Search for Θ+ via π −p → K −X Reaction
near Production Threshold
Koji Miwa

FO

KYOTO

U

ND

JAPAN

97

KY O

T

UNI VE

ITY
RS

O

8
ED 1

A dissertation submitted in partial fulfillment of
the requirements for the degree ofDoctor of Science
Department of Physics
Faculty of Science
Kyoto University
May, 2006

Abstract
We have searched for Θ+ via π − p → K − X reaction using 1.87 and 1.92 GeV/c π − beamat the K2 beam line of the KEK 12 GeV Proton Synchrotron. A SCIFI target ((CH)n )was exposed to 2.9 × 109 π − ’s with momentum of 1.87 GeV/c. For the search for the
Θ+ , a polyethylene target ((CH2 )n )was mainly used to enhance the contribution from free
protons and was exposed to 3.0 × 109 π − ’s of 1.87 GeV/c and 7.4 × 109 π − ’s of 1.92
GeV/c.
In the missing mass of the π − p → K − X reaction at 1.87 GeV/c, any structure corresponding to the Θ+ have not been observed. In the missing mass at 1.92 GeV/c, a bump ofwhich width was consistent with the experimental resolution has been found at the mass
+1.9
2of M = 1530.6+2.2−1.9 (stat.)−1.3 (syst.) MeV/c . However the statistical significance of thebump is only 2.5∼2.7σ which is not sufficient to claim the evidence of the Θ+ . Therefore
we have derived the upper limit of the production cross section via the π − p → K − Θ+reaction. The upper limits of the differential cross sections averaged over 0 deg to 20 deg
in the laboratory frame have been obtained to be 1.6 µb/sr and 2.9 µb/sr at the 90 %confidence level at the beam momenta of 1.87 and 1.92 GeV/c, respectively. The upper
limits of the total cross sections have been obtained to be 1.8 µb and 3.9 µb at 1.87 and1.92 GeV/c, respectively, assuming that the Θ+ is produced isotropically in the center ofmass system. The obtained upper limits are quite smaller than the theoretical calculations
and give a strong constraint to the unknown parameters such as the coupling constantgK ∗ N Θ used in the calculations.

Contents
1 Introduction
1.1 The Θ+ baryon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Theoretical works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.1 Structure of Θ+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.2 K + N scattering and width of Θ+ . . . . . . . . . . . . . . . . . . .
1.3 Experimental review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3.1 Positive evidence for Θ+ . . . . . . . . . . . . . . . . . . . . . . . . .
1.3.2 Experiments with negative results . . . . . . . . . . . . . . . . . . .
1.4 Search for the Θ+ baryon with meson beams . . . . . . . . . . . . . . . . .
1.4.1 Theoretical calculation of the production cross section via π − p →K − X reaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4.2 KEK-PS E522 experiment– Search for the Θ+ baryon via π − p → K − X reaction – . . . . . . .

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2 Experiment
2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 K2 beam line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Beam line spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 Forward spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.1 Spectrometer magnet . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.2 Čerenkov counters . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.3 Trigger hodoscopes . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.4 Drift chambers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5 Target . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5.1 Polyethylene target . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5.2 Scintillating fiber active target . . . . . . . . . . . . . . . . . . . . .
2.6 Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.6.1 First-level trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.6.2 Second-level trigger . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.7 Data acquisition and monitoring . . . . . . . . . . . . . . . . . . . . . . . .
2.8 Data summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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3 Analysis
3.1 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Analysis of π − beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Identification of π − mesons . . . . . . . . . . . . . . . . . . . . . . .
3.2.2 Momentum analysis of π − mesons . . . . . . . . . . . . . . . . . . .
3.3 Analysis of outgoing particles . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 Measurement of momentum . . . . . . . . . . . . . . . . . . . . . . .
3.3.2 Mass reconstruction of outgoing particles . . . . . . . . . . . . . . .

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CONTENTS

3

3.3.3 Momentum correction . . . . . . . . . . . . . . . . . . . . . . . . . .
Vertex reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Summary of the analysis cut . . . . . . . . . . . . . . . . . . . . . . . . . .
Missing mass spectrum of the π + p → K + X reaction . . . . . . . . . . . . .
Missing mass resolution for Θ+ . . . . . . . . . . . . . . . . . . . . . . . . .
Consistency in the (π − , K − ) data . . . . . . . . . . . . . . . . . . . . . . . .
3.8.1 Invariant mass spectrum . . . . . . . . . . . . . . . . . . . . . . . . .
3.8.2 Missing mass spectrum of the π − p → K − pX reaction . . . . . . . .
Cross section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.9.1 Normalization of beam particles . . . . . . . . . . . . . . . . . . . .
3.9.2 Track-finding efficiency of beam particles . . . . . . . . . . . . . . .
3.9.3 Track-finding efficiency of scattered particles . . . . . . . . . . . . .
3.9.4 Overkilling of Čerenkov counters . . . . . . . . . . . . . . . . . . . .
3.9.5 Decay of the outgoing K − . . . . . . . . . . . . . . . . . . . . . . . .
3.9.6 Interaction of the outgoing K − . . . . . . . . . . . . . . . . . . . . .
3.9.7 Efficiency of mass trigger . . . . . . . . . . . . . . . . . . . . . . . .
3.9.8 Data acquisition efficiency . . . . . . . . . . . . . . . . . . . . . . . .
3.9.9 Acceptance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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4 Results
4.1 Missing mass spectra of the π − p → K − X reaction . . . . . . . . . . . . . .
4.2 Discussion about the missing mass spectrum at 1.92 GeV/c . . . . . . . . .
4.2.1 Systematic error of the peak position . . . . . . . . . . . . . . . . . .
4.2.2 Counts of peak . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 The upper limit of production cross section of the π − p → K − X reaction . .
4.3.1 At beam momentum of 1.92GeV/c . . . . . . . . . . . . . . . . . . .
4.3.2 At beam momentum of 1.87GeV/c . . . . . . . . . . . . . . . . . . .
4.3.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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3.4
3.5
3.6
3.7
3.8

3.9

5 Discussion
97
5.1 Comparison with theoretical calculations . . . . . . . . . . . . . . . . . . . . 97
5.2 Relation between the cross sections via π − and K + induced reactions . . . 99
6 Conclusion

102

A Scintillating Fiber Target System
107
A.1 Scintillating Fiber Block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
A.2 Image-intensifier tubes and CCD camera . . . . . . . . . . . . . . . . . . . . 107
A.3 Correction of distorted image . . . . . . . . . . . . . . . . . . . . . . . . . . 108
B KEK-PS E559 experiment110

Chapter 1

Introduction
1.1

The Θ+ baryon

The color interaction between quarks and gluons is described by Quantum Chromodynamics (QCD), a theory of strong interaction. One of the most remarkable successes canbe seen in the good agreement between the experimental results and the calculations by
QCD in the high energy region, where QCD can be treated perturbatively. When we takea look at the low energy region, the properties of hadrons such as spin, parity, magnetic
moment and mass should be explained by QCD. However the framework of QCD in the
low energy region is still in progress due to its non-perturbative nature. Currently mostof the hadron properties have been understood by using the effective models based on theprinciple of QCD; quarks and gluons have quantum number of ”color” with the SU(3)color
symmetry and hadrons, compound of the quarks and the gluons, must be the singlet stateof the SU(3)color symmetry. In the constituent quark model, which is one of the most familiar models based on QCD, mesons and baryons are described by quark and anti-quark
pair and three quarks respectively. The hadrons known so far are well classified by thequark model taking into account the assignment of flavors and spins of the constituent
quarks. The masses of hadrons are also well reproduced by considering the effective color
magnetic interaction between quarks. In these frameworks, the existence of exotic hadrons
such as ”hybrid meson (q q̄g)”, ”baryonium (qq q̄ q̄)”, ”pentaquark (qqqq q̄)” and ”dibaryon(qqqqqq)” has also been predicted theoretically, because QCD requires only that hadrons
should be color singlet, but does not restrict the number of quarks [1]. Although many
experimental efforts to search for these exotics were made, there was no clear evidence ofsuch states.
The pentaquark is the exotic particle which consists of four quarks and one anti-quark.
In particular, the pentaquark with a positive strangeness S = +1 has been attracting
attentions of physicists, because it has a ”s̄” quark as a constituent quark and cannot bea simple three-quark state. Therefore resonance states of K + and nucleon were vigorously
searched for using the partial wave analysis of K + -nucleon scattering from the 1970’s.
These searches resulted in two possibilities, the isoscalar Z0 (1780) and Z0 (1865) [2, 3].
However the evidence of the existence was denied by PDG group because there was noconclusive confirmation for a long time [4]. The comment of PDG group is following, ”Theevidence for strangeness +1 baryon resonances was reviewed in our 1976 edition [5], andmore recently by Kelly [6] and by Oades [7]. Two new partial-wave analyses have appearedsince our 1984 edition [2, 3]. Both claim that the P13 and perhaps other waves resonate.
However, the results permit no definite conclusion- the same story heard for 15 years. The
standards of proof must simply be much more severe here than in a channel in which many
resonances are already known to exist. The general prejudice against baryons not made4

1.1. THE Θ+ BARYON

52

Events/(0.02 GeV/c )

15

10

5

0

1.45 1.5 1.55 1.6 1.65 1.7 1.75 1.8
c2

MM K (GeV/c )Figure 1.1: The first evidence on the existence of the Θ+ reported by SPring-8/LEPS
collaboration. The solid histogram is a missing mass spectrum of γn → K − X reaction
where K + is also detected. The hatched histogram is the estimated background from
γp → K − K + X reaction. The peak with a Gaussian significance of 4.6σ was observed at
1540 ± 10 MeV/c2 . The only upper limit of the width was reported to be less than 25
MeV/c2 because the observed width was consistent with the experimental resolution.

of three quarks and the lack of any experimental activity in this area make it likely that it
will be another 15 years before the issue is decided.”.
It was almost just 15 years after the comment of PDG group that the report on theevidence of the baryon resonance with S = +1, which is now called Θ+ , was made bySPring-8/LEPS collaboration [8]. They measured the γn → K − K + n exclusive reaction
where neutrons in 12 C nuclei were used as a target and showed a peak in mass distributionof the missing mass of the γn → K − X reaction as shown in Figure 1.1. They have claimed
that the mass of the Θ+ is 1.54 ± 0.01 GeV/c2 . The observed width is consistent with its
experimental resolution and the only upper limit of 25 MeV/c2 has been reported.
The analysis at SPring-8 was motivated by the theoretical prediction based on thechiral soliton model by Diakonov, Petrov and Polyakov [9]. They predicted the narrow
resonance state of width less than 15 MeV/c2 at 1530 MeV/c2 . The nice agreement
between the theoretical prediction and the experimental result at SPring-8 stimulated
many physicists. Possible evidences of the narrow baryonic resonance Θ+ with massaround 1530 MeV/c2 and strangeness of +1 and width of about Γ < 15 MeV/c2 werereported one after another by several collaborations [10] using various reactions such as
photo-induced reaction, kaon-nucleon scattering, proton-proton reaction, ν A reaction anddeep inelastic electron scattering.
Such a state is extremely exciting because it is unambiguously exotic in the sensethat it cannot be a simple three-quark state as mentioned above. Therefore much of thetheoretical activity has been aimed at understanding the structure of the exotic state, Θ+[11]. Besides using the chiral soliton model, the most common treatment of this problem
has been based on variants of the quark model where the new baryon is identified as apentaquark [12, 13]. Other approaches treat the Θ+ in terms of meson-baryon binding or
as a kaon-pion-nucleon state [14]. Attempts to identify quantum numbers of the Θ+ andto confirm or deny its existence directly from QCD have been performed within the latticeMonte Carlo simulations [15, 16, 17, 18, 19] and within the QCD sum-rules [20].
One of the most remarkable feature of the Θ+ is its narrow width. In general, the6

CHAPTER 1. INTRODUCTION

Figure 1.2: The proposed anti-decuplet of baryons with J P = 1/2+ by chiral soliton model[9]. The anti-decuplet includes the exotic particles, Θ+ , Ξ+ and Ξ−− at the corners of thisdiagram. The quark content and the predicted masses are shown.

mass and width of a resonance of two particles is related through the depth and range ofthe potential. For a simple attractive potential of range ∼1 fm, the width of a P-wave
resonance 100 MeV/c2 above threshold is above 175 MeV/c2 . To produce a width of orderof 10 MeV/c2 requires a range of about 0.05 fm [12]. Thus the observed width of the Θ+ is
one of the reasons to consider the Θ+ as not a loosely bound state of K + n like a molecule
but a pentaquark state. In order to understand the narrow width, many theoretical models
are proposed considering the additional correlation between quarks. The difference of the
dynamics proposed in several models appears as the difference of the spin and parity of theΘ+ . Therefore experimentally, in addition to confirm the existence, it is quite important
to determine the spin and parity to select theoretical models and to understand the quark
dynamics in the low energy region.
Recently, however, negative results were reported from high energy experiments where
they searched for the Θ+ with much higher statistics [10]. Consequently the status of the
Θ+ is currently becoming controversial. Therefore the confirmation of the Θ+ is urgent
and crucial.
In this thesis, we present the results of the experimental search for the Θ+ via π − p →−K X reaction. In this introduction chapter, theoretical works are reviewed first. Then we
mention about the experimental status with both positive and negative results. Finally,
we describe the importance of the search via hadronic reactions we have executed.

1.2

Theoretical works

1.2.1

Structure of Θ+

The narrow resonance state of width less than 15 MeV/c2 at 1530 MeV/c2 was firstpredicted by D. Diakonov, Petrov and Polyakov using chiral soliton model [9]. The chiralsoliton model is a model of baryons based on the large-Nc (number of color) limit. The”soliton” is another word for the self-consistent pion mean-field in the nucleon in which
the quarks move. The light baryons are regarded as the rotational state in space andflavor SU(3) space. The ordinary baryon octet and decuplet are assigned to the lowest
and first excited states of the rotational states of the soliton and the masses of these1.2. THEORETICAL WORKS

7states are reproduced within accuracy of 1%. The exotic anti-decuplet state including theΘ+ is the next excited state and the members are shown in Figure 1.2. The spin of theanti-decuplet is 1/2 and the parity is positive same as the octet and decuplet baryons in
the chiral soliton model. Diakonov et al. assumed the state N ∗ (1710) to be a memberof the proposed anti-decuplet in order to have a prediction for the absolute mass of theΘ+ . They also calculated the decay width Γ < 15 MeV, which triggered the experimental
searches. In their formalism the narrowness of the Θ+ occurs due to a cancellation ofdifferent contributions in the decay operator.
Jaffe and Wilczek describe the exotic states as pentaquarks composed of two strongly
bound scalar diquarks (ud) interacting with a strange anti-quark [12]. They took particular note of the strong attractive force interacting between diquarks in spin-zero, color andflavor 3̄ configuration. In order to combine with the anti-quark, the two diquarks mustcombine into a color 3, the antisymmetric part of 3̄ × 3̄. Therefore the wave function must
be antisymmetric under space exchange, i.e. P-wave, in order to symmetrize all systemother than color. Their prediction of the Θ+ with J P = 1/2+ is significantly different fromthe assignment of 1/2− by the naive quark model where all quarks stay in S-state. The
model predicts that lowest-lying pentaquark states are a nearly ideally mixed combinationof an SU(3)flavor octet and an SU(3)flavor anti-decuplet. One basic feature of the model isthe prediction of two pentaquark states with nucleon quantum numbers: one with a massof ∼1450 MeV/c2 and the other with a mass of ∼ 1700 MeV/c2 . These states have beententatively identified with the Roper resonance N ∗ (1440) and the N ∗ (1710). In this framework, it is needed for the decay to re-assign quarks from the diquark-diquark-antiquark
configuration to the KN , quark-antiquark and three quarks, configuration. Due to there-assignment, the decay of the Θ+ is considered to be suppressed. They also mention thepossibility of charm and bottom analogues of the Θ+ , Θ0c (uuddc̄) and Θ+b (uuddb̄).
The study of the Θ+ by Lattice QCD is a challenging work. One of the biggest challenge
is how to choose the baryonic operator. Furthermore, since the Θ+ can be close to the
KN threshold, it is essential in any lattice spectroscopy calculation to reliably distinguishbetween genuine five-quark bound states and meson-baryon scattering states. In thesestatus, here, the independent four Lattice calculations are introduced.
Sasaki using double exponential fits, found a state consistent with the Θ+ also in the
I = 0, J P = 1/2− channel [15]. He also managed to identify the charmed analogue of theΘ+ 640 MeV/c2 above the DN threshold.
Csikor et al. using a different operator identified a state in the I = 0, J P = 1/2−
channel with a mass consistent with the observed Θ+ and the lowest mass found in the
opposite parity I = 0, J P = 1/2+ channel was significantly higher [16].
Liu et al. reported that they were not able to see any KN -state compatible with theΘ+ in either parity isosinglet channel [17].
Chiu and Hsieh, in disagreement with the first two studies, found a positive parity
isosinglet state compatible to the observed Θ+ , whereas the lowest state they found in thenegative parity state had much higher mass [18].
Ishii et al. have studied both the positive- and negative-parity pentaquark baryons
with I = 0 and spin J = 1/2 in anisotropic quenched lattice QCD [19]. The lowest
negative-parity pentaquark state is found to have a mass of 1.75 GeV/c2 , while the lowest
one with positive-parity appears at 2.25 GeV/c2 . They claim that the negative-parity
state is not a compact pentaquark state but an S-wave N K-scattering state.

8

CHAPTER 1. INTRODUCTION

Figure 1.3: K + d total cross section corrected for the effects of both the beam momentum
spread and Fermi momentum distribution measured by T. Bowen et al. [21]. Calculations
using a weak scattering approximation for the p-wave resonance by W.R. Gibbs are also
shown by smooth curves [28]. The dash-dotted, solid, and dashed curves correspond towidth of 1.2, 0.9, and 0.6 MeV/c2 , respectively.

1.2.2

K + N scattering and width of Θ+

Because the Θ+ baryon is considered to be a resonance state of K + and neutron, a K + dscattering is the most straightforward way to search for the resonance. However there wasno clear evidence of the resonance in the region around 1530 MeV/c2 from the past K + dscattering data. A question why the Θ+ was missed in the past experiments is raised.
The answer to the question probably lies, at least partly, in the very small width of theΘ+ which appears to be emerging from the step size of momentum of K + . At the firststage from the report by LEPS, discussions whether the Θ+ could be consistent with thepast K + d scattering data have been done vigorously in connection with the width of theΘ+ . Here, at first, the experimental data of the past K + d scattering are reviewed. Then
recent re-analyses with these scattering data are reviewed.
The K + N scatterings such as K + p and K + d scattering were measured mostly withbubble chambers in the 1960’s and 1970’s [21, 22, 23]. The isospin I = 0 amplitude has tobe extracted from the K + d scattering which is the mixture of I = 0 and I = 1 states. To
extract this amplitude, we have to correct the effect of beam momentum spread and Fermi
momentum distribution. If the mass of the Θ+ is assumed to be 1530 MeV/c2 , then the
momentum of K + on resonance in K + n scattering is 420 MeV/c. Such low momentum
K + beams were provided by degrading initial beams of higher momenta. Therefore theresulting beams had momenta with spread of typically 6% (FWHM). Moreover the Fermi
motion of a neutron in a deuteron had to be corrected. Due to the difficulty of treatmentof these unfolding procedures, there was disagreement between the cross sections measured
in different experiments. Figure 1.3 shows one of the results after these corrections by T.
Bowen et al. [21].
One of the first to discuss the relation of the past scattering database and the widthof the Θ+ is Nussinov. He evaluated a peak cross section at the resonance in isospin
I = 0, J P = 1/2+ P-wave channel to be ∼ 37 mb. In the past experiments, the intervalsof measured momentum points were typically 30 MeV/c. If the Θ+ is narrow, it could
escape the detection if there is a gap in the database at the resonant energy. However the1.2. THEORETICAL WORKS

9resonance structure should be spread out by the Fermi momentum of a neutron so thatit should be noticeable. Considering these effects of Fermi motion, he concludes that thewidth of the Θ+ must be less than 6 MeV/c2 [24].
Arndt, who is one of the authors of the reference [25] where partial wave analysis wasdone for the database of K + -nucleon scattering before the report of LEPS , reanalyzed
the database focusing on the energy region around 1540 MeV/c2 . He checked the changeof χ2 in fitting the database considering that there is a resonance structure around 1540
MeV/c2 with some width. From the change of this χ2 , he concludes that the resonancemust have a width of the order of 1 MeV/c2 or less [26].
Cahn and Tilling calculated the width from the result of DIANA experiment [29],where the Θ+ was observed via charge exchange channel of K + n → K 0 p, and obtained
the width of 0.9 ± 0.3 MeV/c2 [27]. They also estimated the upper limit of the width tobe 1 MeV/c2 ∼ 4 MeV/c2 from the K + d scattering data.
Gibbs shows the possible existence of a narrow resonance around 1550 MeV/c2 [28] bycomparing the calculation of K + d total cross section taking into account double scatteringof K + and Fermi motion correction of a neutron with the measured cross section by Bowenet al.. The calculation is shown in Figure 1.3 with the experimental result. The dashdotted, solid and dashed curves correspond to widths of 1.2, 0.9 and 0.6 MeV/c2 forpositive parity resonance, respectively. The dotted curve is the background fit. Assuming
a negative parity resonance gives lower mass.
As reviewed above, all analyses with K + -nucleon data arrive at the conclusion that thewidth of the Θ+ must be less than a few MeV/c2 . Such narrow width is unusual for hadronresonances. If the width of the Θ+ is really narrow, by revealing the decay mechanism of
this resonance we would obtain a new knowledge concerning the quark dynamics in the
low energy region.

10

CHAPTER 1. INTRODUCTION

Figure 1.4: Data from experiments with positive evidence for the Θ+ . This figure is takenfrom Reference [10]1.3

Experimental review

The first report on the evidence of the Θ+ baryon with positive strangeness S = +1
[8] has been immediately confirmed by several collaborations with various reactions suchas photon-induced reactions [30, 31, 33], K + n charge exchange reaction [29], neutrino
scattering [32], deep inelastic electron scatterings [34, 35], proton-proton reaction [36] andp-A reaction [37]. Moreover the possible existences of two more exotic particles, the Ξ−−
and the Θc , have been indicated by NA49 collaboration at CERN [39] and H1 collaboration
at DESY [40], respectively. The Ξ−− baryon with double strangeness S = −2 is one of themember of anti-decuplet and the minimum quark contents are ddssū. The Θc baryon is thecharmed analogue of the Θ+ which has c̄ quark instead of s̄ quark. The results of publishedexperiments with positive evidence are shown in Figure 1.4. When plotted this way, it
is clear that the statistics of all experiments is not sufficient to claim a clear observation
and better statistics is needed. Recently, null results have been reported from several highenergy experiments where they searched for the Θ+ with much higher statistics. However
it should be pointed out that in these experiments many charged particles are produced ina interaction which make a huge combinatorial background. Moreover the Σ∗+ resonancessuch as the Σ(1670) are not seen. Most recently, CLAS collaboration has reported someresults of a series of high statistical searches for the Θ+ . In some of the results, the Θ+
has not been observed [53, 54]. Consequently, the situation of the Θ+ is controversial. In
this section these experimental results with both positive and negative results, which aresummarized in Table 1.1 and 1.2 respectively, are reviewed.

1.3. EXPERIMENTAL REVIEW
Reference
[8]
[29]
[30]
[31]
[32]
[33]
[34]
[35]
[36]
[37]

Group
LEPS
DIANA
CLAS
SAPHIRITEP
CLAS
HERMES
ZEUS
COSY-TOF
SVD

11

ReactionγC → K + K − X
K + Xe → K 0 pX
γd → K + K − p(n)γp → K + K 0 (n)XνA → K 0 pX
γp → π + K + K − (n)e+ d → K 0 pX+
e p → e+ K 0 pX
pp → K 0 pΣ+pA → K 0 pX

Mass(MeV)
1540 ± 101539 ± 2
1542 ± 51540 ± 61533 ± 51555 ± 101526 ± 31522 ± 31530 ± 51526 ± 5

Width(MeV)
<25
<9
<21
<25
<20
<26
13 ± 9
8±4
<18
<24

σ′ s
4.6
4.4
5.2±0.6 1
4.8 2
6.7
7.8
∼5
∼5
4-6
5.6

Table 1.1: Published experiments with evidence for the Θ+ baryon

Reference
[41]
[43]
[44]
[45]
[46]
[47]
[48]
[49]
[50]
[51]
[52]
[53]
[54]

Group
BES
BarBar
Belle
LEP
HERA-BSPHINX
HyperCP
CDF
FOCUS
Belle
PHENIX
CLAS
CLAS

Reactione+ e− → J/Ψ → Θ̄Θ

e+ e− → Υ(4S) → pK 0 X
e+ e− → B 0 B¯0 → pp̄K 0 X
e+ e− → z → pK 0 X
pA → K 0 pX
pC → K 0 pX
pCu → K 0 pX
pp̄ → K 0 pX
γBeO → K 0 pX
K + Si → K 0 pX
AuAu → K − n̄Xγp → K̄ 0 K + n
γd → K + K − p(n)Limit
< 1.1 × 10−5 B.R.
< 1.0 × 10−4 B.R.
< 2.3 × 10−7 B.R.
< 6.2 × 10−4 B.R.
< 0.02 × Λ∗
< 0.1 × Λ∗
< 0.3% K 0 p< 0.03 × Λ∗
< 0.02 × Σ∗
< 0.02 × Λ∗
not given< 0.8 nb
< 0.3 nb

Table 1.2: Published experiments with non-observation for the Θ+ baryon

1This result was denied by the same collaboration with high statistical experiment [54]. In the highstatistical measurement, there was no significant structure in the mass spectrum of nK + . Assuming thatthe histogram of the high statistical measurement represents the true shape of the background, the signal
size estimate of 5.2σ from previous data decreases to 2.9σ.
2The search via the same reaction with high statistics by the CLAS collaboration reported a null result[53]. The 95% C.L. upper limit on the total cross section via γp → K̄ 0 K + n reaction was set to be 0.8 nb.

12

1.3.1

CHAPTER 1. INTRODUCTION

Positive evidence for Θ+

Experiments with tag of S = +1
At LEPS, the photo production of hadrons has been studied using photons with energies of
1.6 ∼ 2.4 GeV produced by Compton backscattering of laser photon from 8 GeV electrons
in the SPring-8 storage ring. The produced charged hadrons are detected by a forward
spectrometer. The Θ+ was searched for via γn → K − Θ+ → K − K + n reaction where theneutrons in 12 C nuclei in Start Counter were used as a target [8]. After the correctionof Fermi motion of neutron, they showed a peak in mass distribution of K + n system asshown in Figure 1.5 (1). They claim that the mass is 1540 ± 10 MeV/c2 and the Gaussian
significance of the peak is 4.6σ. The observed width is consistent with the experimental
resolution of the spectrometer and the upper limit of 25 MeV/c2 is reported.
The DIANA collaboration at ITEP searched for the Θ+ independently of LEPS, according to the prediction by Diakonov et al.. Using K + beam and a Xe bubble chamber,they searched for the Θ+ via K + n charge exchange reaction, K + n → K 0 p [29]. The rangeof each K + beam was required to be larger than 550 mm, which corresponded to the mean
K + momentum of 470 MeV/c at a reaction point. They collected 1,112 events of charged
exchange reaction of K + Xe → KS0 pXe′ . In order to reject events where the proton or KS0
were affected by the final state interaction in the Xe nuclei, they applied a cut for the angleof the proton and KS0 . From the invariant mass spectrum of the proton and KS0 after theseanalyses, the narrow peak with the statistical significance of 4.4σ corresponding to the Θ+
was obtained at 1540 ± 2 MeV/c2 as shown in Figure 1.5 (2). The measured width was
also consistent with the resolution and the upper limit of 9 MeV/c2 has been obtained.
The CLAS collaboration at Thomas Jefferson Laboratory is one of the central placesof the research for the photo production of the Θ+ . Photon beams were produced by
2.474 and 3.115 GeV electrons incident on a bremsstrahlung radiator of thickness of 10−4
radiation length. They have reported the exclusive measurement on deuterium for thereaction γd → K + K − p(n) where the final state neutron is reconstructed from the missing
momentum and energy [30]. The most advantageous feature of this measurement is thatFermi motion correction is not needed. In addition to the cut to eliminate other hadronresonances such as φ meson and Λ(1520) resonance, the missing momentum was required to
be greater than 0.20 GeV/c in order to remove spectator neutrons. Finally they obtainedmass spectrum of the K + n system showing a sharp peak at the mass of 1542 ± 5 MeV/c2
with the width of 21 MeV/c2 corresponding to the experimental resolution as shown in
Figure 1.5 (3). The peak count is 43 and the statistical significance has been estimated to
be 4.6 ∼ 5.8 σ depending on the background shape.
The exclusive measurement on a proton target for the γp → π + K − K + (n) reaction
has also been reported by the CLAS collaboration [33]. The undetected neutron was
selected from the missing mass of γp → π + K − K + X reaction and φ meson was eliminated.
Moreover they required a cut of cos θπ∗ + > 0.8 , where θπ∗ + is the center-of-mass angle
between the π + and the photon beam. This cut corresponds to an enhancement of thet-channel process where the intermediate N ∗ state decays into Θ+ and K − . From thenK + mass spectrum which is shown in Figure 1.5 (5), a narrow baryon state with massM = 1550±10 MeV/c2 and width Γ < 26 MeV/c2 was observed. The peak’s statisticalsignificance is (7.8 ±1.0)σ.
The SAPHIR collaboration at ELSA has reported the evidence for the Θ+ in photoproduction of γp → nK + KS0 reaction [31]. The incident photons are produced by the1.3. EXPERIMENTAL REVIEW13ELSA electron beam via bremsstrahlung in a copper foil radiator. The KS0 was identified
from the invariant mass of π + π − pair and the neutron was also selected from the missing
mass. The Θ+ baryon is seen as a peak in the nK + invariant mass distribution with a 4.8
σ confidence level as shown in Figure 1.5 (4). The observed mass is 1540 ± 4 ± 2 MeV/c2
and an upper limit of the width Γ < 25 MeV/c2 has been obtained.
The Θ+ has been shown from the exclusive measurement of pp → Σ+ K 0 p reaction
by the COSY-TOF collaboration, where hyperon resonances are measured via protonproton reaction using a liquid hydrogen target and proton beams of incident momentum of
2.95 GeV/c [36]. The KS0 was identified by the decay into π + π − pair. The angle between
the π + π − pair was required to be larger than 12 degree to eliminate Λ → π − p events
kinematically. The Σ+ was selected from the missing mass of pp → KS0 pX reaction. Afterthe correction of the acceptance, they have showed a peak with the statistical significanceof 4 ∼ 6 σ at the mass M=1530±5 MeV/c2 in the mass distribution of K 0 p subsystem asshown in Figure 1.5 (6). The production cross section of the proton-proton reaction has
been estimated to be 0.4 ± 0.1(stat.) ± 0.1(syst.) µb.

2

Events/(0.02 GeV/c )

15

10

5

0

1.45 1.5 1.55 1.6 1.65 1.7 1.75 1.8
MMcKŠ (GeV/c2)

35

35

25

30

a

counts40

30

Events

+

25

20

20

15
15

10

10

5
0

5

1.5

1.6
1.7
+
2
M(K n) [GeV/c ]

1.8

1.9

0

1.4

1.6

1.8
+

mass(nK )/GeV

Figure 1.5: Experimental results with positive evidence where the positive strangeness istagged.

14

CHAPTER 1. INTRODUCTION

The pK 0 experiments
Astratyan, Dologolenko and Kubantsev have reported a narrow peak in the mass distribution of pKS0 system produced via neutrino and anti-neutrino collisions with nuclei [32].
This is the re-analysis of past neutrino scattering data with big bubble chambers: WA21,
WA25, WA59 (CERN) and E180, E632 (Fermilab). Three kinds of bubble chambers, hydrogen, deuterium and neon-hydrogen mix were used in these experiments. They haveobtained the pKS0 mass distribution for the neon and deuterium data combined showing
a narrow peak of 27 events at the mass of 1533±5 MeV/c2 as shown in Figure 1.6 (1).
Neutrino data do not allow one to determine the strangeness of the observed resonant
state. They interpret the enhancement as a signal of the formation of the Θ+ , considering
there are no known Σ∗+ states in this mass region.
HERMES collaboration at DESY has reported the evidence for a narrow baryon statewith |S| = 1 in quasi-real photo production on a deuterium target through the decay
channel pKS0 → pπ + π − [34]. The 27.6 GeV positron beams of the HERA storage ringinteract on a longitudinally polarized deuterium gas target. The peak with the mass
M=1528 ± 2.6(stat.) ± 2.1(syst.) and the width Γ = 17 ± 9(stat.) ± 3(syst.) was observedin the mass distribution of pKS0 system as shown in Figure 1.6 (2).
The ZEUS collaboration also at DESY has reported the results of a search for theΘ+ and the Θ̄− in the KS0 p and KS0 p̄ decay channels, respectively, in the central rapidity
region of ep collision at center-of-mass energy of about 300 GeV [35]. The KS0 mesons
were identified by their charged decay mode, KS0 → π + π − . Protons and anti-protons wereselected by the dE/dx distribution in the central tracking detector (CTD). They showed apeak structure in the mass distribution of KS0 p and KS0 p̄ systems at the mass of 1521.5 ±1.5(stat.) GeV/c2 , when they selected events with 4-momentum transfers Q2 > 20 GeV2 ,as shown in Figure 1.6 (3).
The SVD collaboration measured the pA → pK 0 X reaction using the 70 GeV proton
beam at the IHEP [37]. In their analysis, events with no more than five charged particles
from the primary vertex were analyzed to suppress the combinatorial background. The
additional cuts were applied to momentum of proton (4 GeV/c < Pp < 21 GeV/c) andthe angle of the pK 0 system θpK 0 at the center of mass frame (cos θpK 0 ≤ 0). As shownin Figure 1.6 (4), the invariant mass of the pK 0 system shows the excess at 1526 ± 3
MeV/c2 above their background estimated by FRITIOF simulation in addition to theexcess strength in the 1570∼1750 MeV/c2 range, presumably due to Σ∗+ resonance.

1.3. EXPERIMENTAL REVIEW

15

Figure 1.6: Experimental results with positive evidence where the Θ+ was searched forfrom the invariant mass of pKS0 system.

1.3.2

Experiments with negative results

The reports of finding the exotic baryons such as the Θ+ and the Ξ−− in low energy exclusive experiments have given the motivation for collaborations of high energy experiment
to search for these objects. Naively, one might expect that these exotic baryons should
be produced in high-energy experiments through fragmentation processes as the flux tube
breaks when the struck quark exits the nucleon. The searches have been done in bothe+ e− annihilation experiments and the high-energy hadron beam experiments with muchhigher statistics and better detector resolution. In these experiments, mainly the inclusive
measurements of K 0 and proton are reported and mass spectra of pK 0 system show nopeak structure around the expected mass region of 1520 - 1560 MeV/c2 , while the ordinary
hyperons such as Λ(1520) or Ξ(1530) are clearly seen. However, in these experiment many
charged particles are produced in a interaction which make a huge combinatorial background. Moreover the Σ∗+ resonances such as the Σ(1670) are not seen. In this section,
the null experiments are reviewed from the viewpoint of the e+ e− experiments and hadroninteraction experiments.
The e+ e− experiments
The pentaquark production in e+ e− annihilation needs at least 5 quarks and 5 anti-quarks
from zero quark. Therefore experiments with a baryon in the beam or the target might
have some advantage in pentaquark production. However e+ e− interaction is also knownfor ”democratic” production of hadrons. Baryons with nonzero beauty, charm, strangeness(up to three units) and/or orbital angular momentum have been observed with production
rates that appear to depend on the mass and spin, but not quark content as shown in
Figure 1.7. If pentaquarks are produced similarly, then one might expect a pentaquark rate
as high as that for an ordinary baryon of the same mass and spin, i.e. about 8 × 10−4 Θ+16

CHAPTER 1. INTRODUCTIONªªFigure 1.7: Baryon production rates in e+ e− annihilation from experiments at the Z 0√(circles) and s ∼ 10 GeV (squares) as a function of baryon mass [42]. The vertical scaleaccounts for the number of spin and particle+antiparticle states, and the lines are chosen
to guide the eye. The arrows indicate BABAR preliminary upper limits on spin-1/2 Θ+and Ξ−− pentaquark states, assuming the branching fractions shown, and are seen to lie
below the solid line.

√
and about 4 × 10−5 Ξ−− per e+ e− → hadrons event at s = 10.58 GeV. Unfortunately
anyone do not know whether this tendency of baryon production rate is applicable topentaquark production.
The BABAR collaboration has shown the results of inclusive searches for the Θ+ in√data from the BABAR experiment at s = 10.58 GeV, which includes both e+ e− →q q̄, q = udsc, events and the production of Υ(4S) mesons, which decay into B B̄ pairs [43].
They searched for the Θ+ from the invariant mass of the pKS0 system, where KS0 → π + π − .
The invariant mass spectra are shown in Figure 1.8, where there is a clear peak at 2285
0
MeV/c2 from Λ+c → pKS but no other sharp structure. The 95% CL upper limits on theyield per q q̄ event and Υ(4S) decay have been obtained to be 5.0× 10−5 and 18 × 10−5
assuming that the width of the Θ+ is 1 MeV/c2 and the branching ratio of the Θ+ decay
to Ks0 p is 1/4. This results are roughly a factor of eight below the typical values measured
for ordinary octet and decuplet baryons as shown in Figure 1.7.
The ALEPH collaboration has searched for the exotic baryons in the fragmentationof quarks from four million hadronic Z decays as a narrow peak in the invariant massof combinations of reconstructed KS0 and proton tracks with the resolution better than
5 MeV/c2 [45]. They have set the 95% C.L. upper limit on the production rate times
branching ratio of the Θ+ and its antiparticle per hadronic Z decay to be NΘ+ · Br(Θ+ →pKS ) < 6.2 × 10−4 , which yields NΘ+ < 0.0025 assuming that the branching ratio is 25%.
On the other hand, the production rate of Λ(1520) per hadronic Z decay is found to be1.3. EXPERIMENTAL REVIEW

17

5

3

x10
1.5

2

Candidates / (8 MeV/c )2

Candidates / (2 MeV/c )

x10
40

1.0

+
c

0.5

39
38
37
36

~
~
1.500

0.0

1.5

2.0

2.5

3.0
0
pKS Mass

1.550

3.5 2
(GeV/c )

4.0

1.600

4.5

5.0

Figure 1.8: Distribution of the pKS0 invariant mass obtained by the BABAR collaboration[43]. The sharp peak corresponding to Λ+
c is clearly recognized. The same data are plotted2
for the mass range around 1540 MeV/c .

NΛ(1520) = 0.033 ± 0.004 ± 0.003.
The Belle collaboration has reported the upper limit of the production rate of the Θ+
through the B 0 → Θ+ p̄ decay following Θ+ → KS0 p using data sample recorded on theΥ(4S) resonance at the KEKB asymmetric energy e+ e− collider [44]. They obtained the
90% confidence level upper limit of Br(B 0 → Θ+ p̄) · Br(Θ+ → pKS0 ) < 2.3 × 10−7 .

counts / 5 MeV

counts / 3 MeV

High-energy hadron beam experiments
a)
100
50
1.4

p+C
1.475

1.55
0

pKS mass, GeV

1.625

1.7

b) mult < 10
50

p+C
0
1.4

1.475

1.55

1.625

1.7

0

pKS mass, GeV

Figure 1.9: The pKS0 invariant mass distributions obtained by HERA-B collaboration [46].
(a) data from the p + C collisions and the background estimate (continuous line). (b) samedata with requirement that a track multiplicity is less than 10.
HERA-B is a fixed target experiment at the 920 GeV proton storage ring at DESY
utilizing a forward magnetic spectrometer with a large acceptance centered at mid-rapidity.
√
They have searched for the Θ+ from the pKS0 decay in proton-nucleus collisions at s =41.6 GeV using carbon, titanium and tungsten wire targets [46]. The invariant mass
spectrum of the pKS0 pairs is shown in Figure 1.9 for the p + C data with the background
determined from the event mixing. The distribution is smooth shape. The 95% C.L. upper
limit of the particle ratio Θ+ /Λ(1520) at mid-rapidity (ycm ∼ 0) is obtained to be 2.7%.
The SPHINX collaboration has performed a search for the Θ+ in a proton-induced
reaction p + C(N ) → Θ+ K̄ 0 + C(N ) on carbon nuclei at 70 GeV studying nK + , pKS0 and
pKL0 decay channels of the Θ+ where KL ’s and neutrons were detected in their calorimeter[47]. The performance of the calorimeter to detect the neutral particles was studied byreconstructing Λ(1520) → nKS0 and φ → KL0 KS0 decays. There was no significant structure
in all invariant mass spectra of nK + , pKS0 and pKL0 channels as shown in Figure 1.10. They
have set an upper limit of particle ratio Θ+ /Λ(1520) to be less than 0.02 at 90% C.L..

18

CHAPTER 1. INTRODUCTION

Figure 1.10: The mass spectra of (1) pKL0 , (2) pKS0 and (3) nK + obtained by SPHINX
collaboration [47]. The shaded histograms are Monte Carlo simulations.

The HyperCP experiment is designed principally to investigate CP violation in Ξ− /Ξ̄+
decays produced by 800 GeV protons interacting in a copper target. In this experiment,
there was a tungsten collimator just downstream of the copper target to select charged
particles with momenta from about 120 to 220 GeV/c. However over a half of the triggereddata were from events produced in the tungsten near the exit of the defining collimatorand these events were used in the pentaquark search [48]. This experiment did not haveparticle identification. The KS0 mesons are reconstructed from the two charged particles
with the opposite charges. Protons are selected by requiring charged tracks with > 50%of the total momentum. In the total sample of 106,000 KS0 p and KS0 p̄ candidates, there
is no sign of a peak near 1.54 GeV/c2 . They find that the number of the Θ+ is less than
0.3% of the KS0 p candidates.

1.4

Search for the Θ+ baryon with meson beams

As reviewed in the previous section, the present status of the Θ+ is controversial. There
are more than ten experiments which indicated the evidence of the Θ+ , while similar
number of experiments claim the null results. In such a situation, the confirmation ofexistence (or non-existence) of the Θ+ is urgent and crucially important.
It is true that the statistics in all experiments with positive results is not sufficient toclaim a clear observation of the Θ+ , while several high-energy experiments report the null
results obtained from searches with much higher statistics and better resolution. However
Titov et al., using quark constituent coupling rules, shows that the production of the Θ+is suppressed relative to the Λ(1520) resonance by about three orders of magnitude forhigh energy experiments [55]. Therefore, in order to confirm the existence of the Θ+ ,high statistics experiments at low energy region with hadronic reaction become crucial.
Many experimental data of the Θ+ searches are from photo-production experiments. In
general the Θ+ production cross section via hadronic reaction is expected to be muchlarger than that via photo-induced reaction. Now, physical properties such as spin, parity
and width have not been determined experimentally yet. The narrow width of the Θ+ isthe remarkable characteristics. The width of a few MeV or less is expected from the K + nucleon scattering data and is unusually narrow as a hadron resonance of which typical
width is several ten MeV. The suppression of decay to KN mode might be related to theinternal structure of the Θ+ . Therefore determination of spin and parity is indispensable
to understand the reason of the narrowness. The measurement of these values needs morestatistics. From these viewpoints, the study of the Θ+ production using meson beam such

1.4. SEARCH FOR THE Θ+ BARYON WITH MESON BEAMS

19

Figure 1.11: Invariant mass spectra of (1) nK + and (2) pK 0 produced by π − p reactions at
π − beam momentum of 1.5 - 2.4 GeV/c measured in the past bubble chamber experiment[56]. Although the statistics is poor, there is no structure around 1.54 GeV/c2 .

as π − and K + is essential. Therefore we carried out an experiment to search for the Θ+
via π − p → K − Θ+ reaction. In this reaction, the threshold momentum is 1.71 GeV/c. We
used 1.87 and 1.92 GeV/c π − beam.
The π − p → K − X reaction near the Θ+ production threshold was studied in 1960s
using a bubble chamber [56]. The main backgrounds of the (π − , K − ) reaction are φproduction, Λ(1520) production and 3-body phase space as following.
φ production : π − p → φn → K − K + n
0

−

−

0

(σ = 30.0 ± 8.0µb)(1.1)(σ ∼ 25µb)(1.3)

Λ(1520) production : π p → Λ(1520)K → K K p (σ = 20.8 ± 5.0µb)
−

−

+

0

phase space : π p → K (K n/K p)(1.2)

The cross sections of these reactions were measured to be 30.0 ± 8.8µb, 20.8 ± 5.0µb
and ∼ 25µb respectively at beam momenta from 1.8 to 2.2 GeV/c. It is remarkable featurethat in this momentum range the background is small because other channels do not open.
In the past experiment the invariant masses of nK + and pK 0 were surveyed as shown in
Figure 1.11. Any peak structure was not observed. However numbers of nK + and pK 0
events were only 86 and 249 respectively.

1.4.1

Theoretical calculation of the production cross section via π − p →K − X reaction

The understanding of production mechanism is quite important to understand the Θ+ .
Therefore a measurement of the production cross section with a simple reaction is important experimentally. Theoretical calculations with hadronic models using effective interaction Lagrangians and form factors have been made by several authors [57, 58, 59, 60].
They try to understand the Θ+ production mechanism via γN, N N, KN and πN reactions
near the production threshold comprehensively.
For the calculation of the cross section via the π − p → K − Θ+ reaction, the diagrams
shown in Figure 1.12 were taken into account. The parity of the Θ+ was assumed to bepositive. Then the effective Lagrangians are
LKN Θ = −igKN Θ (Θ̄γ5 K + n − Θ̄γ5 K 0 p) + H.c.

(1.4)

20

CHAPTER 1. INTRODUCTION

Figure 1.12: Diagrams for π − p → K − Θ+ reaction.
LπN N= −igπN N N̄γ5 πN(1.5)

for the s-channel. For the K ∗ exchange, they used
LK ∗ N Θ = −gK ∗ N Θ (Θ̄γ µ Kµ∗+ n − Θ̄γ µ Kµ∗0 p) + H.c.
LK ∗ Kπ = −igK ∗ Kπ K̄∂ µ πKµ∗ − ∂ µ K̄πKµ∗ + H.c..

(1.6)

In order to calculate the cross section using this formalism, the coupling constants should
be determined. The coupling constant gK ∗ Kπ fixed by the experimental data for K ∗ → Kπ
decay,
g2 ∗3(1.7)
ΓK ∗ →Kπ = K Kπ
2 |Pπ | ,
2πMK
∗
2
+
is gK ∗ Kπ = 3.2. They also used gπN
N /(4π) = 14 [61]. The coupling term of the Θ is also
estimated from the decay width as follows. The Lagrangian LKN Θ gives the decay widthof Θ+ → KN asΓΘ+ →K + n+K 0p =q2
|PK |(
gKN
Θ2π

2 + P2 − M )
MN
N
K

MΘ

,

(1.8)

where MN and MΘ are the nucleon and Θ+ masses, respectively, and PK is the momentumof the kaon in the Θ+ rest frame 3 . The authors determined the value of gKN Θ considering the experimental upper limit of width around 9–25 MeV/c2 and the KN scattering
analysis. Concerning the coupling gK ∗ N Θ , there is no experimental information, since thedecay of the Θ+ into K ∗ N is not kinematically allowed. The only hint they used is that
coupling constants for the ordinary hyperon production, gK ∗ N Λ and gK ∗ N Σ , are ∼-4.5
and ∼-2.6, respectively, which are smaller than gKN Λ and gKN Σ by a factor of 2.4−3.5
or 1.2−1.8 [62]. From this observation, they expect that gK ∗ N Θ would be smaller thangKN Θ . However, their relative phase is still unfixed. Thus, they treated gK ∗ N Θ as a freeparameter from −gKN Θ to gKN Θ .
In order to estimate the realistic value of the cross section, form factors are needed
at interaction vertices to take into account the finite sizes of hadrons. They adopt the3

In case of negative parity, the decay width Γ and coupling constant gKNΘ are connected with thefollowing equation,p2|PK |( MN+ P2K + MN )g2
Γ = KNΘ
.
(1.9)
2π
MΘ
For example this equation gives gKNΘ = 0.307 with Γ = 5 MeV/c2 , which is about ten times lower thanthat for positive parity (gKNΘ = 2.2 with Γ = 5 MeV/c2 for positive parity). Therefore if the parity is
negative, the cross section is suppressed compared with that for positive parity.

1.4. SEARCH FOR THE Θ+ BARYON WITH MESON BEAMS

21

Figure 1.13: Calculated cross sections for the π − p → K − Θ+ reaction by Y. Oh et al.
[58]. The (a,d) are the results without form factor, (b, e) are that with the form factor
of equation (1.10) with Λ = 0.5 GeV, and (c, f) are that with other form factor (See
Reference [58]). In (a, b, c), the solid, dotted, dashed, and dot-dashed lines are withgK ∗ N Θ = −2.2, −1.1, −0.5 and 0.0, respectively. In (d, e, f), the solid, dotted, dashed, anddot-dashed lines are with gK ∗ N Θ = 2.2, 1.1, 0.5 and 0.0, respectively.

monopole form factor, which is a function of
F (s) =√

s only,Λ2,Λ2 + q2i(1.10)

where Λ is the cut off parameter and qi is the three-momentum of the initial state particles
in the center of mass frame. The cut off parameter is taken to be Λ = 0.5 GeV basedon fitting the measured cross section for the reaction πN → KΛ using similar hadronic
Lagrangians [63].
In Reference [57], Liu and Ko calculated the cross section taking into account only thes-channel diagram. They used gKN Θ = 4.4, which corresponds to 20 MeV/c2 width ofthe Θ+ . They predict that the cross section is about 50 µb. In this framework, the crosssection is controlled by the gKN Θ which is determined from the width by equation (1.8),
because they take into account the only s-channel diagram. Therefore the cross section
is proportional to the width of the Θ+ , since both the cross section and the width are
2
2
proportional to gKN
Θ . If the width is less than 20 MeV/c , smaller cross section will beobtained.
Y. Oh et al. calculated the cross section taking into account the s-channel diagram
and the t-channel diagram where a K ∗ is exchanged [58]. They used gKN Θ =2.2, whichcorresponds to 5 MeV/c2 width of the Θ+ , and the same cutoff value used by C. M.
Ko et al.. Because there is no experimental information about gK ∗ N Θ , they used several
values from −2.2 to 2.2 as gK ∗ N Θ . Figure 1.13 shows their results obtained without form
factor (a, d), with form factor of equation (1.10) (b, e) and with other type of form
factor (c, f) (See Reference [58]). The top ones, (a, b, c), show the calculations using

22

CHAPTER 1. INTRODUCTIONgK ∗ N Θ = −2.2, −1.1, −0.5 and 0.0. The bottom ones, (d, e, f), show the calculations
using gK ∗ N Θ = 2.2, 1.1, 0.5 and 0.0. Due to the interference between the amplitudes of schannel and t-channel, the cross section of the π − p → K − Θ+ reaction is quite dependent
on the magnitude of gK ∗ N Θ . When they used the form factor of equation (1.10), thecalculated cross section ranges from about 2 µb to 190 µb as shown in Figure 1.13 (b,d). Therefore they mention that this reaction is suitable to give a guide to estimate themagnitude of gK ∗ N Θ .
In these calculations, the parameters which are not determined experimentally suchas gKN Θ and gK ∗ N Θ are used. Therefore these calculation should be compared withexperimental cross section. As mentioned above, the total cross section is dependent on
the decay width, because both of them is related to coupling constant gKN Θ . Experimental
information on total cross section is important to determine the decay width, or vise versa.

1.4.2

KEK-PS E522 experiment– Search for the Θ+ baryon via π − p → K − X reaction –The present E522 experiment has been carried out at the K2 beam line of the KEK 12
GeV Proton Synchrotron in November 2002 and March 2004 4 . We took π − p → K − X
data with the motivation of the confirmation of the existence of the Θ+ . Now the K2
beam line is a unique beam line which can provide up to 2 GeV/c π beam and enables us
to study the Θ+ with this reaction near the production threshold. We used a π − beamof 1.87 and 1.92 GeV/c. As a target, we used a scintillation fiber (SCIFI) target ((CH)n )and a bulk target of polyethylene ((CH2 )n ).
In this thesis, we present the production cross section via π − p → K − Θ+ reaction
obtained from the present experiment.

4
The main objective of this experiment was to search for H-dibaryon resonance with (K − , K + ) reaction.
We searched for the enhancement at the threshold region of the double-Λ system, which was first measured
at KEK-PS E224 experiment [64], with much better statistics [65]. The (K − , K + ) data was taken in
November 2002. The (π − , K − ) data to search for the Θ+ was taken in March 2004.

Chapter 2

Experiment2.1

Overview

We have performed the E522 experiment at the K2 beam line of KEK 12 GeV Proton
Synchrotron in 2004. The main objective of this experiment was to search for H-dibaryon
resonance with (K − , K + ) reaction. At KEK-PS E224 experiment, the enhancement wasobserved at threshold region of the double-Λ system [64]. In the present experiment wesearched for this enhancement, which was a candidate of H-dibaryon resonance, with ten
times larger statistics [65]. Besides this reaction, we optionally took π − p → K − X data,
because the search for the Θ+ via mesonic reaction became crucial to confirm its existence
and the K2 beam line was a unique beam line which could provide up to 2 GeV/c π beam.
We used π − beams of 1.87 and 1.92 GeV/c. As a target, we used a scintillation fiber(SCIFI) target ((CH)n ) and a bulk target of polyethylene ((CH2 )n ). The SCIFI target
was 20 cm long, and was the same one used in the hyperon-nucleon scattering experiment(KEK-PS E289) [66]. It was mainly used to detect decay particles from 12 C(K − , K + ΛΛ)reaction for the H-dibaryon resonance search. For (π − , K − ) data, we mainly used the 10
cm long polyethylene target to enhance the contribution from free protons. The SCIFI
target was also used to detect tracks of the charged particles other than K − produced
by reactions. At the beam momentum of 1.87 GeV/c, 2.9×109 and 3.0×109 π − beam
particles were irradiated to the SCIFI and the polyethylene targets, respectively. At 1.92
GeV/c, 7.4×109 π − beam particles were irradiated to only the polyethylene target. For thecalibration we took the following data. In order to estimate the contribution from carbon
in the SCIFI and polyethylene targets, we took data with a carbon target. The (π + , K + )data were analyzed to measure Σ+ peak position for the calibration of the missing mass
spectrum.
The experimental setup consisted of two parts; one part was a beam line spectrometerto analyze momentum of each incident beam particle and the other part was a forward
spectrometer to detect scattered particles.
The K2 beam line is designed to transport charged particles up to 2.0 GeV/c. Figure
2.1 (a) shows the beam line spectrometer. The π − beam was bent by 15 degree at thebending magnet (D2) and focused at the target by two quadrapole magnets (Q6, Q7).
The typical intensity of π − was 3.3×105 counts during 2 sec. spill with primary proton
beam of 1.1 × 1012 . This intensity was determined by adjusting the acceptance slit and themomentum slit considering the memory size of the memory module (MP) used in the dataacquisition system. Each beam particle was defined by the hit of T1 and T2 counters placed
about 7.2m apart each other and π − was selected at a trigger by two aerogel Čerenkov
counters (BAC1,2), of which threshold velocity was 0.971, placed just upstream of the T2
counter. The beam momentum was analyzed with 5 wire chambers placed upstream and23

24

CHAPTER 2. EXPERIMENT

Figure 2.1: The schematic view of E522 experimental setup.

downstream of the D2 magnet. The momentum resolution is estimated to be σ(p) = 8.9
MeV/c from a simulation. Between two quadrapole magnets (Q6, Q7) and the target,
3 proportional chambers were placed to measure the beam direction. The timing for all
detectors was determined by the T2 counter.
The scattered particles were detected by the forward spectrometer shown in Figure
2.1 (b). The KURAMA magnet is 80 cm long and magnetic field strength is 0.93T. The
momentum of each scattered particle was measured using 3 drift chambers (DC1,2,3)
and scintillation hodoscopes (VH, CH) placed upstream and downstream of KURAMA.
The momentum resolution is 1.9 % (r.m.s.) for 0.8 GeV/c K − . The time-of-flight of eachscattered particle was measured by a TOF wall (FTOF) placed at end of the spectrometer.
A typical time resolution was 132 ps. Two Čerenkov counters (BVAC, FAC) were installed
between the target and KURAMA to veto π − . Besides this particle identification withthese Čerenkov counters at trigger level, we selected the charge and momentum rangeof each scattered particle at 1st trigger level using the hit combination of each segmentsof CH hodoscope and FTOF. Momentum of each particle was determined using the hit
combination. By combining time-of-flight information of the hit FTOF segment with thismomentum information, the mass of scattered particle was calculated. We selected K −with this mass trigger (MT) at the 2nd trigger level. This mass trigger rejected mainly
π − which survived due to the inefficiency of the Čerenkov counters.

2.2. K2 BEAM LINE25

K2
container

Figure 2.2: Layout of the K2 beam line at KEK 12 GeV proton synchrotron.

2.2

K2 beam line

In a 12 GeV proton synchrotron, the protons were first accelerated in a Cockcroft-Walton(to 750 keV), and then in a linac (to 40 MeV), before they were injected into the booster.
From the booster, after acceleration, the 500 MeV protons were eventually injected into
the main ring in which they got accelerated to energies of 12 GeV. This experiment was
conducted at East Counter Hall, where proton beams were extracted slowly to the EP2beam line during 2 sec in a 4 second cycle. The accelerated protons were delivered tothe production target in the EP2-A beam line to produce the secondary particles suchas pions and kaons into the K2 beam line. The zero degree production of the secondary
particles was chosen in order to optimize the production rate of secondary particles fromthe primary protons incident on the nuclear target.
The K2 beam line was designed to optimize three important characteristics of low
energy kaon beam, i.e. the kaon beam intensity, the mass separation quality and theoptical beam quality [67]. It consists of two dipole magnets, D1 and D2, six quadrupole
magnets, Q1-Q4 and Q6-Q7, a sextupole magnet, SX, an electromagnetic separator, SEP,a pair of vertical correction magnets, CM1 and CM2. The secondary beam starts fromthe production target. The first dipole magnet (D1) separates the secondary beam fromthe primary beam and deflects the secondary beam with the angle of 23 degree. The
pair of quadrupole magnets (Q1, Q2) transform the beam parallel vertically and focus
the beam horizontally at F1 where the momentum slit is located. The second quadrupole
magnet doublet (Q3, Q4) focuses the beam vertically at F2, where the mass slit is placed.
Finally the beam is focused horizontally and vertically at the final focus (FF) by the final
quadrupole magnet doublet (Q6, Q7). The beam size at the FF, that is the experimental
target, is shown in Figure 2.3. The sextupole magnet, SX, is placed to minimize thechromatic aberration at F2. The unwanted particles are deflected from the central beam
orbit by the electric field of the electrostatic separator (SEP) with the aid of the correction
magnets CM1 and CM2. The SEP has 6 m length, and was operated with ± 300 kV for
kaon beam and ± 150 kV for pion beam between the positive and negative electrodes.
The gap of the electrodes is 10cm and filled with a mixture of Ne (64 %) and He (36 %)gases with the pressure of 2 × 10−4 Torr typically.

CHAPTER 2. EXPERIMENT

2500

CountsCounts

26

2000

2000
1500

1500
1000

1000

500

500

0

-40

-20

0

20

40

Horizontal position (mm)

0

-40

-20

0

20

40

Virtical position (mm)Figure 2.3: Typical beam profile at the experimental target.

anode wire spacing
anode wire diameter
anode wire material
cathode material
operation voltage
gas mixture
BPC1
BPC2
BPC3
BPC4
BPC5

1 mm
10 µm
Au-plated W
graphite
4 kV
Ar 75.3%, Isobutane 23.7%, Freon 1.0%
active area (mm × mm)
efficiency %112 (x) × 64 (y)X:94.6 / Y 89.6
112 (x)X:99.8112 (x) × 64 (y)X:92.1 / Y:95.4
112 (x) × 64 (y)X:96.2 / Y:99.2
80 (x) × 64 (y)X:98.2 / Y:98.2

Table 2.1: Specifications of the BPCs

sense wire spacing
sense wire diameter
potential wire voltage
cathode plane voltage
gas mixture
BDC1
BDC2
BDC3

5 mm
10 µm
1.5 kV
1.45 kV
Ar 80%, Isobutane 20%
active area (mm × mm)
efficiency %160 mm (x and x’)
X:77.3/ X’:54.1
160 mm (x and x’)
X:99.3/ X’:84.3
160 mm (x and x’)
X:97.2/ X’:81.6

Table 2.2: Specifications of the BDCs

2.3. BEAM LINE SPECTROMETER

2.3

27

Beam line spectrometer

The K2 beam line is designed to transport the charged particles up to 2.0 GeV/c beam
momentum. Figure 2.1 (a) shows the setup of the beam line spectrometer which consistsof two scintillation counters (T1, T2) and two aerogel Čerenkov counters (BAC1, 2) for theparticle identification and five proportional chambers (BPC1 - 5) and three drift chambers(BDC1 - 3) to measure the momentum and the direction at the target of each beam
particle.
The T1 and T2 were made of the plastic scintillators (Bicron BC418), of which sizes
were 5-mm thick, 5-cm high and 10-cm and 5-cm wide, respectively. Scintillation lights
were collected by fast photo-multipliers (PMTs), HAMAMATSU H2431-50 from bothhorizontal ends. These counters were placed about 7.2 m apart each other (T1 was placed
upstream of D2 and T2 was placed just upstream of a target), and were mainly used tomeasure the time-of-flight of each incident particle. The obtained time-of-flight resolution
was 70 ps (r.m.s). The T2 also served as the start counter which determined the trigger
timing.
The two aerogel Čerenkov counters, BAC1 and BAC2, were installed just upstreamof T2 for the particle identification of beam particles at the trigger level. Figure 2.4
shows the schematic view and the photograph of BAC1, 2. Each of them consisted ofa hydrophobic-silica-aerogel block, with the size of 10 cm (wide) × 7 cm (high) × 3 cm
(thick) for BAC1 and the size of 8 cm (wide) × 8 cm (high) × 3 cm (thick) for BAC2. The
index of the aerogel was 1.03, which corresponded to the threshold velocity of β = 0.971
for Čerenkov radiation. In the (K − , K + ) trigger, these counters were used as a veto to
reject lighter particles (π, µ, e) than K − mesons. In the (π − , K − ) trigger, these were used
as a coincidence.
beam

Top View

BAC2
mirror
PMT R1584
aerogel8cm(W) 8cm(H) 3cm(T)µ-metalBAC1
mirroraerogel10cm(W) 7cm(H) 3cm(T)iron box

Figure 2.4: Schematic view (up) and photograph (down) of BAC1, 2.

28

CHAPTER 2. EXPERIMENT

Figure 2.5: The cell structure of BDC’s.

For the tracking detectors for beam particles, five multi-wire proportional chambers(BPC1 - BPC5) and three multi-wire drift chambers (BDC1 - BDC3) were used. Eachof BDCs had two planes, X and X’, whose cell structure is shown in Figure 2.5. Mixedgas of argon (80%) and isobutane (20%) was used. BPC1, BDC1, BPC2 and BDC2 wereplaced upstream of the D2 magnet. BDC3 was placed between the exit of the D2 magnet
and the entrance of the Q6 magnet. These chambers were used to analyze the momentumof each incident particle. BPC3, BPC4 and BPC5 were placed between the exit of theQ7 magnet and the target, and these chambers were used to measure the beam directions
and the reaction vertex points. Their specifications are summarized in Table2.1 and 2.2.
The efficiencies of BDCs were significantly low due to the dead channels of the readout
electronics. Figure 2.6 shows the beam profile of BDC3. For the tracking at the entranceof the D2 magnet, there were some redundancies (6 (total planes) - 2 (parameters)) tosolve the straight track by fitting the position information. Therefore the efficiency to findthe upstream track was typically 96.0%. However, in order to analyze the momentum ofeach incident particle we had to connect the upstream track to BDC3 which needed theboth hits at X and X’ planes to solve the left-right ambiguity. Therefore the inefficiency
of BDC3 led up to the inefficiency of the momentum analysis of beam particles directly
as described in Section 3.9.2.
CountsBeam Profile at BDC3x’

CountsBeam Profile at BDC3x

40000

40000
30000

30000

20000

20000

10000

10000

0

0

5

10

15

20

25

30

Channel

0

0

5

10

15

20

25

30

ChannelFigure 2.6: Typical beam profile at BDC3 X (left) and X’ (right). There were some missing
wires due to the dead channels of the readout electronics.

2.4. FORWARD SPECTROMETER

2.4

29

Forward spectrometer

Scattered angle (deg)Scattered K − mesons produced in the π − p → K − X reaction were detected by the forward
spectrometer. Figure 2.7 shows the kinematical relation between momentum and scattering angle of outgoing K − ’s within the acceptance of the forward spectrometer obtained
from a simulation. There is a correlation between the scattering angle and the momentum
in the π − p → K − Θ+ relation since it is two body reaction, as shown by red points in
Figure 2.7. The momentum from the Θ+ production ranges around 0.85 GeV/c. On theother hand, the momentum of K − from the background reaction ranges from 0.4 GeV/c
to 1.1 GeV/c without any correlation. In this section, the detector system to identify K −mesons with momentum from 0.4 GeV/c to 1.1 GeV/c and analyze momenta are describedin detail.
25
Θ+ production
background production

20

15

10

5

0
0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

Momentum (GeV/c)

Figure 2.7: Kinematical relation between the scattering angle and the momentum in theπ − p → K − X reaction within the spectrometer acceptance. The red points represent it forthe Θ+ production. The black boxes represent it from the background reactions including
φ production, Λ(1520) production and phase space.

2.4.1

Spectrometer magnet

The spectrometer magnet (KURAMA) is a window-frame conventional dipole magnet.
The aperture of the magnet was 100(W) × 50(H) cm2 and the iron yokes were 80 cm long.
The KURAMA magnet was sandwiched by two end-guard plates of 10 cm (T) iron. The
downstream end-guard had a 60-cm gap and 110-cm aperture, while the front end-guard
had a 30-cm gap and 50-cm aperture. The front one was smaller than the other in orderto minimize the fringing field at the target point, because the magnetic field distorted
images of tracks in the electrostatic-type IIT. The total length was 164cm including thetwo end-guard plates at the entrance and the exit. The magnet center was located 15 cm
horizontally from the beam axis in order to obtain a large acceptance for particles with
one charge, i.e. positive charged particles in the (K − , K + ) data and negative charged
particles in the (π − , K − ) data.
The spectrometer system was optimized so that the acceptance became maximum
for the scattered K + with mean momentum of 1.1 GeV/c in the (K − , K + ) reaction.
Therefore the acceptance for K − mesons in the (π − , K − ) reaction decreases to about
80% with the same operation of the spectrometer magnet at (K − , K + ) reaction, because
the mean momentum of K − was 0.8 GeV/c. In this experiment, however, the one morepoint to be considered was the missing mass resolution, because the Θ+ is considered

30

CHAPTER 2. EXPERIMENT

to be narrow and better missing mass resolution improves our experimental sensitivity.
Therefore we operated the same magnetic field of about 0.93 Tesla to obtain better missing
mass resolution. The acceptance was 0.14 sr for K − with momentum of 0.8 GeV/c.
The magnetic field was calculated by interpolating from a field map which was measured at past experiment (E224) [68]. The magnetic field is shown in Figure 2.8 with theposition of detectors.

Figure 2.8: The magnetic field of KURAMA. Field strength of Y-direction (vertical) along
the beam direction (Z) at X=0, Y=0 (magnet center in horizontal and vertical). The
position of detectors are illustrated above the histogram.

2.4.2

Čerenkov counters

Two kinds of aerogel Čerenkov counters (BVAC, FAC) were used to reject the unwanted
scattered particles at the trigger level. As shown in Figure 2.1 (b), BVAC was locatedin the center of the front end-guard and had relatively small size. The BVAC covered
only beam spot because in the (K − , K + ) reactions BVAC was mainly used to reject K −beams which did not interact at the target. On the other hand FAC was located justdownstream of the front end-guard and had the same size with the hole of the end-guard
to eliminate the scattered π particles. In (π − , K − ) reaction, both Čerenkov counters wereused to reject π − .
The BVAC consisted of a silica-aerogel block, with the size of 60 mm (wide) × 40
mm (high) × 20 mm (thick). The schematic view of BVAC is shown in Figure 2.9.
The Čerenkov lights were collected from top and bottom with PMTs (HAMAMATSU
R6608ASSY), which were fine-mesh type for operation in strong magnetic field, and had
UV-transparent input windows. The refractive index was 1.05, which corresponded to thethreshold velocity of β = 0.952 for Čerenkov radiation. Therefore, in the (K − , K + ) data,
the non-interacting K + beam of 1.66 GeV/c (β = 0.959) were rejected by BVAC, while
the scattered K + with momentum less than 1.4 GeV/c (β < 0.943) could be alive. In the(π − , K − ) data, the momentum range of K − was 0.4∼1.1 GeV/c. The BVAC was used todiscriminate the π particles.
The FAC consisted of a silica-aerogel block, with the size of 300 mm (wide) × 210

2.4. FORWARD SPECTROMETER

31

PMT
R6608ASSYGORETEXbeam
Aerogelwidth: 60 mm
height: 40 mm
thickness: 20 mm(Front View)

Figure 2.9: Schematic drawing and photograph of BVAC

300m

210mm

m

PMT
HAMAMATSU
R5543ASSY

Aerogel
Block
beam
mm

60

Figure 2.10: Schematic drawing and photograph of FAC

mm (high) × 60 mm (thick). The schematic view of FAC is shown in Figure 2.10. It wasviewed by six fine-mesh-type PMTs, HAMAMATSU R5543ASSY, from top and bottom
ends. The refractive index was 1.041 and the corresponding Čerenkov β-threshold was
0.962.
The efficiencies of the Čerenkov counters were measured at five β points using π − and−K beams of 1.67 and 1.4 GeV/c and π − beam of 230 MeV/c. The typical ADC spectra
are shown in Figure 2.11 where the open histograms were data for 1.67 GeV/c π − and thehatched histograms were data for 1.4 GeV/c K − . The threshold of the discriminator was
shown by arrows. Figure 2.12 shows the efficiencies of BVAC and FAC as a function ofβ. The efficiency of FAC for π’s with β > 0.99 was slightly low value of 95.4%, while the
BVAC had sufficient efficiency more than 99.9%. The π particles which passed throughthe FAC veto were eliminated with the charge trigger and the mass trigger (see section
2.6). The over-killing rates of the K − ’s with momenta less than 1 GeV/c were 6.9±1.0%

32

CHAPTER 2. EXPERIMENT

array direction# of channels
thickness [mm]width [mm]spacing [mm]PMT type
scintillator typeeffectivearea[mm(x)×mm(y)]

VH
x
y
32
18
2
2
6.6
9.0
4.4
6.0
R5600U R3164-10
SCSN-50 SCSN-50

CH
x
24
2
19
17.5
H3165-01
SCSN-50

YH
y
6
5
200
180
H1161
SCSN-56

FTOF
x
24
30
80
75
H1949
SCSN-56

143×110421.5×300

1700×1100

1805×1200

Table 2.3: Specifications of the plastic scintillator hodoscopes. All PMTs are HAMAMATSU and all scintillators are KURARAY.

and 4.7±0.8% for BVAC and FAC, respectively.
FAC ADC

4Counts/2ch

Counts/4ch

BVAC ADC

101.67 GeV/c π1.4 GeV/c K

3

-

10

90

1.67 GeV/c π-80

1.4 GeV/c K-

70
60

2

50

10

40
30

10

20
10

1
0

200

400

600

800

1000

1200

ADC (channel)

0
0

100

200

300

400

500

600

ADC (channel)

Figure 2.11: The typical ADC spectra of BVAC (left) and FAC (right). These spectra
were linear sums of signals of all PMTs connected to each Čerenkov counters. The open
histograms were data for 1.67 GeV/c π − and the hatched histograms were data for 1.4
GeV/c K − . The arrows represent the threshold positions of the discriminators.

2.4.3

Trigger hodoscopes

Four kinds of scintillator hodoscopes (VH, CH, YH and FTOF) were used in the forward
spectrometer. The VH and CH were used as not only online trigger counters but also
tracking detectors. The YH defined the acceptance of the spectrometer and were used as
online trigger counter. The FTOF was used as not only online trigger counters but also
time-of-flight counter. The specifications of these hodoscopes are summarized in Table
2.3.
Vertex hodoscope
The Vertex Hodoscope (VH) was located just downstream of the target. The schematic
view of VH is shown in Figure 2.13. The VH consisted of 32 and 18 segments of scintillator2.4. FORWARD SPECTROMETER

33

Figure 2.12: The efficiencies of BVAC (black circle) and FAC (open circle) as a function ofβ. The dashed line at β = 0.952 and the dot-dashed line at β = 0.962 are corresponding to
the thresholds for Čerenkov radiation of BVAC and FAC, respectively. For the π − beams
with β more than 0.99, which was main background for (π − , K − ) reaction, efficiency of
FAC was a little low (95.4%), while efficiency of BVAC was more than 99.9%. The overkilling rates for the K − ’s of which momenta were less than 1.0 GeV/c were 6.9±1.0% and4.7±0.8% for BVAC and FAC, respectively.

for horizontal (X) and vertical (Y) directions, respectively. The size of each X segment
was 6.6 mm (wide) × 110 mm (high) × 2 mm (thick) and each segment was staggeredwith overlapping of 2.2 mm each other. The size of each Y segment was 9 mm (wide)× 143 mm (high) × 2 mm (thick) and each segment was staggered with overlappingof 3 mm each other. The scintillation lights were collected by one PMT connected tovertical end for X segments and horizontal end for√ VH was used as a
√ Y segments. This
tracking detector with position resolution of 2.2/ 12 mm and 3.0/ 12 mm for X and Y
segments, respectively. The VH was also used as trigger counter to reject neutral particle
events such as K 0 production where the neutral particle decayed after VH and the decay
products made triggered event.

Charge hodoscope
The Charge Hodoscope (CH) was installed just upstream of the pole pieces of KURAMA
as shown in Figure 2.14, in order to select the charge of each scattered particle together
with hit information of FTOF. The CH was used for the first-level trigger as well as thesecond-level trigger. The CH consisted of 24 scintillators each of which was 19 mm wide,
300 mm height and 2.0 mm thick. The signals were read by one PMT connected via longlight guide.

34

CHAPTER 2. EXPERIMENT

Figure 2.13: Schematic view of VH.

Figure 2.14: Schematic view of CH and the KURAMA magnet.

Y hodoscope
The geometrical acceptance of vertical direction was defined by the Y hodoscope (YH)
which was located in front of FTOF. The YH consisted of 6 segments of scintillation
counter with the size of 1700 mm (wide) × 200 mm (high) × 5 mm (thick) as shown in
Figure 2.15. The signals of the scintillators were read from both horizontal ends connected
to PMTs via lucite light-guides. These segments were also staggered with overlapping of
10 mm each other. In order to minimize the reaction events at YH, thin scintillators with
5 mm thickness were used.

2.4. FORWARD SPECTROMETER

35

Forward TOF

Time-of-flight information of each scattered particle was measured by TOF wall (FTOF)
located in the most downstream of the forward spectrometer. The schematic view of FTOF
is shown in Figure 2.15. The FTOF consisted of 24 segments of scintillation counter withthe size of 80 mm (wide) × 1200 mm (high) × 30 mm (thick). Each segment was madeof the plastic scintillators (SCSN-56) and its scintillation lights were collected by two
PMTs (HAMAMATSU 1949) via lucite light guide. These segments were staggered withoverlapping of 5 mm each other. The FTOF was located at the distance of 3333 mm fromthe target position and rotated from the beam direction by 10 degree to maximize thespectrometer acceptance. The resolution of time-of-flight from T2 to FTOF was obtained
to be 132 ps as the mean value of all segments. The FTOF was also employed to measurevertical hit positions of particles on FTOF, which were given by the time difference of thetwo signals from the PMT’s on the top and bottom.

Figure 2.15: Schematic view of YH and FTOF.

36

CHAPTER 2. EXPERIMENT

plane# of read wire
spacing (mm)diameter (µm)
HV (V)
material
diameter (µm)HV(V)
material
position resolution (µm rms)

DC1
DC2
X X’ Y U
X X’ Y Y’
XX’:48 / Y:32 / U:40
XX’:128 / YY’:96
anode wire
10.0
9.0
20.0
20.0
Au-plated W
Au-plated W
potential wire
75
200
-1850
-1900
Au-plated Cu-Be
AlDC3
X X’ Y Y’
XX’:32 / YY’:16
X: 56.0/ Y: 60.0
20.0
1000.0Au-plated W
150
-3000
Au-plated Cu-Be

XX’:200 / Y:200 / U:400

XX’:210 / YY’ 200

XX’:230 / YY’:240

X : 99.6
X’ : 99.6
Y : 98.6
U : 98.1

X : 94.1
X’ : 99.7
Y : 97.5
Y’ : 99.4

X : 99.0
X’ : 99.9
Y : 99.9
Y’ : 99.6

500×350

1200×1200

1800×900

efficiency (%)

effectivearea[mm(x)×mm(y)]gas mixture

Ar 50%, C2 H6 50%

Table 2.4: Characteristics and performance of Drift Chambers.

2.4.4

Drift chambers

The trajectories of scattered particles were reconstructed using drift chambers (DC1, DC2
and DC3) together with VH and CH. The characteristics of the drift chambers are summarized in 2.4.
The effective area of DC1 was 500 mm in width and 350 mm in height. The DC1
was installed between the front end-guard and pole pieces of KURAMA. There were four
planes to measure the X, X’, Y and U coordinates. The X and X’ planes were staggeredby the drift space of 5 mm. In the U plane, the sense wires were tilted by 15 degrees fromthe vertical direction. The cell structure of DC1 is shown in Figure 2.16 (a). The cathodeplane were made of 15-µm-thick Kapton foils with aluminum coating on both sides.
The DC2 had an effective area of 1200 × 1200 mm2 with 4 planes of X, X’, Y and
Y’. The DC2 was located at the end point of downstream end-guard and covered the fullaperture of the magnet. The sense wires were surrounded by hexagonally located potential
wires as shown in Figure 2.16 (b).
The DC3 had a sensitive area of 1800 mm in horizontal direction and 900 mm invertical direction. The DC3 was located 530 mm downstream of DC2. The chamber had
4 planes of X, X’, Y and Y’ and the cell structure are shown in Figure 2.16 (c) for X, X’and (d) for Y, Y’.
The mixed gas of Ar-ethane (1:1) was used for all drift chambers.
The typical efficiencies of each chamber plane are also summarized in Table 2.4. To
estimate this efficiency, at first, the trajectory of particle which did not decay was selectedby connecting the tracks upstream and downstream of KURAMA by Runge-Kutta method.
Then we checked the hit information of each plane corresponding to the track. The
efficiencies of DC2X and DC2Y is a little low due to dead channels of readout electronics.

2.4. FORWARD SPECTROMETER

37

Figure 2.16: Cell structure of (a) DC1, (b) DC2, (c) DC3-X X’ planes and (d) DC3-Y Y’planes.

38

2.5

CHAPTER 2. EXPERIMENT

TargetWe used two kinds of targets.The first one was the Scintillating Fiber (SCIFI) target((CH)n ) which was mainly used as an active target to measure the tracks of charged
particles at a reaction point in the (K − , K + ) reaction. The other one was a bulk targetof polyethylene ((CH2 )n ) to enhance the contribution from free protons. In the (π − , K − )reaction, the polyethylene target was mainly used.

2.5.1

Polyethylene target

The polyethylene ((CH2 )n ) target with thickness of 10 cm and cross section of 10 × 10
cm2 was used. The density was 1.0 g/cm3 .

2.5.2

Scintillating fiber active target

The scintillating fiber (SCIFI) target was 20 cm long and was the same one used in
the hyperon-nucleon scattering experiment (KEK-PS E289). It worked as a 4π tracking
detector to measure tracks of charged particles produced in the (K − , K + ) and (π − , K − )reactions. By reading out from two directions, we can reconstruct the event topologies
three-dimensionally. Figure 2.17 shows a schematic view of the SCIFI active target system.
The SCIFI active target system consisted of a SCIFI block, four image intensifier tubes
to amplify the photon image, and CCD to read out and digitize the image data. Event
topology around the reaction vertex was obtained with this system as image data of u-z
and v-z projections. The SCIFI target had a large effective volume (10 × 10 × 20 cm3 )and consisted of thinner scintillating fibers (300 × 300 µm2 square cross section). The
material of the fiber was polystyrene ((CH)n ) and the density was 1.03 g/cm3 . The detail
description of each parts is given in Appendix A.
The typical image of 12 C(K − , K + ΛΛ) and π − p → K − K 0 p reactions are shown in
Figure 2.18 and 2.19, respectively.

2.5. TARGET

39

ibers)(c) SCIFI Active Target system
Figure 2.17: Schematic view of the SCIFI active target system. (a) photograph of the
SCIFI target. (b) schematic view of the structure of the SCIFI block. The SCIFI block
was assembled by stacking the fiber sheets, each of them contained about 330 fibers. The
fiber sheets of each direction were bundled at the readout arms to make readout surfacesof 100 mm × 100mm. (c) schematic view of the total target system including readoutdevices. The target system was located in the direction of u and v which are rotated ±45
degree from the y axis. The shaded region is the effective volume of 100 mm × 100 mm.
The readout system consisted of four IITs and a CCD camera. The first and second stages
were electrostatic-type image intensifiers. The third and fourth one were micro-channel
plate (MCP) type and were gatable. The CCD camera was also gatable type.

40

CHAPTER 2. EXPERIMENT

100

100

75

75

50

50

25

25

0

0

-25

-25

-50

-50

-75

-75

-100

-100
-100 -75

-50

-25

0

25

50

75

100

-100 -75

-50

-25

0

25

50

75

100

Figure 2.18: A typical image of 12 C(K − , K + ΛΛ) reaction. The two image data are corresponding to the v-z and u-z projections taken from each side of the SCIFI target. The sizeof the fiducial areas are shown by the ellipses. Double Λ’s were produced at the (K − , K + )reaction vertex. The Λ decaying into π − and proton is shown as a clear V-topology.

100

100

75

75

50

50

25

25

0

0

-25

-25

-50

-50

-75

-75

-100

-100
-100 -75

-50

-25

0

25

50

75

100

-100 -75

-50

-25

0

25

50

75

100

Figure 2.19: A typical image of π − p → K − K 0 p reaction. The green and yellow dottedlines were reconstructed tracks of π − and K − using the position detectors (wire chambers,
hodoscopes). The KS0 decaying into π + and π − is shown as a clear V-topology. The proton
stopped in the SCIFI target.

2.6. TRIGGER

2.6

41

Trigger

The experimental setup was optimized for the (K − , K + ) reaction. The trigger system wasalso designed to have a sufficient performance for the selection of the true (K − , K + ) eventsfrom many background events. In the (π − , K − ) reaction, the trigger was made with somemodifications of the (K − , K + ) trigger. Therefore, an explanation of the (K − , K + ) trigger
is given before we describe the (π − , K − ) trigger.
In the (K − , K + ) reaction, the main analysis was focused on the image data taken by
the SCIFI active target system. Because the SCIFI system needed a long data taking
time of several milli seconds, the sufficient rejection power of unwanted events at thetrigger level was indispensable. The K − beams were selected using the Čerenkov counters(BAC1, 2). For the forward spectrometer part, we had to select K + particles from the large
backgrounds of π + and proton. Scattered π + and non-interacted K − beam were rejectedby the Čerenkov counters (BVAC, FAC). The charge of each scattered particle was selectedusing the hit combination of each segments of CH and FTOF (Charge Trigger). At thisstage, the main background event of the (K − , K + ) reaction was the (K − , p) event. To
eliminate these (K − , p) events, we used the Mass Trigger, which used digitized time-offlight information of the hit FTOF segment, as the second level trigger. After the selection
using this trigger system, the trigger rate was 30 events/spill for 23,000 K − beams per
spill. This trigger rate was acceptable for the operation of the SCIFI system.
In the (π − , K − ) reaction, the scattered K − particle was selected in the same way.
While the main background for the scattered K + in the (K − , K + ) reaction was proton
event, an anti-proton could not be produced in the (π − , K − ) and this enabled us to selectthe K − particle more easily.

2.6.1

First-level trigger

The role of the first-level trigger was to select a π − beam and an outgoing K − particle using
fast signals from scintillation hodoscopes and Čerenkov counters. The logic diagram of thefirst-level trigger is shown in Figure 2.20. The incident beam particles were tagged by thesignals of T1 and T2. In order to select π − beams, BAC1, 2 were used as a coincidence.
The main background for scattered K − particles was π − which was eliminated by BVAC
and FAC. However, some π − beam-through events and elastic scattering events survived
due to the inefficiency of FAC (4.6%). In order to eliminate these π − events, we adjusted
the accepted region of the Charge Trigger (CT) as described below. The Charge Trigger
module was a programmable matrix coincidence module and selected the charge of thescattered particle by checking whether the hit combination of CH and FTOF was within
the accepted region which is surrounded by the red line in Figure 2.21. The CT also
selected momenta of scattered particles roughly. Momenta of π − events were around 1.9
GeV/c and are corresponding to the hatched ellipse region in Figure 2.21. On the other
hand, momenta of K − ranged from 0.4 GeV/c to 1.1 GeV/c as shown by boxes (not filled)
in Figure 2.21. Therefore we adjusted this region to accept almost all momentum range ofK − within the spectrometer acceptance and reject high momentum π − particles. Finally,the ”OR”ed signal of YH was required to cut off the neutral particles hitting FTOF.
Thus the first-level trigger was defined by
T 1 ⊗ T 2 ⊗ BAC ⊗ BAV C ⊗ F AC ⊗ CT ⊗ Y H.

(2.1)

Gate signals of ADCs and common start/stop signals of TDCs for detectors of thespectrometer were made by the first-level trigger. For the operation of SCIFI target, thegate signals of the third and fourth IITs were also made by this signal. The rate of the42

CHAPTER 2. EXPERIMENT......

......

......

first-level trigger was typically 320/spill for the beam intensity of 3.3 × 105 π − /spill.

Figure 2.20: Logic diagram of the first-level trigger.

2.6. TRIGGER

43

Charge Hodoscope segment

25
Low momentum
High momentum

gi
on

20

m

πre

15

K

-

K- (0.7<P(GeV/c)<0.9)

m
om
en

tu

Positive particle

H
ig
h

10

5
Negative005Positive
10

15

20
25
FTOF segment

Figure 2.21: The combination of the hit CH and FTOF segments. The open, shaded andhatched histograms are the combinations for K − ’s, K − ’s with momentum of 0.7 GeV/c< p < 0.9 GeV/c and positive particles, respectively. The particle identifications weredone by offline analysis. The region surrounded by the red line was the accepted regionof the CT. From the hit combination the momenta of the scattered particles are roughly
selected; to the direction of the arrow titled ”High momentum”, momenta become larger
and to the direction of the arrow titled ”Low momentum”, momenta become lower. The
momenta of π − beam-through events and elastic scattering events are corresponding to
the hatched ellipse region.

2.6.2

Second-level trigger

The second-level trigger was defined by
1st level trigger ⊗ (V Hx ⊗ V Hy) ⊗ M T.

(2.2)

We required the hit of VH to eliminate the background triggers caused by the neutral
particles such as KS0 mesons. The mass trigger (MT) was the main component of thesecond-level trigger and the detail explanation of MT are given bellow. This mainly
rejected the π − mesons accepted at the first-level trigger.
Mass trigger
As described at the explanation of CT, the momenta of outgoing particles were determinedusing the hit combination of CH and FTOF. For events with the same hit combination,
the difference of their masses should appear as the difference of their time-of-flight. The
typical time-of-flight spectra are shown in Figure 2.22 where the peaks corresponding toK − and π − are clearly seen. The particle identification can be done by setting a suitablewindow against time-of-flight for each combination of CH and FTOF.

44

CHAPTER 2. EXPERIMENT150

All events

100

K-

50

MT gete100π- (×1/30)

CountsCountsCounts

The trigger scheme for the mass trigger is illustrated in Figure 2.24. The timing
information of the CH and FTOF signals were digitized with LeCroy 4303 TFC (Time-toFera Converter) and LeCroy 4300B FERA (Fast Encoding and Read out Adc) modules(FERET). The hit addresses and the timing information of FTOF were stored in thememories in the FERA modules, and the hit information of CH was stored in a LeCroy
2375 Data Stack module. The hit addresses of CH and FTOF were send to a LeCroy
2372 MLU (Memory Lookup Unit) module and decoded into momentum information.
Another MLU stored the trigger windows against the FTOF TDC data for corresponding
combinations of CH and FTOF. It selected the particle masses by combining the FTOF
timing data and the momentum information obtained by the first MLU.
The decision time of the mass trigger was about 14 µs. The trigger rate was 85 per spill
for the π − beam intensity of 3.3×105 . The contamination due to the π − ’s were reduced
to typically 42% with the mass trigger. The overkilling rate of K − mesons was 4.3% (seeSection 3.9.7)

K- selected

7000
1st level trigger

6000

2nd level trigger

5000
4000

50

Suppression factor = 0.58
Counts3000
150

π- selected

2000

100

1000

50
0
100

0
0
150

200

250

300
350
400
TDC channel

0.1

0.2

0.3

0.4

0.5

0.6

0.7

2

Mass (GeV/c )Figure 2.22: Time-of-flight spectra be- Figure 2.23: Mass distribution of outgotween T2 and FTOF against the events ing particles with the first level trigger
where there were hits at CH segment 13, (open histogram) and the 2nd level trig−
14 and FTOF segment 9. The top spec- ger (hatched histogram). The π particles
trum is for all particles. The peaks cor- were reduced to typically 42%.
responding to K − ’s and π − ’s are clearly
seen. The middle and bottom spectra arefor K − ’s and π − selected in the offline
analysis. The red lines are the accepted
window for the mass trigger. The data
outside of this window were collected forthe check of the efficiency of the mass trigger with the prescale factor of 30.

2.6. TRIGGER

45

)

)

5 bits+Figure 2.24: Logic scheme of the mass trigger.

46

2.7

CHAPTER 2. EXPERIMENT

Data acquisition and monitoring

Figure 2.25: Schematic diagram of the data flow during the data acquisition and monitoring. See text for detail.
The data flow of the data acquisition is illustrated in Figure 2.25. The signals ofcounters and chambers of the spectrometer were digitized by ADCs and TDCs of CAMAC
and TKO standard. The conversions of the signals were started at the timing of the firstlevel trigger. When the second-level trigger was accepted, the digitized data were send
to CAMAC memory modules (Buffer Memory, TKO MP). When the second-level trigger
was rejected, the data were cleared. Data were stored during one spill in the memory
modules and were collected at the end of the spill by the DAQ system which is called”Spectrometer DAQ” here to distinguish from ”Image DAQ” for SCIFI sub DAQ system.
The Spectrometer DAQ was operated by a Unix operating system on a VME on-board
computer (FORCE SPARC CPU-50T). The data of the spectrometer as well as scaler andsome trigger flags were acquired by a ”collector” process from CAMAC memory modules
via VME-CAMAC interface modules.
For the data acquisition of SCIFI image data, the independent sub DAQ systems called”Image DAQ” were used for each CCD camera. The Image DAQ was also operated by a
Unix operating system on a VME on-board computer (FORCE SPARC CPU-50T). The
CCD camera we used was Kodac MEGAPLUS Camera ES310. The readout of the CCD
data was triggered by the external signal made from the second-level trigger. The digital2.8. DATA SUMMARY

47

data were compressed from 8 bit to 4 bit using the real time image processing module(Imaging Technology Coop. MVC 150/40). At the end of the spill, the image data weretransfered to the ”collector” process of the Spectrometer DAQ via Ethernet. The Image
DAQ also collected scaler data such as ”spill”, ”number of 2nd accept”, ”number of CCD
accept” for each event. These scaler information were used for the event matching between
the spectrometer and CCDs.
The data during one spill of the spectrometer and CCDs (if we used the SCIFI target)
were transfered to the ”collector” process of the Spectrometer DAQ. The collected data
were managed by a NOVA buffer manager, and recorded in a AIT2 tape by a ”recorder”
process. In order to monitor the data during the data acquisition, some on-line analyzers
were executed on a personal computer operated by a Linux 2.0 operating system. A”decoder” process took the raw data from the NOVA buffer of the Spectrometer DAQ
and decoded for some on-line analyzers. The decoded data were managed by a linux-local
NOVA buffer manager. The data of the spectrometer were monitored by two ”analyzer”
program. One was ”raw data analyzer” which checked raw data such as ADC, TDC
spectra and hit profiles of wire chambers. Another one was ”spectrometer analyzer” whichcalculated momenta and masses of scattered particles, and so on. The ”spectrometer
analyzer” was much helpful to adjust the CT accept region at the online level. The CCD
images were sent to an online monitoring software directory from the Spectrometer DAQ
buffer manager and monitored by human eyes. The run control (start, stop, pause or
resume) was carried out from the Linux PC via Ethernet.

2.8

Data summary

Table 2.5 shows the data summary. For the π − p → K − X reaction, we used π − beams
of 1.87 and 1.92 GeV/c. At 1.92 GeV/c, only the polyethylene target was used. In orderto estimate the contribution from carbon in the SCIFI and polyethylene targets, carbon
target data were taken. The (π + , K + ) data were taken to measure Σ+ for the calibration of
the missing mass spectrum. The (K − , K + ) data were also used for momentum correction
and only the analyzed data size is listed in Table 2.5.
Pbeam (GeV/c)reaction

1.87(π − , K − )(π + , K + )(π − , K − )

1.92
1.67

(π + , K + )(K − , K + )targetSCIFI
polyethylene
12 C
polyethylene
polyethylene
12 C
polyethylene
SCIFI

NBeam (×108 )
29
30
8.4
1.4
74
8.4
4.3
14

data taking time
20.5 hour
14.5 hour
2.5 hour2 hour31.5 hour
2.5 hour
3.5 hour∼ 3 day

Table 2.5: Data summary, where Pbeam is the beam momentum and NBeam is the numberof beam particles irradiated on each target.

Chapter 3

Analysis
3.1

OutlineThe goal of our analysis is to obtain the missing mass spectrum of the π − p → K − X
reaction and derive the production cross section of the Θ+ with the π − induced reaction.
In this chapter, the analysis procedures are described. The contents consist of three parts
as explained bellow.
In the first part, the analysis procedure to find good (π − , K − ) events will be describedwith attention to the performance of the analysis and the cut points. The outline of thefirst part is following.
1. Selection of the incident π − and determination of the momentum (Section
3.2).
The particle identification was done by the time-of-flight between T1 and T2. To calculate
the momentum, the trajectory was reconstructed using the hit information of beam line
chambers and a transfer matrix.
2. Determination of the momentum of the outgoing particle and selection ofK − (Section 3.3).
The trajectory of the outgoing particle was reconstructed using the information of tracking detectors and field map of KURAMA. The mass was obtained from the momentum
information and time-of-flight between T2 and FTOF.
3. Determination of the reaction vertex (Section 3.4).
The reaction vertex was obtained as the closest distant point between the incident π − andthe outgoing K − .

In the second part, momentum resolutions for incident and outgoing particles arestudied by reconstructing the Σ+ from the missing mass spectrum of the π + p → K + X
reaction (Section 3.6). Then the expected missing mass resolution for the Θ+ is shown(Section 3.7). Good performance of the analysis is also confirmed by using the (π − , K − )data (Section 3.8).

48

3.1. OUTLINE

49

In the final part, for the preparation of deriving the cross section, various efficiencies
such as decay factor of the outgoing K − and the acceptance of the spectrometer are
obtained (Section 3.9 ).
Monte Carlo simulation
In order to estimate not only these values such as decay factor and the acceptance of thespectrometer but also the missing mass resolution for the Θ+ , we have developed the Monte
Carlo simulation program based on the GEANT4 [72]. All materials of the spectrometerare included in this program. It simulates trajectories of particles through the experimental
apparatus taking into account decay in flight, energy loss, multiple scattering, and hadronic
reaction of the particles. The realistic chamber performances such as resolutions andefficiencies are also taken into account. The output data produced by the simulation wereanalyzed by the same analysis code used for the real data.

50

CHAPTER 3. ANALYSIS

3.2

Analysis of π − beam

3.2.1

Identification of π − mesons

The incident particles were identified with the information of time-of-flight between the T1
and T2 counters placed about 7.2 m apart. Figure 3.1 shows spectra of the time-of-flight.
The typical time resolution after the ADC pulse height correction was 72 ps. We selected±3σ region of its time resolution as good events as shown by arrows in Figure 3.1. The
bump around −750 ps might be considered to be K − because it is consistent with thetime difference between π − and K − . Therefore the contamination of K − in the selected
region was negligible. By this cut, 94.2% of the total events were accepted.

4

3

2

Figure 3.1: TOF spectra of incident particles (a) in a linear scale and (b) in a logarithmic
scale . The arrows indicate the selection window for π − mesons which is the ±3σ regionof its time resolution. The bump around −750 ps might be K − mesons.

3.2.2

Momentum analysis of π − mesons

The momenta of the incident particles were calculated by fitting the hit positions of thebeam line chambers upstream and downstream of the D2 magnet (BDC1, 2, 3 and BPC1,
2) with the second order transfer matrix calculated by TRANSPORT [70]. The conceptof beam optics and the detail procedure of momentum analysis are described here.
A beam line is comprised of a set of magnetic elements such as bending magnets or
quadrupole magnets placed sequentially at intervals along an assumed reference trajectory.

3.2. ANALYSIS OF π − BEAM51

The trajectory moving along the beam line can be described by the beam optics. At any
specified position in the system, an arbitrary charged particle is represented by a vector
X defined below.




x
 θ 




X= y 


 φ 
δ

Definitions:(3.1)

x = the horizontal displacement of the arbitrary ray with respect tothe assumed central trajectory.
θ = the horizontal angle of the ray with respect to the assumed
central trajectory.
y = the vertical displacement of the ray with respect to the assumed
central trajectory.
φ = the vertical angle of the ray with respect to the assumed
central trajectory.
δ = δp/p is the fractional momentum deviation of the ray fromthe assumed central trajectory.
The optical element such as magnets can be represented by a matrix and the positionof the charged particle after the optical elements is represented by the equation
Xi (l) =X

Rij Xj (0) +jX

Tijk Xj (0)Xk (0),

(3.2)

jk

where X(0) is the initial coordinate vector and X(l) is the final coordinate vector of
the particle, and R and T are the the first order and the second order transfer matrices
respectively.
The first and second order transfer matrices were calculated using TRANSPORT,
which is the program code developed for the design of static-magnetic beam transportsystem [70]. In this analysis, we used hit positions of BPC1, 2 and BDC1, 2, 3 and thematrix of the D2 magnet. In this case, the position vector was three components vector(x, θ, δ) and the first order transfer matrix was 3 × 3 matrix. The initial values of x andθ were given by the local tracks at the entrance of the D2 magnet obtained by fitting thehit positions at these chambers. The trajectory of beam was connected to BDC3 using
the transfer matrix. The particle momentum was determined by minimizing the following
χ2 value. The χ2 value is defined as

χ

2

≡

n =

8
1 X
Hi
n − 3 i=1

8
X

−
→ !2
Pi − fi ( X in )
wi

(3.3)

Hi

(3.4)

1 if ith plane has a hit
0 if ith plane has no hit

(3.5)

i=1

Hi =

(

52

CHAPTER 3. ANALYSISCountswhere Pi and wi denote the hit position and resolution of i-th plane. The calculated−→−→
position by the transfer matrix at i-th plane is denoted by fi ( X in ), where X in is the initialcoordinate vector at the entrance of D2 magnet. The particle momentum is denoted byp = p0 (1 + δ), where p0 is the central momentum.
The typical χ2 distribution of 1.92 GeV/c π − beam is shown in Figure 3.2. The χ2 distributions with each degrees of freedom, that is (number of hit planes − 3), are also shownin Figure 3.2, where the smooth lines represent the expected reduced χ2 distributions withthe corresponding degrees of freedom. The obtained χ2 distribution was consistent withthe expectation except a tail towards large χ2 . We selected confidence level = 95% regionfor χ2 cut when the number of hit planes was 5, 6 and 7. In case of hit number of 8, theχ2 distribution was slightly broader. Therefore we selected confidence level = 99% region.
The selected regions are shown by arrows in Figure 3.2 for each degrees of freedom. The
efficiency of this cut was 84.6% as the result of rejecting the large χ2 events. The obtained
momentum distributions are shown in Figure 3.3. The events of which momenta wereless than 1.8 GeV/c or larger than 2.0 GeV/c were rejected considering the momentum
acceptance of the beam line.

χ2 distribution of beam fitting

hit=8

200

900
100

total

800
700

hit=7

400

600

200

hit=7
500
400
300

200
150
100
50

hit=6

40

hit=5

hit=8
200

30

100
0
0

hit=6

20
10

hit=5
0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

χ /dof
2

0
0

1

2

3

4

5

χ2/dofFigure 3.2: χ2 distributions of the beam tracking using the transfer matrix. The smoothlines represent the expected reduced χ2 distributions with the corresponding degrees of
freedom. Right figures represent the χ2 distributions for each degrees of freedom. The
arrows show the cut positions which are corresponding to 95% confidence level for hit
plane number of 5, 6 and 7 and 99% confidence level for hit plane number of 8.
The momentum resolution of this tracking method was estimated with a Monte Carlosimulation. Figure 3.4 shows the results of the same analysis using the hit information foreach chamber produced in the simulation. The χ2 and momentum distribution are shownin (a) and (b), respectively, and these are consistent with the real data. Figure 3.4 (c)3.3. ANALYSIS OF OUTGOING PARTICLES

53Countsis the plot of the differences between generated momenta and calculated momenta. From
this plot, the momentum resolution was obtained to be σ=8.9 MeV/c. This resolution was
taken into account in the Monte Carlo simulation to estimate the missing mass resolutionof this spectrometer system.

600

PBeam=1.87

400

Counts200

1000

PBeam=1.92

500

0
1.75

1.8

1.85

1.9

1.95
2
Momentum (GeV/c)

Figure 3.3: Obtained momentum distributions for the beam momenta of 1.87 GeV/c (top)and 1.92 GeV/c (bottom).

The beam direction at the target was measured by three proportional chambers (BPC3,4, 5) located with the distance of 1 m for BPC3 − BPC4 and 2 m for BPC4 − BPC5.
The angular resolutions were estimated to be 0.008 degree for both horizontal and verticaldirections.

3.3

Analysis of outgoing particles

3.3.1

Measurement of momentum

The trajectories of outgoing particles were reconstructed using the position information of
the drift chambers (DC1,2,3) and the hodoscopes (VH,CH) and the magnetic field strength
calculated with the field map. First, straight tracks were defined locally at the entrance
and exit of the KURAMA magnet by VH·DC1·CH and DC2·3 using a least-square method,respectively. To find tracks, all combinations of the left/right ambiguity were examined,
because the trajectory had a large angle and we could not use the pair plane information.
The trajectory with minimum χ2 was selected as the reconstructed track. In multi track
events, chamber hits corresponding to each track were required not to be duplicate for allplanes.
From here, we call the local track at the entrance ”up-track” and the local track at
the exit ”down-track”. Then, we have to combine the up-track with the down-track. In

CHAPTER 3. ANALYSIS

200

(a)

CountsCounts

54

150
100
50
0
0

160
140

(c)

120
1

2

3

4

5

σ=8.9 MeV/c100

reduced χ2Counts

80
150

60

(b)

40

100

20
50

0
-50 -40 -30 -20 -10
0
1.8

1.85

1.9

1.95

2

0

10 20 30 40 50∆ p (MeV/c)

Momentum (GeV/c)

Figure 3.4: Results obtained from a Monte Carlo simulation. (a) χ2 distribution. (b)momentum distribution. (c) the differences between generated momenta and calculated
momenta. The momentum resolution was obtained to be σ=8.9 MeV/c.

order to find a good combination of these tracks, the following consistencies were checked.
Finally, the trajectory was reconstructed using the Runge-Kutta tracking method [71].
Consistency between FTOF and down-track
The consistency between the down-track and the hit FTOF segment was checked to reject
events where outgoing particles decayed before arriving at FTOF. Figure 3.5 (left) shows
the difference between the horizontal position at FTOF calculated from the down-track
and the center position of hit segment. Figure 3.5 (right) shows the difference between thevertical position at FTOF calculated from the down-track and the y position calculatedby the time difference from the signals of the top and bottom PMTs. The vertical position
resolution of FTOF was typically 22 mm (σ). The cut positions are shown by arrows.
Consistency between up-track and down-track in vertical plane
If there was no x component in the magnetic field, the up-track and down-track would be
identical in the vertical plane. In reality, the magnetic field had some x components and thetwo tracks in the vertical plane were a little different. However the difference should not be
so large. Figure 3.6 shows the difference between the y position at DC1Y calculated fromdown-track and the hit information of DC1Y and the difference between slopes (dy/dz)
of up-track and down-track in the vertical plane. In order to reject decay events, we set
the accept regions for each plot shown by the arrows. This region was determined by theMonte Carlo simulation. In order to connect the up-track and down-track in the verticalplane, the combination with the smallest difference was chosen.
Consistency between up-track and down-track in horizontal plane
In the horizontal plane, the trajectory was bent in the magnetic field. We defined thefollowing values, ”bendpoint”, ”lup ” and ”ldown ”. The bendpoint is the crossing point of
the up-track and down-track in the horizontal plane. The lup and ldown are the distance3.3. ANALYSIS OF OUTGOING PARTICLES
Difference between track and FTOF X

55

Difference between track and FTOF YCountsCounts

1600
1400

2500

1200

2000

1000

1500

800
600

1000

400
500

200
0
-150 -100

-50

0

50

100

0
-150 -100

150

-50

0

50

(mm)

100

150

(mm)

Figure 3.5: (left) Difference between the horizontal position at FTOF calculated from thedown-track and the center position of the hit FTOF segment. (right) Difference between
the vertical position at FTOF calculated from the down-track and the y position calculatedby the time difference of the top and bottom PMTs. The arrows show the cut positions.

Difference between track and DC1Y

Difference between track2 and track3

CountsCounts

3500
3000

2000

2500
1500

2000
1500

1000

1000
500
500
0
-100-80 -60 -40 -20 0 20 40 60 80 100

(mm)

0

-0.05

0

0.05

Difference of slope

Figure 3.6: (left) Difference between the y position at DC1Y calculated from down-track
and the hit information of DC1Y. (right) Difference between slopes (dy/dz) in the verticalplane of up-track and down-track. The arrows show the cut positions.

between the entrance point of the KURAMA and the bendpoint and the distance between
the bendpoint and the exit point of the KURAMA. Figure 3.7 shows the difference between
lup and ldown . We accepted the events within the arrows. In order to connect the up-trackand down-track in the horizontal plane, the combination with the minimum difference waschosen.

Runge-Kutta tracking
In order to connect the up-track and down-track considering the equation of motion of theparticle in the magnetic field, we used the Runge-Kutta tracking method [71]. The fieldstrength was calculated using the field map mentioned in Section 2.4.1. The Runge-Kutta
tracking has the following five parameters to be determined,CHAPTER 3. ANALYSISCounts

56

2500
2000
1500
1000
500
0
-200-150-100 -50 0

50 100 150 200mm

Figure 3.7: Difference between lup and ldown . The arrows show the cut positions.

xF T OF: x coordinate of hit position at FTOF,

yF T OF: y coordinate of hit position at FTOF,

aF T OF: slope in the horizontal plane (dx/dz) at FTOF,

bF T OF: slope in the vertical plane (dy/dz) at FTOF,

p0 : Q/p charge divided by momentum.
The momentum was determined as p = 1/p0 . The values obtained from the local
tracking were used as initial values of these parameters. These parameters were calculated to minimize the χ2 value defined below and the calculation was iterated until theconvergence criterion of δχ2 = (χ2k+1 −χ2k )/χ2k < 10−3 was satisfied, where k is the numberof iterations and χ2k is the χ2 value for the k-th iteration. The χ2 value of each track isdefined as
χ2RGK =n
1 X
xtracking− xdataiin − 5 i=1
wi

!2

,

(3.6)

are the hit
where n is the number of the chamber planes with a hit, xtracking
and xdataiipositions on the i-th plane in the tracking and the data, respectively, and wi is the position
resolution of i-th plane. The typical number of the iteration was five.
Figure 3.8 shows the obtained χ2 distributions for the (π − , K − ) and (π + , K + ) data.
The calculated momentum distribution for the (π − , K − ) trigger data is shown as the open
histogram in Figure 3.9. The momentum distribution for K − ’s is also shown in Figure
3.9 by the hatched histogram where K − ’s were selected by mass cut discussed in Section
3.3.2. In the (π − , K − ) reaction, the momenta of scattered K − ’s ranged from 0.4 to 1.1
GeV/c. Therefore the effect of multiple scattering made the χ2 distribution of the RungeKutta tracking broader than ideal one. To study the cut position, we compared with the
distribution obtained by the Monte Carlo simulation as shown by the hatched histogramin Figure 3.8. The simulated χ2 distribution reproduced real data except for a long tailtowards large χ2 , not only for the (π − , K − ) data but also for the (π + , K + ) data as shownin Figure 3.8 (b) where the typical momenta of K + ’s were around 1.6 GeV/c. From thisstudy, we selected χ2 < 6.0 region where the χ2 distribution was almost consistent withthe simulation.

Counts

3.3. ANALYSIS OF OUTGOING PARTICLES

57-(a) 1.92GeV/c (π-, K )real data

1500

Simulation
1000

500

0
0

5

10

15

20

25

30

Countsχ2

400+(b) 1.92GeV/c (π+, K )real data
300

Simulation

200

100

0
0

5

10

15

20

25

30

χ2

Figure 3.8: The χ2 distributions of the Runge-Kutta tracking (a) for the (π − , K − ) data and(b) for the (π + , K + ) data at the beam momentum of 1.92 GeV/c. The open histogramshows the obtained distribution from real data and the hatched histogram shows one
obtained by the simulation. The arrow shows the cut position of the χ2 cut which was
determined considering that the data and simulation were almost consistent for the eventswith smaller χ2 than this cut position.

CHAPTER 3. ANALYSISCounts/0.01(GeV/c)

58

12000
10000
8000
6000
4000

K-

2000
0
0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

momentum(GeV/c)

Figure 3.9: Reconstructed momentum using the Runge-Kutta tracking for the (π − , K − )trigger data. The hatched histogram represents the momentum distribution for K − selected by mass cut discussed in Section 3.3.2. The peak around 1.9 GeV/c is corresponding
to the π − beam-through events. The events with momenta between 0.45 GeV/c and 1.1
GeV/c were suppressed if the particle was not K − because we rejected particles otherthan K − using the mass trigger.

3.3.2

Mass reconstruction of outgoing particles

The mass of each outgoing particle was reconstructed using the information of the momentum, flight length and flight time. The momentum and flight length were obtainedby the Runge-Kutta tracking as discussed in Section 3.3.1. The flight time was obtained
from the time-of-flight between T2 and FTOF. Because this time-of-flight included boththe flight time of π − between T2 and the reaction point and the flight time of K − between
the reaction point and FTOF, we subtracted the contribution of π − using the distance
between T2 and the obtained vertex point which will be described in Section 3.4. Then
we obtained the flight time of K − . The velocity and mass of the outgoing particle were
calculated by the following equations,

β =
M

L
,
T ×c

= P×

(3.7)

p

1 − β2,β(3.8)

where L, T and P denote the flight length, flight time and momentum, respectively. Figure
3.10 shows the obtained mass spectrum.
In order to adjust the absolute value of the mass, the calibration of the time-of-flightbetween T2 and FTOF is important. The calibration was done in the following way. At
first, the outgoing particles which might be considered to be π − were selected using only
time-of-flight information. Then we calculated the predicted time-of-flight (Tpred ) using
the momentum, flight length, and mass of π − . We obtained the time difference (∆T )between the Tpred and the measured time-of-flight (Tmeasure ),∆T = Tpred − Tmeasure .

(3.9)

2

Counts/0.004(GeV/c )3.3. ANALYSIS OF OUTGOING PARTICLES

59

π-

104

K

p

-

103

π+

K+
d

2

10

10

1
-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2

mass× charge(GeV/c )Figure 3.10: Distribution of obtained masses of outgoing particles

The time offset was adjusted to make ∆T be zero. The mass resolution of π − was almost
determined by the resolution of the time-of-flight. Conversely, there were few effects
propagated from the error of the momentum measurement. Therefore we used π − for thecalibration. The time resolution was obtained from ∆T spectra to be 132 ps as the meanvalue of 24 segments of FTOF.
Mass resolution
Figure 3.11 shows the mass resolution (σ of mass square) as a function of momentum
for proton, K − and π − . In case of proton and K − , we divided into two event sets with
χ2RGK < 5 and χ2RGK > 5 and obtained mass resolution for each event set. We recognizedthat the resolution became worse for larger χ2RGK events.
The mass resolution is parametrized by the following equation,
4
2σM
2 = 4M

1+



M
p

2 !

a21 + 4M 4 p2 a22 + 4p2 (p2 + M 2 )



c
a3
L

2

,

(3.10)

where a1 , a2 and a3 are parameters, M is the nominal values (PDG values) of mass of
π − , K − and proton and c is the speed of light. The flight length (L) is set to 3280 mm
which is the typical value for the spectrometer. The first and second term of equation(3.10) represent the contribution of momentum resolution. The momentum resolution canbe evaluated as


σp
p

2

=

a21
+ p2 a22 .
β2(3.11)

The first term is the contribution of multiple scattering. The second term represents thecontribution of the resolution of the spectrometer.The third term of equation (3.10) is thecontribution of the time-of-flight.

CHAPTER 3. ANALYSIS

2

2

σ of M (GeV )

60

0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
0

protonχ2 < 5 selectχ2 > 5 select

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2

2

σ of M (GeV )momentum(GeV/c)
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
0

kaon

χ2 < 5 selectχ2 > 5 select

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2

2

σ of M (GeV )momentum(GeV/c)
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
0

pion

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

momentum(GeV/c)

Figure 3.11: Mass resolution as a function of momentum for proton (top), K − (middle)
and π − (bottom). The solid lines represent the expected resolution from the equation(3.10). The dotted lines show the contribution of the time-of-flight resolution. For proton
and K − , the momentum resolutions were obtained for two event samples. The circle
points show the obtained resolution for events where the the χ2 is less than 5. The star
points show the resolution for events where the the χ2 is larger than 5. For π − , the mass
resolution is almost determined by the resolution of time-of-flight and the solid and dottedlines are same.

The parameter a1 and a2 were obtained by fitting the same plot as Figure 3.11 obtained
from the Monte Carlo simulation with the equation of (3.10). The obtained values werea1 = 0.00557 and a2 = 0.0091. We used a3 = 132 ps as the resolution of time of flight. The
solid lines in Figure 3.11 show the expected mass resolution obtained from equation (3.10)
using these parameters. The dotted lines show contribution of time-of-flight resolution.
It is not shown for π − because it is same with the solid line. The mass resolution wasalmost reproduced by the parameterization function. The contribution from momentum
resolution appears in the mass resolution significantly for proton, while the mass resolution
for other particles were almost determined by time-of-flight resolution. For proton, theobtained mass resolution was almost consistent with the expected one. Therefore webelieve that the best possible intrinsic-resolution of the spectrometer is obtained. The
momentum resolution was obtained to be 1.0% (rms) for 0.8 GeV/c K − .

3.3. ANALYSIS OF OUTGOING PARTICLES

61

Selection of the scattered K − mesons
Because the mass resolution is a function of momentum, the scattered K − ’s were selectedby the mass gate which was dependent on the momentum. In order to determine themass gate, the mass spectrum for each momentum was fitted with two Gaussian peaks
and an exponential background of contamination of π − as shown in Figure 3.12 (a). The
gate was determined as ±3σ region of the broader Gaussian peak for each momentum asshown by the red lines in Figure 3.12 (b). The K − identification efficiency is expected tobe larger than 99.7%. The π − contamination ratio within the mass gate was estimatedby integrating the background function obtained by the fitting between the mass gate andis shown in Figure 3.12 (c). For the momentum range of 0.6 < p < 0.9 GeV/c which iscorresponding to the Θ+ production, the π − contamination was obtained to be ∼3%.

Figure 3.12: (a) Mass spectrum of outgoing particles with momentum of 0.8 GeV/c < p <0.9 GeV/c. The histogram was fitted with the two Gaussian peaks and an exponential
background. The arrows show the ±3σ region of the broader Gaussian peak. (b) Scatteredplot of momentum and mass. The lines represent the mass gate obtained as ±3σ region
for each momentum. (c) Contamination ratio of π − within the mass gate.

62

CHAPTER 3. ANALYSIS

3.3.3

Momentum correction

dx/dz at target

dx/dz at target

We found that there was the correlation between momenta and scattering angles in thehorizontal plane at the target ( dxdz ) of scattered particles by investigating the scattered plotdx+
of dz and Σ peak position obtained from the (π + , K + ) reaction as shown in the left figureof Figure 3.13. This correlation appears to be caused by imperfection of the used field map.
Because the field map was measured at the experiment several years ago and in the present
experiment the additional materials such as the magnetic shields of image intensifier tube
(IIT) for SCIFI detector were added, there can be some differences between the field map
and the real magnetic field. In order to obtain better missing mass resolution, we have tocorrect momentum to remove such correlation. Because the Σ+ events were not sufficient
statistically and the momentum range was larger than that of the (π − , K − ) reaction, the(K − , p) reaction was used to correct the momentum as described following.
The same kind of correlation existed between dx
dz and the calculated proton mass at−+(K , K ) data set as shown in Figure 3.14 (bottom). Because the effect of momentum
for mass of π + and K + is smaller than that for proton as described in Section 3.3.2, thecorrelation for π + and K + did not appear. We corrected the momentum so as to make thecalculated proton mass constant in every dx
dz region as shown in 3.14 (top) where eventswith momentum of 0.4 GeV/c < p < 1.1 GeV/c were selected in order to obtain thecorrected momentum of the same range with the (π − , K − ) reaction. The missing mass
spectrum of the (π + , K + ) reaction applied this correction is shown in the right figure of
Figure 3.13, where this correlation is removed. We also applied this correction to the(π − , K − ) data.

w/o Correction

0.3

Σ

+

0.2
0.1

0.2
0.1
0

-0.1

-0.1

-0.2

-0.2

1

Σ

+

0

-0.3

w/ Correction

0.3

-0.3
1.1

1.2

1.3

1.4

1.5

1.6
2

Missing mass(GeV/c )

1

1.1

1.2

1.3

1.4

1.5

1.6
2

Missing mass(GeV/c )Figure 3.13: Scattered plot between missing mass of the (π + , K + ) data and the scattering
angle in the horizontal plane at the target ( dxdz ) without momentum correction (left) andwith momentum correction (right). The loci are corresponding to Σ+ .

2

Mass(GeV/c )3.4. VERTEX RECONSTRUCTION

63

1.05
1

0.4 < p(GeV/c) <1.1

0.95

2

Mass(GeV/c )

0.9

1.2
p
1
0.8
K+

0.6
0.4

π+

0.2
0
-0.4

-0.3

-0.2

-0.1

-0
0.1
0.2
0.3
Slope of track at ZX-plane

Figure 3.14: Scattered plots between the ( dxdz ) at the target and masses obtained from(K − , K + ) data set. Top figure is the expansion around proton mass where the momentum
range of 0.4 GeV/c < p < 1.1 GeV/c was selected.

3.4

Vertex reconstruction

The reaction vertex point (xvtx , yvtx , zvtx ) was obtained by the closest distance between
tracks of beam and outgoing particles. Figure 3.15 shows the vertex distribution of the(π − , K − ) reaction. The beam size (1.4 × 1.3 cm2 ) was small enough in comparison withthe target size. Therefore any cut was not applied for xvtx and yvtx . In the distribution of
zvtx , the image corresponding to the polyethylene target and the VH are clearly recognized.
We required the vertex point to be less than 80 mm from the target center as shown by thearrows in Figure 3.15. The background events attributed to materials other than the target
were estimated from the analysis of the empty target data and the contamination ratio
was obtained to be 0.6%. Because the SCIFI target enabled us to see particle trajectories
as image data, we could estimate the efficiency of this vertex cut precisely by comparing
the vertex position calculated by the spectrometer (vtxSP ) and one obtained by the image
data (vtxSCIF I ). Figure 3.16 (top) shows the typical SCIFI image which zooms into thevertex point. The vtxSCIF I was obtained by human eyes. Figure 3.16 (bottom) shows
the vtxSP distribution for events with −50 mm < vtxSCIF I < 50 mm , where ±50mm isthickness of the polyethylene target. By applying the cut of −80 mm < vtxSP < 80 mm
for these events, the efficiency of this vertex cut was obtained to be 92.8±0.5%.
We also checked the distribution of the closest distance between tracks of beam andoutgoing particles at the vertex point as shown in Figure 3.17. The events where the closest
distance was greater than 7mm, which corresponded to 3σ, were rejected considering thatbeam or outgoing particles reacted more than 2 times in the target.
Scattering angle was determined by the local tracks of the π − beam and scattered K − .
The scattering angle for the (π − , K − ) events ranged from 0 degree to 20 degree and meanvalue of the scattering angle was 8.2 degree as shown in Figure 3.18.

64

CHAPTER 3. ANALYSIS
y vertex

CountsCountsz vertex

CH2 target

1000

2500
2000
1500
1000

800

500
0
-50 -40 -30 -20 -10600

010 20 30 40 50

y (mm)

VH

Countsx vertex

400

2000
1500

200
1000

0
-400 -300 -200 -100500

0100 200 300 400

z (mm)

0-50 -40 -30 -20 -10

010 20 30 40 50

x (mm)

Figure 3.15: Vertex distributions of the (π − , K − ) reaction. The arrows show the cut
position for the vertex cut.

30

30

20

20

10

10

0

0

-10

-10

-20

-20
-20

-10

0

10

20

30

-20

-10

0

10

20

30

Countsz vertex tagged by SCIFI image

50

Accept event
Reject event

40
30
20
10
0
-200 -150 -100

Cut region
-50

0

50

100

150

200

z(mm)

Figure 3.16: (top) Typical SCIFI image around the vertex point. The vtxSCIF I and vtxSP
are the vertex point obtained from image data and analysis of spectrometer, respectively.
(bottom) vtxSP distribution for events with −50 mm < vtxSCIF I < 50 mm , where±50mm is thickness of the polyethylene target. The open and solid histogram represent
the accepted and rejected event by the vertex cut. The accepted ratio was 92.8±0.5%.

Counts

3.4. VERTEX RECONSTRUCTION

65

900

Closest Distance Approach at vertex point

800-(π-, K ) data

700
600
500
400
300
200
100
0
0

2

4

6

8

10

12

14

16

18

20

Counts

(mm)

220
200

Closest Distance Approach at vertex point

180(π+,K event)

+

160
140
120
100
80
60
40
20
0
0

2

4

6

8

10

12

14

16

18

20

(mm)

Figure 3.17: Distribution of the closest distance between tracks of beam and outgoingparticles at the vertex point. The solid lines show the fitting results with a Gaussianfunction. The accepted region is shown by an arrow which corresponds to the 3σ point of
the fit.

900
800

Scatterd angle of K

700

Mean = 8.235

600

RMS = 3.784

-

500
400
300
200
100
0
0

5

10

15

20

25

30
degreeFigure 3.18: Scattering angle distribution of the (π − , K − ) reaction.

66

CHAPTER 3. ANALYSIS
cut

criteria

efficiency(%)π − selection
Time-of-Flight cut
beam χ2 cut
beam momentum cut
mass-momentum cut
Runge-Kutta χ2 cutvertex cut
closest distance cut
total

3σ region
C.L. 95% region
1.8 < Pπ− (GeV/c) < 2.0
K − selection
3σ region (p dependent)
χ2RGK < 6vertex selection−80 < zvtx (mm) < 80
< 7mm (3σ)

93.8 ± 0.1
84.6 ± 0.1
94.8 ± 0.1> 99.772.7±0.292.8± 0.5
97.8 ±0.1
49.6±0.3

Table 3.1: Summary of the analysis cuts and their efficiencies. Errors are statistical ones.
This is a cut summary applied for the events where beam and outgoing particles are foundin the analysis program.

3.5

Summary of the analysis cut

We have mentioned the analysis procedure of the (π − , K − ) data. In order to select good(π − , K − ) events, we applied the following cuts for the events where beam and outgoingparticles were found in the analysis program,
1. selection of π − in the beam and its momentum analysis,
2. identification of the scattered K − and its momentum analysis,
3. selection of the reaction vertex point,
as described in the previous sections. Here, we summarize the criteria and efficiencies ofthese cuts in Table 3.1. The efficiencies will be used to derive the production cross sectionof the Θ+ .

3.6

Missing mass spectrum of the π + p → K +X reaction

In the missing mass spectrum of the π − p → K − X reaction, there might not be any
peaks of hadron resonances other than the Θ+ . Therefore it is quite important to checkthe validity of the analysis from the missing mass spectrum of calibration data. In thisexperiment, we measured the π + p → K + Σ+ reaction for this purpose.
Missing mass is defined as the invariant mass of an undetected residual system assuming
the target particle to be at rest. In the reaction 1 + 2 → 3 + X, where 1 is the incident
particle, 2 is the target particle, and 3 is the outgoing particle, the missing mass MX is
calculated as,q
MX =(E1 + M2 − E3 )2 − (p21 + p23 − 2p1 p2 cos θ),(3.12)

where Ei and pi is the energy and momentum of particle i, M2 is the rest mass of the target
particle, and θ is the scattering angle of the particle 3 from the direction of the particle 1.
The p1 and p3 is the momentum at the reaction point. The energy loss in the target wascorrected using the reconstructed momenta of the incident and outgoing particles with
their directions and the calculated vertex point. The vertex resolution decreased for the3.6. MISSING MASS SPECTRUM OF THE π + P → K + X REACTION

67

Counts/8MeV/c2

events with small scattering angle. When the scattering angle was less than 4 degree, theenergy loss was corrected assuming that the reaction vertex was the center of the target.
Figure 3.19 shows the missing mass spectrum of the (π + , K + ) reaction at the beam
momentum of 1.92 GeV/c. The peak due to Σ+ is clearly observed. The beam momentum was normalized so as to make the obtained Σ+ peak consistent with the PDG value.
We fitted this spectrum with two Gaussian functions assuming that the broad peak was
attributed to quasi-free reactions in carbon and the narrow one was attributed to free protons. The obtained width of the narrow peak was 33.3±4.8 MeV/c2 (FWHM) which was
almost consistent with the expected value of 28.3 MeV/c2 from the Monte Carlo simulation. To estimate the missing mass resolution in the simulation, the position resolutions of
the drift chambers, the momentum resolution of the beam spectrometer and the effects ofthe energy loss and the multiple scattering in materials for incident and outgoing particles
were taken into account.

140

Σ+

120

M=1189.9 ± 1.8 MeV/c
2
Γ=33.3 ± 4.8 MeV/c

100

2

80
60
40
20
0
0.9

1

1.1

1.2

1.3

1.4

1.5

1.6
2

Missing Mass(GeV/c )Figure 3.19: Missing mass spectrum of the (π + , K + ) reaction with a polyethylene target.
The beam momentum was adjusted so as to make the obtained Σ+ peak consistent with
the PDG value. The hatched spectrum is the expected spectrum from the simulation. The
obtained peak width of 33.3 ± 4.8 MeV/c2 (FWHM) is almost same with the expectedvalue of 28.3 MeV/c2 .

68

3.7

CHAPTER 3. ANALYSIS

Missing mass resolution for Θ+CountsUsing the same Monte Carlo simulation, the missing mass resolution for the Θ+ wasestimated to be 13.4 MeV/c2 (FWHM). In the Θ+ production, the momentum of theoutgoing particle is much lower than that in the Σ+ production. Therefore the missing
mass resolution for the Θ+ is better than that for the Σ+ hyperon.

600

SimulationΘ+Γ = 13.4 MeV/c2

500
400
300
200
100
0

1.4

1.45

1.5

1.55
1.6
1.65
1.7
2
Missing Mass(GeV/c )Figure 3.20: Expected missing mass spectrum for the Θ+ . The missing mass resolution
was obtained to be 13.4 MeV/c2 (FWHM).

3.8

Consistency in the (π − , K −) data

In Section 3.6, we confirmed that the expected resolution was obtained using the π + p →K + Σ+ reaction. Because the polarities of the KURAMA magnet and magnets in the beamline were inverse in the (π + , K + ) and (π − , K − ) reactions, it was desirable to confirm thevalidity of the missing mass resolution for the Θ+ by reconstructing some particles froma missing mass or invariant mass using the (π − , K − ) data. For this purpose, we checkedby the following two ways. The first one was to reconstruct the invariant mass for themulti-track events detected in the forward spectrometer and check the width and peak
position of the reconstructed particle. The other was to reconstruct KS0 meson from themissing mass of the π − p → K − pX reaction using the image data.

3.8.1

Invariant mass spectrum

The forward spectrometer had a small acceptance for multi particles with different charges,
because it was designed to have the maximum acceptance for particles with negative
charge. However there were some multi-track events, of which fraction was small, where
the both particles were detected in the spectrometer. Figure 3.21 shows the invariant mass
spectrum of π − and proton system. We can recognize the sharp peak corresponding to Λ
hyperon. The blue histogram is the background shape estimated using the mixed event
technique and reproduces well the spectrum other than the peak. The hatched histogramis the expected spectrum obtained from the Monte Carlo simulation. The mass and width3.8. CONSISTENCY IN THE (π − , K − ) DATA

69

were obtained to be M = 1113.7 ± 0.4 MeV/c2 and σ = 2.4 ± 0.3 MeV/c2 , respectively,by fitting the histogram after the subtraction of the estimated background as shown in
Figure 3.21 (b). The width was consistent with the expectation. The obtained mass was
slightly shifted from the world average value of M = 1115.683 ± 0.006 MeV/c2 .
Figure 3.22 shows the invariant mass distribution of K − and proton system where thepeak corresponding to Λ(1520) is seen. The histogram was fitted with a Gaussian function
and background which was assumed to be an exponential function. The obtained results
were that the mass was M = 1520.5 ± 2.6 MeV/c2 and the width was σ = 13.4 ± 2.2
MeV/c2 . The obtained width was consistent with the simulated value of 12.7 MeV/c2
obtained from the Monte Carlo simulation within the error. The world average mass is1519.5±1.0 MeV/c2 and the obtained mass was consistent within the error.
From these results, we checked that the obtained widths for the reconstructed particles
were consistent with the simulated values. Therefore we concluded that we obtained the
expected momentum resolution for outgoing particles. The obtained peak positions wereslightly shifted from the world average values. The shift will be discussed in relation to
the systematic error of absolute value in the missing mass of the π − p → K − X reaction in
Section 4.2.1.

–

Figure 3.21: (a)Invariant mass spectrum of π − and proton system. The peak around 1.115
GeV/c2 is the Λ(1115). The histogram with the blue solid line is the background estimatedusing the mixed event technique. The hatched histogram shows the expected peak shapeobtained from the Monte Carlo simulation. (b) Peak structure after the subtraction of
the estimated background. By fitting this histogram with a Gaussian function, the mass
and width were obtained to be M = 1113.7 ± 0.4 MeV/c2 and σ = 2.4 ± 0.3 MeV/c2 ,respectively. The hatched histogram is the same one with the simulated histogram shownin (a).

CHAPTER 3. ANALYSISCounts/10MeV

70

35
30
25

Λ(1520)20

M = 1520.5 ± 2.6 MeV/c2
σ = 13.4 ± 2.2 MeV/c
2

15
10
5
0

Simulation
1.4

1.45

1.5

1.55

1.6
1.65
2
Mass(GeV/c )Figure 3.22: Invariant mass spectrum of K − and proton system. The peak of Λ(1520) is
seen. The mass and width was obtained to be M = 1520.5±2.6 MeV/c2 and σ = 13.4±2.2
MeV/c2 , respectively. The hatched histogram shows the expected peak shape obtained
from the Monte Carlo simulation.

3.8.2

Missing mass spectrum of the π − p → K − pX reaction

In order to check the performance of the missing mass measurement in the (π − , K − ) data,
we reconstructed the KS0 meson from the missing mass of π − p → K − pX reaction using theimage data. By the analysis of the spectrometer, the momenta of the incident π − and theoutgoing K − were measured. In addition, much more information was obtained by using
the image data, because the SCIFI detector was the 4π tracking detector. In particular,
the tagging of KS0 meson decaying into π + and π − mesons and the measurement of thescattering angle of the proton were the key points in this analysis. The analysis procedure
is following. Figure 3.23 shows a supporting illustration of the analysis procedure.
1. Tag the KS0 production events by selecting the ”V” topology which indicated that aneutral particle, after some flight length, decayed into two charged particles.
2. Require that the number of the charged particles produced at the reaction point was
two. The two tracks were corresponding to the K − meson and the proton. Whenthe π − beam interacted with 12 C nucleus, the additional tracks of the fragmentation
production from the nucleus were seen. These events were rejected because these
events made the broad background due to the Fermi motion of proton in the nucleus.
3. Reconstruct the scattering angle, that is the direction vector, of the proton from thetwo sets of 2-dimensional image.
4. As the events where the particles in the final state were the K − , KS0 and proton,
the following two reactions are considered,3.8. CONSISTENCY IN THE (π − , K − ) DATA71

π − p → K − KS0 p (phase space),
π − p → K 0 Λ(1520) → K − KS0 p (Λ(1520) production).
We assumed that K − and proton were the decay products from Λ(1520). Because thescattering angle of the proton were measured using the image data, the momentum
could be calculated.
5. Calculate the momentum of the proton to make the invariant mass of the proton
and the K − be the mass of Λ(1520). Although the Λ(1520) has the natural width of
15.6±1.0 MeV/c2 , the central value of the mass was used. Therefore there was theuncertainty due to the width in the calculated momentum.
6. From these information, the missing mass of the π − p → K − pX reaction was calculated. For the phase space events, the calculated momenta of the protons were
not correct, because we assumed that K − and proton were the decay products fromΛ(1520). Therefore phase space events made the continuous background. On theother hand, the true Λ(1520) production events should make the peak corresponding
to the K 0 meson.

Figure 3.23: Supporting illustration of the derivation of the missing mass of the π − p →K − pX reaction.

Figure 3.24 shows the missing mass of the π − p → K − pX. The peak corresponding to
the KS0 meson can be recognized. The simulated spectra for the phase space events andΛ(1520) production events are also shown by the hatched spectra. Because the momentumof proton was calculated using the central value of the mass of Λ(1520), the shape of thereconstructed KS0 meson became a Lorentz function. The obtained missing mass spectrum
can be understood as the sum of these contributions. The peak position was obtained to
be M = 498.1 ± 5.2 MeV/c2 by fitting this spectrum with the Lorentz function. The
obtained mass was consistent with the PDG value of 497.67 MeV/c2 .
As discussed above, the obtained peak position of the KS0 meson was consistent with the
PDG value. The shape of the spectrum was consistent with the Monte Carlo simulation.
Therefore we consider that the analysis for both incident and outgoing particles has been
executed correctly. From these studies, we conclude that the missing mass resolution of
13.4 MeV/c2 for the Θ+ calculated by the Monte Carlo simulation is reliable.

CHAPTER 3. ANALYSISCounts/10MeV

72

12

K0

data
MC (phase space)

M=498.1 ± 5.2 MeV/c2

10
MC (Λ (1520) event)

8
6
4
2
0
0.2

0.3

0.4

0.5

0.6

0.7
2

Mass (GeV/c )Figure 3.24: Missing mass spectrum of the π − p → K − pX reaction where the K 0 meson
was tagged by selecting the ”V” topology in the image data. The peak corresponding to
the K 0 meson is recognized. The peak position was obtained to be 498.1 ± 5.2 MeV/c2
by fitting with the Lorentz function. The blue and green hatched histograms show theMonte Carlo simulations for the phase space events and the Λ(1520) events, respectively.

3.9. CROSS SECTION
fbeam
ǫK2
ǫtrackfČerenkov
fdecayfK − int
ǫM T
ǫDAQ
ǫana

73

beam normalization factor
tracking efficiency of K2 beamline
tracking efficiency of scattered particle
Čerenkov overkilling factor
decay factor−
K interaction factor
efficiency of mass trigger
DAQ live time
efficiency of analysis

83.6 ± 1.3%
72.7 ± 2.0%
84.6 ± 2.0%
90.8 ± 0.8%
57.6 ± 0.1% / 55.0 ± 0.1%
89.8 ± 0.1% / 90.7 ± 0.1%
95.7 ± 0.1%
93.5 ± 0.2%
49.6 ± 0.3%

Table 3.2: Summary of the various efficiencies for the calculation of the production crosssection. The fK − int and fdecay were obtained for 1.87 GeV/c and 1.92 GeV/c, respectively.
The former value is for 1.92 GeV/c and the latter value is for 1.87 GeV/c.

3.9

Cross section

After the derivation of the missing mass spectrum of the π − p → K − X reaction, we discuss
the production cross section of the Θ+ . In order to obtain the cross section, detection
and analysis efficiencies have to be estimated. The cross section is calculated from theexperimental yields as



dσ
dΩ



NtargetǫKU RAM A

1
1
NΘ +
,
·
·
Ntarget Nbeam · fbeam · ǫK2 ǫDAQ ǫKU RAM A · ǫana · dΩ
2 · (ρx) · NAvo(ρx) · NAvo=
(polyethylene),(SCIF I),1413
= ǫtrack · fdecay · fK − int · fČerenkov · ǫM T .
=1·

Here NΘ+ , Nbeam and Ntarget represent the number of Θ+ , beam particles and protons
in the target. The solid angle covered by the forward spectrometer at laboratory frame
is represented by dΩ. Other ǫ’s and f ’s represent various experimental efficiencies, andare summarized in Table 3.2. The efficiencies include µ− , e− contamination effect in thebeam, track-finding efficiency of incident particles, track-finding efficiency of scatteredparticles, overkilling of the Čerenkov counters, the decay and interaction of the outgoing
K − , the DAQ live time, the efficiencies of the mass trigger and the analysis cut. Eachefficiency was calculated with various calibration data and the Monte Carlo simulation.
The acceptance was calculated with the Monte Carlo simulation. The coefficient ǫana isthe analysis cut efficiency and summarized in Table 3.1. In this section, we discuss how
they were obtained.

3.9.1

Normalization of beam particles

The coefficient fbeam is the correction factor to obtain the number of π − . In this experiment, we could not distinguish e− and µ− from π − . We referred the past experiments
where a gas Čerenkov counter was used to distinguish e− and µ− and estimated that thiscontamination was 12.4±1.3% [67, 73]. We also calculated the absorption rate of π − inthe target with the GEANT simulation and obtained to be 4%. Adding these two values,
we estimated fbeam to be 83.6±1.3%.

74

CHAPTER 3. ANALYSIS

3.9.2

Track-finding efficiency of beam particles

The coefficient ǫK2 is the track-finding efficiency for beam particles. The efficiency wasestimated as a ratio of the number of events accepted as a good trajectory to that of good
beam particles defined from the time-of-flight between T1 and T2. The analysis of beam
particles was composed of the momentum reconstruction using BDC1,2,3 and BPC1,2 andthe track measurement of the incident beam using BPC3,4,5. The former was 76.3% dueto the inefficiency of BDC3 as described in Section2.3. The latter was 94.7%. The total
efficiency including these two factors was obtained to be 72.7±2.0%.

3.9.3

Track-finding efficiency of scattered particles

The efficiencies of track-finding routine used in the analysis program for scattered particles
have to be estimated, because the routine has criteria to find tracks such as minimum
number of hit chambers and can not find out some tracks due to the inefficiency of thedrift chambers or multi hit events.
The tracking efficiency is defined by the following equations,ǫdown−track(ZX) = 1 − (ǫ(min) + ǫ(χ2 cut) + ǫ(F T OF missX)),

ǫdown−track(Y Z) = 1 − (ǫ(min) + ǫ(χ2 cut) + ǫ(F T OF missY ) + ǫ(KIN Kcut1)),
ǫup−track(ZX) = 1 − (ǫ(min) + ǫ(χ2 cut) + ǫ(bendpoint)),

ǫup−track(Y Z) = 1 − (ǫ(min) + ǫ(χ2 cut) + ǫ(KIN Kcut2)),ǫtrack = ǫdown−track(ZX) × ǫdown−track(Y Z) × ǫup−track(ZX) × ǫup−track(Y Z) ,where ǫdown−track(ZX) , ǫdown−track(Y Z) denote the track-finding efficiencies at the exit of
KURAMA in the horizontal and vertical planes, respectively, and ǫup−track(ZX) , ǫup−track(Y Z)
denote the same efficiencies at the entrance of KURAMA. The other ǫ’s of right-hand side
represent inefficiencies due to the algorithm in the analysis program. The ǫ(min) represents the inefficiency due to the lack of the hit planes. In the analysis program, we required
at least three hit planes to execute straight track search. The ǫ(χ2 cut) represents the inefficiency due to the χ2 cut for local tracks, where the criterion of χ2 < 100 was required.
The others represent the factors which come from the consistency check between up-trackand down-track as described in Section 3.3.1. The ǫ(F T OF missX) and ǫ(F T OF missY )are the inefficiencies which come from the check between FTOF and down-track as shownin Figure 3.5 (left) and (right), respectively. The ǫ(KIN Kcut1) and ǫ(KIN Kcut2) are
the inefficiencies due to the inconsistency between up-track and down-track in the verticalplane as shown in Figure 3.6 (left) and (right), respectively. Finally the ǫ(bendpoint) is
the inefficiencies corresponding to the inconsistency between up-track and down-track in
the horizontal plane as shown in Figure 3.7.
The coefficient ǫtrack was obtained by analyzing the data produced by the Monte Carlosimulation with the same analysis program. In this Monte Carlo simulation, the measured
efficiencies of the chamber planes summarized in Table 2.4 were taken into account andthe decay process was not included.
Before we discuss the track-finding efficiency in the (π − , K − ) data, the validity of thisestimation was checked using scattered proton events taken with (K − , K + ) trigger data,
because proton does not decay and this made the estimation more easy. The scatteredprotons could be selected by using hit combination of CH and FTOF and the time-of-flightwithout tracking as discussed in the section of the mass trigger. Figure 3.25 shows thescattered plot between hit segment of the CH and time-of-flight of FTOF of segment 4,
where there were two loci corresponding to protons and π + ’s. In order to select proton3.9. CROSS SECTION

75

events, we applied the TOF gate shown in the solid lines in Figure 3.25, which corresponded
to the 1.5σ region in order to reject contamination of other particles. We estimated thetrack-finding efficiency by analyzing such pre-selected proton events and obtained theresults listed in the column of ”proton select” of Table 3.3. The efficiencies were comparedwith the results obtained by analyzing the Monte Carlo data which is also listed in thecolumn of ”simulation” of Table 3.3. The difference larger than 1.0% was found in χ2
cut. The difference is considered to be caused by the wrong TDC information of the drift
chambers most likely due to the multi hit events in the same cell or some noises in thereal data. Figure 3.26 shows the XT curve of DC3. In this Figure there were some events
located in the wrong relation and these events were rejected by the χ2 cut. Because thiseffect was not taken into account in the simulation, we concluded that the difference in χ2
cut came from this effect. The other factors were consistent within less than 1.0%.
Because we checked the validity of the simulation, we estimated the track-finding
efficiency for the (π − , K − ) event using the Monte Carlo simulation. However the factorof the χ2 cut was estimated with the real data. The estimated track-finding efficiency isgiven in the column of ”(π − , K − ) simulation” and ǫtrack was obtained to be 84.6±2.0%.
The error was estimated from the difference between pre-selected proton events and theMonte Carlo events.

TOF (nsec)

FTOF 4ch

24
22

proton

20
18
16
14

π+

12
10

2

4

6

8

10

12

14

16

CH (channel)

Figure 3.25: Scattered plot between hit segment of the CH and time-of-flight of the FTOF
of segment 4 in the (K − , K + ) data. There were two loci corresponding to protons and π + ’s.
The solid lines are the selection region of time-of-flight of FTOF which is corresponding
to 1.5σ region.

76

CHAPTER 3. ANALYSIS

Figure 3.26: XT plots of DC3 before the χ2 cut (left) and after the χ2 cut (right). By
applying the χ2 cut the events with the bad XT relation were rejected.

3.9.4

Overkilling of Čerenkov counters

The coefficient fČerenkov represents the correction factor due to the overkilling rates of
BVAC and FAC. Although the velocity of K − ’s produced in the (π − , K − ) reaction ismuch smaller than the threshold values for each Čerenkov counter, some events were discriminated due to the δ-rays produced along the passage in the counters and the accidentalveto under the high counting rate.
At first, we discuss the overkilling rates due to the δ-ray, fδ (BV AC) and fδ (F AC),for each counter. Figure 2.12 shows the efficiencies of each counter as the function ofβ. In this plot, the efficiency, that is overkilling rate for the K − ’s now, were measured
using π − beam of 230 MeV/c and obtained to be 6.9±1.0% for BVAC and 4.7±0.8% for
FAC, respectively. While FAC had the acceptance for all outgoing particles detected in
the spectrometer, BVAC had the acceptance for only particles with smaller scattering
angles. The acceptance of BVAC for the K − ’s was measured from the (π − , K − ) dataand obtained to be 21.3%. The overkilling rate for BVAC was obtained by the following
equation, fδ (BV AC) = (6.9 ± 1.0) × 0.213 = 1.5 ± 0.2%. The overkilling rate for FAC was
obtained to be fδ (F AC) = 4.7 ± 0.8%.
Next we discuss the overkilling rates due to the accidental coincidence, facc (BV AC)
and facc (F AC), under the beam intensity of 3.3 × 105 /spill. The single counting rates
were 142±13 kHz and 250±22 kHz for BVAC and FAC, respectively. Considering that thegate widths for BVAC and FAC were 100 ns and 70 ns, respectively, the overkilling rates
were obtained to be facc (BV AC) = 1.42 ± 0.13% and facc (F AC) = 1.75 ± 0.15%. Taking
into account the all effects, we calculated the fČerenkov by the following equation,fČerenkov = (1 − fδ (BV AC)) · (1 − fδ (F AC)) · (1 − facc (BV AC)) · (1 − facc (F AC)). (3.13)
The fČerenkov was obtained to be 90.8±0.8%.

3.9.5

Decay of the outgoing K −The coefficient fdecay represents the correction factor due to the decay ratio of the K − ’sbefore arriving at FTOF. The βγcτ of the K − with the momentum of 0.8 GeV/c is 6 m.
A part of K − ’s decayed on the way of the spectrometer, of which typical flight length was
3.3 m. Using the βγcτ and the flight length of 3.3 m, the rough estimation of the survival
rate was 58%. In order to study this factor for the π − p → K − Θ+ reaction in detail, we
executed the Monte Carlo simulation for the beam momentum of 1.92 GeV/c and 1.87
GeV/c. In this simulation the Θ+ was produced isotropically in the center of mass system.
The survival rate for 1.92 GeV/c was obtained to be 57.6±0.1%. Similarly the survival
rate for 1.87 GeV/c was 55.0±0.1%.

3.9. CROSS SECTION

ǫ(min)
ǫ(χ2 cut)ǫ(F T OF missX)
ǫ(min)
ǫ(χ2 cut)ǫ(F T OF missY )ǫ(KIN Kcut1)
ǫ(min)
ǫ(χ2 cut)ǫ(bendpoint)ǫ(min)
ǫ(χ2 cut)ǫ(KIN Kcut2)ǫtrack77(K − , p)(π − , K − )proton select simulation simulation
down-track(ZX)
0.763
0.073
0.104
1.87
1.42
0.00
0.241
0.535
0.293
down-track(YZ)
0.225
0.00
0.028
1.49
1.53
0.00
0.066
0.084
0.134
2.64
2.00
2.35
up-track(ZX)
0.03
0.011
0.00
1.83
0.17
0.032
1.49
1.51
1.43
up-track(YZ)
5.41
3.39
3.40
2.11
1.09
1.05
0.670
1.05
0.860
Tracking efficiency
85.4
90.5
84.6

Table 3.3: Summary of the estimations of the track-finding efficiencies of the (K − , p)
and the (π − , K − ) data. For the (K − , p) event, the results obtained from the pre-selected
proton and Monte Carlo simulation are shown. There is a difference larger than 1% inthe ǫ(χ2 ) between results obtained from the pre-selected data and simulation. This might
be caused due to the wrong TDC information (see text for detail description). Estimatedtracking efficiency in the π − p → K − Θ+ reaction using Monte Carlo simulation is givenin the column of ”(π − , K − ) simulation”. As the ǫ(χ2 ), we adopted inefficiencies obtained
from the real data.

78

CHAPTER 3. ANALYSIS

Target(CH2 )
VHX
VHY
BVAC
FAC
CH
YH

length (cm)
5.0
0.2
0.2
6.0
6.0
0.2
0.5

density (g/cm3)
1.0
1.07
1.07
0.200
0.164
1.07
1.07

thickness (g/cm2)
5.0
0.214
0.214
1.20
0.984
0.214
0.535

λI (g/cm2)
57.0
58.3
58.3
64
64
58.3
58.3

Table 3.4: Summary of the materials in the forward spectrometer. λI denotes the interaction length.

3.9.6Interaction of the outgoing K −The coefficient fK −int represents the correction factor due to the interaction rate of K −in the materials of the target and the forward spectrometer. The cross section of the K − preaction at the momentum around 0.8 GeV/c has relatively large value of about 40 mb,
half of which is the elastic scattering. Along the path of the outgoing K − , there werematerials of which total thickness was 8.36 g/cm2 , as summarized in Table 3.4. Therefore
some outgoing K − ’s interacted with these materials and disappeared. The interaction
rate of K − with these materials was roughly calculated to be about 13% considering theinteraction length of each material. In order to estimate this interaction rate in detail,
we also executed the Monte Carlo simulation based on the GEANT4. As the elastic andinelastic interaction, we used the packages included in the GEANT4. Figure 3.27 shows
the interaction points or decay points of K − ’s obtained by the simulation. The blue points
were the survival events where the outgoing K − arrived at FTOF without the decay orinteraction. The black points were the decay points of K − ’s. The red points indicatedthe inelastic reaction points. As expected, the inelastic reaction points were concentrated
on the materials in the spectrometer. The green points showed the events where there
were elastic scatterings with the materials and the K − ’s went off from the acceptanceand stopped at the end-guard or the yoke of KURAMA. For the correction due to theinteraction of K − , we took into account the last two effects due to the inelastic and elastic
interactions. The interaction rates were obtained to be 10.2±0.1% and 9.3±0.1% for the
beam momenta of 1.92 GeV/c and 1.87 GeV/c, respectively. Therefore the coefficient
fK −int were obtained to be 89.8±0.1% and 90.7±0.1% for 1.92 GeV/c and 1.87 GeV/c,
respectively.

x(mm)

3.9. CROSS SECTION

79

1400
1200
1000

survival event
decay event
inelastic reaction event
elastic reaction event

800
600
400
200
0
-200
-400
-600
-500

0

500

1000

1500

2000

2500

3000

3500

400

End guard

600

KURAMAEnd guard

y(mm)

z(mm)

200

CH

VH
BVAC
FAC

-200

target

0

YH

-400
-600
-500

0

500

1000

1500

2000

2500

3000

3500

z(mm)

Figure 3.27: Interaction points or decay points of K − ’s obtained by the Monte Carlosimulation based on the GEANT4. The top figure shows the horizontal projection and thebottom one shows the vertical projection. The blue points represent the survival events
which arrived at the FTOF without the decay or interaction. The black points are thedecay points of K − ’s. The red points indicate the inelastic interaction points. The green
points show the events where there were elastic scatterings with the materials and the K − ’swent off from the acceptance and stopped at the end-guard or the yoke of KURAMA.

3.9.7

Efficiency of mass trigger

The coefficient ǫM T is the efficiency of the second-level mass trigger. In addition to theordinal data accepted by the mass trigger (dataM T on ) we also took data rejected by themass trigger (dataM T of f ) with the prescale factor of 30. Figures 3.28 (a), (b) show themass spectra for dataM T on and dataM T of f , where K − ’s are also identified in dataM T of f .
The efficiency of the mass trigger, ǫM T , was estimated by the following equation,
ǫM T = 1 −30 × Nof f,
Non + 30 × Nof f(3.14)

where Non and Nof f are the number of K − ’s in dataM T on and dataM T of f , respectively.
Figure 3.28 (c) shows the efficiencies for each momentum region. For all momentum region,

80

CHAPTER 3. ANALYSIS

the ǫM T was obtained to be 95.7±0.5% where the error was statistical error. The systemerror due to the contributions of π − was estimated to be less than 0.2%.
2400
2200
2000
1800
1600
1400
1200
1000
800
600
400
200
0
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7(a)2

mass(GeV/c )2Counts/2MeV/c

1

0.99
0.98

(c)

0.97

0.96
0.95

Mass trigger Off
6

Efficiency

Counts/2MeV/c

2

Mass trigger On

(b)

0.94

5

0.93

Preset:30

4
3

0.92

2

0.4 0.5 0.6 0.7 0.8 0.9 1
Momentum(GeV/c)

1
00.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7
2

mass(GeV/c )Figure 3.28: (a) Mass spectrum for dataM T on . (b) Mass spectrum for dataM T of f . (c) Efficiency of the mass trigger. The solid circles represent the efficiencies for each momentum
region. The red line is the efficiency obtained for all momentum region and the hatchedregion shows the error.

3.9.8

Data acquisition efficiency

The data acquisition efficiency (ǫDAQ ), caused by the dead time of the data acquisition
system, was obtained as a ratio of the number of the first-level trigger events acceptedby the DAQ and that of the first-level trigger requests. The ǫDAQ was obtained to be
93.5±0.2%.

3.9.9

Acceptance

The effective solid angle of the forward spectrometer was calculated with the Monte Carlosimulation. In the event generator, the distribution of the beam profile defined as afunction of (xb , yb , ub , vb ) was produced from the experimental data, where xb , yb , ub andvb were the horizontal and vertical positions and their derivatives of a beam particle atthe target. The outgoing K − ’s were generated uniformly from θ − 12 ∆θ to θ + 12 ∆θ inthe polar angle, from 0 to 2π in the azimuthal angle and from p − 21 ∆p to p + 12 ∆p in
the momentum. In the simulation, the Charge Trigger was also taken into account. The
effective solid angle was calculated as a function of scattering angle θ and momentum p
as follows,dΩ(θ, p) = 2π

Z θ+ 1 ∆θ
2

θ− 12 ∆θd cos θ ×

number of accepted events.
number of generated events(3.15)The results are shown in Figure 3.29. Assuming that the Θ+ was produced isotropicallyin the center of mass system, the expected momentum distribution has mean momentumof 0.825 GeV/c with momentum spread of 0.040 GeV/c (r.m.s) as shown in Figure 3.30.
In order to calculate the differential cross section, we used 0.141±0.004 sr where 0.141 sr

3.9. CROSS SECTION

81

1.1

0.016

1

0.014

0.9

0.012
0.01

0.8

(sr/deg)

Momentum(GeV/c)

was corresponding to the acceptance for momentum of 0.825 GeV/c and the error of 0.004
sr attributed to the momentum spread of 0.040 GeV/c. Similarly, we used 0.133±0.005 sr
for 1.87 GeV/c.
When we assume that the Θ+ was produced isotropically in the center of mass system, 10.4% of the outgoing K − ’s were accepted for the beam momentum of 1.92 GeV/c.
Similarly 11.0% of K − ’s were accepted for 1.87 GeV/c. These values were used to derive
the total cross section assuming that the Θ+ was produced in the S-wave.

0.008
0.7
0.006
0.6

0.004

0.5

0.002

(sr/deg)

5

10

15

20

0

25

θ(degree)

0.012

PK-=0.8GeV/c

0.01
0.008
0.006
0.004
0.002

Solid Angle(sr)

0
0

5

10

15

20

25

θ(degree)

0.16
0.14
0.12
0.1
0.08
0.06
0.04

0.4

0.5

0.6

0.7

0.8

0.9

1

Momentum(GeV/c)

Figure 3.29: Solid angle of the forward spectrometer in the laboratory system. (Top)Contour plot of the solid angle as a function of the scattering angle and the momentum.
(Middle) Solid angle at the momentum of 0.8 GeV/c. (Bottom) Solid angle as a functionof the momentum. In this plot, the solid angle was integrated in all scattering angle. The
solid angle for the momentum of 0.825 GeV/c which is the expected mean momentum ofthe Θ+ production at beam momentum of 1.92 GeV/c is 0.141 sr. Similarly that for the
momentum of 0.749 GeV/c is 0.133 sr.

82

CHAPTER 3. ANALYSISCountsMomentum of K-

400

P π-=1.87GeV/c
Mean = 0.749
RMS = 0.042200Counts0500

P π-=1.92GeV/c
Mean = 0.825
RMS = 0.040

0
0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1
Momentum (GeV/c)

Figure 3.30: Simulated momentum distributions of the K − ’s in the π − p → K − Θ+ reaction
at the beam momenta of 1.87 GeV/c (top) and 1.92 GeV/c (bottom).

Chapter 4

Results
4.1

Missing mass spectra of the π − p → K −X reaction

The missing mass spectra for the π − p → K − X reaction are shown in Figure 4.1, 4.2
for the beam momenta of 1.87 GeV/c and 1.92 GeV/c. Considering the expected missing
mass resolution of 13.4 MeV/c2 (FWHM), i.e. σ=5.7 MeV/c2 , three spectra with different
binnings of 2MeV/c2 , 3MeV/c2 and 4MeV/c2 per bin are presented to study the effects
which result from the difference of the binning.
In order to display the contribution from carbon nuclei in the SCIFI and polyethylene
targets, carbon target data are also shown as the hatched spectra, which are normalized
by the number of beam particles and the number of carbon nuclei in each target. The
statistics of the carbon target data is about ten times lower than that of the polyethylene
target data. The net contribution from free protons is represented as the excess fromthe hatched histogram and is compatible with the expectation from the cross sectionsof the π − p → K − X reactions measured in the past experiment using a bubble chamber[56]. Because half of data at beam momentum of 1.87 GeV/c was taken with the SCIFI
target, the contribution from free protons at 1.87 GeV/c is smaller than that at 1.92
GeV/c. Naively the low missing mass region is corresponding to high momentum of thescattered K − . When a reaction with a free proton is considered, a momentum, which isso high as to correspond to the missing mass region less than about 1.45 GeV/c2 , is notallowed kinematically. Therefore this missing mass region is attributed to contributions
from quasi-free reactions in carbon nuclei. In fact, this missing mass region is represented
well by the carbon target data.
In the missing mass spectrum at 1.87 GeV/c, data taken with the SCIFI and thepolyethylene targets are combined. Any peak with the width compatible with the experimental resolution has not been observed in this spectrum.
In the missing mass spectrum at 1.92 GeV/c, it seems that there is a bump around1.53 GeV/c2 which is consistent with the mass reported by several experiments. However
there is a possibility that the structure is only a statistical fluctuation. In the following
section, we discuss the bump in this missing mass spectrum.

83CHAPTER 4. RESULTSCounts/2MeV/c 2

84

350
300

EntriesPπ-=1.87GeV/c

22732
12

Entries( C) 1916

250
200
150
100

Counts/3MeV/c2

50

500
400
300
200

Counts/4MeV/c 2

100

700
600
500
400
300
12

C data

200
100
0
1.3

1.35

1.4

1.45

1.5

1.55

1.6

1.65

1.7
2

Missing Mass (GeV/c )Figure 4.1: Missing mass spectra of the π − p → K − X reaction at the beam momentumof 1.87 GeV/c with the different binnings of 2MeV/c2 (top), 3MeV/c2 (middle), and
4MeV/c2 (bottom) per bin. These histograms are the sum of data with the SCIFI target
and the polyethylene target. The hatched histograms are the carbon target data which arenormalized by the number of target and beam particles. The statistics of the carbon target
data is about ten times lower than that of the polyethylene and SCIFI data. These hatchedhistograms show the contribution from carbon nuclei in the SCIFI and the polyethylene
targets.

Counts/2MeV/c 2

4.1. MISSING MASS SPECTRA OF THE π − P → K − X REACTION

350

Pπ-=1.92GeV/c

Entries

85

26842
12

Entries( C) 2214

300
250
200
150
100

Counts/3MeV/c2

50

500
400
300
200

Counts/4MeV/c 2

100

700
600
500
400
300
12

C data

200
100
0
1.3

1.35

1.4

1.45

1.5

1.55

1.6

1.65

1.7
2

Missing Mass (GeV/c )Figure 4.2: Missing mass spectra of the π − p → K − X reaction at the beam momentumof 1.92 GeV/c with the different binnings of 2MeV/c2 (top), 3MeV/c2 (middle), and
4MeV/c2 (bottom) per bin. The hatched histograms are the carbon target data which
are normalized by the number of target and beam particles. The statistics of the carbon
target data is about ten times lower than that of the polyethylene data. These hatchedhistograms show the contribution from carbon nuclei in the polyethylene target.

86

4.2

CHAPTER 4. RESULTS

Discussion about the missing mass spectrum at 1.92
GeV/c

In this section, we discuss whether it is possible to regard the bump in the missing mass
spectrum at 1.92 GeV/c as the Θ+ from the viewpoint of the peak position, the width
and the statistical significance.
We fitted this histogram with the background of a cubic function and a Gaussian
peak as shown in Figure 4.3 (a). In this fitting, at first, the initial parameters of the
background were estimated by fitting with only a cubic function, where the bump region
was excluded from the fitting. Then the histogram was fitted with the Gaussian peak
and the background function simultaneously. Figure 4.3 (b) shows the residual plot fromthe background function obtained in the fitting. The peak position has been obtained to+2.2
2
be 1530.6 −1.9
(stat.)+1.9−1.3 (syst.) MeV/c . The explanation of the systematic error will be
described in Section 4.2.1. The obtained value is consistent with the masses reported by2
the several experiments. The width has been obtained to be Γ=9.8+7.1−3.4 MeV/c (FWHM)
which is consistent with the expected resolution of 13.4 MeV/c2 within the error. The
count of the peak has been obtained to be 139+86−67 (stat.)±10(syst.) by calculating thearea of the Gaussian function obtained by fitting the histogram. The uncertainty of countresulting from varying the fitting range and binning is considered as the systematic error.
The systematic error of the peak count will be explained in Section 4.2.2.
Because the obtained width is consistent with the experimental resolution, we also
fitted this spectrum with the fixed width of 13.4 MeV/c2 as shown in Figure 4.4. The
count of this bump has been obtained to be 183±71(stat.)±10(syst.). The statisticalsignificance of this bumpq two expressions. The first expression is theq was considered by
2σ
2σ
2σ
2σ
∼
naive estimator Ns / Ns + Nb (= Ns / Nb2σ ) where Ns2σ is the peak count within 2σregion from the center and Nb2σ is the background within the same region. The significanceof 2.7σ √is obtained by the first expression. The second estimate of significance is given
by Ns / ∆Ns , where Ns is full area of the Gaussian peak obtained by the fitting of thehistogram and ∆Ns is its fully correlated uncertainty. The significance of 2.5σ is obtainedby the second expression.
Although we assumed that there was a bump around 1.53 GeV/c2 in the discussion
above, we also fitted the histogram with only the background of a cubic function assumingthat there was no peak structure. The fitting result is shown by a dashed line in Figure
4.3 (a). The difference between backgrounds obtained from two fits, the Gaussian peakplus the background and only the background, was represented by the solid line in Figure
4.3 (b). The obtained reduced χ2 was less than one and the assumption of the non-peakstructure could not be excluded. However the reduced χ2 was dependent on the fitting
range and was almost determined by the residuals at the region other than the bump.
Therefore we also checked the statistical significance of the bump from this backgroundobtained with the assumption of the non-peakstructure The significance is estimated toq
2σ
2σ
be 1.9σ using the first expression, Ns / Ns + Nb2σ .

Counts/4MeV/c 2

4.2. DISCUSSION ABOUT THE MISSING MASS SPECTRUM AT 1.92 GEV/C

87

Gaussian peak+cubic B.G.

700
600
500

(a) Fitting results

cubic B.G. onlyχ /nof = 16.5/28
22
M=1530.6 +2.2
-1.9 MeV/c2
Γ=9.8 +7.1
-3.4 MeV/c

400
300
200

Counts/4MeV/c 2

100

100

(b) Residual plot

Gaussian peak+cubic B.G.
Difference between B.G. of two fits

50
0
-50
-100
1.3

1.35

1.4

1.45

1.5

1.55
1.6
1.65
1.7
2
Missing Mass(GeV/c )Figure 4.3: Fitting results of the missing mass spectrum of the π − p → K − X reaction at thebeam momentum of 1.92 GeV/c. (a) We fitted this spectrum with third order polynomial
background and a Gaussian peak (solid line). In this fitting, the width was a parameter2
and obtained to be 9.8+7.1−3.4 MeV/c (FWHM) which was consistent with the expected valueof 13.4 MeV/c2 within the error. The dashed line represents the fitting result with only
third order polynomial background assuming that there is no peak structure. (b) Residual
plot from the background function obtained from the fitting with third order polynomial
background and a Gaussian peak. The difference between backgrounds obtained from twofits, the Gaussian peak plus the background and the background only, is represented by
the solid line.

CHAPTER 4. RESULTSCounts/4MeV/c 2

88Gaussian peak+cubic B.G.

700(a) Fitting results

cubic B.G. only

χ2/nof = 16.9/29
600
500
400

2
M=1530.8 +2.4
-2.4 MeV/c

Γ=13.4 MeV/c2 (Fix)Gaussian peakCounts=187.1 +70.8-70.8+ cubic function

300
200

Counts/4MeV/c 2

100

100

(b) Residual plot

Gaussian peak+cubic B.G.
Difference between B.G. of two fits

50
0
-50
-100
1.3

1.35

1.4

1.45

1.5

1.55
1.6
1.65
1.7
2
Missing Mass(GeV/c )Figure 4.4: (a)Results of fitting the missing mass spectrum of the π − p → K − X reaction
at the beam momentum of 1.92 GeV/c with the same function as Figure 4.3. However, in
this fitting, the width was a fixed value of the expected resolution of 13.4 MeV/c2 . The
solid line represents the fitting result. The dashed line is the same as that in Figure 4.3 andrepresents the fitting result with only third order polynomial background assuming that
there is no peak structure. (b) Residual plot from the background function obtained fromthe fitting with third order polynomial background and a Gaussian peak. The difference
between backgrounds obtained from two fits, the Gaussian peak plus the background andthe background only, is represented by the solid line.

4.2. DISCUSSION ABOUT THE MISSING MASS SPECTRUM AT 1.92 GEV/C

4.2.1

89

Systematic error of the peak position

Missing mass is calculated with the momenta of incident and outgoing particles and thescattering angle as described in Equation (3.12). We estimated the systematic error of theabsolute value of the missing mass from the systematic error of these variables.
The momenta of beam particles were calibrated in order that the peak of the Σ+
obtained in the (π + , K + ) reaction became consistent with the PDG value. However thestatistics of the Σ+ was not enough. There is an uncertainty due to the statistical error of the determination of the peak position. This uncertainty is corresponding to the2
uncertainty of the Θ+ mass of ∆M =+1.8−0.9 MeV/c .
For the scattered particles, the important variables are the momentum and the scattering angle to determine the missing mass. We did not take into account the systematic
error of the momentum, because the obtained central values of masses of K − and π − wereconsistent with the PDG value. The scattering angle was calculated using the straight
track at the entrance of KURAMA, where there was the fringing field and the trajectories
of outgoing particles were bent by the fringing field. Therefore the obtained scattering
angle has the systematic error due to this effect. We assumed that the systematic error of
the missing mass came from only the systematic error of the scattering angle. The systematic error of the scattering angle was estimated from the masses of Λ(1115) and Λ(1520)
obtained from the invariant mass spectra of the π − and proton system and the K − andproton system, respectively. The observed mass of Λ(1115) was 1113.7±0.4 MeV/c2 (thePDC value is 1115.683±0.006 MeV/c2 ). Assuming that the shift is attributed to the errorof the scattering angle, the error of the scattering angle is ∆θ = +0.5 degree, which iscorresponding to the error of the missing mass of ∆M = +0.6 MeV/c2 . The observed massof Λ(1520) was 1520.5±2.6 MeV/c2 (the PDC value is 1519.53±1.0 MeV/c2 ). Similarly,
the error of the scattering angle is ∆θ = −0.5 degree and the error of the missing mass is∆M = −0.9 MeV/c2 .
Considering the effects of the beam momentum and the scattering angle, we determined
2that the systematic error of the missing mass is ∆M =+1.9−1.3 MeV/c .

4.2.2

Counts of peak

The count of the peak was calculated as the area of the Gaussian function obtained by fitting the missing mass histogram with the Gaussian peak and the polynomial background.
The background shape obtained from the fitting is dependent on the fitting range. Therefore the count of the peak also varies with the fitting range. In addition, because thestatistics of the histogram is not sufficient, the yield of the peak depends on the binning of
the histogram. The uncertainty due to the difference of the fitting range and the binningis treated as the systematic error of the peak count. In order to study the systematic
error, we investigated the yield of the peak for the histograms with different binnings of
2 MeV/c2 , 3 MeV/c2 and 4 MeV/c2 per bin. The dependence of the fitting range waschecked by fitting with five different fitting ranges, where the fitting range was incremented
by 10 MeV/c2 for both sides from the closest fitting range between 1.49 GeV/c2 and 1.57
GeV/c2 . The maximum value of the upper side of the fitting range was set to 1.6 GeV/c2 .
Figures 4.5 and 4.6 show the dependences of the reduced χ2 , the count of the peak andthe statistical significance for the different binnings and fitting ranges. Figure 4.5 is theresult for the fitting with the width as a parameter. Figure 4.6 is the result for the fittingwith the fixed width. From the reduced χ2 , as shown in (a) of these figures, the fittings
are considered to be reasonable for all fitting ranges. The result for the count of the peakis shown in (b) of these figures, where the error bars represent the statistical error. The
final value and the systematic error of the yield were obtained as the mean value and the

90

CHAPTER 4. RESULTS

standard deviation of the counts, as shown by the red line and the hatched region in (b) of
these figures, respectively. In case of the fit with the width as a parameter, the peak countis 138+86−67 (stat.) ± 10(syst.). In case of the fit with the fixed width, similarly, the peakcount is 183 ± 71(stat.) ± 10(syst.). The (c) of these figures show the dependences of thestatisticalstatistical significance is considered by the two expression
q significance where the
√
2σ
2σ
2σ
of Ns / Ns + Nb and Ns / ∆Ns as described in page 86. When the standard deviation of the distribution is considered as the error of the significance, the significances forthe fitting with the width as a parameter have been obtained to be 2.5±0.1 σ for the firstexpression and 2.0±0.2 σ for the second expression. For the fitting with the fixed width,
similarly, the significances have been obtained to be 2.7±0.1 σ and 2.5±0.1 σ, respectively.

4.2.3

Summary

The obtained results are summarized by following,+1.9
2
Mass : 1530.6+2.2−1.9 (stat.)−1.3 (syst.) MeV/c ,2
Width : 9.8+7.1−3.4 MeV/c .

The obtained mass is consistent with ones reported by several experiments whichclaimed the evidence of the Θ+ . The width is consistent with the experimental resolution.
This fact is also similar with other experiments. From the result of the fitting with thefixed width, the yield and the significance are
Yield : 183 ± 71(stat.) ± 10(syst.),Significance : 2.5 ∼ 2.7 σ.

The statistical significance is not sufficient to claim this bump as the evidence of the
However it is quite important to estimate the upper limit of the production crosssection of the Θ+ via the π − p → K − Θ+ reaction. Therefore we have obtained the upper
limit of the production cross section. To derive the upper limit, the peak count obtained
from the fitting with the fixed width is used at beam momentum of 1.92 GeV/c. We used asingle tail approach assuming that the peak count fluctuatesq based on Gaussian statistics.
22+ ∆Nsyst.
=274 at 90%
Then the upper limit of the peak count is Ns + 1.28 × ∆Nstat.
confidence level, where Ns denotes the peak count obtained from the fitting and ∆Nstat. ,∆Nsyst. denote the statistical and systematic errors respectively, and we use this count for
the following calculations.
Θ+ .

reduced χ 2

4.2. DISCUSSION ABOUT THE MISSING MASS SPECTRUM AT 1.92 GEV/C

0.8
0.75
0.7
0.65
0.6
0.55
0.5
0.45
0.4

91

(a)

2MeV/bin
3MeV/bin
4MeV/bin

1.44 1.445 1.45 1.455 1.46 1.465 1.47 1.475 1.48
Fit range

N
N

Figure 4.5: Study of the systematic error due to the difference of the fitting range andthe binning for the fitting with the width as a parameter. In all plots, the open cross,solid star and open star represent the results for the histogram with binning of 2 MeV/c2 ,3 MeV/c2 and 4 MeV/c2 , respectively. The x axis is the lower side of the fitting range.
(a) The χ2 distribution of the fitting with the Gaussian peak and polynomial backgroundfor each binning and fitting range. (b) Count of the peak distribution for each binningand fitting range. The error bars represent the statistical errors. The red line is themean value of the count which is 138.0 and the hatched region represents the standard
deviation of this distribution which is treated as the systematic error. (c) Dependence ofthe statistical significance.
The red points represent the significances calculated by the firstq
2σ
2σ
expression of Ns / Ns + Nb2σ . The blue points represent the significances calculated√by the second expression of Ns / ∆Ns . The mean values and the standard deviationsof these distributions are obtained to be 2.5±0.1σ and 2.0±0.2σ for the first and second
expressions, respectively.

CHAPTER 4. RESULTS

reduced χ 2

92

0.8
0.75
0.7
0.65
0.6
0.55
0.5
0.45
0.4

(a)

2MeV/bin
3MeV/bin
4MeV/bin

1.44 1.445 1.45 1.455 1.46 1.465 1.47 1.475 1.48
Fit range

N

Figure 4.6: Study of the systematic error due to the difference of the fitting range and thebinning for the fitting with the fixed width. In all plots, the open cross, solid star andopen star represent the results for the histogram with binning of 2 MeV/c2 , 3 MeV/c2
and 4 MeV/c2 , respectively. The x axis is the lower side of the fitting range. (a) The χ2
distribution of the fitting with the Gaussian peak and polynomial background for eachbinning and fitting range. (b) Count of the peak distribution for each binning and fitting
range. The error bars represent the statistical errors. The red line is the mean value ofthe count which is 182.5 and the hatched region represents the standard deviation of this
distribution which is treated as the systematic error. (c) Dependence of the statisticalsignificance.
The red points represent the significances calculated by the first expressionq2σ2σ
of Ns / Ns + Nb2σ . The blue points represent the significances calculated by the second√
expression of Ns / ∆Ns . The mean values and the standard deviations of these distributions are obtained to be 2.7±0.1σ and 2.5±0.2σ for the first and second expressions,
respectively.

4.3. THE UPPER LIMIT OF PRODUCTION CROSS SECTION OF THE π − P → K − X REACTION93

4.3

The upper limit of production cross section of the π − p →K −X reaction

In order to derive the upper limit of the cross section, we used the equation (3.13) as
described in Section 3.9. The efficiencies listed in Table 3.2 were used. Scattering angles
of outgoing particles at the laboratory system range from 0 degree to 20 degree and themean value of the scattering angle is 8.2 degree. The differential cross section in thelaboratory system is derived in this scattering angle range.

4.3.1

At beam momentum of 1.92GeV/c

For the derivation of the upper limit, the count of the peak obtained by the fitting withthe fixed width was used. The numbers of beam particles and protons in the target are
Nbeam = 7.40 × 109 and Ntarget = 8.6 × 1023 , respectively.
The upper limit of the differential cross section via the π − p → K − Θ+ reaction at thebeam momentum of 1.92 GeV/c has been obtained to bedσ< 2.9 µb/sr (90% confidence level)dΩLat 90% confidence level. Assuming that K − is produced isotropically in the center of mass
system, 10.4% of K − is accepted by the spectrometer. Therefore, if the K − is producedin the S-wave, the upper limit of the total cross section has been obtained to be
σ < 3.9 µb (90% confidence level)at 90% confidence level.

4.3.2

At beam momentum of 1.87GeV/c

We obtained the upper limit of the cross section from the 1.87 GeV/c data as well as 1.92
GeV/c data. Because we used two different targets, we derived the upper limit for eachtarget.
In the missing mass spectrum at 1.87 GeV/c, we could not find any obvious√peak
structure. We estimated that the signal from the Θ+ (NΘ+ ) is less than 1.28× N2σ
at 90 % confidence level, where N2σ represents the count in the missing mass spectrum
corresponding to ±2σ region from the peak position (1530.6 MeV/c2 ) obtained from 1.92
GeV/c data. We calculated that NΘ+ were 62 and 52 for the SCIFI target and thepolyethylene target, respectively.
SCIFI target
The numbers of beam particles and protons in the target are Nbeam = 2.88 × 109 andNtarget = 9.53 × 1023 , respectively. From the SCIFI target data, the upper limit of thedifferential cross section via π − p → K − Θ+ reaction at the beam momentum of 1.87 GeV/c
has been obtained to bedσ< 1.7 µb/sr (90% confidence level)dΩLat 90% confidence level. Assuming that the Θ+ is produced isotropically in the center ofmass system, the upper limit of the total cross section has been obtained to be
σ < 2.1 µb (90% confidence level)at 90% confidence level.

94

CHAPTER 4. RESULTS

Polyethylene target
The numbers of beam particles and protons in the target are Nbeam = 2.97 × 109 andNtarget = 8.56 × 1023 , respectively. From the polyethylene target data, the upper limit ofthe differential cross section at the beam momentum of 1.87 GeV/c has been obtained tobedσ< 1.6 µb/sr (90% confidence level)dΩLat 90% confidence level. The upper limit of the total cross section has been obtained tobeσ < 1.8 µb (90% confidence level)at 90% confidence level.

4.3.3

Summarydσ/dΩL (µb/sr)

σ (µb)The obtained upper limits of cross sections and differential cross sections are summarized
in Figure 4.7 as a function of beam momentum. At the beam momentum of 1.87 GeV/c,
the results from the two targets are consistent each other.

4.5
4
3.5
3
2.5
2
1.5
1
0.5
4.5
4
3.5
3
2.5
2
1.5
1
0.5
1.7

polyethylene target
SCIFI target

1.75 1.8

1.85 1.9 1.95 2 2.05 2.1
π- beam momentum (GeV/c)

Figure 4.7: Upper limits of the total and differential cross sections of the π − p → K − Θ+reaction. For the derivation of the total cross section, we assume that the Θ+ is produced
isotropically in the center of mass system. The differential cross section is derived in the
scattering angle from 0 to 20 degree at the laboratory frame.

4.3. THE UPPER LIMIT OF PRODUCTION CROSS SECTION OF THE π − P → K − X REACTION95

σ (µb)In the above discussion, we have derived the upper limit for the mass region of theobtained peak position (1530.6 MeV/c2 ). However, the mass of the Θ+ has not been
determined demonstrably, because there are some differences between the masses reported
by several collaborations which claim the evidence of the Θ+ . The significance for the peakobserved in the present experiment is insufficient as the evidence of the Θ+ . Therefore
we have derived the 90 % confidence level upper limits of the total and differential crosssections as a function of the mass of the Θ+ . Because the momentum of the outgoingK − is related to the mass of the Θ+ , the decay factor (fdecay ), the K − interaction factor(fK − int ) and the acceptance (dΩ) were obtained for each mass of the Θ+ . Figures 4.8 and4.9 show the obtained upper limits for the beam momenta of 1.87 GeV/c and 1.92 GeV/c.

4.5
4
3.5
3
2.5
2

Pπ-=1.87 GeV/c

90% C.L. upper limit

1.51dσ/dΩL (µb/sr)

0.5
3.5
3

90% C.L. upper limit

2.5
2
1.5
1
0.5
0

1.48

1.5

1.52

1.54

1.56

1.58
1.6
2
Mass (GeV/c )Figure 4.8: Upper limits of the total and differential cross sections of the π − p → K − Θ+reaction as a function of the mass of the Θ+ for the beam momentum of 1.87 GeV/c. Thisis the result obtained from the polyethylene target data.

CHAPTER 4. RESULTS

σ (µb)

96

4.5
4
3.5
3
2.5
2

Pπ-=1.92 GeV/c

90% C.L. upper limit

1.51dσ/dΩL (µb/sr)

0.5
3.5
3

90% C.L. upper limit

2.5
2
1.5
1
0.5
0

1.48

1.5

1.52

1.54

1.56

1.58
1.6
2
Mass (GeV/c )Figure 4.9: Upper limits of the total and differential cross sections of the π − p → K − Θ+reaction as a function of the mass of the Θ+ for the beam momentum of 1.92 GeV/c.

Chapter 5

Discussion
5.1

Comparison with theoretical calculations

Once the existence of the Θ+ is established, its production mechanism will become quite
important issue. Here we compare our experimental results with theoretical calculations.
The theoretical calculations of the production cross section via π − p → K − Θ+ reaction
have been done by W. Liu and C. M. Ko [57] and Y. Oh et al. [58]. They calculated
the production cross section taking into account the Feynman diagrams shown in Figure
1.12, where nucleon resonance or K 0∗ was exchanged. Unknown parameters such as thecoupling constant gK ∗ N Θ and the cut off parameter Λ of the form factor were used in theircalculations. In their calculation, they used the same form factor, which is a function of√s only,Λ2,(5.1)
F (s) = 2
Λ + q2iwhere Λ is the cut off parameter and qi is the three-momentum of the initial state particles
in the center of mass frame. They used the cut off parameter of Λ = 0.5 GeV basing on
fitting the measured cross section for the reaction πN → KΛ using similar hadronic
Lagrangians [63].
In Reference [57], Liu and Ko calculated the cross section taking into account only
the s-channel diagram. They used gKN Θ = 4.4, which corresponds to 20 MeV/c2 widthof the Θ+ . They predict that the cross section is about 50 µb. In their formalism, thecross section is controlled by the gKN Θ , because they took into account the only s-channel
diagram. The cross section is proportional to the width, since both the cross section and2
the width are proportional to gKN
Θ . If parameters other than gKN Θ are correct, thepresent experimental results mean that the width of the Θ+ is less than 1.6 MeV/c2 .
Y. Oh et al. calculated the cross section taking into account the s-channel diagram andt-channel diagram where the K ∗ is exchanged. They used gKN Θ =2.2, which corresponds
to 5 MeV/c2 width of the Θ+ , and the same cutoff value used by C. M. Ko et al.. Because
there is no information about gK ∗ N Θ , they used several values from −2.2 to 2.2 as gK ∗ N Θ .
They point out that the behavior of the cross section of the π − p → K − Θ+ reaction isquite dependent on the magnitude of gK ∗ N Θ as shown in Figure 5.1. The calculated crosssection ranges from about 2 µb to 190 µb. Therefore this reaction is suitable to give a
guide to estimate the magnitude of gK ∗ N Θ . Present results are quite smaller than most of
the theoretical calculations as shown in Figure 5.1. If the parameters other than gK ∗ N Θ
are correct, the calculations other than using gK ∗ N Θ = 2.2 are excluded by the present
results.
Currently, although we do not know the correct values of gKN Θ , gK ∗ N Θ and which kind97

98

CHAPTER 5. DISCUSSION

cross section σ (µb)

of form factor is realistic, the present results give a strong constraint to these unknown
parameters.

220

Theoretical calculation
by Y. Oh et al.

200
180

gK*NΘ=-2.2
gK*NΘ=-1.1
gK*NΘ=-0.5
gK*NΘ=0.0
gK*NΘ=0.5
gK*NΘ=1.1
gK*NΘ=2.2

160
140
120
100
80
60
40
20
0
1.6

1.8

2
2.2
2.4
2.6
2.8
π- beam momentum (GeV/c)

Figure 5.1: Comparison with the experimental 90% C.L. upper limits of the production
cross section of π − p → K − Θ+ reaction and theoretical calculations by Y. Oh et al. [58].
They calculated the total cross section for J P = 1/2+ using gKN Θ =2.2 and several values
as gK ∗ N Θ from −2.2 to 2.2.

5.2. RELATION BETWEEN THE CROSS SECTIONS VIA π − AND K + INDUCED REACTIONS99

Figure 5.2: Feynman diagram for the three-body decay of the N ∗ resonance and Feynman
diagrams with two-meson coupling for the π − and K + induced reactions for the Θ+
production. In the calculation by T. Hyodo and A. Hosaka [74], the coupling constants ofΘKπN are estimated from that of N ∗ ππN calculated from the decay width of N ∗ → N ππ.

5.2

Relation between the cross sections via π − and K + induced reactions

A theoretical study of production mechanism via hadronic reactions has been done by T.
Hyodo and A. Hosaka [74]. Figure 5.3 shows the obtained upper limit of the cross section
for each π − beam momentum together with their theoretical calculations. They took
particular note of the importance of two meson coupling and calculated the total crosssections of the reaction π − p → K − Θ+ and K + p → π + Θ+ in case of J P = 1/2+ and 3/2−
taking into account Feynman diagrams shown in Figure 5.2. They obtained the scalarand vector coupling constants of ΘKπN , gs and gv , using the flavor SU(3) symmetry
from the decay width of N ∗ (1710) → ππN . Without the two meson coupling, all theamplitudes for the Θ+ production are proportional to the gKN Θ coupling, which is fixedby the small decay width of the Θ+ as was done in the calculation by W. Liu and C.M.
Ko. However, even with the extremely narrow width of the Θ+ , sizable cross section canbe obtained with the two meson coupling determined from the decay width of N ∗ (1710).
The obtained coupling constants have uncertainty due to the experimental uncertainties
of the branching ratio. They restricted the coupling constants to be consistent with ourpresent results for the dotted, dot-dashed and dashed lines in Figure 4.7. Moreover the
relative phase between scalar and vector coupling constants could not be determined by the
information of decay width of N ∗ (1710). This relative phase is quite important because it
affects the interference term of two amplitudes. If gs and gv have the same phase, the two
amplitudes interfere constructively for π − p → K − Θ+ channel, while in K + p → π + Θ+ caseit shows the destructive interference. On the other hand, if gs and gv do not have the same
phase, the constructive and destructive interference appears in opposite way. Considering
the small cross section obtained in the present experiment, they selected the latter case.
Therefore the behavior near the threshold in this calculation is different from that by Y.
Oh et al. due to the destructive interference between scalar and vector amplitudes.
The ratio of cross sections of π − and K + induced reactions can be calculated morereliably than the absolute value of the cross section, because there is uncertainty due toselection of a form factor in the derivation of the absolute value. By using the coupling
constant which explains the present data, they find that the ratio is very different forcross section σ (µb)

100

CHAPTER 5. DISCUSSION

70
60
50

Theoretical calculation
by T. Hyodo et al.
v

JP=1/2+ gs=1.37, g =-0.23v
JP=1/2+ gs=1.80, g =-0.31v
JP=3/2- gs=0.104, g =-0.209v
P- s
J =3/2 g =0.22, g =-0.44

40
30
20
10
0
1.6

1.8

2
2.2
2.4
2.6
2.8
π- beam momentum (GeV/c)

Figure 5.3: The upper limits of the production cross section of π − p → K − Θ+ reaction atbeam momenta of 1.87 and 1.92GeV/c. The theoretical calculations by T. Hyodo and A.
Hosaka [74] are also shown together. They calculated the total cross section for J P = 1/2+
and 3/2− using scalar and vector meson coupling constants, gs and gv , respectively. The
dot-dashed and dashed lines are calculations for J P = 1/2+ with (gs , gv ) = (1.37, −0.23)
and (1.80, −0.31) respectively. The dotted and solid lines are calculations for J P = 3/2−
with (gs , gv ) = (0.104, −0.209) and (0.22, −0.44) respectively.

two J P assignments. In the case of J P = 1/2+ the ratio of the cross section, σ(K + p →π + Θ+ )/σ(π − p → K − Θ+ ), is ∼ 50, while in the case of J P = 3/2− it is ∼ 3.3. Anexperiment to search for the Θ+ via K + p → π + Θ+ has been performed at the K6 beamline with high statistics and good missing mass resolution using the SKS spectrometer at
KEK (KEK-PS E559) (see Appendix B for the detailed description). One of the most5.2. RELATION BETWEEN THE CROSS SECTIONS VIA π − AND K + INDUCED REACTIONS101
important purposes is the determination of the width utilizing the spectrometer systemwith the excellent missing mass resolution of 2.4 MeV/c2 (FWHM), if we observe the Θ+ .
In this experiment, about 25,000 events for the K + p → π + X reaction have been collected.
The expected sensitivity is less than 10 µb. This experiment together with the present
results will provide deeper understanding on the existence of the Θ+ .

Chapter 6

Conclusion
Since the report on the evidence of the exotic baryon Θ+ , many studies from both theoretical and experimental aspects have been conducted. The Θ+ is predicted by Diakonov
et al. using chiral soliton model and is considered to be manifestly exotic baryon which
has unusual quark contents of uudds̄. The observation at SPring-8/LEPS was immediately confirmed by several experiments. Recently, however, null results have been reported
from several high-energy experiments where investigators searched for the Θ+ using higher
statistics. In such a situation, the confirmation of the existence (or non-existence) of the
Θ+ is urgent and crucially important. Therefore high statistics experiments at low energy
region with hadronic reaction become crucial.
The present experiment has been carried out to search for the Θ+ via π − p → K − X
reaction at the K2 beam line of the KEK Proton Synchrotron (KEK-PS E522). We used
π − beams of 1.87 and 1.92 GeV/c. A SCIFI target was exposed to 2.9 × 109 π − ’s with
momentum of 1.87 GeV/c. For the search for the Θ+ , a polyethylene target was mainly
used to enhance the contribution from free protons and was exposed to 3.0 × 109 π − ’s of
1.87 GeV/c and 7.4 × 109 π − ’s of 1.92 GeV/c. The analysis was done carefully paying
attention to the resolution of the spectrometer, since the Θ+ is expected to be narrow.
The missing mass resolution for the Θ+ is estimated to be 13.4 MeV/c2 (FWHM) from
the Monte Carlo simulation. The cut positions to select good (π − , K − ) events were also
determined by clear criteria. In the missing mass of the π − p → K − X reaction at 1.87
GeV/c, any structure corresponding to the Θ+ has not been observed. In the missing mass
at 1.92 GeV/c, a bump with a width consistent with the experimental resolution has been
+1.9
2
found at the mass of M = 1530.6+2.2−1.9 (stat.)−1.3 (syst.) MeV/c . However the statisticalsignificance of the bump is only 2.5∼2.7σ which is not sufficient to claim the evidence ofthe Θ+ . Therefore we have derived the upper limit of the production cross section via
π − p → K − Θ+ reaction. The upper limit of the differential cross sections for the scattering
angle from 0 degree to 20 degree at the laboratory frame have been obtained to be 1.6µb/sr and 2.9 µb/sr at the 90 % confidence level at the beam momenta of 1.87 and 1.92
GeV/c, respectively. The upper limits of the total cross sections have been obtained to be
1.8 µb and 3.9 µb at 1.87 and 1.92 GeV/c, respectively, assuming that the Θ+ is produced
isotropically in the center of mass system.
The obtained upper limits are quite smaller than the theoretical calculations and givea strong constraint to the unknown parameters such as the coupling constant gK ∗ N Θ usedin the calculations. Using the present results, the cross section of the K + p → π + Θ+reaction has been studied by T. Hyodo and A. Hosaka. They find that the ratio of thecross sections of π − and K + induced reactions are quite different for two J P assignmentsof the Θ+ . In the case of J P = 1/2+ , σ(K + p → π + Θ+ )/σ(π − p → K − Θ+ ) is ∼50, whilein the case of J P = 3/2− it is ∼3.3. An experiment to search for the Θ+ via K + p → π + X
102

103
reaction has been performed at KEK. This experiment together with the present results
will provide deeper understanding on the existence of the Θ+ .

Acknowledgments
During my research at graduate school, fortunately I have been given chances to joinmany experiments; LEPS, KEK-PS E325, E509, E518, E521, E522, E559, E566. These
were quite invaluable opportunity not only to learn various experiences for experiments
but also to be acquainted with many people. I have spent a long time with them andbeen supported by them with their collaboration, advice and encouragement. I deeply
appreciate kindness and warm advice of all who have helped me until completion of thisthesis work.
First of all, I would like to express my sincere gratitude to Prof. Ken’ichi Imai, who
has been my supervisor. He guided me to an exciting world of the experimental hadronic
and nuclear physics. He gave me so many chances to join experiments which are myirreplaceable asset. He always encouraged me with his warm advice and vivid sense forphysics when I had a trouble in the experiment and data analysis. I have also learned
from him about attitudes to the physical research as a physicist.
I have spent my graduate school days as a member of the ”Experimental Nuclear andHadronic Physics (NH)” group in Kyoto University. I would like to acknowledge Prof.
Naohito Saito for his advice and encouragement. I am very impressed by his leadershipnot only to physics discussion but also to the management of our laboratory. It is mygreat pleasure to complete my thesis work before his movement to the KEK. I would liketo express my thanks to Prof. Haruhiko Funahashi for his guidance from early days when
I was the fourth grade of the undergraduate school. I wish to acknowledge the help andencouragement by Prof. Harutaka Sakaguchi, Prof. Masanobu Nakamura, Prof. Masaru
Yosoi and Dr. Tetsuya Murakami and all members of NH group. The NH group has beena hospitable place for me.
I have joined two experiment to search for the Θ+ , KEK-PS E522 and E559, during
my doctoral course. I would address my thanks to all the members of KEK-PS E522 andE559 collaboration. I could not complete this thesis work without their great effort. I
would like to express great thanks to Prof. Jung-Keun Ahn and Mr. Choong-Jae Yoon.
The E522 experiment was impossible without their great effort of design and preparationof the experiment. I am grateful to Mr. Yoon for his contribution for setting up andmanagement of the experiment. I am also grateful to Prof. Ahn for useful discussion on
the analysis. I wish to thank to Dr. Hitoshi Takahashi for his kindness during my longstay at KEK. I learned from him many things about experimental and analysis technique.
He also brought me to the restaurant out side of KEK at every week end, which released
my stress and anxiety caused by the long preparation and long beamtime. I would liketo express my thanks to Prof. Kazuma Nakazawa for his continuous collaboration forboth experiments. He came to the experimental area as much as possible and encouraged
me during the long beam time. I would like to express my thanks to Dr. Kazuhiro
Yamamoto for his contribution at the early stage of the experiment. The starting up of
the experiment was going well thanks to his experiences on the (K − , K + ) reaction. I wish
to thank Mr. Tomokatsu Hayakawa for his great contributions for the set up and analysis
104

105
of the experiment.
I would express my gratitude to Prof. Shin’ya Sawada and Prof. Toshiyuki Takahashi
for supports for the designing and managing the E559 experiment. Prof. Sawada always
relaxed and encouraged me and other graduate students. Prof. Takahashi is one of thespecialist of the experiment at SKS and I learned many things from his experience on theexperiment from both aspects of the hard ware and soft ware. I wish to thank to Mr.
Masahi Hayata, Mr. Seishi Dairaku and Mr. Daisuke Nakajima for their great efforts
to the design and operation of the range counter, large acceptance chamber and liquidhydrogen target, respectively. I would express my gratitude to Prof. Tomofumi Nagae,
who is the leader of the SKS group, for his helps and suggestions based on his experiencesof the experiment at SKS. I am grateful to Dr. Shigeru Ishimoto and Dr. Shoji Suzuki.
They made great efforts to construct the liquid hydrogen target system and operate it
quite stably. I would wish to thank to Dr. Tomofumi Maruta and Mr. Hiroyuki Fujioka
for their sizable contributions during not only the experimental shift time but also the
preparation and analysis periods. I would wish to thank to Dr. Michiko Sekimoto forexperimental supports at the test experiment and the E559 experiment. I would like tothank to Dr. Shuhei Ajimura, who is the specialist of the trigger system of SKS, for help
to make the (K + , π + ) trigger.
I cordially thank the beam channel group for their support to provide beam with theexcellent condition during both experiments. Especially I thank Prof. Masaharu Ieiri for
his effort for the maintenance of the electrostatic separator. I am also thankful to Prof.
Hiroyuki Noumi, Dr. Yoshinori Sato and Dr. Akihisa Toyoda for their great efforts toprovide K + beams with good condition. They re-tuned the beam condition whenever I
asked them.
I would like to express my gratitude to Prof. Hirokazu Tamura, who is the leader ofHyperball group. He gave me a chance to join E509 experiment and write the results as
my master thesis. After the E509 experiments, he gave me many opportunities to join his
experiments and he and his students also helped my experiments. I am sincerely gratefulto Dr. Kiyoshi Tanida, who was also supervisor when I was a master student. I am very
impressed by his vivid sense for physics and his kindness for collaborators. I would like tothank to Dr. Mifuyu Ukai for her encouragements. I would like to thank to Dr. Yusuke
Miura for his great support at many experiments I joined.
I would like to express my gratitude to Prof. Takashi Nakano and Prof. Kenneth H.
Hicks, who triggered experimental search for Θ+ at many collaborations. Discussion withthem gave me many motivations for my analysis and was quite useful for me. I would liketo express my thanks to Prof. Atsushi Hosaka and Dr. Tetsuo Hyodo for their theoretical
calculation.
I would address my thanks to all the members of KEK-PS E522 and E559 collaboration,
Dr. Hiroki Sato. Mr. Yoshinori Fukao, Ms Hiromi Okada, Mr. Kazuya Aoki, Mr. Kaoru
Taketani, Mr. Kohei Shoji, Mr. Tetsuya Hibi, Mr Haruyuki Nishikawa, Mr. S.J. Kim, Mr.
B.H. Choi, Mr. Tomohiro Kameyama, Dr. Takaomi Watanabe, Dr. Megumi Naruki, Dr.
Hisako Fujimura, Mr. Yoshichika Seki, Mr. Satoru Kamigaito, Mr. Katsuyuki Senzaka,
Mr. R. Zavislak, Prof. Tomokazu Fukuda, Ms. Sari Kinoshita, Dr. Takeshi Koike, Mr.
Yue Ma, Mr. Koutaro Shirotori, Prof. Jacques Arvieux and Mr. Tomonori Takahashi.
During my master course, I joined experiments at SPring-8/LEPS. I would address
my thanks to all members of LEPS collaboration. Especially I would like to thanks Dr.
Takatsugu Ishikawa, Mr. Manabu Miyabe and Mr. Masayuki Niiyama. They taught mequite many things about experimental technique through the experiment at LEPS andconstruction of TPC, analysis procedure from very elementary points, when I was in first
grade of my master course.

106

CHAPTER 6. CONCLUSION

I would like to thank members of NH group in the same grade, Mr. Yoshinori Fukao,
Mr. Terunao Nakura, Ms. Hiromi Okada, Mr. Shinsuke Ota, Mr. Satoru Terashima, Mr.
Manabu Togawa for their friendships and encouragements. Talk and discussion with themmake my graduate school days fruitful and enjoyable.
Finally, I would address my heartfelt thanks to my parents, Mr. Norio Miwa and
Ms. Chizuko Miwa and my brother, Dr. Yohei Miwa. They have supported me not only
financially but also mentally with their warm encouragement. I could not finish this thesis
work without their continuous support, patience and encouragement.

Appendix A

Scintillating Fiber Target System
A.1

Scintillating Fiber Block

The SCIFI block consisted of 300 µm × 300 µm square plastic scintillating fibers (KURARAY SCSF-78). The core of the fiber was 288 µm × 300 µm and its material waspolystyrene ((CH)n ). The refractive index of the core was 1.59 and the density was 1.03
g/cm3 . The cladding was made of polymethylmethacrelate (PMMA, C5 H8 O2 ) with refractive index of 1.49 and density of 1.19 g/cm3 . The wave length of transmitted light was
peaked at 450 nm. All fibers were coated with white paint as an extra mural absorber(EMA). The attenuation length of SCSF-78 (300 µm square) was 114 cm. The attenuation length was defined as the longer decay constant obtained with the two components
exponential fitting. The length of the fibers which used for the SCIFI target was about
30 cm, and the effective volume of the target corresponded to from 0 cm to 10 cm.

A.2

Image-intensifier tubes and CCD camera

Figure A.1: Schematic drawing of the structure of IIT chain for SCIFI target system.
The first and second stages were electrostatic-type image intensifier tubes. The firststage (HAMAMATTSU V4440PX) had a large input window (100 m φ) which was madeof glass fibers. The quantum efficiency of photo-cathode was 19 %. The applied anode
107

108

APPENDIX A. SCINTILLATING FIBER TARGET SYSTEM

voltage of the first IIT was 20 kV. The phosphor of the first IIT was PS-5 whose decay time
was measured to be 1.3 µs. The diameter of the fiber-optic output window was 25 mm φ,i.e. the image was demagnified by a factor of four with the electrostatic lens system.
The second IIT (DEP PP0030X) was used in order to obtain sufficient number ofphotons before a micro-channel plate (MCP) in the next stage. The diameters of both
input and output fiber-optic windows were 25 mm φ. The phosphor of 300 ns decay time(P46) was used for second IIT.
The third and fourth stages were MCP type image intensifiers (PROXITRONIC BV2563
QG). The diameters of the input and output windows were 25 mm φ. These IITs were
gatable. The first-level trigger opened these gates for 2 µs to cover the decay time of thefirst phosphor of 1.3 µs. The decay time of the phosphor (P20) for the these IITs were 20µs, whereas the decision time of the second-level trigger was about 14 µs.
The image amplified by four IITs was digitalized by CCD camera (Kodac MEGAPLUS
Camera ES310). The CCD camera consisted of 648 × 484 pixels where the size of eachpixel was 9 µm × 9 µm. The readout of the charge on the CCD was started by the external
trigger. The digital data were compressed from 8 bit to 4 bit using the real time image
processing module (Imaging Techmology Coop. MVC 150/40).

A.3

Correction of distorted image

Images are distorted mainly due to the pin-hole distortion caused by the electro-static
lenses of IITs. The distortion can be expressed as,
X′
Y′

!

= (a0 + a1 r + a2 r 3 + a3 r 5 + · · ·)

X
Y

!

,

′
′
where (X,
√ Y ) and (X , Y ) represent original coordinates and distorted ones, respectively,
22
and r is X + Y . The coefficients ai are correction parameters. Since SCIFI target were
installed very close to the spectrometer, their images were also distorted by the magnetic
field (about 0.01 or 0.02 T), although we minimized the distortion by covering each IIT
chain with a double magnetic shield made of iron and µ-metal. Therefore, the pin-holedistortions as well as the effect due to the remaining magnetic field were corrected withfollowing expression,(

X ′ = b0 + b1 X + b2 Y + b3 X 2 + b4 XY + b5 Y 2 + b6 X 3 + b7 X 2 Y + b8 XY 2 + b9 Y 3
Y ′ = c0 + c1 X + c2 Y + c3 X 2 + c4 XY + c5 Y 2 + c6 X 3 + c7 X 2 Y + c8 XY 2 + c9 Y 3

The correction parameters, bi and ci , were determined using the images of a plate witha grid-pattern LED. Figure A.2 (a) shows the grid image viewed by left-sided IIT and
Figure A.2 (b) shows that after the correction using above equation. After this correction
image reconstruction was performed.

A.3. CORRECTION OF DISTORTED IMAGE

109

pixel

(a) Before correction
450
400
350
300
250
200
150
100
50
100

150

200

250

300

-20

0

350

400

450

500
pixel

mm

(b) After correction
40
30
20
10
0
-10
-20
-30
-40
-80

-60

-40

20

40

60

80
mm

Figure A.2: The grid image viewed by the left-sided IIT (a) before and (b) after thecorrection.

Appendix B

KEK-PS E559 experiment– Search for the Θ+ baryon via K +p → π + X reaction –After the E522 experiment, we proposed an experiment to search for the Θ+ via K + p →π + X reaction to give a conclusive information on the existence of the Θ+ . Although
theoretical prediction expected large production cross section in this reaction (more thanseveral ten µb), the experiment was designed to have sensitivity until small production
cross section (about 10 µb) because the cross section is also expected to be small considering the small cross section via π − p → K − Θ+ reaction.
We have performed the E559 experiment to search for the Θ+ via the K + induced
reaction at the K6 beam line with high statistics and good missing mass resolution using
SKS spectrometer at KEK 12 GeV Proton Synchrotron (KEK-PS E559). The experimental periods were about one month from June 2005 and two weeks from December 2005.
We used K + beams of 1.2 GeV/c and total 6.1 × 109 kaons were irradiated. By using
K + beams including s̄ quark, the strangeness of the reconstructed system by the missing mass of the K + p → π + X reaction was a priori known to be positive. Naively the
production cross section via K + p → π + Θ+ reaction is expected to be larger than thatvia π − p → K − Θ+ reaction, because K + beams already include s̄ quark. Therefore thehigh statistics search is expected to be possible. One of the most important purpose is
the determination of the width of the Θ+ by utilizing spectrometer system, SKS and K6
beam line, with the excellent missing mass resolution of 2.4 MeV/c2 (FWHM). Therefore
this experiment will give the information to understand the narrow width and give theinsight about non-perturbative QCD, if we observe the Θ+ . Figure B.1 shows the experimental setup of the E559 experiment. As a target, a new liquid hydrogen target system
was constructed for both this experiment and future experiments at J-PARC [75]. The
thickness of the liquid hydrogen target was 12.5 cm. The momentum of each beam particle
was analyzed using the K6 beam line spectrometer of which resolution is expected to be∆p/p=0.047% (FWHM). Scattered particles were detected using SKS spectrometer.
The background of the measurement is divided into two parts. One is the physicalbackground such as ∆ and K ∗ production. Another background is the 3 body decayof K + such as K + → π + π + π − or K + → π + π 0 π 0 . The latter background was quite
severe and the rejection of these decay backgrounds was essential for the Θ+ search. In
decay events, one or three charged particles were emitted to a forward angle, whereas ina hadronic reaction such as ∆ production or Θ+ production, two charged particles were
emitted with a large scattering angle. Therefore we installed a large acceptance chamber
just downstream of the target to detect the charged particles [76]. We selected two charged
particle events to reject decay events in offline analysis. To improve S/N ratio by detecting
K + from the decay of Θ+ , we also installed a range counter system at the downstream of
110

111
this chamber [77].
Let us now describe the present analysis status of the (K + , π + ) data. The momentum
analyses of incident and outgoing particles are done well, since the Σ+ is clearly reconstructed with almost expected resolution using the π + p → K + X reaction taken for thecalibration as shown in Figure B.2. The vertex distribution after the rejection of decay
events is shown in Figure B.3 together with the distribution of the empty target data
(blue-hatched histogram). The 12.5 cm liquid hydrogen image is clearly observed. We
took approximately 15,000 and 10,000 events of K + p → π + X reaction in the first andsecond run, respectively. However, there are still background events which is shown in thehatched histogram. These events might be the contaminations of the K + decay eventsand reaction events at the timing counter upstream of the target (BH2). We will compare
the vertex distribution attributed to these background events with a simulation in futurestudies.
The analysis of the K + p → π + X reaction is still preliminary and the analysis of themissing mass is in progress.

Figure B.1: Experimental setup of the KEK-PS E559. As a target, a liquid hydrogen target was used. The shape of the container was a cylinder, of which length was 12.5 cm anddiameter was 6.8 cm. Beam line spectrometer consisted of 4 drift chambers (BDC1,2,3,4)
and trigger counters (BH1,2 and BAC) located upstream and downstream of QQDQQ
magnet system. The SKS spectrometer consisted of 4 drift chambers (SDC1,2,3,4) andtrigger counters (TOF, LC). The magnetic field of the SKS was set to 1.6 T which wascorresponding to the central momentum of 0.55 GeV/c. In order to suppress the background due to the decay of K + beams and improve S/N ratio by detecting K + , a large
acceptance chamber and a range counter system were installed after the target to detect
the charged particles.

APPENDIX B. KEK-PS E559 EXPERIMENTCounts/0.4MeV/c 2

112

180
160
140

Σ+

120

M = 1189.39 ± 0.03 MeV/c
Γ = 1.92 ± 0.07 MeV/c

100

2

2

80
60
40
20
0
1.18

1.185

1.19

1.195
1.2
2
Mass(GeV/c )CountsFigure B.2: Missing mass spectrum of the π + p → K + X reaction. The peak corresponding to Σ+ was clearly observed with the expected experimental resolution of 1.92±0.07
MeV/c2 .

1200
1000

LH2 Target
Empty Target
Subtraction

800
600
400
200
0
-500 -400 -300 -200 -1000

100 200 300 400 500z(mm)Figure B.3: Vertex distribution of K + p → π + X reaction obtained from first run. The
blue hatched histogram represents the background event estimated from the empty target
data. The red hatched histogram shows the net contribution of K + p interaction events.

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