorbed
or rescattered in the nucleus. The K and K̄ absorptions decrease the observed cross section
while do not change the invariant mass spectrum. However, the KN and K̄N rescatterings
aﬀect both the cross section and the invariant mass spectrum. The eﬀects of KN and K̄N
rescattering were studied using JAM.
We chased φ → K + K − decays in JAM, and then the daughters were ﬂagged when they wereabsrobed or rescattered in the nucleus. The obtained yields of these events are summarized inTable 3.8, and the invariant mass distributions are shown in Fig. 3.62. It can be concluded
that the probability of the rescattering is small, less than 3% even in the Cu nucleus, and thatthe rescattered events cannot be identiﬁed as φ mesons. We neglect such a rescattering eﬀect
in the later analysis, which at the same time implies that the experiment is not sensitive to afew % level of the mass shape modiﬁcation.
When we deﬁne the φ-meson which decays inside the half-density radius of the Woods-Saxon
distribution as the inside decay in the nucleus, as described in Sec. 4.4, probabilities of the inside
decay are estimated to be 1.3% and 3.3% in the carbon and copper nucleus respectively. So
the daughters of φ → K + K − decays which decays inside in the nucleus are almost absorbed or
rescatterd 3 .
12

63
C
Cu
+ −
generated φ → K K
52.2k 100.0% 72.4k 100.0%
w/o kaon absorption
51.5k 98.6% 69.3k 95.8%
w/o kaon absorption and rescattering 50.8k 97.3% 67.9k 93.8%

Table 3.8: The numbers of generated φ → K + K − decays and kaon absroptions and rescatterings.

 

Figure 3.62: The φ → K + K − invariant mass distributions obtained by JAM. The black lines
represent all the φ → K + K − events before the rescattering. The red and blue lines represent
the events with the rescattering before and after the rescattering, respectively.

3
When we deﬁne the φ-meson which decays inside the 1/10-density radius as the inside decay, probabilitiesof the inside decay are estimated to be 3.1% and 5.1% in the carbon and copper nucleus respectively.

3.5. Detector Simulation for φ97

Mass Acceptance for K + K − Decays

AcceptanceAcceptance

The acceptance of the K + K − invariant mass spectrum was studied through the detector simulation, as same as the e+ e− pair case as explained before. This time a ﬂat mass distribution
from 2mK ± (0.987) to 1.15 GeV/c2 was used.
The obtained mass acceptances for each target disk are shown in Fig. 3.63(a). Because of
the small opening angle of φ → K + K − decays, there is a high probability that K + and K −tracks cross each other in a chamber drift cell. In such case, the chamber hit information in
the cell is correct for one track and lost from other track, and a pair reconstruction eﬃciency
for such event becomes worse. Therefor the mass acceptance decreases kinematically on the
low mass side of the φ-meson peak. The obtained acceptances are almost equivalent between
the C target and the average of the Cu targets, as shown in Fig. 3.63(b). The small but visible
diﬀerence in Fig. 3.63(b) will be considered later in Sec.4.3.2. In the later discussions in Sec. 4.2,
we divide the data into three bins in βγ, rapidity, and pT . With these divisions, we obtained themass acceptances as shown in Fig. 3.64. The acceptance at the φ-meson peak (1.02 GeV/c2 )was about 0.12%.

K+K- Invariant Mass (GeV/c2)(a)K+K- Invariant Mass (GeV/c2)(b)

Figure 3.63: (a)The mass acceptances for each target disk in K + K − decays. (b)The mass
acceptances for the C target and the averaged one for the Cu targets.

1.7< <2.2

1<rapidity<1.2

pT<0.8K+K- Invariant Mass (GeV/c2)

AcceptanceAcceptance

K+K- Invariant Mass (GeV/c2)

K+K- Invariant Mass (GeV/c2)

0.8<pT<1

K+K- Invariant Mass (GeV/c2)

2.2<

K+K- Invariant Mass (GeV/c2)

Acceptance

rapidity<1

K+K- Invariant Mass (GeV/c2)

AcceptanceAcceptance

K+K- Invariant Mass (GeV/c2)

1.2<rapidity

K+K- Invariant Mass (GeV/c2)

Acceptance<1.7

Acceptance

Chapter 3. Data Analysis

AcceptanceAcceptance

98

1<pT

K+K- Invariant Mass (GeV/c2)

Figure 3.64: The mass acceptances for Cu targets in K + K − decays divided into three bins in
βγ (top), rapidity (middle), and pT (bottom).

3.5.3

Momentum Resolution

Single Track Resolution
The eﬀects of the detector materials and the chamber resolution were studied with use of thedetector simulation. We evaluated the momentum resolution for e, π, K, and p as shown in
Fig. 3.65(a), and the diﬀerences of the obtained momenta from the original value are shownin Fig. 3.65(b). The sources of the momentum resolution are from the chamber resolution,
coulomb multiple scattering, and the energy losses as shown in Fig. 3.66. The energy losses
here include external bremsstrahlung, ionization, and δ-ray processes. It should be noted thatin the electron curves in Fig. 3.66(a), the amount of an energy-loss tail from the externalbremsstrahlung is not taken into account in the evaluation since we used the values of theGaussian-ﬁtting width.

3.5. Detector Simulation for φ99

difference
difference(%)

resolution(%)

resolution

momentum(GeV/c)momentum(GeV/c)(a) momentum resolution(b) diﬀerence of momentum

Figure 3.65: (a)The momentum resolution for e, π, K, and p. (b)The diﬀerence of the obtained
momenta from the original values.

resolution(%)

kaon

resolution(%)

electronmomentum(GeV/c)(a) electron

momentum(GeV/c)(b) kaon

Figure 3.66: Breakdown of the sources in the momentum resolution, (a) for e and (b) for K.

Momentum Resolution with Common-Vertex Track Fitting
In the analysis of e+ e− and K + K − pairs, we constrained the vertex position onto the target position (see Sec. 3.3.4). This “Common Vertex Track Fitting” (CVTF) improved the momentum
resolution as shown in Fig. 3.67.

100

Chapter 3. Data Analysis

+ -

e e

K in



+

-

K K

resolution(%)



resolution(%)

e in

momentum(GeV)

momentum(GeV)(a) e in φ → e+ e−(b) K in φ → K + K −Figure 3.67: The momentum resolution (a) for e in φ → e+ e− and (b) for K in φ → K + K − .
The resolution “without CVTF” and “with CVTF” are plotted.

3.6

Background Estimation

3.6.1

Background in the φ → e+ e− Channel

The sources of the background were uncorrelated pairs of e+ and e− , which mainly come fromπ 0 Dalitz decays, γ-conversions in the targets and the detector materials, and miss-identiﬁed
pions. Because all the correlated background from Dalitz decays and γ-conversions fall in
below the π 0 and η mass, all the e+ e− pairs around the φ mass region must be originated from
uncorrelated pairs of π 0 or η which decay into e+ e− γ or γγ followed by eventual conversions. In
order to evaluate the amount of e+ π − , e− π + , or π + π − pairs originated from the miss-identiﬁed
pions in the background, we examined the signal to noise ratio S/N in the φ mass region.
The invariant mass spectra were ﬁtted with the simulated φ resonance shape and a quadratic
background curve. The ﬁt region was from 0.85 GeV/c2 to 1.2 GeV/c2 except that the mass
region from 0.95 to 1.00 GeV/c2 , where the excess signal was observed [31], was excluded fromthe ﬁt. The amount of the signal was deﬁned by subtracting the background from the datain the mass region from 0.99 to 1.04 GeV/c2 . Although S does not contain the miss-identiﬁed
pion, N contains the pion contamination. Thus, we consider N = e + c, where e is from puree+ e− pairs and c is from contamination. When the electron selections are tightened enough toreject miss-identiﬁed pions completely, the ratio S/N should become better and saturate. So
we obtained the S/N by varying the electron identiﬁcation condition to strict ones (ID=1 to
14 in Fig. 3.68). The ﬁtted spectra for ID = 1 and 9 are shown in Fig. 3.69. The maximum(S/N )max = S/e was obtained to be 2.01 ± 0.06 when ID is greater than 8.
The S/N in the present analysis (ID=1) was obtained to be 1.21 ± 0.03. Since (S/N )max is
independent of the electron purity, the contaminations can be obtained as
c=N−

S
.
(S/N )max(3.29)

We conclude that the φ mass region from 0.99 to 1.04 GeV/c2 contains 54.7 ± 1.0 % of the3.6. Background Estimation

101

S/N

signal (φ → e+ e− ), 27.2 ± 0.9 % of combinatorial e+ e− background, and 18.1 ± 0.8 % of particle
miss-identiﬁcations (e+ π − , e− π + , and π + π − ).
With a separate study described later in Sec. 3.6.2 and also in Ref. [35], we found the π + π −invariant mass distribution is well reproduced by the event-mixing method except for a small
peak from K0s → π + π − decays. Thus we can safely assume that the background shape of thee+ e− mass spectra is reproducible also by the event-mixing. Nevertheless we used a quadratic
function for the background shape in the later analysis to leave a room to take a possible tailfrom the ρ/ω region into account.

ID
1
2
3
4
5
6
7
8
9
10
11
12
13
14

eID strictness

threshold above pedestal(ADC counts)
FGC ADC RGC ADC lead-glass E/p
200
50
0.5
400
50
0.5
600
50
0.5
800
50
0.5
400
50
0.6
400
50
0.7
400
100
0.7
400
150
0.7
400
100
0.8
600
100
0.8
800
100
0.8
600
150
0.8
600
100
0.9
800
150
0.9

Figure 3.68: The S/N with a various electron identiﬁcation conditions. The condition is severe
with larger IDs. The conditions are listed in the right panel.

events [/10MeV/c2]

events [/10MeV/c2]

e e Invariant Mass [GeV/c ]+ -(a) ID = 1

2

e e Invariant Mass [GeV/c ]+ -2(b) ID = 9

Figure 3.69: The e+ e− mass distributions with the ﬁt results for (a) ID = 1 and (b) ID = 9 inFig. 3.68. The data for all the targets are summed. The closed circles represent the data and thethin crosses represent the excluded region from the ﬁt. The red, green and blue lines represent
the ﬁt results, the quadratic backgrounds and the expected φ → e+ e− shapes, respectively. The
arrows indicate the region to examine the S/N .

102

3.6.2

Chapter 3. Data Analysis

Background in the φ → K + K − Channel

The sources of the background in φ → K + K − decays are non-resonant K + K − pairs like
K + K ∗− → K + K − π 0 , K ∗0 K¯∗0 → K + π − K − π + , and so on, and pairs due to miss-identiﬁed
pions and protons. The purity of the K + K − pair samples was estimated to be 85.6 ± 4.7(stat)± 0.7(syst) % as described in Sec. 3.3.6, so that the miss-identiﬁcation is not a major issue.
The correlation in non-resonant K + K − pairs, however, are not well known. If the non-resonant
K + K − pairs have no correlation, it is reasonable to use the event-mixing method for the K + K −background estimation in which a K + -track from one event is combined with a K − -track fromother event which comes from the same target as K + -track. We need to impose the trackcrossing eﬀect described in Sec. 3.5.2 in the event mixing. So we reconstructed the tracksof the mixed event as same as the real-data analysis, i.e., the track ﬁnding, the ﬁtting by
the Runge-Kutta method, and Common Vertex Track Fitting. In the following sections, we
examine;• whether it is reasonable to use the mixed event for the combinatorial background or not,• whether the non-resonant K + K − pairs have correlation or not.

3.6. Background Estimation

103

Study of π + π − Data

event [/10MeV/c2]

event [/10MeV/c2]

First, we checked usability of the event-mixing method to reproduce the shape of the combinatorial background. In this study, we used π + π − pairs which were assumed to be uncorrelated 4 .
Figure 3.70(a) and (b) show the invariant mass spectra of π + π − pairs with CVTF for the singlearm events and the double-arm events, respectively, compared to the mixed-event spectra. It
can be concluded that the invariant mass spectra of π + π − pairs are well reproduced with themixed event.

CCuinvariant mass [GeV/c2]

invariant mass [GeV/c2]

event [/20MeV/c2]

event [/20MeV/c2](a) single-arm eventsCCuinvariant mass [GeV/c2]

invariant mass [GeV/c2](b) double-arm events

Figure 3.70: The invariant mass spectra of π + π − pairs with CVTF for (a) the single-arm eventsand (b) the double-arm events (LR events only). The closed circles and lines represent the data
and the mixed event, respectively.

4This assumption is safe since the ρ → π + π − mass distribution is wide and we have a small acceptance forthose. A peak of K0s → π + π − is negligible as long as we do not apply a delayed-decay condition.

104

Chapter 3. Data Analysis

Study of Non-Resonant K + K − by JAM

event [/4MeV/c2]

event [/4MeV/c2]

Next, we examined whether the non-resonant K + K − pairs have a correlation or not. The
mass and kinematical distributions of non-resonant K + K − pairs were obtained by JAM, andexperimental eﬀects were taken into account using the detector simulation. Figure 3.71(a) and(b) show the invariant mass spectra of non-resonant K + K − pairs with CVTF for the singlearm events and the double-arm events, respectively, which are well reproduced with the mixed
event. So the non-resonant K + K − pairs in JAM can be considered to have no correlation.

C

Cu

invariant mass [GeV/c2]

invariant mass [GeV/c2]

event [/4MeV/c2]

event [/4MeV/c2](a) single-arm events

C

Cu

2

invariant mass [GeV/c ]2

invariant mass [GeV/c ](b) double-arm events

Figure 3.71: The invariant mass spectra of non-resonant K + K − pairs with CVTF for (a) the
single-arm events and (b) the double-arm events (LR events only) obtained by JAM. The closed
circles and lines represent the simulated data and those after the event-mixing, respectively.

3.6. Background Estimation

105

Study of Double-Arm K + K − Data
In addition to the results using JAM described above, we studied the non-resonant K + K − pairs
using the double-arm K + K − event data. Because of the small Q value in φ → K + K − decays,
the φ → K + K − events were negligible in the double-arm K + K − events (see Appendix B). So
the double-arm K + K − events should consist of the non-resonant K + K − pairs and contaminations from miss-identiﬁed pions and protons. As same as Sec. 3.3.6, we evaluated the purityof the kaon in the double-arm data as listed in Table 3.9 for reference. Figure 3.72 show theinvariant mass spectra of K + K − pairs with CVTF for the double-arm events. The invariant
mass spectra of K + K − pairs are well reproduced with the mixed event, so that the double-arm
K + K − pairs can be considered to contain only uncorrelated pairs.
+

K
K−
K +K −

purity(%)
84.7 ± 5.4(stat) ± 0.3(syst)
81.8 ± 7.3(stat) ± 0.1(syst)
69.3 ± 7.6(stat) ± 0.3(syst)

event [/20MeV/c2]

event [/20MeV/c2]

Table 3.9: The purity of the kaon in the double-arm data (LR events only).

Cinvariant mass [GeV/c2]

Cu

invariant mass [GeV/c2]

Figure 3.72: The invariant mass spectra of K + K − pairs with CVTF for the double-arm events(LR events only). The closed circles and lines represent the data and the mixed events, respectively.

106

Chapter 3. Data Analysis

Combinatorial Background for the Final K + K − Sample
Considering the conﬁrmations described above, it is reasonable to use the event-mixing method
to estimate the K + K − background shape. Below we describe the method in detail.
The event-mixing method is usually used in heavy-ion experiments by simply taking K +and K − from diﬀerent events. In our experiment, the signal to noise ratio (S/N ) is much better,
S/N is about unity at the φ → K + K − resonances, compared with heavy-ion experiments. Thus
we considered the distortion of the background shape due to the K − or K + originated fromthe resonance itself. To eliminate such a distortion, the weights to the pairs in the resonanceregions (correlated pairs) were reduced according to the S/N in the mass region from 1.002
to 1.038 GeV/c2 which was determined by the ﬁt. At the ﬁrst step, we chose arbitrary values
as the input weights for the correlated pairs in the event-mixing, and obtained the tentative
background shape. Next, we ﬁtted the spectra with this background shape and the simulated φresonance shape to obtain the S/N . The obtained S/N was used as the input weights in making
the new combinatorial background shape. We repeated this procedure until the backgroundshape got stabilized (converged).
To study a systematic uncertainty in the background estimation, we made the diﬀerent
background shape by setting the weights to 1 or 0 to the tracks belonging to the resonanceregion. In other words, we considered three types of backgrounds;
Type 1: including all tracks belong the resonance mass-region (“all-in” in Fig. 3.73),
Type 2: using the tracks in the resonance mass-region with the weights determined by S/N(“S/N ” in Fig. 3.73), andType 3: excluding all tracks belong the resonance mass-region (“all-ex” in Fig. 3.73).
Figure. 3.73 shows the shapes of those backgrounds normalized with the number of entries. In
the following analysis, we used the Type 2 (S/N ) background for the ﬁt, and used the Type 3(all-ex) background for the study of systematic errors 5 .

CuCinvariant mass [GeV/c2]

invariant mass [GeV/c2]

Figure 3.73: Three types of the combinatorial background shape obtained by the event-mixing
and normalized by the number of the mixed events. The red, black, and blue lines represent
Type 1, 2, and 3, respectively (see text).
5

The obtained yields of the φ mesons used the Type 1 and Type 3 background are almost symmetric about
the yields used the Type 2 background. So we used only the Type 3 background for the systematic-error study.

3.7. Mass Scale and Resolution for φ

107

3.7

Mass Scale and Resolution for φ

3.7.1

φ → e+ e− Decays

We examined the reproducibility of the detector simulation using Ks0 → π + π − and Λ → pπ −decays as described in Sec. 3.3.3. The observed resolution and centroids of the resonances were
well reproduced by the simulation.
For φ → e+ e− decays, we estimated the mass resolution to be 10.7 MeV/c2 in the data,
and to be 10.1 MeV/c2 in the detector simulation. Since φ → e+ e− events were required tobe “double-arm event”, the uncertainty of the mass scale and the resolution emerged from theremaining errors due to the alignment of the chambers as described in Sec. 3.2.3. In otherwords, the BDC alignment was not precise enough in this mass scale and the resolution (afew MeV/c2 ). It should be noted that such a problem due to the chamber miss-alignment was
negligible in “single-arm event”, i.e. for φ → K + K − , K0s → π + π − , and Λ → pπ − .
Thus we examined the amount of changes in the mass scale and the resolution by ﬁtting
the mass spectra with the detector simulation. First, we shifted the simulated φ → e+ e− shape
step by step using parameter δm with an interval of 0.1 MeV/c2 , and we also smeared theshape step by step with a Gaussian of a width δσ with an interval of 0.1 MeV/c2 . Next, inthe high βγ region (βγ > 1.5), we ﬁtted the data with these modiﬁed φ → e+ e− shapes anda quadratic background. The obtained best values and the associated errors of δm and δσ aresummarized in Table 3.10. The systematic errors contain contributions from the uncertainty
due to the background shape, the binning of histograms, and the ﬁt region. We used these
modiﬁed shapes with the mass resolution of 10.7 MeV/c2 to ﬁt the e+ e− spectra in the analysis
presented in Sec. 4.1. Please note that, although this treatment is somewhat arbitrarily, thevalues applied for δm and δσ are consistently understood within one σ error of the uncertainty
in the BDC alignment (see Table 3.2 in Sec. 3.2.3). Detailed analysis is described in Sec. 3.3.2
in Ref. [36].

LR
additional mass scale δmadditional resolution δσ

2001
0.7 ± 0.9+0.0
−0.6

RL
2002
2001
2002
+0.0
+0.5
−0.7 ± 0.6−0.4 0.6 ± 2.8−0.6 4.2 ± 1.3+0.1−0.2
3.6 ± 1.3+1.2−0.0

Table 3.10: The obtained best values in the additional mass scale δm and the resolution δσ,
in a unit of [MeV/c2 ]. The values are obtained separately for the LR and RL events and theyear 2001 and 2002, due to the expected nature of the BDC alignments. The ﬁrst errors are
statistical and the seconds are systematic.

3.7.2

φ → K + K − Decays

For φ → K + K − decays, we evaluated the mass centroid and the resolution in the data by ﬁtting
the spectra with the combinatorial background and the relativistic Breit-Wigner shape with
the natural width of 4.26 MeV/c2 after folded with a Gaussian. The combinatorial background
was obtained by the event-mixing method as described in Sec. 3.6.2, and the relativistic BreitWigner was modiﬁed by using the mass acceptance as described in Sec. 3.5.2. For the detector
simulation spectra, we evaluated the values as same as the data but without a background. The
obtained values are summarized in Table. 3.11, and the ﬁtting results for the data are shown in
Fig. 3.74. The systematic errors contain contributions from the uncertainties in the backgroundestimation as described in Sec. 3.6.2 and the binning of histograms. The agreements are quite
remarkable, and we used the simulated mass shape in the ﬁt described in Sec. 4.2.

108

Chapter 3. Data Analysis

mass centroid
mass resolution
DATA 1019.38 ± 0.31 ± 0.13 2.19 ± 0.42 ± 0.30
CMC
1019.53
2.35
DATA 1019.43 ± 0.21 ± 0.04 1.91 ± 0.29 ± 0.23
CuMC
1019.49
2.24
Table 3.11: The obtained values of the mass centroid and the resolution for the data (DATA)
and the detector simulation (MC) in a unit of [MeV/c2 ]. The ﬁrst errors are statistical and theseconds are systematic.

CuC 2/dof=49/89

 2/dof=72/89

K K Invariant Mass [GeV/c ]+-2

K K Invariant Mass [GeV/c ]+-2

Figure 3.74: The invariant mass spectra of the ﬁnal K + K − sample. The closed circles represent
the data. The blue and red lines represent the ﬁt results and the combinatorial backgrounds
respectively.

Chapter 4
Results and Discussions
4.1

Spectral Shape and Yield of φ Meson in the e+e−
ChannelThe invariant mass spectra of the ﬁnal e+ e− sample in the mass region from 0.85 to 1.2 GeV/c2
are shown in Fig. 4.1 for C and Cu targets. We ﬁtted each mass spectrum with a resonanceshape of φ → e+ e− and a quadratic background curve. For the φ meson resonance shape, weused the simulated shape as described in Sec. 3.5.1. The ﬁt region was from 0.85 to 1.2 GeV/c2
excluding the region from 0.95 to 1.00 GeV/c2 , where the excess attributed to the φ meson
modiﬁcation was observed. Detailed studies on the modiﬁcation of the φ meson are made in
Ref [31, 36]. In this manuscript, we just set a focus to evaluate the φ-meson yields to compare
the nuclear mass-number dependences of φ → e+ e− with φ → K + K − .
Figures 4.2, 4.3, and 4.4 show the invariant mass spectra in the four kinematical regions ofβγ (=p/m), rapidity (y), and transverse momentum (pT ) of observed e+ e− pairs, respectively.
It should be noted that an excess visible on the low-mass side of the φ meson peak in βγ < 1.25of the Cu target data (Fig. 4.2) looks somewhat diﬀerent from the one in Ref. [31, 36]. This isbecause the analysis cuts applied in the present work are diﬀerent from the cuts in Ref. [31, 36],
where the S/N for the φ peak is optimized while the yield statistics are optimized in the present
work.
The relative abundances of the φ mesons and the parameters of the quadratic backgroundwere obtained from the ﬁt. The yields of φ mesons are listed later in Table 4.5(a). They
were obtained by integrating the mass region from 0.9 and 1.1 GeV/c2 after subtracting thebackground. Thus the excess observed in Ref. [31, 36] is in principle included in the φ meson
yields here. As listed as χ2 /dof in Fig. 4.2, 4.3, and 4.4, all the ﬁts were satisfactory performed.

109

110

Chapter 4. Results and Discussions

events [/10MeV/c2]

events [/10MeV/c2]

C

Cu

2

2

/dof=41/26/dof=25/26

e e Invariant Mass [GeV/c ]+ -2e e Invariant Mass [GeV/c ]+ -2Figure 4.1: The invariant mass spectra of the ﬁnal e+ e− sample. The closed circles represent
the data and the thin crosses represent the excluded region from the ﬁt. The red, green andblue lines represent the ﬁt results, the quadratic backgrounds and the expected φ → e+ e−
shapes, respectively.

4.1. Spectral Shape and Yield of φ Meson in the e+ e− Channel

events [/10MeV/c2]



C

111

events [/10MeV/c2]



Cu

<1.25

2

2

/dof=34/26/dof=20/26

e e Invariant Mass [GeV/c ]+ -events [/10MeV/c2]

e e Invariant Mass [GeV/c ]2+ -events [/10MeV/c2]


1.25< <1.75

C

2/dof=24/26/dof=32/26

e e Invariant Mass [GeV/c ]+ -events [/10MeV/c2]

Ce e Invariant Mass [GeV/c ]2events [/10MeV/c2]22/dof=25/26/dof=23/26

e e Invariant Mass [GeV/c ]e e Invariant Mass [GeV/c ]2events [/10MeV/c ]2
1.75< <2.5

Cu

1.75< <2.5

+ -

2


1.25< <1.75

Cu

2

+ -

<1.25

+ -

2

events [/10MeV/c ]

2

2

C

2.5<



Cu

2.5<

2

2

/dof=29/26/dof=22/26

e e Invariant Mass [GeV/c ]
+ -



2

e e Invariant Mass [GeV/c ]+ -2Figure 4.2: The invariant mass spectra of the ﬁnal e+ e− sample divided into four βγ bins. The
closed circles represent the data and the thin crosses represent the excluded region from theﬁt. The red, green and blue lines represent the ﬁt results, the quadratic backgrounds and the
expected φ → e+ e− shapes, respectively.

112

Chapter 4. Results and Discussions

events [/10MeV/c2]

events [/10MeV/c2]

C

Cu

y<1

y<1

2

2

/dof=36/26/dof=22/26

e e Invariant Mass [GeV/c ]+ -e e Invariant Mass [GeV/c ]2events [/10MeV/c2]+ -2

events [/10MeV/c2]

CCu

1<y<1.25

1<y<1.25

22/dof=20/26/dof=19/26

e e Invariant Mass [GeV/c ]+ -e e Invariant Mass [GeV/c ]2events [/10MeV/c2]+ -2

events [/10MeV/c2]

C

Cu

1.25<y<1.5

1.25<y<1.522/dof=20/26/dof=25/26

e e Invariant Mass [GeV/c ]+ -e e Invariant Mass [GeV/c ]2events [/10MeV/c ]+ -2events [/10MeV/c ]

2

2

C

Cu

1.5<y

1.5<y

2

2

/dof=29/26/dof=28/26

e e Invariant Mass [GeV/c ]+ -2e e Invariant Mass [GeV/c ]+ -2Figure 4.3: The invariant mass spectra of the ﬁnal e+ e− sample divided into four rapidity bins.
The closed circles represent the data and the thin crosses represent the excluded region fromthe ﬁt. The red, green and blue lines represent the ﬁt results, the quadratic backgrounds andthe expected φ → e+ e− shapes, respectively.

4.1. Spectral Shape and Yield of φ Meson in the e+ e− Channel

events [/10MeV/c2]

113

events [/10MeV/c2]

C

Cu

pT<0.25

pT<0.2522/dof=32/26/dof=23/26

e e Invariant Mass [GeV/c ]+ -e e Invariant Mass [GeV/c ]2events [/10MeV/c2]+ -2

events [/10MeV/c2]

C

Cu

0.25<pT<0.4

0.25<pT<0.422/dof=49/26/dof=31/26

e e Invariant Mass [GeV/c ]+ -e e Invariant Mass [GeV/c ]2events [/10MeV/c2]+ -2

events [/10MeV/c2]

C

Cu

0.4<pT<0.6

0.4<pT<0.622/dof=35/26/dof=32/26

e e Invariant Mass [GeV/c ]+ -e e Invariant Mass [GeV/c ]2events [/10MeV/c ]+ -2events [/10MeV/c ]

2

2

C

Cu

0.6<pT

0.6<pT2

2/dof=22/26/dof=13/26

e e Invariant Mass [GeV/c ]+ -2e e Invariant Mass [GeV/c ]+ -2Figure 4.4: The invariant mass spectra of the ﬁnal e+ e− sample divided into four pT bins. The
closed circles represent the data and the thin crosses represent the excluded region from theﬁt. The red, green and blue lines represent the ﬁt results, the quadratic backgrounds and the
expected φ → e+ e− shapes, respectively.

114

Chapter 4. Results and Discussions

4.2

Spectral Shape and Yield of φ Meson in the K +K −ChannelThe invariant mass spectra of the ﬁnal K + K − sample are shown in Fig. 4.5. We ﬁtted eachmass spectrum with the resonance shape of φ → K + K − and the combinatorial backgroundshape described in Sec. 3.5.2 and 3.6.2 respectively, in the mass region from 2mK ± (0.987) to
1.15 GeV/c2 . The ﬁts were performed by using the maximum likelihood method. To examine
the quality of the ﬁt, the “likelihood chi-square χ2λ ”, which is deﬁned in Ref. [69] asχ2λ = 2∑[yi − ni + ni ln (ni /yi )],

(4.1)

i

where ni is the number of events in the i-th bin and yi is the number of events predicted by theﬁt, is calculated and shown in each ﬁgure. The likelihood chi-square χ2λ asymptotically obeys
a chi-square distribution.
Figure 4.6, 4.7, and 4.8 show the invariant mass spectra in the three kinematical regions ofβγ, rapidity, and pT of the observed K + K − pairs, respectively.

events [/4MeV/c2]

events [/4MeV/c2]

CCu 2/dof=38/39

 2/dof=35/39

K K Invariant Mass [GeV/c ]+-2

K K Invariant Mass [GeV/c ]+-2

Figure 4.5: The invariant mass spectra of the ﬁnal K + K − sample. The closed circles represent
the data. The red, green and blue lines represent the ﬁt results, the combinatorial backgrounds
and the expected φ → K + K − shapes, respectively.

4.2. Spectral Shape and Yield of φ Meson in the K + K − Channel

events [/4MeV/c2]

115

events [/4MeV/c2]



C



Cu

<1.7

 2/dof=43/39

 2/dof=33/39

K K Invariant Mass [GeV/c ]
+

-

<1.7

K K Invariant Mass [GeV/c ]2events [/4MeV/c2]

+

-

2

events [/4MeV/c2]



C



Cu

1.7< <2.2

1.7< <2.2

 2/dof=24/39

 2/dof=46/39

K K Invariant Mass [GeV/c ]+-K K Invariant Mass [GeV/c ]2events [/4MeV/c2]

+

-

2

events [/4MeV/c2]

C

2.2<



Cu

2.2<

 2/dof=53/39

 2/dof=36/39

K K Invariant Mass [GeV/c ]
+

-



2

K K Invariant Mass [GeV/c ]+-2

Figure 4.6: The invariant mass spectra of the ﬁnal K + K − sample divided into three βγ bins.
The closed circles represent the data. The red, green and blue lines represent the ﬁt results,
the combinatorial backgrounds and the expected φ → K + K − shapes, respectively.

116

Chapter 4. Results and Discussions

events [/4MeV/c2]

events [/4MeV/c2]

C

Cu

y<1

y<1

 2/dof=34/39

 2/dof=38/39

K K Invariant Mass [GeV/c ]+-K K Invariant Mass [GeV/c ]2events [/4MeV/c2]

+

-

2

events [/4MeV/c2]

CCu

1<y<1.2

1<y<1.2

 2/dof=35/39

 2/dof=39/39

K K Invariant Mass [GeV/c ]+-K K Invariant Mass [GeV/c ]2events [/4MeV/c2]

+

-

2

events [/4MeV/c2]

C

Cu

1.2<y

1.2<y

 2/dof=55/39

 2/dof=46/39

K K Invariant Mass [GeV/c ]+-2

K K Invariant Mass [GeV/c ]+-2

Figure 4.7: The invariant mass spectra of the ﬁnal K + K − sample divided into three rapidity
bins. The closed circles represent the data. The red, green and blue lines represent the ﬁt
results, the combinatorial backgrounds and the expected φ → K + K − shapes, respectively.

4.2. Spectral Shape and Yield of φ Meson in the K + K − Channel

events [/4MeV/c2]

117

events [/4MeV/c2]

C

Cu

pT<0.8pT<0.8

 2/dof=58/39

 2/dof=33/39

K K Invariant Mass [GeV/c ]+-K K Invariant Mass [GeV/c ]2events [/4MeV/c2]

+

-

2

events [/4MeV/c2]

C

Cu

0.8<pT<1.0

0.8<pT<1.0 2/dof=38/39

 2/dof=32/39

K K Invariant Mass [GeV/c ]+-K K Invariant Mass [GeV/c ]2events [/4MeV/c2]

+

-

2

events [/4MeV/c2]

C

Cu

1.0<pT

1.0<pT 2/dof=39/39

 2/dof=26/39

K K Invariant Mass [GeV/c ]+-2

K K Invariant Mass [GeV/c ]+-2

Figure 4.8: The invariant mass spectra of the ﬁnal K + K − sample divided into three pT bins.
The closed circles represent the data. The red, green and blue lines represent the ﬁt results,
the combinatorial backgrounds and the expected φ → K + K − shapes, respectively.

118

Chapter 4. Results and Discussions

The observed K + K − spectra are well reproduced by the ﬁt in all the βγ bins (and all others).
Therefore, the changes in mass spectra are not statistically signiﬁcant in the φ → K + K −channel. Indeed, we have observed mass-shape modiﬁcation in the φ → e+ e− channel in thevery low βγ region (βγ < 1.25) for the copper target data [31, 36]. In Fig. 4.9, we compare
the acceptances of the K + K − and e+ e− channels. In the region of βγ < 1.25, we have very
limited statistics for φ → K + K − , and we cannot obtain a reasonable ﬁt for the K + K − datawhen βγ < 1.25 is selected. Thus, it is impossible to compare the φ → K + K − shape directlywith the modiﬁed shape observed in the e+ e− channel. It can be concluded that in the region
βγ > 1.25, both φ → K + K − and φ → e+ e− do not show any signs of shape modiﬁcation.
The relative abundances of the φ mesons and the background were obtained from the ﬁt.
The yields of φ mesons are listed later in Table 4.5(b). They were obtained by integrating themass region from 2mK ± to 1.07 GeV/c2 after subtracting the background.
eventsevents

(b)

(a)
+ -



e e
K+K=1.25

(c)rapidity
pT

eventspT(d)rapidity

Figure 4.9: The observed kinematical distributions of φ → e+ e− and φ → K + K − , as functionsof (a) βγ, (b) rapidity, (c) pT , and (d) pT and rapidity. The points blue represent φ → e+ e−
and the red histograms and contours represent φ → K + K − . The dotted lines in (a) represent
βγ = 1.25. The histograms for φ → K + K − are scaled up by a factor of about 3.

4.3. Nuclear Mass Number Dependences α in the φ → e+ e− and φ → K + K − Channels

4.3

119

Nuclear Mass Number Dependences α in the φ →e+e− and φ → K +K − Channels

The cross section for a nuclear target of mass number A is parameterized as σ (A) = σ0 × Aα .
When the φ meson and/or kaon is modiﬁed in a medium and Γφ→K + K − /Γφ→e+ e− changes, theratio of the φ-meson yield R = Nφ→K + K − /Nφ→e+ e− becomes dependent on the mass number
since a larger number of φ mesons are to be modiﬁed in a larger nucleus. Consequently, by using
two diﬀerent nuclear targets A1 and A2 , the diﬀerence in the α parameter between φ → e+ e−(αφ→e+ e− ) and φ → K + K − (αφ→K + K − ) can be related to R as follows:∆α = αφ→K + K − − αφ→e+ e−
{ [
]
[
]}/
Nφ→K + K − (A1 )Nφ→e+ e− (A1 )
=
ln
− ln
ln (A1 /A2 )Nφ→K + K − (A2 )Nφ→e+ e− (A2 )= ln [R (A1 )/R (A2 )]/ln (A1 /A2 ).

(4.2)

It is important that most of the experimental eﬃciencies are canceled in obtaining α as describedin Sec. 4.3.2. The major eﬀects are present in geometrical acceptance, trigger eﬃciency, andtracking and analysis eﬃciencies.

4.3.1

Determination of α Parameters in the φ → e+ e− and φ → K + K −Channels

The production cross section of φ meson, σφ , is written as σφ = Nφ /(Np · Nt · η), where Nφ isthe number of the observed φ mesons, Np is the number of beam protons, Nt is the number
density of nucleus per unit area of the target, and η is the correction factor which includes
geometrical acceptance, trigger eﬃciency, and tracking and analysis eﬃciencies. Since Np wascommon for C and Cu targets in the present experiment, we can extract the α parameter as
[

]/

(

)

Nφ (Cu) Nt (C) ηCACu
α = ln··ln
Nφ (C) Nt (Cu) ηCu
AC
]/ (
(
)/ (
[
)
)
ACu
ACu
ηC
Nφ (Cu) Nt (C)
ln
ln
= ln
·
+ ln
Nφ (C) Nt (Cu)
AC
ηCu
AC
[
]/ (
)
ACu
Nφ (Cu) Nt (C)
= ln
·
ln
+ δα.
Nφ (C) Nt (Cu)
AC

(4.3)

Although most of the experimental eﬀects are canceled in obtaining α, small experimental
eﬀects remain as the second term in Eq. 4.3, i.e., δα 6= 0 if ηC is diﬀerent from ηCu .
The values of Nt (C) and Nt (Cu) were determined by measuring the dimensions and theweights of the target materials used for the experiment. These information is summarized inAppendix C. We obtained Nt (C)/Nt (Cu) = 3.354 ± 0.016 and 3.348 ± 0.028 for 2001 and 2002
respectively. Since the ratios are almost identical between the two data taking periods, weconsidered the ratios were the same, and treated the measurement errors as a systematic error
in α. The values used in the analysis are listed in Table 4.1. For the e+ e− channels we used
the average ratio of 2001 and 2002, and for the K + K − channel we used the ratio of 2001.

120

Chapter 4. Results and Discussions+ −for φ → e e
for φ → K + K −Nt (C)/Nt (Cu)
3.351 ± 0.031
3.354 ± 0.016

systematic error in α
0.006
0.003

Table 4.1: The values of Nt (C)/Nt (Cu) for φ → e+ e− (average of 2001 and 2002) and for
φ → K + K − (2001 only). The systematic errors in α from the errors in Nt (C)/Nt (Cu) are also
listed.

In the rest of this section, we describe how to estimate ηC /ηCu and its error. As a result,the most signiﬁcant correction was obtained from the geometrical acceptance, and we corrected
the values of α. Next, there was a correction from the trigger eﬃciency, which we included in
the systematic error. The corrections from the other eﬃciencies were negligibly small.
Diﬀerence in Geometrical Acceptance
The targets were aligned in-line, like Cu-C-Cu or Cu-Cu-C-Cu-Cu depending on the data taking
year. Since these conﬁgurations were symmetric about the C target, we considered that the
average of the Cu targets is equivalent to that of the C target. However this assumption was
not perfect, particularly in the φ → K + K − channel as described in Sec. 3.5.2. Table 4.2 shows
the geometrical acceptance eﬀects on ηC /ηCu (φ → K + K − ) and δαφ→K + K − obtained with thenuclear cascade code JAM as described in Sec. 3.5.2. We estimated the systematic errors inthem to be 0.006 and 0.004 for ηC /ηCu (φ → K + K − ) and δαφ→K + K − , respectively, mainly due tothe Monte Carlo statistics. Apparently this correction is signiﬁcant at low pT and low rapidity,i.e., in the small-angle region. The reason is that the center of the kinematical distribution of
the φ-meson is on the edge of the detector acceptance for K + K − pairs as shown in Fig. 4.10(b),and consequently the number of accepted mesons is very sensitive to the target position.
On the other hand, in the φ → e+ e− channel in which e+ and e− are widely separated,ηC /ηCu (φ → e+ e− ) is consistent with unity within a systematic error of 0.011 which corresponds
to 0.006 in αφ→e+ e− . This is because the center of the kinematical distribution of the φ-mesonis on the center of the detector acceptance unlike φ → K + K − , as shown in Fig. 4.10(a).
Table 4.2 was used to correct αφ→K + K − , and the above-mentioned systematic errors (bothφ → K + K − and φ → e+ e− ) were included as the error of δα.

allβγ

rapiditypT

1 – 1.7
1.7 – 2.2
2.2 – 3.5
0.5 – 1
1 – 1.2
1.2 – 1.5
0.4 – 0.8
0.8 – 1
1 – 1.5

ηC /ηCu (φ → K + K − )
1.021
1.009
1.010
1.040
1.063
1.011
0.992
1.030
1.016
1.020

δαφ→K + K −
0.012
0.005
0.006
0.024
0.037
0.007
−0.005
0.018
0.010
0.012

Table 4.2: The geometrical acceptance eﬀects in ηC /ηCu (φ → K + K − ) and δαφ→K + K − obtainedwith the nuclear cascade code JAM and the detector simulation.

121

pT

pT

4.3. Nuclear Mass Number Dependences α in the φ → e+ e− and φ → K + K − Channels

rapidity(a) φ → e+ e−

rapidity(b) φ → K + K −Figure 4.10: The simulated detector acceptances for (a) φ → e+ e− decays and (b) φ → K + K −decays are plotted as the color maps. The acceptances are calculated using a ﬂat kinematical
distribution in the region of 0 < y < 3 and 0 < pT < 2, and include not only the geometricalacceptance but also the detector eﬃciencies and all other conditions used in the present analysis.
The kinematical distribution of the generated φ-meson yield obtained by JAM is also plottedas the contour plot in each panel.

Diﬀerence in Experimental Eﬃciencies
The ratio ηC /ηCu can diﬀer from unity due to the particle multiplicity diﬀerence between the
C and Cu targets.
We ﬁrst discuss the particle identiﬁcation eﬃciencies. In the case of φ → e+ e− decays,ηC /ηCu can be considered to be multiplicity independent, because the two tracks are well
separated and there is no veto logic neither in the trigger nor in the analysis. In the case of
φ → K + K − decays, the situation is diﬀerent because the two tracks are close to each otherand the veto logic exists in the particle identiﬁcation. The following two situations are worth
considered.
1. If a fast pion overlaps with a kaon within the same trigger segment in AC (consists ofthree physical AC segments), the kaon is overkilled.
2. If a fast pion overlaps with a kaon within the same TOF counter, the kaon is miss-identiﬁed
and overkilled.
These two possibilities can be multiplicity dependent. We denote these overkilling probabilities
as PAC (arm, target) and PTOF (arm, target), where arm is L (the left arm) or R (right) andtarget is C (the carbon target) or Cu (copper). We evaluated these two cases using the ﬁnal
K + K − sample as follows.
We obtained a probability that an event has one or more AC hits in the arm in whicha K + K − pair was detected. By scaling the AC hit multiplicity to the entire AC segments
including the ones used for the veto logic, we evaluated the overkilling probabilities for K + K −pairs in AC to be PAC (L,C)=0.138±0.006, PAC (R,C)=0.101±0.005, PAC (L,Cu)=0.123±0.006,
and PAC (R,Cu)=0.105±0.004. For TOF, we obtained the FTOF hit multiplicity in the armin which a K + K − pair was detected and then we calculated a probability that one FTOF
segment contained a kaon and other particles which change the TOF value to outside the122

Chapter 4. Results and Discussions

kaon identiﬁcation window. The overkilling rates thus obtained in TOF for K + K − pairs were
PTOF (L,C)=0.013, PTOF (R,C)=0.017, PTOF (L,Cu)=0.010, and PTOF (R,Cu)=0.014.
To check the estimations above, we also introduced the event-mixing technique. We combined the AC hits from one event with the kaon tracks from an other event, and we evaluated the overkilling probability in AC to be PAC (L,C)=0.146±0.004, PAC (R,C)=0.097±0.002,
PAC (L,Cu)=0.124±0.006, and PAC (R,Cu)=0.099±0.004. For TOF, we combined the kaon
tracks and the associated FTOF hits from one event with the FTOF hits which are not associated with the kaon tracks from another event. Considering the timing window for thekaon used for the kaon identiﬁcation, we evaluated the overkilling probability in TOF to be
PTOF (L,C)=0.010, PTOF (R,C)=0.007, PTOF (L,Cu)=0.009, and PTOF (R,Cu)=0.008.
The overkilling probabilities in the AC and TOF are summarized in Table 4.3. We took theaverages of above two estimations and the diﬀerences as the errors. It should be noted that only
the diﬀerence of the overkilling probabilities between C and Cu aﬀects the α parameters. The
overkilling in the TOF changes αφ→K + K − by a maximum value of 0.002, which is negligible,
whereas the overkilling in AC changes αφ→K + K − by a maximum value of 0.016. The lattervalue was included in the systematic error.
(a) AC

AC
C
Cu

L-arm
0.142 ± 0.005
0.123 ± 0.006(b) TOFR-arm
0.099 ± 0.003
0.102 ± 0.004

TOF
C
Cu

L-arm
0.011 ± 0.002
0.009 ± 0.000

R-arm
0.012 ± 0.005
0.011 ± 0.003

Table 4.3: The overkilling probabilities in (a) AC and (b) TOF.

Second, we consider δα caused by the track multiplicity diﬀerence between the C and Cu
targets. Using the relations between the tracking eﬃciency and the track multiplicity describedin Sec. 3.4.2 in Ref. [38], we compare it with the multiplicity diﬀerence between the C andCu targets. Table 4.4 lists the track multiplicities in the ﬁnal data sample. We estimated thediﬀerences in the average tracking eﬃciency between the C and Cu targets to be 0.3% at most,which corresponds to the correction on α of 0.002 and is negligibly small.
(a) e+ e−

e+ e−
C
Cu

L-arm
1.194 ± 0.001
1.230 ± 0.001(b) K + K −R-arm
1.166 ± 0.001
1.206 ± 0.001

K +K −
CCu

L-arm
2.10 ± 0.01
2.16 ± 0.01

R-arm
2.05 ± 0.01
2.11 ± 0.01

Table 4.4: Track multiplicity in the ﬁnal data sample, (a) for e+ e− and (b) for K + K − .

4.3. Nuclear Mass Number Dependences α in the φ → e+ e− and φ → K + K − Channels

4.3.2

123

Obtained φ-meson Yields and α Parameters

We obtained the φ-meson yields for the K + K − and e+ e− decay channels as functions of βγ,
rapidity, and pT . In the K + K − decay channel, the φ-meson yields were obtained by integrating
the data from 2mK ± to 1.07 GeV/c2 after subtracting the background. In the e+ e− decay channel, the yields were obtained by integrating the data from 0.9 to 1.1 GeV/c2 after subtracting
the background.
Table 4.5(a) and (b) summarize the yields for both decay channels with the systematic errors
mainly from the uncertainties in the background estimation described in Sec.3.6.2. Additionally,
we change the excluded region from the ﬁt, and check the stability of the ﬁt in the φ → e+ e−
decays.
In the tables, the α parameters are corrected for the target dependence of the experimental
eﬃciencies, i.e., ηC /ηCu . The most signiﬁcant correction was from the diﬀerence in the geometrical acceptance for each target position. The other corrections were estimated to be small andwere included in the systematic errors together with those from the background estimations
and the target thicknesses. In the analysis thereafter, the errors in α are the quadratic sumsof the statistical and systematic errors.
The observed α parameters are plotted as functions of βγ in Fig. 4.11(a) and as functions of
the rapidity and pT in (b) and (c), respectively. The e+ e− and K + K − decay channels cannot
be compared directly because of the diﬀerence in the detector acceptance between the e+ e−
and K + K − decay channels, as shown in Fig. 4.9. Table 4.6 shows how the acceptances were
diﬀerent in each bin of βγ, rapidity, and pT . In the table, we list the mean value and RMS ofeach bin for φ → e+ e− and φ → K + K − decays. Here the target dependence is neglected andthe C and Cu target data are summed. Figure 4.12 demonstrates how they look in the y-pT
plane.

124

Chapter 4. Results and Discussions(a) φ → e+ e−
Nφ→e+ e− (C)2528 ± 101 ± 6
331 ± 32 ± 6
702 ± 51 ± 9
945 ± 62 ± 14
579 ± 52 ± 4
397 ± 35 ± 6
649 ± 50 ± 5
828 ± 57 ± 11
687 ± 57 ± 6794 ± 57 ± 3
748 ± 53 ± 2
646 ± 51 ± 2
370 ± 39 ± 3

allβγ < 1.25
1.25 < βγ < 1.75
1.75 < βγ < 2.5
2.5 < βγy<11 < y < 1.25
1.25 < y < 1.5
1.5 < yp T < 0.25
0.25 < p T < 0.4
0.4 < p T < 0.6
0.6 < p T

Nφ→e+ e− (Cu)3302 ± 121 ± 25
703 ± 50 ± 26
899 ± 63 ± 41096 ± 71 ± 12
626 ± 56 ± 5774 ± 54 ± 26
854 ± 62 ± 3
937 ± 65 ± 12
758 ± 61 ± 2
987 ± 70 ± 18993 ± 63 ± 12
899 ± 61 ± 1
474 ± 46 ± 1

αφ→e+ e−0.89 ± 0.03 ± 0.01
1.18 ± 0.07 ± 0.02
0.87 ± 0.06 ± 0.02
0.81 ± 0.06 ± 0.01
0.77 ± 0.08 ± 0.01
1.13 ± 0.07 ± 0.02
0.89 ± 0.06 ± 0.01
0.80 ± 0.06 ± 0.01
0.79 ± 0.07 ± 0.01
0.86 ± 0.06 ± 0.02
0.90 ± 0.06 ± 0.01
0.92 ± 0.06 ± 0.01
0.87 ± 0.09 ± 0.01(b) φ → K + K −Nφ→K + K − (C)426 ± 41 ± 49
99 ± 20 ± 18
142 ± 24 ± 18
177 ± 26 ± 11
113 ± 22 ± 17
162 ± 25 ± 19
139 ± 24 ± 10
175 ± 23 ± 16
132 ± 24 ± 19
122 ± 24 ± 12allβγ < 1.7
1.7 < βγ < 2.2
2.2 < βγy<11 < y < 1.2
1.2 < yp T < 0.8
0.8 < p T < 1
1<pT

Nφ→K + K − (Cu)849 ± 54 ± 79
285 ± 29 ± 27
279 ± 32 ± 30
269 ± 33 ± 21
318 ± 32 ± 31
301 ± 33 ± 24
217 ± 29 ± 22329 ± 31 ± 29
283 ± 31 ± 27
237 ± 32 ± 21

αφ→K + K −1.15 ± 0.07 ± 0.03
1.38 ± 0.13 ± 0.07
1.14 ± 0.12 ± 0.03
0.99 ± 0.12 ± 0.03
1.35 ± 0.13 ± 0.05
1.10 ± 0.11 ± 0.04
1.02 0.13 ± 0.04
1.14 ± 0.10 ± 0.02
1.19 ± 0.13 ± 0.05
1.12 ± 0.14 ± 0.03

Table 4.5: The yields and the α parameters for (a) φ → e+ e− and (b) φ → K + K − . The ﬁrst
errors are statistical and the second are systematic.



+ -

e e
+ K K


(a) βγrapidity(b) rapiditypT(c) pT

Figure 4.11: α parameters of φ → e+ e− (closed circle) and φ → K + K − (open circle) as
functions of (a) βγ, (b) rapidity, and (c) pT . The horizontal error bars are the RMS values of
the horizontal bins.

4.3. Nuclear Mass Number Dependences α in the φ → e+ e− and φ → K + K − Channels

125(a) φ → e+ e−
βγ valuemean RMS
1.89
0.67
1.00
0.21
1.51
0.15
2.08
0.22
2.89
0.29
1.06
0.24
1.56
0.21
2.07
0.28
2.78
0.36
1.65
0.64
1.85
0.65
1.96
0.63
2.37
0.61

all
βγ < 1.25
1.25 < βγ < 1.75
1.75 < βγ < 2.5
2.5 < βγy<11 < y < 1.25
1.25 < y < 1.5
1.5 < ypT < 0.25
0.25 < pT < 0.4
0.4 < pT < 0.6
0.6 < pT

rapidity valuemean RMS
1.26
0.31
0.81
0.16
1.12
0.11
1.38
0.12
1.66
0.14
0.82
0.16
1.13
0.07
1.37
0.07
1.66
0.11
1.22
0.33
1.27
0.32
1.27
0.30
1.33
0.26

pT valuemean RMS
0.38
0.21
0.28
0.15
0.35
0.17
0.40
0.20
0.49
0.26
0.34
0.18
0.38
0.21
0.41
0.22
0.40
0.21
0.16
0.06
0.33
0.04
0.49
0.05
0.75
0.13

(b) φ → K + K −allβγ < 1.7
1.7 < βγ < 2.2
2.2 < βγy<11 < y < 1.2
1.2 < ypT < 0.8
0.8 < pT < 1
1 < pTβγ valuemean RMS
2.02
0.54
1.41
0.22
1.95
0.15
2.60
0.30
1.52
0.36
2.03
0.34
2.56
0.36
1.60
0.36
2.11
0.42
2.46
0.44

rapidity valuemean RMS
1.08
0.20
0.88
0.13
1.09
0.11
1.25
0.14
0.86
0.11
1.10
0.06
1.31
0.08
1.01
0.18
1.14
0.20
1.12
0.18

pT valuemean RMS
0.90
0.25
0.70
0.15
0.88
0.17
1.09
0.22
0.83
0.27
0.92
0.25
0.96
0.19
0.67
0.09
0.89
0.05
1.20
0.17

( -slice)(rapidity-slice)

rapidity(a) βγ-slice

pT

+ -

e e
+ K K

pT

pT

Table 4.6: The mean and RMS values of each kinematical bin for (a) φ → e+ e− and (b)φ → K +K −.

(pT-slice)

rapidity(b) rapidity-slice

rapidity(c) pT -slice

Figure 4.12: The mean and RMS values of each bin of φ → e+ e− (closed circle) and φ → K + K −(open circle) in the y-pT plane for (a) βγ-slice, (b) rapidity-slice, and (c) pT -slice. The error
bars are the RMS values in each kinematical bin.

126

Chapter 4. Results and Discussions

α Parameters in the Overlapped AcceptanceThe detector acceptance is diﬀerent between the e+ e− and K + K − decay channels, however,there is overlapped region as shown in Fig. 4.13(d); which is enclosed by the lines connecting thefour points in the (y,pT) plane, (0.7,0.5), (1.1,0.5), (1.6,1.0), and (1.2,1.0). So we evaluated thevalues of α in the overlapped region to check the consistency with αφ→e+ e− and αφ→K + K − . The
mean and RMS values of βγ, rapidity, and pT for φ → e+ e− and φ → K + K − in the overlapped
acceptance are listed in Table 4.7. Figure 4.14(a) and (b) show the invariant mass spectra of thee+ e− and K + K − pairs with the ﬁt result in the overlapped acceptance, respectively. Table 4.8
summarizes the yields for both decay channels with the systematic errors. In the table, the αparameters are corrected for the target dependence of the experimental eﬃciencies. The ratioηC /ηCu (φ → K + K − ) and δαφ→K + K − are obtained to be 1.028 and 0.017, respectively. As listed
in Table 4.8, we obtained ∆α = 0.18 ± 0.14. Although the center value has a ﬁnite value, ∆α
is statistically consistent with zero within the large error.
eventsevents(b)(a)
e+eK+K-(c)rapidity
pT

eventspT(d)rapidity

Figure 4.13: The kinematical distributions of φ → e+ e− and φ → K + K − in the overlapped
region shown with the rectangle in (d), as functions of (a) βγ, (b) rapidity, (c) pT . The closed
circles represent φ → e+ e− and the lines represent φ → K + K − .

φ → e+ e−
φ → K +K −βγ value
rapidity value
pT valuemean RMS mean RMS mean RMS
1.81 0.48 1.11
0.17
0.67 0.13
1.96 0.44 1.15
0.16
0.75 0.12

Table 4.7: The mean and RMS of kinematic variables for φ → e+ e− and φ → K + K − decays in
the overlapped acceptance.

4.3. Nuclear Mass Number Dependences α in the φ → e+ e− and φ → K + K − Channels

events [/10MeV/c2]

events [/10MeV/c2]

C

Cu

2

2

/dof=23/26/dof=26/26

e e Invariant Mass [GeV/c ]
+ -

127

e e Invariant Mass [GeV/c ]

2

+ -

2

(a) φ → e+ e−
events [/4MeV/c2]

events [/4MeV/c2]

CCu 2/dof=53/39

 2/dof=41/39

K K Invariant Mass [GeV/c ]+-2

K K Invariant Mass [GeV/c ]+-2(b) φ → K + K −Figure 4.14: (a) The invariant mass spectra of the e+ e− sample in the overlapped acceptance.
The closed circles represent the data and the thin crosses represent the excluded region from theﬁt. The red, green and blue lines represent the ﬁt results, the quadratic backgrounds and the
expected φ → e+ e− shapes, respectively. (b) The invariant mass spectra of the K + K − sample
in the overlapped acceptance. The closed circles represent the data. The red, green and bluelines represent the ﬁt results, the combinatorial backgrounds and the expected φ → K + K −shapes, respectively.

+ −

φ→e e
φ → K +K −Nφ (C)Nφ (Cu)α
214 ± 27 ± 0 293 ± 34 ± 1 0.91 ± 0.10 ± 0.01
226 ± 27 ± 20 408 ± 35 ± 35 1.10 ± 0.09 ± 0.02

Table 4.8: The yields and the α parameters for φ → e+ e− and φ → K + K − in the overlapped
acceptance. The ﬁrst errors are statistical and the second are systematic.

128

4.3.3

Chapter 4. Results and Discussions

Comparison of αφ→e+ e− and αφ→K + K −The e+ e− and K + K − decay channels cannot be compared directly because of the diﬀerencein the detector acceptance. Therefore, we determined αφ→e+ e− two-dimensionally on the y-pT
plane under the assumption that αφ→e+ e− is linearly dependent on y and pT , and estimated thevalues corresponding to the kaon acceptance windows (see Appendix D for the detail).
The y-pT dependence of αφ→e+ e− is parameterized as α(y, pT ) = a × y + b × pT + c, and wedetermined the parameters as follows:
1. The e+ e− data was divided into 3 × 3 bins in the y-pT plane as shown in Fig. 4.15.
2. The value of αφ→e+ e− in each bin was obtained as listed in Table 4.9.
3. The values were ﬁtted with the above function.

pT

We obtained a = −0.32 ± 0.11, b = 0.13 ± 0.17, c = 1.24 ± 0.15, and χ2 /dof = 4.2/6, indicatingthat the above assumption is statistically acceptable. Since the ﬁt was statistically reasonable,
we estimated α(y, pT ) of each K + K − data point according to its kinematical coverage and weused the estimated values for the comparison of αφ→e+ e− and αφ→K + K − .

+ -

e e

#1
#2
#3
#4
#5
#6
#7
#8
#9

#3 #6 #9
#2 #5 #8
#1 #4 #7y < 1.1
y < 1.1
y < 1.1
1.1 < y < 1.4
1.1 < y < 1.4
1.1 < y < 1.4
1.4 < y1.4 < y1.4 < ypT < 0.3
0.3 < pT < 0.5
0.5 < pT
pT < 0.3
0.3 < pT < 0.5
0.5 < pT
pT < 0.3
0.3 < pT < 0.5
0.5 < pT

rapidity valuemean RMS
0.87
0.19
0.91
0.15
0.93
0.15
1.25
0.09
1.26
0.09
1.26
0.10
1.60
0.14
1.59
0.14
1.57
0.11

pT valuemean RMS
0.18
0.07
0.40
0.05
0.63
0.15
0.19
0.07
0.39
0.06
0.67
0.16
0.20
0.07
0.39
0.05
0.67
0.13

rapidity

Figure 4.15: The mean and RMS values of each bin of φ → e+ e− decays divided into 3 × 3 inthe y-pT plane. The error bars are the RMS values. The ID number (#x) in the ﬁgure for eachdata point corresponds to the number in the table showing the actual values.

#1
#2
#3
#4
#5
#6
#7
#8
#9

Nφ→e+ e− (C)280 ± 30 ± 4
243 ± 27 ± 1
137 ± 20 ± 1
407 ± 39 ± 3
359 ± 34 ± 5
257 ± 30 ± 2
388 ± 42 ± 2
306 ± 38 ± 8296 ± 36 ± 2

Nφ→e+ e− (Cu)495 ± 43 ± 15377 ± 38 ± 12
223 ± 28 ± 1
454 ± 47 ± 4426 ± 41 ± 5
319 ± 37 ± 1
391 ± 46 ± 2
389 ± 42 ± 1
386 ± 39 ± 1

αφ→e+ e−1.07 ± 0.08 ± 0.02
0.99 ± 0.09 ± 0.03
1.02 ± 0.11 ± 0.01
0.79 ± 0.08 ± 0.01
0.83 ± 0.08 ± 0.01
0.86 ± 0.10 ± 0.01
0.73 ± 0.10 ± 0.01
0.87 ± 0.10 ± 0.02
0.89 ± 0.10 ± 0.01

Table 4.9: The yields and the α parameters for the φ → e+ e− decays divided into 3 × 3 bins in
the y-pT plane. The ﬁrst errors are statistical and the second are systematic.

4.3. Nuclear Mass Number Dependences α in the φ → e+ e− and φ → K + K − Channels

129

In Fig. 4.16, we show the estimated values of αφ→e+ e− in the kaon acceptance windows as
hatched bands; these can be compared to the measured values of αφ→K + K − . The diﬀerence∆α’s in the kaon acceptance are plotted in Fig. 4.17, and listed in Table 4.10. We expect that∆α should be zero when Γφ→K + K − /Γφ→e+ e− does not change in a nuclear media. Although it
is interesting to observe that ∆α increases when βγ decreases, ∆α at the lowest βγ bin is 0.33
± 0.17. The averaged value, which is obtained by using all kinematical region for the K + K −channel, is 0.14 ± 0.12. It seems that these values have discrepancies from zero, however,
αφ→e+ e− and αφ→K + K − are consistent with each other within errors in the measured kinematic
region.


+ -

e e
+ K K


rapidity(a) βγpT(b) rapidity(c) pT

Figure 4.16: The α parameters of φ → e+ e− (closed circle) and φ → K + K − (open circle) as
functions of (a) βγ, (b) rapidity, and (c) pT , before the acceptance correction. The corrected
αφ→e+ e− with the errors for the K + K − acceptance are shown as the hatched bands.









(a) βγrapidity(b) rapiditypT(c) pT

Figure 4.17: The diﬀerences between αφ→K + K − and αφ→e+ e− , ∆α, in the kaon acceptance asfunctions of (a) βγ, (b) rapidity, and (c) pT . The average value and error are also plotted as
the hatched bands.

130

Chapter 4. Results and Discussions

allβγ < 1.7
1.7 < βγ < 2.2
2.2 < βγy<11 < y < 1.2
1.2 < ypT < 0.8
0.8 < pT < 1
1 < pT

rapidity valuemean RMS
1.08
0.20
0.88
0.13
1.09
0.11
1.25
0.14
0.86
0.11
1.10
0.06
1.31
0.08
1.01
0.18
1.14
0.20
1.12
0.18

pT valuemean RMS
0.90
0.25
0.70
0.15
0.88
0.17
1.09
0.22
0.83
0.27
0.92
0.25
0.96
0.19
0.67
0.09
0.89
0.05
1.20
0.17

αφ→K + K −estimated αφ→e+ e−∆α1.15 ± 0.07 ± 0.03
1.38 ± 0.13 ± 0.07
1.14 ± 0.12 ± 0.03
0.99 ± 0.12 ± 0.03
1.35 ± 0.13 ± 0.05
1.10 ± 0.11 ± 0.04
1.02 ± 0.13 ± 0.04
1.14 ± 0.10 ± 0.02
1.19 ± 0.13 ± 0.05
1.12 ± 0.14 ± 0.03

1.01 ± 0.10
1.05 ± 0.08
1.00 ± 0.10
0.98 ± 0.12
1.07 ± 0.10
1.01 ± 0.10
0.94 ± 0.10
1.00 ± 0.07
0.99 ± 0.09
1.03 ± 0.15

0.14 ± 0.12
0.33 ± 0.17
0.14 ± 0.16
0.01 ± 0.17
0.28 ± 0.17
0.09 ± 0.16
0.08 ± 0.17
0.14 ± 0.12
0.20 ± 0.17
0.09 ± 0.20

Table 4.10: αφ→K + K − and estimated αφ→e+ e− in the kaon acceptance window. The ﬁrst errors
are statistical and the second are systematic. For “estimated αφ→e+ e− ” and “∆α”, the errors
are the quadratic sums of the statistical and systematic errors.

4.4

Discussion on the Possible Modiﬁcation of Γφ→K +K −and Γφ→e+e−

On the basis of the obtained results, the possible modiﬁcation of the decay widths is discussed
below. In medium, we suppose the total and partial decay widths Γ to change to Γ∗ according
to the relation//Γ∗φ Γ0φ = 1 + ktot (ρ/ρ0 ) ,Γ∗φ→K + K − Γ0φ→K + K − = 1 + kK (ρ/ρ0 ) ,
/

(4.4)

Γ∗φ→e+ e− Γ0φ→e+ e− = 1 + ke (ρ/ρ0 ) ,where Γ0 is the value in vacuum, ρ0 is the normal nuclear density, and ktot , kK , and ke are width
broadening parameters (see Appendix E). We expect ktot ' kK since the φ meson mainly decays
into K K̄ as long as such decays are kinematically allowed.
To estimate the relation between ∆α, kK , and ke , we performed the Monte Carlo calculation.
We considered that φ mesons were uniformly generated in the target nucleus according to the
nuclear density. This is because the mass-number dependence of the φ meson production crosssection α is obtained to be about unity as described in Sec. 4.3. Generated φ mesons weretraced until the decay point with the modiﬁed decay width according to the nuclear density
distribution. The decay probability increases in the medium due to the width broadening. We
used the Woods-Saxon form as shown in Fig. 4.18 for the nuclear density distribution;
ρ/ρ0 ∝ (1 + exp((r − R)/τ ))−1 ,(4.5)

where R = 4.1(2.3) fm, and τ = 0.50(0.57) fm for the Cu(C) target. In the plane of kK and
ke , the expected values of ∆α were obtained. The results are shown in Fig. 4.19, in which themeasured ∆α provides constraints for kK and ke .

131

/ 0

4.4. Discussion on the Possible Modiﬁcation of Γφ→K + K − and Γφ→e+ e−CCur (fm)
Figure 4.18: The Woods-Saxon distribution for C and Cu nuclei.

0.2

20

0.15

.10

)

ke



=-0

)
02
.
=0

(

15

0.05

(
1

2

10

0.1

0
-0.05

5

0
0

5

ter
cen

10

(
15

14)
=0.
20

-0.1
-0.15
-0.2

kK

Figure 4.19: The values of expected ∆α shown in color, which are obtained by the Monte Carlocalculation. The measured ∆α and its error band are shown with the lines.
Next, we considered how the K + K − spectra could provide constraints on kK . Since weobserved a signiﬁcant excess on the low-mass side of the φ-meson peak in the φ → e+ e−channel [31, 36], we consider that a similar excess can exist in the φ → K + K − spectra. We
thus reanalyzed the φ → K + K − spectra with the same ﬁtting procedure as described earlier,except that the mass range from 2mK ± (0.987) to 1.01 GeV/c2 (0.01 GeV/c2 below the φ peak)
was excluded from the ﬁt, as shown in Fig. 4.20. Due to the statistical limitation, we combined
all the kinematical bins into one.
This procedure gives the amount of excess Nex as a surplus over the natural φ-meson peak
and the background. Since the K + K − acceptance is a function of the invariant mass as described in Sec. 3.5.2 (Fig. 3.63(b)), we corrected obtained values as listed in Table 4.11. In this

132

Chapter 4. Results and Discussions

table, the systematic errors contain the uncertainty in the background estimation. Althoughthese surpluses Nex are close to zero, they statistically limit the number of modiﬁed φ mesonsin the K + K − spectra. The ratio Nex /Nφ can be considered as the ratio of the number of φmesons decayed inside the nucleus to that outside it, i.e., Nex /Nφ = Nφin /Nφout .

events [/4MeV/c2]

events [/4MeV/c2]

CCu

K K Invariant Mass [GeV/c ]+-2

K K Invariant Mass [GeV/c ]+-2

Figure 4.20: The invariant mass spectra of the ﬁnal K + K − sample. The closed circles represent
the data and the thin crosses represent the excluded region, from 2mK ± (0.987) to 1.01 GeV/c2 ,for the ﬁt. The red, green and blue lines represent the ﬁt results, the combinatorial backgrounds
and the expected φ → K + K − shapes, respectively.

Nφ
Nex
Nex /Nφbefore the mass acceptance correction
CCu
454 ± 33 ± 29
880 ± 44 ± 50
23 ± 20 ± 37
90 ± 28 ± 54
0.051 ± 0.045 ± 0.073 0.103 ± 0.032 ± 0.053

after the mass acceptance correction
CCu
356k ± 12k ± 23k
697k ± 16k ± 40k
16k ± 13k ± 23k
53k ± 18k ± 34k
0.044 ± 0.037 ± 0.058 0.076 ± 0.025 ± 0.043

Table 4.11: The number of φ meson Nφ , the excess Nex , and Nex /Nφ before and after the mass
acceptance correction. The ﬁrst errors are statistical and the second are systematic.

The relation between Nφin /Nφout and kK was also obtained by the Monte Carlo calculation.
We assumed that the decays inside the half-density radius of the Woods-Saxon distribution
contribute to Nφin . Figure 4.21 shows the relation between Nφin /Nφout and kK for C and Cu
nuclei obtained by the Monte Carlo calculation. Using the relation in Fig. 4.21, we obtained
the allowed region of kK with a constraint by the observed Nex /Nφ as listed in Table 4.12. By
averaging the kK for C and Cu, we obtained kK = 1.4 ± 1.1 (stat) ± 2.1 (syst), and plotted inFig. 4.22.

N in/N out

4.4. Discussion on the Possible Modiﬁcation of Γφ→K + K − and Γφ→e+ e−

133

1

0.8

0.6

0.4

0.2

0

0

5

10

15

20

kK

Figure 4.21: The relation Nφin /Nφout and kK for C and Cu nuclei obtained by the Monte Carlocalculation.

kK
3.4 ± 4.8 ± 7.6
1.3 ± 1.1 ± 1.8
1.4 ± 1.1 ± 2.1

CCu
weighted mean

Table 4.12: The obtained kK from the observed Nex /Nφ in Table 4.11 and the calculated
Nφin /Nφout -kK relation in Fig. 4.21. The ﬁrst errors are statistical and the second are systematic.

ke


0.2

20

0.15
15

5



0

2 (kK=7.8)

10

0.05

1 (kK=4.6)

center (kK=1.4)

0.1

-0.05



-0.1
-0.15

0
0

5

10

15

20

-0.2

kK

Figure 4.22: The constraint given by the Nex /Nφ ratio in the plane of kK and ke .

134

Chapter 4. Results and Discussions

Using the above two constraints in the plane of kK and ke , the 90% conﬁdence limits are
obtained and shown in Fig. 4.23. We have renormalized the probability distribution functions
eliminating an unphysical region corresponding to Γ∗ /Γ0 < 0. These are the ﬁrst experimental
limits assigned to the in-media broadening of the partial decay widths.

ke


20

%
0
9
om
r
(f

15

kK=1.4

90% C.L.
(from kK=1.4)

10

5

0.2

L. .14)
.
C =0

0.15
0.1
0.05
0
-0.05
-0.1

4

1
=0.

-0.15

0
0

5

10

15

20

-0.2

kK

Figure 4.23: The obtained constraints on the in-medium modiﬁcation of the partial decay
widths of φ → K + K − and φ → e+ e− . The 90% conﬁdence limits, which are renormalized
for the probability distribution functions by eliminating an unphysical region corresponding toΓ∗ /Γ0 < 0, are plotted.

1354.4. Discussion on the Possible Modiﬁcation of Γφ→K + K − and Γφ→e+ e−With our previous result of the φ → e+ e− decay channel, the constraints on the in-medium
modiﬁcation of the partial decay widths of φ → K + K − and φ → e+ e− , and the constraint
obtained in Ref. [31], parameterk2tot , are plotted in Fig. 4.24. Here the parameter of k2tot in/
Ref. [31] is deﬁned as Γ∗φ Γ0φ = 1 + k2tot (ρ/ρ0 ) with an assumption that Γφ /Γφ→e+ e− are notchanged in a medium, and obtained to be k2tot = 2.6+1.8−1.2 . In the ﬁgure, our two works are
consistent with each other.

ke


20

%
90
om
r
(f

15

ta
e+
eda

5

0.15
0.1
0.05
0

90% C.L.
(from kK=1.4)

10

0.2

. 4)
L
C. =0.1

-0.05
-0.1
-0.15

0
0

5

10

15

20

-0.2

kK

Figure 4.24: The obtained constraints on the in-medium modiﬁcation of the partial decay
widths of φ → K + K − and φ → e+ e− , and the constraint obtained in Ref. [31].

Although the present analysis gave “null” results on the decay width modiﬁcation of Γφ→e+ e−and Γφ→K + K − as well as on the mass shape modiﬁcation in the φ → K + K − decay channel,
the data can set limits on the in-media broadening using a simple model calculation witha minimal assumption that the modiﬁed φ appears in the low mass side of the φ peak as
experimentally shown by our previous work [31, 36]. It should be noted that the remarkable
S/N ratio (compared to the high-energy A + A reactions) of the present experiment enabled us
to perform this analysis. Such an analysis was impossible by the past experiments. Therefore,
it is very meaningful to set those experimental limits to be compared with various theoreticalmodels for the width broadening as described in Sec. 1.2.

Chapter 5
Conclusion
The experiment KEK-PS E325 has measured the invariant mass spectra of e+ e− and K + K −pairs in 12 GeV p + A reactions. The goal of the experiment is to detect a possible signature of
the partially-restored chiral-symmetry at normal nuclear density to appear as modiﬁcation of
the spectral shape of vector mesons. We have searched for a possible change of the branchingratio Γφ→K K̄ /Γφ→e+ e− , which is theoretically predicted as a consequence of a change in the
spectral functions of φ and/or kaon in medium, using the nuclear mass-number dependences ofthe φ → e+ e− and φ → K + K − yields.
The spectrometer was newly constructed at the high-intensity primary beam-line in KEK todetect slowly moving vector mesons in the ρ → e+ e− , ω → e+ e− , φ → e+ e− , and φ → K + K −decay modes simultaneously. The e+ e− data described in this manuscript was taken in the year
2001 and 2002, and the K + K − data was taken in 2001.
The clear peaks of the φ → e+ e− and φ → K + K − decays were obtained both in the carbon
and copper targets data, and we have observed a mass shape modiﬁcation in the φ → e+ e−channel in the very low βγ region (βγ < 1.25) for the copper target data [Phys. Rev. Lett.
98, 042501 (2007)]. The observed K + K − spectra are well reproduced by the relativistic BreitWigner distribution with a combinatorial background shape. Because of the diﬀerence in thedetector acceptances between φ → e+ e− and φ → K + K − , we have very limited statistics for
φ → K + K − in the region βγ < 1.25. Thus, it is impossible to compare the φ → K + K − shape
directly with the modiﬁed shape observed in the e+ e− channel, and it can be concluded thatin the region βγ > 1.25, both φ → K + K − and φ → e+ e− do not show any shape modiﬁcation.
The nuclear mass number dependences of φ meson production are compared between the+ −e e and K + K − channels, using the parametrization of σ (A) = σ0 × Aα . Because of the diﬀerence in the detector acceptances, we extrapolated αφ→e+ e− two-dimensionally on the rapidity(y) and transverse momentum (pT ) plane to the kaon arm acceptance under the assumption,
which is veriﬁed with the data, that αφ→e+ e− changes linearly on both rapidity and pT . We
obtain ∆α = αφ→K + K − − αφ→e+ e− to be 0.33 ± 0.17 at the lowest βγ region, βγ < 1.7. The
averaged value of ∆α is obtained to be 0.14 ± 0.12 in the full βγ region, 1 < βγ < 3.5. It seems
that these values have discrepancies from zero, however, αφ→e+ e− and αφ→K + K − are consistent
with each other within errors in the measured kinematic region. This is the ﬁrst measurementof the branching ratio Γφ→K + K − /Γφ→e+ e− in a nuclear medium.
Using a simple Monte Carlo calculation, we related ∆α to the in-media broadening parameters kK for Γφ→K + K − and ke /for Γφ→e+ e− , and the observed ∆α set the limit on kK and ke .
Here kx is deﬁned as Γ∗φ→x+ x− Γ0φ→x+ x− = 1 + kx (ρ/ρ0 ) . We also searched for possible massmodiﬁcation signals on the low mass side of the φ → K + K − peak. We found zero-consistentsignal which set the limit on kK . Using the above two constraints in the plane of kK and ke ,the 90% conﬁdence limits are obtained in the kK -ke plane for the ﬁrst time.

136

Acknowledgments
First of all, I would like to express my gratitude for Professor Hideto En’yo who has been the
spokesman of the present experiment. He has continuously encouraged, advised, and supported
me at every stage of this work. I gratefully acknowledge Prof. K. Imai and Prof. N. Saito for
their guidance, discussions, and support for myself to accomplish the present works.
I wish to acknowledge all the collaborators of the E325 experiment. I express my thanks
to Prof. J. Chiba, Dr. M. Sekimoto, Prof. H. Funahashi, Dr. T. Murakami, and Prof.
H. Hamagaki for their helpful advice at every stage of the experiment, including the design,
construction, data-taking, and analysis. I greatly acknowledge Prof. M. Ieiri, Prof. K.H.
Tanaka, and Prof. M. Takasaki who constructed and maintained the EP1B beam line, for theirhelpful support. I would like to thank Dr. S. Yokkaichi, Dr. T. Tabaru, Dr. M. Naruki, Dr.
R. Muto, Dr. K. Ozawa, Dr. M. Ishino, and Dr. S. Mihara. They are the major players
who carried out this experiment. They have also provided clear and helpful advice. I would
also like to say thanks to Mr. T. Miyashita and Mr. Y. Yoshimura for the construction andthe maintenance of the spectrometer. Thanks are also delivered to Dr. M. Kitaguchi, Dr. S.
Yamada, Mr. Y. Fukao, Dr. K. Miwa, Mr. T. Nakura, and Mr. M. Togawa for their tirelesseﬀorts during the data-taking period. I also thank Dr. H. Kanda and for assistance during thebeam time.
The experiment was fully supported by the staﬀs of KEK, including the PS beam channelgroup, the PS ﬂoor staﬀ, the on-line group, the electronics division, and the accelerator division.
This work was partly supported by the Japan Society for the Promotion of Science and a
Grant-in-Aid for Scientiﬁc Research from the Japan Ministry of Education, Culture, Sports,
Science and Technology (MEXT). Finally, we also thank the staﬀ members of RIKEN Super
Combined Cluster system and RIKEN-CCJ.
Finally, I express my appreciation to my wife Karen and my parents for their lasting assistance and encouragements.

137

Appendix A
Squared-Mass Distribution in Kaon
SampleAs described in Sec. 3.3.6, we obtained the momentum-sliced M2 distributions from Fig. 3.25,
and each M2 distribution was ﬁtted by three peaks, pion, kaon and proton using a double
Gaussian distribution. All the results are shown in Fig. A.1 and A.2, and Fig. A.3 shows thesum of the sliced M2 distributions.
0.4<p<0.6

0.6<p<0.8

squared-mass [(GeV/c ) ]0.8<p<1.0

squared-mass [(GeV/c ) ]2 2

squared-mass [(GeV/c ) ]2 2

1.0<p<1.2

2 2

1.2<p<1.4

squared-mass [(GeV/c ) ]1.4<p<1.6

squared-mass [(GeV/c ) ]2 2

squared-mass [(GeV/c ) ]2 2

1.6<p<1.8

2 2

1.8<p<1.9

squared-mass [(GeV/c ) ]2 2

squared-mass [(GeV/c ) ]2 2

Figure A.1: The distributions of the squared-mass for positive particles with momentum slices
of every 0.2 GeV/c step. The distributions were ﬁtted using a double Gaussian distribution.
The vertical magenta lines indicate the regions for the kaon selection.
138

139

0.4<p<0.6

0.6<p<0.8

squared-mass [(GeV/c ) ]0.8<p<1.0

squared-mass [(GeV/c ) ]2 2

squared-mass [(GeV/c ) ]2 2

1.0<p<1.2

2 2

1.2<p<1.4

squared-mass [(GeV/c ) ]1.4<p<1.6

squared-mass [(GeV/c ) ]2 2

squared-mass [(GeV/c ) ]2 2

1.6<p<1.8

2 2

1.8<p<1.9

squared-mass [(GeV/c ) ]2 2

squared-mass [(GeV/c ) ]2 2

Figure A.2: The distributions of the squared-mass for negative particles with momentum slices
of every 0.2 GeV/c step. The distributions were ﬁtted using a double Gaussian distribution.
The vertical magenta lines indicate the regions for the kaon selection.

squared-mass [(GeV/c ) ]2 2(a) + chargesquared-mass [(GeV/c ) ]2 2(b) – charge

Figure A.3: The distributions of the squared-mass for (a) positive and (b) negative particles.
The ﬁt results, which were the sum of the ﬁts on the momentum-sliced M2 distributions asshown in Fig. A.1 and A.2, was also plotted.

Appendix B
Double-Arm φ → K +K − Event
Because of the small Q value in φ → K + K − decays, the number of φ → K + K − events were
negligible in the double-arm K + K − event, which has larger opening angle than that of thesingle-arm event. Here, “double-arm event” means that K + is detected in the left arm andother is detected in the right arm of the spectrometer (LR event), and vice versa (RL event).
Since the mass acceptance of RL events is largely suppressed in the mass region near threshold,as same as e+ e− events, we used LR events for the analysis. Table 3.9 in Sec. 3.6.2 listed thepurity of the kaon in the double-arm data (LR events).
Figure B.1 shows the invariant mass spectra of K + K − pairs in the double-arm events (LRevents) in the mass range from 0.95 to 1.15 GeV/c2 . Small peaks of double-arm φ → K + K −decays are seen. We ﬁtted each mass spectrum with a resonance shape of φ → K + K − anda combinatorial background shape in the mass region from 2mK ± (0.987) to 1.15 GeV/c2 , andthe ﬁts were performed by using the maximum likelihood method. For the φ meson resonanceshape, we used the simulated shape as described in Sec. 3.5.2, but the double-arm events wererequired. And for the combinatorial background shape, we used the mixed event as describedin Sec. 3.6.2. The relative abundance of the φ mesons and the background were obtained fromthe ﬁt.
events [/6MeV/c2]

events [/6MeV/c2]

CCu 2/dof=30/25

 2/dof=31/25

K K Invariant Mass [GeV/c ]+-2

K K Invariant Mass [GeV/c ]+-2

Figure B.1: The invariant mass spectra of the double-arm K + K − sample. The closed circles
represent the data. The red, green and blue lines represent the ﬁt results, the combinatorial
backgrounds and the expected φ → K + K − shapes, respectively.

140

141

Table B.1 summarizes the φ-meson yields. The yields were obtained by integrating the mass
region from 1.01 to 1.03 GeV/c2 after subtracting the background. In the table, the α parameteris corrected for the target dependence of the experimental eﬃciencies as described in Sec. 4.3.2.
For this correction, the overall eﬃciency ratio ηC /ηCu (φ → K + K − ) and the correction value
δαφ→K + K − were obtained to be 0.859 and -0.092, respectively. Figure B.2 shows the detector
acceptance for the double-arm K + K − pairs (LR event only). In Fig. B.3, we compare theacceptances of double-arm φ → e+ e− , single-arm φ → K + K − , and double-arm φ → K + K − .
The observed α parameters are plotted as a function of βγ in Fig. B.4(a) and as functions of
the rapidity and pT in (b) and (c), with the single-arm φ → K + K − data and the double-arm
φ → e+ e− data.
Nφ (C)Nφ (Cu)α11.2 ± 4.3 ± 0.1 15.9 ± 5.4 ± 0.3 0.85 ± 0.31 ± 0.04

pT

Table B.1: The yields and the α parameters for double-arm φ → K + K − decays. The ﬁrst
errors are statistical and the second are systematic.

rapidity

Figure B.2: The simulated detector acceptance for double-arm φ → K + K − decays (LR event
only) is plotted as the color map. The acceptance is calculated using a ﬂat kinematical distribution in the region of 0 < y < 3 and 0 < pT < 2, and includes not only the geometricalacceptance but also the detector eﬃciencies and all other conditions used in the present analysis. The kinematical distribution of the generated φ-meson yield obtained by JAM is alsoplotted as the contour plot.

Appendix B. Double-Arm φ → K + K − Event

142

eventsevents

(b)

(a)


=1.25

e+eK+Kdouble-arm K+K-



(c)

rapidity
pT

events(d)pT

rapidity

Figure B.3: The observed kinematical distributions of double-arm φ → e+ e− , single-arm φ →K + K − , and double-arm φ → K + K − (LR event only), as functions of (a) βγ, (b) rapidity, (c)pT , and (d) pT and rapidity. The points represent φ → e+ e− , the red lines represent singlearm φ → K + K − , and the pink lines represent double-arm φ → K + K − . The histograms for
single-arm and double-arm φ → K + K − are scaled by a factor of about 3 and 13, respectively.



+ -

e e
+ K K
+ double-arm K K
(a) βγrapidity(b) rapiditypT(c) pT

Figure B.4: α parameters of φ → e+ e− (closed circle), φ → K + K − (open circle), and the
double-arm φ → K + K − (star) as functions of (a) βγ, (b) rapidity, and (c) pT . The horizontal
error bars are the RMS values of the horizontal bins.

Appendix C
Target Thickness
Table C.1 and C.2 list the detailed description of the targets used in 2001 and 2002, respectively.
The errors in the tables are the precision in the measurements of the sizes and weights of thetargets. The target dimensions in the tables are the values we received those materials fromcompanies. Actual target disks used in the experiment were cut away from those, into thedimensions summarized in Table 2.4 in Sec. 2.4.1. The ratio of the target number densities
Nt (C)/Nt (Cu) were almost equivalent between 2001 and 2002, i.e. Nt (C)/Nt (Cu) = 3.354 ±0.016 and 3.348 ± 0.028 for 2001 and 2002 respectively.
total weight [g]C
2.30230± 0.00001

Cu1
0.45663± 0.00001

Cu2
0.45980± 0.00001

Cu (sum)
0.91643± 0.00001

2.30230± 0.00001
50.00± 0.0550.05± 0.0570.70± 0.0550.00± 0.0550.05± 0.0525.025± 0.071
0.09200± 0.00026
46.126± 0.130

0.45663± 0.00001
25.00± 0.0525.05± 0.0535.25± 0.0525.25± 0.0525.00± 0.056.287± 0.035
0.07263± 0.00041
6.883± 0.038

0.45980± 0.00001
25.30± 0.0525.05± 0.0535.50± 0.0525.25± 0.0525.15± 0.05
6.344± 0.035
0.07248± 0.00040
6.869± 0.038

0.91643± 0.00001

paper weight [g]target weight [g]L1 [mm]
L2 [mm]
L5 [mm]
L3 [mm]
L4 [mm]target area [cm2 ]target density [g· cm−2 ]Nt /1020 [cm−2 ]









12.631± 0.050
0.07255± 0.00029
13.752± 0.054

Table C.1: The detailed description of the targets used in 2001, and the measured dimensions,L1 ∼ L5.

143

144

Appendix C. Target Thickness

total weight [g]paper weight [g]target weight [g]L1 [mm]
L2 [mm]
L5 [mm]
L3 [mm]
L4 [mm]target area [cm2 ]target density [g· cm−2 ]Nt /1020 [cm−2 ]C
4.81935± 0.00001
0.21277± 0.00001
4.60658± 0.00001
50.05± 0.0550.00± 0.0570.65± 0.0550.05± 0.0550.05± 0.0525.037± 0.071
0.18399± 0.00052
92.247± 0.260

Cu1
0.17911± 0.00001

0.17911± 0.00001
9.80± 0.0525.10± 0.0527.00± 0.059.90± 0.0524.90± 0.052.462± 0.0400.07275± 0.00117
6.894± 0.111Cu2
0.39197± 0.00001
0.21277± 0.00001
0.17920± 0.00001
9.85± 0.0524.80± 0.0526.60± 0.059.90± 0.0525.10± 0.052.463± 0.0390.07276± 0.00114
6.895± 0.108Cu3
0.17841± 0.00001

0.17841± 0.00001
9.90± 0.0525.25± 0.0526.60± 0.059.80± 0.0524.80± 0.052.463± 0.0390.07243± 0.00114
6.864± 0.108Cu4
0.39199± 0.00001
0.21277± 0.00001
0.17922± 0.00001
9.90± 0.0525.00± 0.0526.75± 0.059.80± 0.0525.00± 0.052.462± 0.0390.07279± 0.00116
6.898± 0.110Cu (sum)
1.14148± 0.00002
0.42554± 0.00001
0.71594± 0.00002

9.850± 0.078
0.07268± 0.00058
27.551± 0.219

Table C.2: The detailed description of the targets used in 2002.

Appendix D
Linear Assumption on α Parameter
We assumed α(y, pT ) is linearly dependent on y and pT . Indeed, the pair acceptance depends
quadratically on the rapidity interval, but the α parameter does not show such a dependence
because the acceptance term is almost canceled out by taking the ratio in calculating of α.
We found that the linear assumption is statistically valid for the present data, and we also
examined the assumption for a result of the intra-nuclear cascade calculation, as follows.
For the real data, as described in Sec. 4.3.3, the two-dimensional linear ﬁt for the e+ e− data,
which were divided into 3 × 3 bins in the y-pT plane, was successful with χ2 /dof = 4.2/6. This
supports the fact that the “linear” assumption is valid within the e+ e− acceptance. Using theﬁt result, we estimated the values corresponding to the kinematical coverage of the K + K − data
points. The comparison between αφ→K + K − and αφ→e+ e− (in the K + K − acceptance) yielded
Fig. 4.17, which shows that the value of ∆α = αφ→K + K − – αφ→e+ e− is consistent with zero
within the present statistics. If we assume that there are no diﬀerences between αφ→e+ e− and
αφ→K + K − the “linear” assumption can be tested using both with the e+ e− and K + K − data
together. We performed the ﬁt for the e+ e− data of 3 × 3 bins and the K + K − data of 3 binsin the βγ regions simultaneously, and obtained χ2 /dof = 8.7/9, which is quite reasonable.
To test the assumption for the case of the intra-nuclear cascade calculation, we generated
the events by JAM, 10 times as large statistics as the real data, as listed in Table D.1 and D.2.
The obtained α(y, pT ) are diﬀerent from the data but the “linear” ﬁt was successful. Table D.3summarizes the ﬁt qualities for both the data and the cascade calculations. Therefore, theassumption that α is linearly dependent on y and pT in the detector acceptance is considered
to be reasonable.

145

146

Appendix D. Linear Assumption on α Parameter

#1
#2
#3
#4
#5
#6
#7
#8
#9

Nφ→e+ e− (C)1184 ± 30
1041 ± 27
679 ± 20
1906 ± 39
1719 ± 34
1509 ± 302163 ± 42
1952 ± 38
1545 ± 36

Nφ→e+ e− (Cu)4825 ± 434501 ± 38
3023 ± 287761 ± 47
7298 ± 416517 ± 37
7891 ± 467553 ± 426359 ± 39

αφ→e+ e−1.150 ± 0.016
1.185 ± 0.016
1.203 ± 0.018
1.149 ± 0.013
1.175 ± 0.012
1.185 ± 0.013
1.084 ± 0.012
1.119 ± 0.012
1.156 ± 0.015

Table D.1: The simulated yields and the α parameters for the φ → e+ e− decays divided into
3 × 3 bins in the y-pT plane. The errors are statistical. The ID numbers (#x) in the tablecorrepond to the number in Fig. 4.15.

βγ < 1.7
1.7 < βγ < 2.2
2.2 < βγ

Nφ→K + K − (C)666 ± 26
1110 ± 33
1673 ± 41

Nφ→K + K − (Cu)2163 ± 47
3605 ± 60
5124 ± 72

αφ→K + K −1.263 ± 0.027
1.263 ± 0.021
1.228 ± 0.017

Table D.2: The simulated yields and the α parameters for the φ → K + K − decays divided into
three βγ bins. The errors are statistical.

DATA
MC

3x3(e+ e− )3x3(e+ e− )+3(K + K − )3x3(e+ e− )3x3(e+ e− )+3(K + K − )χ2 /dof
4.2/6
8.6/9
8.5/6
13.8/9a-0.32 ± 0.11
-0.39 ± 0.11
-0.09 ± 0.02
-0.10 ± 0.02

b
0.13 ± 0.17
0.22 ± 0.11
0.11 ± 0.02
0.12 ± 0.02c1.24 ± 0.15
1.31 ± 0.14
1.23 ± 0.03
1.24 ± 0.02

Table D.3: The results of the ﬁt with α(y, pT ) = a×y +b×pT +c, using values of α in Table 4.5,
4.9, D.1, and D.2.

Appendix E
Linear Assumption on Width
Broadening
The assumption that the width broadening is linearly dependent on the nuclear density as
Eq. 4.4 is not based on a particular theoretical prediction. However, this assumption is considered to be reasonable by referring to E.Oset and A.Ramos [9], for example, who gave theoretical predictions on Γ∗ as functions of density and the φ meson mass. From Fig.4 of Ref. [9](=Fig. E.1), the values of Γ∗ at 1020 MeV/c2 as a function of the density are read oﬀ by theeye as listed in Table E.1. When we ﬁt the values with a linear function Γ∗ /Γ0 = 1 + k(ρ/ρ0 )as Eq. 4.4, the ﬁt reproduces their prediction reasonably well and generates k = 4.4 ± 0.2 asshown in Fig. E.2.
40

[MeV]

30



     0 0
0

20

10

0
950

1000

1050

1100

0

q [MeV]

Figure E.1: Width of the φ meson in nuclear matter at three densities (ρ = 0.25ρ0 , 0.5ρ0 , ρ0 )as a function of the φ energy (Fig. 4 of Ref. [9]).

ρ/ρ0Γ (MeV/c2 )

0
4.26

0.25
5±1

0.5
10 ± 1

1
22 ± 1

Table E.1: The values of Γ∗ at 1020 MeV/c2 as a function of density read from Fig E.1 (Fig. 4of Ref. [9]) by the eye.

147

Appendix E. Linear Assumption on Width Broadening

2[MeV/c ]

148



3.988
P1
P2

/ 2
4.260
18.70

0.1000E-03
0.8728/ 0

Figure E.2: The ﬁt result of the values in Table E.1.

Appendix F
Eﬀects of Target Thickness on
Invariant Mass Spectrum
One of the key points in the E325 experiment is to use thin targets in order to suppress
the background from γ-conversions in the e+ e− channel. Moreover, thick targets increase aradiative tail on the invariant mass peaks, caused mainly by the energy loss of the electrons bybremsstrahlung. So we evaluated the eﬀects of the target thickness on the e+ e− invariant mass
spectrum using Geant4 simulation. We used the non-relativistic Breit-Wigner distribution as
the φ-meson mass shape with the internal radiative corrections described in Sec. 3.5.1. Their
kinematical distribution was generated by JAM. We compared 8 kinds of targets:• C-target, thickness = 1.0mm = 0.227g/cm2 (E325 in 2002) 1 ,• C-target, thickness = 10mm = 2.27g/cm2 ,• C-target, thickness = 20mm = 4.54g/cm2 ,• C-target, thickness = 4.42mm = 1.0g/cm2 ,• Cu-target, thickness = 0.08mm = 0.072g/cm2 (E325 in 2001/2002),• Cu-target, thickness = 0.8mm = 0.72g/cm2 ,• Cu-target, thickness = 1.6mm = 1.44g/cm2 , and• Cu-target, thickness = 1.12mm = 1.0g/cm2 .
The φ mesons were decayed into the e+ e− pairs at the center of the target thickness. When e+ e−pairs escaped out the target, we calculated the invariant mass from their momenta. Figure F.1
shows the distortion of the mass spectrum caused by the target material. The targets used in
the E325 experiment hardly change the mass spectrum as shown in the two ﬁgures (top-centerand top-right).
In addition to the target material eﬀect, we show the decomposition of various eﬀects inthe simulated φ-meson spectrum by the detector simulation in Fig. F.2. The ﬁgure shows
how the mass spectra of (1) the non-relativistic Breit-Wigner distribution get distorted with
(2) internal radiative eﬀects, (3) the target material, (4) the detector materials, and (5) the
chamber position resolution as described in Sec. 3.3.2, for the C and Cu targets.

1
The measured target thickness of C-target in the 2002 run was 0.184g/cm2 , so we overestimated the target
thickness of about 20% in the detector simulation. However the following results show that the eﬀect is negligibly
small.

149

150

Appendix F. Eﬀects of Target Thickness on Invariant Mass Spectrum

2

no target materiale e Invariant Mass [GeV/c ]+ -2C, 1.0mm=0.227g/cm

2

Cu, 0.08mm=0.072g/cm

e e Invariant Mass [GeV/c ]
+ -

2

2

2

2

e e Invariant Mass [GeV/c ]
+ -

2

2

C, 20mm=4.54g/cm

Cu, 1.6mm=1.44g/cm

e e Invariant Mass [GeV/c ]22e e Invariant Mass [GeV/c ]
+ -

2

2

C, 4.42mm=1.0g/cm

Cu, 1.12mm=1.0g/cm

e e Invariant Mass [GeV/c ]+ -2Cu, 0.8mm=0.72g/cm

e e Invariant Mass [GeV/c ]

+ -

+ -

2

C, 10mm=2.27g/cm+ -e e Invariant Mass [GeV/c ]2

e e Invariant Mass [GeV/c ]+ -Figure F.1: The invariant mass spectra of φ → e+ e− decays for diﬀerent target thickness of C
and Cu. The red, black, and blue lines represent the Breit-Wigner distribution, the spectrumwith the internal radiative eﬀects, and the distorted mass spectrum by the target material,
respectively. The mass spectra are normalized by their peak count to unity.

2

151

C

Cu

e e Invariant Mass [GeV/c ]
+ -

(a) C

2

e e Invariant Mass [GeV/c ]+ -2(b) CuFigure F.2: The expected invariant mass spectra of φ → e+ e− obtained by the detector simulation. The pink, black, green, red, and blue lines correspond to the contribution from (1) to (5)described in the text. Both LR and RL events are included. The mass spectra are normalized
by their peak count to unity.

Appendix G
Run List used for the Present Analysis
Table G.1(a) and (b) list the run shows used for the present analysis for the year 2001 and
2002, respectively. The list for 2001 is common to the e+ e− and K + K − data.
(a) the year 2001

1
2
3
4
5
6
7
8
9
10
11
12
13
14

1
6010
6042
6068
6091
6112
6131
6148
6261
6300
6337
6377
6412
6447
6479

2
6022
6044
6069
6092
6113
6133
6153
6266
6306
6344
6382
6415
6451
6482

3
6023
6051
6072
6094
6114
6134
6155
6272
6308
6347
6383
6418
6454
6487

4
6025
6053
6077
6098
6116
6137
6157
6274
6313
6350
6386
6424
6455
6490

5
6026
6054
6078
6100
6117
6138
6159
6281
6314
6353
6389
6427
6456
6493

6
6027
6056
6079
6101
6121
6139
6235
6285
6317
6357
6395
6430
6462
6501

7
6029
6058
6083
6103
6122
6140
6242
6289
6320
6360
6398
6433
6464

8
6036
6060
6086
6107
6123
6142
6247
6290
6323
6363
6401
6436
6469

9
6038
6062
6088
6108
6126
6143
6248
6293
6327
6372
6404
6442
6472

10
6040
6064
6089
6109
6127
6145
6254
6296
6330
6373
6407
6444
6476

7
7036
7064
7096
7121
7150
7170
7190
7212
7235
7265
7290
7334

8
7038
7067
7098
7123
7152
7172
7193
7214
7242
7267
7292
7338

9
7040
7069
7100
7127
7154
7174
7195
7216
7243
7269
7294
7345

10
7046
7070
7102
7128
7156
7176
7197
7218
7245
7272
7296
7347

(b) the year 2002

1
2
3
4
5
6
7
8
9
10
11
12
13

1
7017
7051
7072
7106
7130
7158
7178
7199
7220
7251
7273
7322
7352

2
7022
7053
7074
7109
7134
7160
7180
7202
7222
7253
7277
7324
7355

3
7024
7055
7081
7111
7140
7162
7182
7204
7224
7257
7281
7326
7357

4
7027
7056
7086
7115
7142
7164
7183
7206
7226
7259
7283
7328
7359

5
7029
7060
7088
7118
7144
7166
7185
7208
7231
7261
7285
7330
7362

6
7031
7062
7091
7120
7148
7168
7187
7210
7233
7263
7287
7332
7365

Table G.1: The run lists used for the present analysis, (a) for the year 2001 [136 runs] and (b)for 2002 [126 runs].

152

Appendix H
Search for J/ψ Production in 12 GeV
p + A Reactions
Understanding the production mechanism of J/ψ in high-energy hadronic collisions is an important topic in QCD. Although the structures of cc̄ mesons are well understood in terms ofquark model, the production mechanism of them is not clear yet. Understanding of such mechanism is particularly important to give the basement both in the search for quark-gluon plasma
and the study of the spin structure of nucleon. There are some theoretical models to investigate the J/ψ production mechanism which assumes a diﬀerent theoretical assumption andtreatment; the color-evaporation model (CEM) [70, 71], the color-singlet model (CSM) [72, 73],and the color-octet model (COM) [74] for example. These theoretical models are successful toexplain experimental results of J/ψ production in various energy ranges to some extent, but
not complete yet.
Experimentally, there are many experiments of J/ψ production in p + p, p + A, and A + A
collisions. Figure H.1 shows the proton-induced J/ψ total cross-sections in energy ranges√
from sN N = 6.8 to 200 GeV [75]. Theoretical models predict that J/ψ production throughquark-antiquark annihilation gives the largest contribution at large xF , while gluon-gluon fusion dominates the production at small xF [76]. The present experiment, KEK-PS E325, is√
performed at sN N = 5.1 GeV, so that searching for J/ψ production in the present energy is
attractive for the investigation of the production mechanism of J/ψ near threshold (threshold√energy is sN N = 4.9 GeV at p + p → J/ψ + p + p), which is not well studied theoretically andexperimentally yet.

153

Appendix H. Search for J/ψ Production in 12 GeV p + A Reactions

( b)

154

10
1

10
10
10
10

-1

-2

     !!#"$ 

-3

-4

10

10

2

s



√Figure H.1: The J/ψ total cross-sections at various s [73, 77, 78, 79]. The curves are thecalculations of the color-octet model using diﬀerent parton distribution functions.
In the present J/ψ → e+ e− analysis, the electron identiﬁcation was performed as follows.
Tracks were required to have position-matched hits in both the ﬁrst and the second stage
electron counters, particle momentum ptrack > 0.4 GeV/c (shown in Fig. H.2), counter position
matching (within ± 1.0 counter size), ADC of the gas-Čerenkov counters ADCFGC > 200 and
ADCRGC > 50 channels (shown in Fig. H.3), the time diﬀerence between the measured TOF
value (TFGC − TSTC ) and the expected TOF value (Texp ) to be within ± 10 ns, and energy
deposit of the EM calorimeters E > 0.3 GeV and E/p > 0.2 (shown in Fig. H.4). Note thatpions with momentum larger than 2.7 GeV/c produce Čerenkov light in GC’s, as visible inFig. H.2 ∼ H.4.

155

+

e (C)

+

e (Cu)

GeV/c

-

GeV/c

-

e (C)

e (Cu)

GeV/c

GeV/c

Figure H.2: The momentum distributions of electrons candidates. Pion contamination is visible
above 2.7 GeV/c. The upper ﬁgures are for e+ and the lower ﬁgures are for e− , for the targets
C and Cu as indicated in the ﬁgures.

156

Appendix H. Search for J/ψ Production in 12 GeV p + A Reactions



 






 


+

       


 




! +

              


 


"



       Figure H.3: The correlations between ADC pulse-hight and track momentum in FGC (upper)
and in RGC (lower). The left ﬁgures are for e+ and the right ﬁgures are for e− . Events fromthe C and Cu targets are summed.

157 +       +      (a) RLG       +      (b) SLG              (c) FLG

Figure H.4: The correlations between E/p and track momentum in (a) RLG, (b) SLG, and (c)FLG. The left ﬁgures are for e+ and the right ﬁgures are for e− . Events from the C and Cu
targets are summed.

158

Appendix H. Search for J/ψ Production in 12 GeV p + A Reactions

We also calculated expected detector responses to e, µ, and π using Geant4, as shown in
Fig. H.5 and H.6. The E/p of electrons, the ratio of energy deposit to momentum, decreases
as momentum increases, since the back-end leakage of 7.5 λ0 radiator is increases.

,

 





 
  
%
)

&
*

'
(
+
     ! " # $Figure H.5: The simulated correlations between Čerenkov-photon-yields and track momentum
when particles pass through 600 mm iso-butane gas. The blue, green, red points represent
photon-yields by e, µ, and π, respectively.









   

(a) e

(b) µ

      (c) πFigure H.6: The simulated correlations between E/p and track momentum when particles passthrough 126 mm lead-glass block, for (a) e, (b) µ, and (c) π.

159

The obtained invariant mass spectra are shown in Fig. H.7, which contain the LR and RL
events and the 2001 and 2002 data. A small peak is seen around 3 GeV/c2 in the C-target data,
although there is no peak in the Cu-target data. When the mass spectrum for the C-targets
was ﬁtted with a Gaussian shape and a combinatorial background shape in the mass region
from 2.4 to 3.4 GeV/c2 as shown in Fig. H.8, we obtained the peak position to be 3.073 ±0.014 GeV/c2 , the Gaussian σ to be 43 ± 14 MeV/c2 , and the entry of the peak to be 25.9
± 8.0 events. Where the combinatorial background shape was evaluated by the event-mixing
method. Using the detector simulation described in Sec. 3.5, the simulated J/ψ shape gave thepeak position to be 3.079 GeV/c2 and the Gaussian σ to be 55 MeV/c2 . The agreements arequite remarkable. We obtained the entry of the peak for the Cu-targets to be 4.7 ± 6.9 eventsusing the above ﬁtting procedure, except that the Gaussian peak and σ were ﬁxed to the valuesof the C-targets data.

   
 
                  

Figure H.7: The e+ e− invariant mass spectra for the C-targets (left) and for the Cu-targets(right).

160

Appendix H. Search for J/ψ Production in 12 GeV p + A Reactions    ! "


 






   
Figure H.8: The e+ e− invariant mass spectrum for the C-targets. The solid and dotted lines
represent the ﬁt result and the combinatorial background, respectively.

However when the E/p cuts in the EM calorimeters were tightened from E/p > 0.2 to
E/p > 0.3, the peak structure around 3 GeV/c2 in the C-target data vanished, as shown in
Fig. H.9. In the present experiment, the dynamic-range of ADC modules used for the EM
calorimeters was limited (typically up to about 2 GeV/c2 as the energy deposit), so that theenergy deposit from the high momentum electron should saturate around 2 GeV/c2 . In otherwords, the values of E/p at the higher momentum region should be ﬂatten against the saturation
values; E/p ' 0.4 at p = 5 GeV/c for example. Although these saturations were expected in
the J/ψ mass region, there were no such tendencies observed as shown in Fig. H.11.
Therefore we cannot conclude that the J/ψ peak is observed in the present experiment√( sN N = 5.1), because the electron identiﬁcations in the higher momentum region have lessreliability. Nevertheless, we plot the data in Fig. H.7 as the acceptance-corrected cross sectionof p + C → J/ψ + X and the 90% onﬁdence limit of the cross section of p + Cu → J/ψ + X in
Fig. H.12, as a record.

161


   "!$#&%('  ,-)!$#.%/'       )!*#&%(+       )!*#&%(+

        

Figure H.9: The e+ e− invariant mass spectra for the C-targets (left) and for the copper targets(right). The upper ﬁgures are E/p > 0.2 in the EM calorimeters, and the lower ﬁgures are
E/p > 0.3.

162

Appendix H. Search for J/ψ Production in 12 GeV p + A Reactions



 






 


+

       


 





       


 


! +

       







!

       Figure H.10: The correlations between ADC pulse-hight and track momentum in the mass
region from 2.95 to 3.2 GeV/c2 in the C-target data, for FGC (upper) and RGC (lower) . The
left ﬁgures are for e+ and the right ﬁgures are for e− .

163



 +        +        +                            Figure H.11: The correlations between E/p and track momentum in the mass region from 2.95
to 3.2 GeV/c2 in the C-target data, for RLG (upper), SLG (middle), and FLG (lower). The
left ﬁgures are for e+ and the right ﬁgures are for e− .

Appendix H. Search for J/ψ Production in 12 GeV p + A Reactions

(nb)

164

J/





s(GeV)

Figure H.12: The J/ψ total cross-sections, added the E325 data for the C-targets (open circle)
and Cu-targets (linelevel). The curve is the ﬁt resultwith a empirical( for 90% conﬁdence
) {(
) (
)β }
√
ΓJ/Ψ
(m +2mp )sequation, σ = α ××× 1 − J/Ψ√s, where α and β are
3(mJ/Ψ +2mp )(mJ/Ψ +2mp )ﬁt parameters.

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List of Figures
1.1
1.2

1.3

1.4
1.5

A chiral condensation |hq̄qi| as a function of temperature T and density ρ. The
density is given in units of the nuclear matter density ρ0 ' 0.17fm−3 . . . . . . .
Masses of ρ, ω, and φ mesons as functions of density, which is normalized by
the normal nuclear density ρ0 , predicted by Hatsuda and Lee [6]. The hatchedregions represent the theoretical uncertainty which is caused in estimating quark
condensates from limited experimental information. The uncertainty for ρ and¯ N , the u and d quark contents in the nucleon. Forω mesons is from hūu + ddi
φ meson, there is an extra error from the strange contents in the nucleon, y =¯ N ). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2hs̄siN /(hūuiN + hddi
The spectrum of the φ meson in vacuum (dashed) and in nuclear matter at ρ = ρ0(solid curve) predicted in Ref. [8]. The data are from the reaction e+ e− → K + K −[12]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(c) The ω → π 0 γ spectrum at CBELSA/TAPS [22]. (b) The low-mass e+ e−spectrum in Pb+Au at CERES [26]. (c) The ρ → µ+ µ− spectrum at NA60 [25].
Transverse mass distribution of φ mesons measured in K + K − at NA49 (squares),µ+ µ− at NA50 (diamonds), K + K − at CERES (triangles), and e+ e− at CERES(circles) [30]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.1
2.2

1

2

3
4

5

Schematic view of the E325 spectrometer, the top view. . . . . . . . . . . . . . . 8
Schematic view of the E325 spectrometer, the cross section along the center of
the kaon arm, 33 degrees from the beam line, is shown. . . . . . . . . . . . . . . 8
2.3 Photographs of the E325 spectrometer for (a) the top view and (b) the front view. 9
2.4 Schematic view of Beam Line (EP1B). . . . . . . . . . . . . . . . . . . . . . . . 10
2.5 Schematic view of spectrometer magnet. The dashed lines indicate the electron
acceptance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.6 The calculated magnetic ﬁeld map (z = -400 mm). . . . . . . . . . . . . . . . . 14
2.7 The region of the magnetic ﬁeld measurements. The three areas, A, B, and C
are with diﬀerent settings of the measuring device. . . . . . . . . . . . . . . . . . 14
2.8 The measured magnetic ﬁeld map (z = -363 mm). . . . . . . . . . . . . . . . . . 15
2.9 Possible uncertainty of the momentum determination due to the magnetic ﬁeld
map. Test tracks were generated with the measured map and reconstructedwith the calculated map. The diﬀerences of the reconstructed momenta fromthe generated momenta were plotted as a function of the vertical angle in (A),and the horizontal angle in (B). The histogram (C) gives the projection of all
the diﬀerences. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.10 Diﬀerences between the measured magnetic ﬁeld strength and the calculation
with TOSCA. Deﬁnition of the vertical axis is the ratio of the diﬀerences to themeasured values. The horizontal axis is the z position of the measured points. . 17
2.11 The magnetic ﬁeld strength for each run measured with a NMR probe. The
jumps were caused by switching on and oﬀ the power supply. . . . . . . . . . . 17
2.12 Schematic view of Target in 2002. . . . . . . . . . . . . . . . . . . . . . . . . . . 18
170

List of Figures

2.13 Schematic view of Target and Beam Pipe. . . . . . . . . . . . . . . . . . . . . .
2.14 Interaction rate as a function of the beam position. . . . . . . . . . . . . . . . .
2.15 Schematic view of CDC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.16 The cell structures of CDC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.17 (a)The simulated drift line in the outer super-layer (3 layers) in the magnetic
ﬁeld of 0.61T, which is the magnetic ﬁeld strength at this location when the
spectrometer magnet is fully excited. (b)The calculated relation between thedrift time and the drift length of the X layer. . . . . . . . . . . . . . . . . . . . .
2.18 The cross section of the aluminum end plate and the ceramic plate. . . . . . . .
2.19 (a) Schematic view of the feedthrough structure for the ceramic plate of CDC.
(b) Schematic view (not to the scale) of the feedthrough structure for the oneon the aluminum ribs of CDC. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.20 Photographs of (a) ASD board and (b) LVDS-ECL converter. . . . . . . . . . .
2.21 (a)Block diagram of the ASD chip. (b)Pin assignment of the ASD IC. . . . . . .
2.22 Schematic view of BDC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.23 The cell structure of BDC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.24 Schematic view of VTC. The target arrangement in 2001 is also shown. . . . . .
2.25 The cell structures of VTC (a) for the backward cells and (b) for the forwardcells. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.26 Feedthrough structures (a) for the backward cells and (b) for the forward cells.
2.27 The read-out and high-voltage circuit (a) for the backward cells and (b) for thefroward cells. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.28 Photograph of the VTC and the targets in 2000. . . . . . . . . . . . . . . . . .
2.29 (a) The simulated drift line in the forward layer in the magnetic ﬁeld of 0.71T,
which is the magnetic ﬁeld strength at this location when the spectrometer magnet is fully excited. (b) The calculated relation between the drift time and thedrift length of the layer-4 under the magnetic ﬁeld of 0.71T. . . . . . . . . . . .
2.30 The breeder circuit of the photomultiplier used for STC (Hamamatsu H6154). .
2.31 Schematic view of FGC,RGC and RLG. . . . . . . . . . . . . . . . . . . . . . .
2.32 The eﬃciencies (upper ﬁgure) and the averaged number of photo-electrons (lower
ﬁgure) of the FGC test module for 0.5 GeV/c electrons as a function of the vertical incident angle. The circles and the squares show eﬃciencies with thresholdat one and two photo-electron levels, respectively. . . . . . . . . . . . . . . . . .
2.33 The eﬃciencies (upper ﬁgures) and the averaged number of photo-electrons(lower ﬁgures) of the FGC test module for 0.5 GeV/c electrons as functionsof the horizontal incident angle. The left ﬁgures were measured when the vertical incident angle was 0.1 rad, and the right ﬁgures were when that was 0.3 rad.
The open marks are mirror image of the closed marks. . . . . . . . . . . . . . .
2.34 FGC response for 1 GeV/c pions. The horizontal axis is normalized to thenumber of photo-electrons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.35 The eﬃciency (top panels) and the number of photo electron (bottom panels) of
the RGC test module as functions of (a) the vertical angle of incident electronsand (b) the horizontal angle of incident electrons. . . . . . . . . . . . . . . . . .
2.36 RGC response for 1 GeV/c pions. . . . . . . . . . . . . . . . . . . . . . . . . . .
2.37 Schematic view of FGC and SLG. . . . . . . . . . . . . . . . . . . . . . . . . . .
2.38 (a)Vertical position dependence of the light yield for SLG. The open rectangles
and closed circles are the light yields from the top and the bottom PMT’s. The
closed rectangles are for the sum. (b)The vertical position dependence of theenergy resolution for electrons (top) and the pion rejection power (bottom) of
SLG, measured with 0.5, 1.0, and 1.5 GeV/c electrons and pions. . . . . . . . .
2.39 Schematic view of FLG. The hatched areas are lead-glass radiators. . . . . . . .

171

19
20
21
22

23
24

24
25
26
27
27
28
29
30
30
30

31
32
33

34

34
35

36
36
37

38
39

172

List of Figures

2.40 Schematic view of AC and the light collection scheme. . . . . . . . . . . . . . . .
2.41 Pulse height distributions of AC for 1.4 GeV/c positive pions and protons. . . .
2.42 A diagram of the trigger control system. . . . . . . . . . . . . . . . . . . . . . .
2.43 The schematic view of Data Acquisition System. . . . . . . . . . . . . . . . . . .
2.44 Screen shot of the GUI environment on X window system. . . . . . . . . . . . .

40
40
41
44
45

3.1
3.2

47

Typical TDC spectrum and its diﬀerential. . . . . . . . . . . . . . . . . . . . . .
Run dependence of typical time-oﬀset adjustment, (a) in the year 2001 and (b)in the year 2002. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 The correlations between the CDC residual as a function of the drift length (a)and of the incident angle of tracks (b). (c) shows the over all resolution. . . . . .
3.4 The residual distributions between BDC hit positions and the CDC extrapolated
tracks. The upper ﬁgures show the residuals in the horizontal position at the
BDC location, the lower are in the vertical position. . . . . . . . . . . . . . . . .
3.5 The correlation between RLG energy and momentum. The region E/p > 0.5 ischosen for the electron selection. . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6 The E/p ratios in all the segments of RLG/SLG/FLG. The segment id is numbered from top to bottom PMT, from forward to backward, and from left toright arm. The error bars only show the statistical errors. . . . . . . . . . . . . .
3.7 (a)Before the STC slewing correction, the distribution of the time diﬀerence
between the measured time and the expected time is shown at top. The ADC
distributions at middle, and the slewing eﬀect at bottom. (b)As same as (a) but
after the STC slewing correction. . . . . . . . . . . . . . . . . . . . . . . . . . .
3.8 The resolution of the ﬂight time measurements of any combinations between the
STC and FTOF counters after the slewing correction. . . . . . . . . . . . . . . .
3.9 Reduced χ2 distribution in the Runge-Kutta ﬁtting. . . . . . . . . . . . . . . . .
3.10 The typical chamber residual and track χ2 /N distribution for the data (DATA)
and the tuned detector simulation (MC) in the ﬁnal e+ e− sample. . . . . . . . .
3.11 The typical chamber residual and track χ2 /N distribution for the data (DATA)
and the tuned detector simulation (MC) in the ﬁnal K + K − sample. . . . . . . .
3.12 (a) Invariant Mass spectrum of p π − showing the Λ peak. The curve is the ﬁt
result with the simulated mass shape over a linear background. (b) Invariant
Mass spectrum of π + π − showing the K0s peak. The curve is the ﬁt result withthe simulated shape over a quadratic background. . . . . . . . . . . . . . . . . .
3.13 Vertex distribution for double-arm e+ e− events in 2001 (left) and 2002 (right).
Vertex distribution in the xy-plane (upper) and the projection in the x-axis(lower). The indicated rectangles in the upper ﬁgure are the cut regions for thevertex position in the x-y plane. . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.14 Vertex distribution for single-arm K + K − events in 2001. (a)Vertex distribution
in the xy-plane (upper) and the projection in the x-axis (lower). (b)Vertex
distribution in the xy-plane (upper) and the projection in the direction of thecorresponding arm (lower). The left ﬁgure is for left arm events, the right ﬁgure
is for right arm events. The indicated rectangles in the upper ﬁgure are the cut
regions for the vertex position in the x-y plane. . . . . . . . . . . . . . . . . . .
3.15 The momentum distributions of electrons in the ﬁnal sample. The upper ﬁgures
are for e+ and the lower ﬁgures are for e− . The left ﬁgure is for the C targets
and the right ﬁgure is for the Cu targets. . . . . . . . . . . . . . . . . . . . . . .
3.16 Horizontal matching between electron tracks and electron-counter hits in theﬁnal e+ e− sample. The arrows indicate the region for the electron selection, andthe x coordinate is in a unit of the counter size. . . . . . . . . . . . . . . . . . .

48
48

50
51

51

53
53
55
56
57

58

59

60

61

62

List of Figures173

3.17 The time diﬀerence between the measured TOF value (Tcounter − TSTC ) and the
expected TOF value (Texp ). The arrows indicate the region for the electron
selection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.18 The correlation between RLG energy and momentum. The region E/p > 0.5 ischosen for the electron selection. . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.19 (a)The opening angle distribution of the pure electron candidates. The region
lower than the arrow was used to select pure electrons. (b)Invariant mass distribution of electron pair in the low mass region. The region lower than the arrow
was used to select pure electrons. . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.20 The correlation between RLG energy and momentum for the pure electron sample. The solid lines show the region for the electron identiﬁcation. . . . . . . . . 65
3.21 The electron identiﬁcation eﬃciency as a function of track momentum. . . . . . 66
3.22 Horizontal matching between kaon tracks and the kaon identiﬁcation counters inthe ﬁnal K + K − sample. The arrows indicate the region for the kaon selection,and the x coordinate is in a unit of the counter size. (The ﬁgures are shown after
the matching cuts were applied.) . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.23 Vertical matching between kaon tracks and diﬀerential timings of two PMT’s in
the kaon identiﬁcation counters in the ﬁnal K + K − sample. The right ﬁgures
show projection along the correlation line of the left ﬁgures. The indicatedrectangles in the left ﬁgures and the arrows in the right ﬁgures are the cut
regions for the matching. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.24 The momentum distributions of kaons in the ﬁnal sample. The upper ﬁgures arefor K+ and the lower ﬁgures are for K− . The left ﬁgures are for the C target andthe right ﬁgures are for the Cu targets. . . . . . . . . . . . . . . . . . . . . . . . 68
3.25 The distributions of the momentum versus squared-mass for (a) positive and (b)negative particles, after the AC veto is applied. The indicated regions are theselected regions for the kaon identiﬁcation. . . . . . . . . . . . . . . . . . . . . . 69
3.26 The distributions of the squared-mass, when the momentum from 0.8 to 1.0
GeV/c is selected. The distributions were ﬁtted with a sum of double-Gaussian
distributions. The lines indicate the approximate region for the kaon selection. . 70
3.27 (a) Horizontal matching between pion tracks and AC hits in the pion sample.
(The ﬁgures are shown after the matching cuts were applied.) (b) Hit-timing
diﬀerence between AC and associated FTOF counters. The arrows indicate thecut regions for the AC hit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.28 Correlation between the track vertical position and the asymmetry of the top
and bottom photomultipliers of AC. . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.29 The momentum dependence of the AC eﬃciencies, (a) for pions and (b) for protons. 72
3.30 The vertical position dependence of the AC eﬃciencies, (a) for pions whose
momentum was larger than 1.0 GeV/c and (b) for protons . . . . . . . . . . . . 73
3.31 The deﬁnition of LR (blue) and RL (red) event. . . . . . . . . . . . . . . . . . . 74
3.32 The e+ e− invariant mass spectra of the ﬁnal data sample for the carbon targets(left) and for the copper targets (right). . . . . . . . . . . . . . . . . . . . . . . . 75
3.33 The e+ e− invariant mass spectra. The spectra of the LR events and the RL
events are shown separately. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.34 The e+ e− invariant mass spectra, close up views of Fig. 3.32 and 3.33 to the φmeson peak. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.35 The e+ e− invariant mass spectra divided into each target disk. . . . . . . . . . . 77
3.36 The e+ e− invariant mass spectra, close up views of Fig. 3.35 to the φ meson peak. 77
3.37 The K + K − invariant mass spectra for C (left) and Cu (right) targets. . . . . . . 78
3.38 The K + K − invariant mass spectra divided into each target disk. . . . . . . . . . 79
3.39 The K + K − invariant mass spectra divided into the L and R arm events. . . . . 79

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3.40 The E325 spectrometer implemented in the detector simulation using Geant4
toolkit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
3.41 The non-relativistic (red) and the relativistic (blue) Breit-Wigner distributions
for the φ → e+ e− decays. The distributions are normalized by their peak countto unity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
3.42 The kinematical distributions of the generated φ mesons using JAM (black lines)
and for the accepted φ → e+ e− in the detector (red lines). . . . . . . . . . . . . 82
3.43 The kinematical distributions of the generated φ mesons for C (black lines) andCu (red lines), normalized with the number of entries. . . . . . . . . . . . . . . 82
3.44 The decay angular distributions for the data (closed circles) and the simulation(lines), (a) in the Gottfried-Jackson frame and (b) in the helicity frame. The
LR and RL events are summed. The scaling is determined arbitrarily. (c) In the
Gottfried-Jackson frame, z-axis parallel to the beam direction in the φ rest frame.
(d) In the helicity frame, z-axis parallel to the φ direction in the center-of-massframe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
3.45 The momentum distributions of the observed (closed circles) and simulated(lines) daughter e+ (upper panels) and e− (bottom panels) in the φ → e+ e−
decays, for C (left panels) and for Cu (right panels). The LR and RL events are
summed. The scaling is determined arbitrarily. . . . . . . . . . . . . . . . . . . 84
3.46 The kinematical distributions of the observed (closed circles) and simulated(lines) φ → e+ e− pairs, for C (left four panels) and for Cu (right four panels). In the scatter plots of pT versus rapidity, only the observed events areshown. The LR and RL events are summed. The scaling is determined arbitrarily. 85
3.47 The kinematical distributions of the observed (closed circles) and simulated(lines) φ → e+ e− as Fig. 3.46. Here the LR and RL events are represented
in red and blue, respectively. The scaling is determined arbitrarily, but the ratioof the number of LR events to RL events is not changed in the data and thesimulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.48 The separation of the signal region and the side-band (background) regions. . . 86
3.49 Internal bremsstrahlung in V → e+ e− decays. . . . . . . . . . . . . . . . . . . . 86
3.50 The internal radiative eﬀects in φ → e+ e− decays. The red spectra are withinternal radiative eﬀects, and the blue are without. (a)The detector eﬀects are
not considered. (b)The detector eﬀects are considered. The green line is theﬁt result to the blue spectrum with the Breit-Wigner function folded with aGaussian. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
3.51 Feynman diagrams of the vertex correction term (left) and the vacuum polarization term (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
3.52 Atomic Electromagnetic Field Scattering . . . . . . . . . . . . . . . . . . . . . . 89
3.53 The mass acceptances for e+ e− decays in the 2001 run. The acceptances of eachtarget disk for the all events (left), LR events (center), and RL events (right) are
shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
3.54 The mass acceptances for e+ e− decays for the C and the averaged Cu targets,for the all events (left), LR events (center), and RL events (right). . . . . . . . 90
3.55 The mass acceptances for e+ e− decays divided into four bins in βγ (top), rapidity(middle), and pT (bottom). The acceptances for the averaged Cu targets for the
all events, LR events, and RL events are shown. . . . . . . . . . . . . . . . . . 91
3.56 The non-relativistic (red) and the relativistic (blue) Breit-Wigner distribution
for φ → K + K − decays. The distributions are normalized by their peak count tounity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

List of Figures175

3.57 The kinematical distributions of the generated φ mesons using JAM (black lines)
and of the accepted φ → K + K − in the detector (red lines). The accepted
φ → K + K − are scaled up by a factor of 50. . . . . . . . . . . . . . . . . . . . . 93
3.58 The decay angular distributions for the data (closed circles) and the simulation(lines), (a) in the Gottfried-Jackson frame and (b) in the helicity frame. The
scaling is determined arbitrarily. . . . . . . . . . . . . . . . . . . . . . . . . . . 93
3.59 The momentum distributions of the observed (closed circles) and simulated(lines) daughter K + (top panels) and K − (bottom panels) in the φ → K + K −decays, for C (left panels) and for Cu (right panels). The scaling is determined
arbitrarily. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
3.60 The kinematical distributions of the observed (closed circles) and simulated(lines) φ → K + K − pairs, for C (left four panels) and for Cu (right four panels).
In the scatter plots of pT versus rapidity, only the observed events are shown.
The scaling is determined arbitrarily. . . . . . . . . . . . . . . . . . . . . . . . . 95
3.61 The separation of the signal region and the side-band (background) regions. . . 95
3.62 The φ → K + K − invariant mass distributions obtained by JAM. The black lines
represent all the φ → K + K − events before the rescattering. The red and bluelines represent the events with the rescattering before and after the rescattering,
respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
3.63 (a)The mass acceptances for each target disk in K + K − decays. (b)The mass
acceptances for the C target and the averaged one for the Cu targets. . . . . . 97
3.64 The mass acceptances for Cu targets in K + K − decays divided into three bins in
βγ (top), rapidity (middle), and pT (bottom). . . . . . . . . . . . . . . . . . . . 98
3.65 (a)The momentum resolution for e, π, K, and p. (b)The diﬀerence of the obtained
momenta from the original values. . . . . . . . . . . . . . . . . . . . . . . . . . 99
3.66 Breakdown of the sources in the momentum resolution, (a) for e and (b) for K. 99
3.67 The momentum resolution (a) for e in φ → e+ e− and (b) for K in φ → K + K − .
The resolution “without CVTF” and “with CVTF” are plotted. . . . . . . . . . 100
3.68 The S/N with a various electron identiﬁcation conditions. The condition issevere with larger IDs. The conditions are listed in the right panel. . . . . . . . 101
3.69 The e+ e− mass distributions with the ﬁt results for (a) ID = 1 and (b) ID = 9 inFig. 3.68. The data for all the targets are summed. The closed circles represent
the data and the thin crosses represent the excluded region from the ﬁt. The
red, green and blue lines represent the ﬁt results, the quadratic backgrounds andthe expected φ → e+ e− shapes, respectively. The arrows indicate the region to
examine the S/N . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
3.70 The invariant mass spectra of π + π − pairs with CVTF for (a) the single-arm
events and (b) the double-arm events (LR events only). The closed circles andlines represent the data and the mixed event, respectively. . . . . . . . . . . . . 103
3.71 The invariant mass spectra of non-resonant K + K − pairs with CVTF for (a) the
single-arm events and (b) the double-arm events (LR events only) obtained by
JAM. The closed circles and lines represent the simulated data and those after
the event-mixing, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
3.72 The invariant mass spectra of K + K − pairs with CVTF for the double-arm events(LR events only). The closed circles and lines represent the data and the mixed
events, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
3.73 Three types of the combinatorial background shape obtained by the event-mixing
and normalized by the number of the mixed events. The red, black, and bluelines represent Type 1, 2, and 3, respectively (see text). . . . . . . . . . . . . . 106

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3.74 The invariant mass spectra of the ﬁnal K + K − sample. The closed circles represent the data. The blue and red lines represent the ﬁt results and the combinatorial backgrounds respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
The invariant mass spectra of the ﬁnal e+ e− sample. The closed circles represent
the data and the thin crosses represent the excluded region from the ﬁt. The
red, green and blue lines represent the ﬁt results, the quadratic backgrounds andthe expected φ → e+ e− shapes, respectively. . . . . . . . . . . . . . . . . . . . . 110
4.2 The invariant mass spectra of the ﬁnal e+ e− sample divided into four βγ bins.
The closed circles represent the data and the thin crosses represent the excluded
region from the ﬁt. The red, green and blue lines represent the ﬁt results, thequadratic backgrounds and the expected φ → e+ e− shapes, respectively. . . . . 111
4.3 The invariant mass spectra of the ﬁnal e+ e− sample divided into four rapidity
bins. The closed circles represent the data and the thin crosses represent the excluded region from the ﬁt. The red, green and blue lines represent the ﬁt results,
the quadratic backgrounds and the expected φ → e+ e− shapes, respectively. . . 112
4.4 The invariant mass spectra of the ﬁnal e+ e− sample divided into four pT bins.
The closed circles represent the data and the thin crosses represent the excluded
region from the ﬁt. The red, green and blue lines represent the ﬁt results, thequadratic backgrounds and the expected φ → e+ e− shapes, respectively. . . . . 113
4.5 The invariant mass spectra of the ﬁnal K + K − sample. The closed circles represent the data. The red, green and blue lines represent the ﬁt results, thecombinatorial backgrounds and the expected φ → K + K − shapes, respectively. . 114
4.6 The invariant mass spectra of the ﬁnal K + K − sample divided into three βγ bins.
The closed circles represent the data. The red, green and blue lines represent theﬁt results, the combinatorial backgrounds and the expected φ → K + K − shapes,
respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
4.7 The invariant mass spectra of the ﬁnal K + K − sample divided into three rapidity
bins. The closed circles represent the data. The red, green and blue lines represent the ﬁt results, the combinatorial backgrounds and the expected φ → K + K −shapes, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
4.8 The invariant mass spectra of the ﬁnal K + K − sample divided into three pT bins.
The closed circles represent the data. The red, green and blue lines represent theﬁt results, the combinatorial backgrounds and the expected φ → K + K − shapes,
respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
4.9 The observed kinematical distributions of φ → e+ e− and φ → K + K − , as functions of (a) βγ, (b) rapidity, (c) pT , and (d) pT and rapidity. The points blue
represent φ → e+ e− and the red histograms and contours represent φ → K + K − .
The dotted lines in (a) represent βγ = 1.25. The histograms for φ → K + K − arescaled up by a factor of about 3. . . . . . . . . . . . . . . . . . . . . . . . . . . 118
4.10 The simulated detector acceptances for (a) φ → e+ e− decays and (b) φ → K + K −decays are plotted as the color maps. The acceptances are calculated using a
ﬂat kinematical distribution in the region of 0 < y < 3 and 0 < pT < 2, andinclude not only the geometrical acceptance but also the detector eﬃciencies andall other conditions used in the present analysis. The kinematical distributionof the generated φ-meson yield obtained by JAM is also plotted as the contour
plot in each panel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
4.11 α parameters of φ → e+ e− (closed circle) and φ → K + K − (open circle) as
functions of (a) βγ, (b) rapidity, and (c) pT . The horizontal error bars are theRMS values of the horizontal bins. . . . . . . . . . . . . . . . . . . . . . . . . . 124
4.1

List of Figures177

4.12 The mean and RMS values of each bin of φ → e+ e− (closed circle) and φ →K + K − (open circle) in the y-pT plane for (a) βγ-slice, (b) rapidity-slice, and (c)pT -slice. The error bars are the RMS values in each kinematical bin. . . . . . . 125
4.13 The kinematical distributions of φ → e+ e− and φ → K + K − in the overlapped
region shown with the rectangle in (d), as functions of (a) βγ, (b) rapidity, (c)pT . The closed circles represent φ → e+ e− and the lines represent φ → K + K − . 126
4.14 (a) The invariant mass spectra of the e+ e− sample in the overlapped acceptance.
The closed circles represent the data and the thin crosses represent the excluded
region from the ﬁt. The red, green and blue lines represent the ﬁt results, thequadratic backgrounds and the expected φ → e+ e− shapes, respectively. (b) The
invariant mass spectra of the K + K − sample in the overlapped acceptance. The
closed circles represent the data. The red, green and blue lines represent the ﬁt
results, the combinatorial backgrounds and the expected φ → K + K − shapes,
respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
4.15 The mean and RMS values of each bin of φ → e+ e− decays divided into 3 × 3
in the y-pT plane. The error bars are the RMS values. The ID number (#x) in
the ﬁgure for each data point corresponds to the number in the table showing
the actual values. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
4.16 The α parameters of φ → e+ e− (closed circle) and φ → K + K − (open circle) as
functions of (a) βγ, (b) rapidity, and (c) pT , before the acceptance correction.
The corrected αφ→e+ e− with the errors for the K + K − acceptance are shown as
the hatched bands. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
4.17 The diﬀerences between αφ→K + K − and αφ→e+ e− , ∆α, in the kaon acceptance asfunctions of (a) βγ, (b) rapidity, and (c) pT . The average value and error are
also plotted as the hatched bands. . . . . . . . . . . . . . . . . . . . . . . . . . 129
4.18 The Woods-Saxon distribution for C and Cu nuclei. . . . . . . . . . . . . . . . 131
4.19 The values of expected ∆α shown in color, which are obtained by the Monte
Carlo calculation. The measured ∆α and its error band are shown with the lines. 131
4.20 The invariant mass spectra of the ﬁnal K + K − sample. The closed circles represent the data and the thin crosses represent the excluded region, from 2mK ± (0.987)
to 1.01 GeV/c2 , for the ﬁt. The red, green and blue lines represent the ﬁt results, the combinatorial backgrounds and the expected φ → K + K − shapes,
respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
4.21 The relation Nφin /Nφout and kK for C and Cu nuclei obtained by the Monte Carlocalculation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
4.22 The constraint given by the Nex /Nφ ratio in the plane of kK and ke . . . . . . . 133
4.23 The obtained constraints on the in-medium modiﬁcation of the partial decay
widths of φ → K + K − and φ → e+ e− . The 90% conﬁdence limits, which arerenormalized for the probability distribution functions by eliminating an unphysical region corresponding to Γ∗ /Γ0 < 0, are plotted. . . . . . . . . . . . . . . . . 134
4.24 The obtained constraints on the in-medium modiﬁcation of the partial decay
widths of φ → K + K − and φ → e+ e− , and the constraint obtained in Ref. [31]. . 135
A.1 The distributions of the squared-mass for positive particles with momentum
slices of every 0.2 GeV/c step. The distributions were ﬁtted using a double
Gaussian distribution. The vertical magenta lines indicate the regions for thekaon selection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
A.2 The distributions of the squared-mass for negative particles with momentum
slices of every 0.2 GeV/c step. The distributions were ﬁtted using a double
Gaussian distribution. The vertical magenta lines indicate the regions for thekaon selection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

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A.3 The distributions of the squared-mass for (a) positive and (b) negative particles.
The ﬁt results, which were the sum of the ﬁts on the momentum-sliced M2
distributions as shown in Fig. A.1 and A.2, was also plotted. . . . . . . . . . . 139
B.1 The invariant mass spectra of the double-arm K + K − sample. The closed circles
represent the data. The red, green and blue lines represent the ﬁt results, thecombinatorial backgrounds and the expected φ → K + K − shapes, respectively. . 140
B.2 The simulated detector acceptance for double-arm φ → K + K − decays (LR event
only) is plotted as the color map. The acceptance is calculated using a ﬂat
kinematical distribution in the region of 0 < y < 3 and 0 < pT < 2, and includes
not only the geometrical acceptance but also the detector eﬃciencies and allother conditions used in the present analysis. The kinematical distribution of
the generated φ-meson yield obtained by JAM is also plotted as the contour plot. 141
B.3 The observed kinematical distributions of double-arm φ → e+ e− , single-arm
φ → K + K − , and double-arm φ → K + K − (LR event only), as functions of (a) βγ,(b) rapidity, (c) pT , and (d) pT and rapidity. The points represent φ → e+ e− , thered lines represent single-arm φ → K + K − , and the pink lines represent doublearm φ → K + K − . The histograms for single-arm and double-arm φ → K + K −are scaled by a factor of about 3 and 13, respectively. . . . . . . . . . . . . . . 142
B.4 α parameters of φ → e+ e− (closed circle), φ → K + K − (open circle), and the
double-arm φ → K + K − (star) as functions of (a) βγ, (b) rapidity, and (c) pT .
The horizontal error bars are the RMS values of the horizontal bins. . . . . . . 142
E.1 Width of the φ meson in nuclear matter at three densities (ρ = 0.25ρ0 , 0.5ρ0 , ρ0 )as a function of the φ energy (Fig. 4 of Ref. [9]). . . . . . . . . . . . . . . . . . 147
E.2 The ﬁt result of the values in Table E.1. . . . . . . . . . . . . . . . . . . . . . . 148
F.1 The invariant mass spectra of φ → e+ e− decays for diﬀerent target thickness of C
and Cu. The red, black, and blue lines represent the Breit-Wigner distribution,
the spectrum with the internal radiative eﬀects, and the distorted mass spectrumby the target material, respectively. The mass spectra are normalized by theirpeak count to unity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
F.2 The expected invariant mass spectra of φ → e+ e− obtained by the detector simulation. The pink, black, green, red, and blue lines correspond to the contribution
from (1) to (5) described in the text. Both LR and RL events are included. The
mass spectra are normalized by their peak count to unity. . . . . . . . . . . . . 151√
H.1 The J/ψ total cross-sections at various s [73, 77, 78, 79]. The curves are thecalculations of the color-octet model using diﬀerent parton distribution functions. 154
H.2 The momentum distributions of electrons candidates. Pion contamination isvisible above 2.7 GeV/c. The upper ﬁgures are for e+ and the lower ﬁgures arefor e− , for the targets C and Cu as indicated in the ﬁgures. . . . . . . . . . . . . 155
H.3 The correlations between ADC pulse-hight and track momentum in FGC (upper)
and in RGC (lower). The left ﬁgures are for e+ and the right ﬁgures are for e− .
Events from the C and Cu targets are summed. . . . . . . . . . . . . . . . . . . 156
H.4 The correlations between E/p and track momentum in (a) RLG, (b) SLG, and(c) FLG. The left ﬁgures are for e+ and the right ﬁgures are for e− . Events fromthe C and Cu targets are summed. . . . . . . . . . . . . . . . . . . . . . . . . . 157
H.5 The simulated correlations between Čerenkov-photon-yields and track momentum when particles pass through 600 mm iso-butane gas. The blue, green, redpoints represent photon-yields by e, µ, and π, respectively. . . . . . . . . . . . . 158

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179

H.6 The simulated correlations between E/p and track momentum when particles
pass through 126 mm lead-glass block, for (a) e, (b) µ, and (c) π. . . . . . . . . 158
H.7 The e+ e− invariant mass spectra for the C-targets (left) and for the Cu-targets(right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
H.8 The e+ e− invariant mass spectrum for the C-targets. The solid and dotted lines
represent the ﬁt result and the combinatorial background, respectively. . . . . . 160
H.9 The e+ e− invariant mass spectra for the C-targets (left) and for the copper
targets (right). The upper ﬁgures are E/p > 0.2 in the EM calorimeters, andthe lower ﬁgures are E/p > 0.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
H.10 The correlations between ADC pulse-hight and track momentum in the mass
region from 2.95 to 3.2 GeV/c2 in the C-target data, for FGC (upper) and RGC(lower) . The left ﬁgures are for e+ and the right ﬁgures are for e− . . . . . . . . 162
H.11 The correlations between E/p and track momentum in the mass region from 2.95
to 3.2 GeV/c2 in the C-target data, for RLG (upper), SLG (middle), and FLG(lower). The left ﬁgures are for e+ and the right ﬁgures are for e− . . . . . . . . 163
H.12 The J/ψ total cross-sections, added the E325 data for the C-targets (open circle)
and Cu-targets (line for 90%
is the ﬁt result with a }( conﬁdence level).
) {( The curve )
(
)
√
ΓJ/Ψ
(mJ/Ψ√+2mp ) βsempirical equation, σ = α×
×
×
1
−
,
3
s
(mJ/Ψ +2mp )(mJ/Ψ +2mp )where α and β are ﬁt parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . 164

List of Tables
1.1

Theoretical predictions for the φ meson modiﬁcation in a medium. Where Tc isthe critical temperature (∼ 170 MeV). . . . . . . . . . . . . . . . . . . . . . . .

2.1
2.2

The collimator width setting. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
List of the materials and their radiation lengths from the center of CDC to theradius of 1680 mm where BDC’s were located. . . . . . . . . . . . . . . . . . . .
2.3 The measured and calculated magnetic ﬁelds for ﬁve values of z. The voltage
was set to 1985.45A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 The target dimensions, interaction lengths, and radiation lengths used in theexperiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5 CDC wire conﬁguration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.6 BDC wire conﬁguration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.7 VTC wire conﬁguration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.8 Characteristics of SF6W [51]. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.9 Trigger rates in a typical spill of 1.8 sec-long in the year 2001 and 2002. . . . .
2.10 The pattern of the matrix coincidence for the FGC segments and the RGC, RLG,
and SLG segments in the electron ﬁrst-level logic. The counters were numberedfrom forward to backward in each arm. . . . . . . . . . . . . . . . . . . . . . . .
2.11 The pattern of the matrix coincidence for the FTOF segments and the HC segments in the kaon ﬁrst-level trigger logic. The counters were numbered fromforward to backward in each arm. . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1
3.2

3.3
3.4

3.5
3.6

3.7
3.8
3.9

3
11
13
16
18
22
26
28
36
42

42

43

The number of beam protons and triggered events. . . . . . . . . . . . . . . . . 46
The shifts and rotations parameters of BDC with respect to the nominal position.
The unit of dx, dy and dz are [mm], and τx , τy and τz are [×10−3 radian]. The
period I corresponds to from run 6000 to 6292 in 2001, the period II from run
6293 to 6999 in 2001, and the period III from run 7000 to 7999 in 2002. . . . . 49
Estimated eﬃciency of each chamber layer. . . . . . . . . . . . . . . . . . . . . . 56
Estimated resolution of the chamber layers. The values σ1 are the widths for themain component of the double Gaussian distribution, σ2 are those for the second
component, and “ratio” are the second/main ratios. . . . . . . . . . . . . . . . . 57
The mean values (target position) and precisions of the vertex determination for
double-arm e+ e− events. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59(a)The parameters of the eﬃciency curves for the electron identiﬁcation counters.
The parameter b and c were ﬁxed to zero for RGC and FLG. (b)The averaged
eﬃciencies including the oﬀ-line cuts for single electron tracks in the ﬁnal e+ e−sample. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
The kaon purity of the ﬁnal sample. . . . . . . . . . . . . . . . . . . . . . . . . . 70
The numbers of generated φ → K + K − decays and kaon absroptions and rescatterings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
The purity of the kaon in the double-arm data (LR events only). . . . . . . . . . 105

180

List of Tables

181

3.10 The obtained best values in the additional mass scale δm and the resolution
δσ, in a unit of [MeV/c2 ]. The values are obtained separately for the LR and
RL events and the year 2001 and 2002, due to the expected nature of the BDCalignments. The ﬁrst errors are statistical and the seconds are systematic. . . . 107
3.11 The obtained values of the mass centroid and the resolution for the data (DATA)
and the detector simulation (MC) in a unit of [MeV/c2 ]. The ﬁrst errors are
statistical and the seconds are systematic. . . . . . . . . . . . . . . . . . . . . . 108
The values of Nt (C)/Nt (Cu) for φ → e+ e− (average of 2001 and 2002) andfor φ → K + K − (2001 only). The systematic errors in α from the errors in
Nt (C)/Nt (Cu) are also listed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
4.2 The geometrical acceptance eﬀects in ηC /ηCu (φ → K + K − ) and δαφ→K + K − obtained with the nuclear cascade code JAM and the detector simulation. . . . . . 120
4.3 The overkilling probabilities in (a) AC and (b) TOF. . . . . . . . . . . . . . . . 122
4.4 Track multiplicity in the ﬁnal data sample, (a) for e+ e− and (b) for K + K − . . . 122
4.5 The yields and the α parameters for (a) φ → e+ e− and (b) φ → K + K − . The
ﬁrst errors are statistical and the second are systematic. . . . . . . . . . . . . . . 124
4.6 The mean and RMS values of each kinematical bin for (a) φ → e+ e− and (b)φ → K + K − . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
4.7 The mean and RMS of kinematic variables for φ → e+ e− and φ → K + K − decays
in the overlapped acceptance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
4.8 The yields and the α parameters for φ → e+ e− and φ → K + K − in the overlapped
acceptance. The ﬁrst errors are statistical and the second are systematic. . . . 127
4.9 The yields and the α parameters for the φ → e+ e− decays divided into 3 × 3 binsin the y-pT plane. The ﬁrst errors are statistical and the second are systematic. . 128
4.10 αφ→K + K − and estimated αφ→e+ e− in the kaon acceptance window. The ﬁrst
errors are statistical and the second are systematic. For “estimated αφ→e+ e− ”
and “∆α”, the errors are the quadratic sums of the statistical and systematic
errors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
4.11 The number of φ meson Nφ , the excess Nex , and Nex /Nφ before and after themass acceptance correction. The ﬁrst errors are statistical and the second aresystematic. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
4.12 The obtained kK from the observed Nex /Nφ in Table 4.11 and the calculated
Nφin /Nφout -kK relation in Fig. 4.21. The ﬁrst errors are statistical and the second
are systematic. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
4.1

B.1 The yields and the α parameters for double-arm φ → K + K − decays. The ﬁrst
errors are statistical and the second are systematic. . . . . . . . . . . . . . . . . 141
C.1 The detailed description of the targets used in 2001, and the measured dimensions, L1 ∼ L5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
C.2 The detailed description of the targets used in 2002. . . . . . . . . . . . . . . . 144
D.1 The simulated yields and the α parameters for the φ → e+ e− decays divided into
3 × 3 bins in the y-pT plane. The errors are statistical. The ID numbers (#x)
in the table correpond to the number in Fig. 4.15. . . . . . . . . . . . . . . . . 146
D.2 The simulated yields and the α parameters for the φ → K + K − decays divided
into three βγ bins. The errors are statistical. . . . . . . . . . . . . . . . . . . . 146
D.3 The results of the ﬁt with α(y, pT ) = a × y + b × pT + c, using values of α inTable 4.5, 4.9, D.1, and D.2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

182

List of Tables

E.1 The values of Γ∗ at 1020 MeV/c2 as a function of density read from Fig E.1 (Fig.
4 of Ref. [9]) by the eye. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
G.1 The run lists used for the present analysis, (a) for the year 2001 [136 runs] and(b) for 2002 [126 runs]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152