Search for the pentaquark Θ+
via the π −p → K −X reaction at J-PARC

U

ND

JAPAN

97

T

KY O
FO

KYOTO

ITY
RS

O

UNI VE

8
1
ED

Manabu Moritsu
Department of Physics, Kyoto University
A dissertation submitted in partial fulﬁllment of
the requirements for the degree of Doctor of Science

November, 2014

Abstract
A pentaquark Θ+ (1540) is a genuine exotic hadron with its minimal quark conﬁgurationof uudds̄. A search for the Θ+ pentaquark via the π − p → K − X reaction was performed
at J-PARC using a beam momentum of 2.01 GeV/c. A liquid hydrogen target witha thickness of 0.85 g/cm2 was exposed to 8.1 × 1010 beam pions. The missing-mass
spectrum of the π − p → K − X reaction was obtained with a mass resolution of 2.13 MeV(FWHM). The spectrum has no distinct structure and no clear peak was observed. The
upper limit on the production cross section averaged over scattering angles from 2◦ to
15◦ in the laboratory frame was found to be less than 0.28 µb/sr at the 90% conﬁdence
level in a mass region of 1500-1560 MeV/c2 . It is on the same level as the previous dataobtained at an incident momentum of 1.92 GeV/c. The systematic uncertainty of theupper limit was controlled within 10%.
The cross section of the π − p → K − Θ+ reaction is related to the Θ+ decay width on
the basis of the reaction mechanism. Combining with the previous data together witha theoretical calculation using the eﬀective Lagrangian approach, we evaluated the Θ+
decay width. The upper limits on the Θ+ width were estimated to be 0.36 and 1.9 MeV
in a possible Θ+ mass region for the Θ+ spin-parity of 1/2+ and 1/2− , respectively. The
upper limits of the width were improved by half of the previous limits. The upper limit of
the width for the 1/2+ case is more stringent than the upper limit of 0.64 MeV reportedby the Belle Collaboration. It is comparable to the width of 0.34 ± 0.10 MeV reportedby the DIANA Collaboration. The consistency is subtle but the present result does notcompletely exclude the DIANA result.

Contents
1 Introduction
1.1 Pentaquark Θ+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Width of Θ+ from K + d scattering data . . . . . . . . . . . . . . . . . . .
1.3 Theoretical works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4 Experimental review . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4.1 Low-energy photoproduction experiments . . . . . . . . . . . . . .
1.4.2 Formation experiments . . . . . . . . . . . . . . . . . . . . . . . .
1.4.3 Experiments using high-energy beams . . . . . . . . . . . . . . . .
1.4.4 Low-energy hadron-induced experiments . . . . . . . . . . . . . .
1.4.5 Isospin of Θ+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4.6 Other pentaquarks . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4.7 Summary of experimental results . . . . . . . . . . . . . . . . . .
1.5 Θ+ production via meson-induced reactions . . . . . . . . . . . . . . . .
1.6 Present experiment: J-PARC E19 . . . . . . . . . . . . . . . . . . . . . .

1
1
2
3
6
7
9
10
14
15
16
17
18
20

2 Experimental Apparatus
2.1 J-PARC and hadron experimental facility . . . . . . . . . . . . . . . . . .
2.2 K1.8 beam line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Beam spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.1 Tracking chambers for the beam spectrometer . . . . . . . . . . .
2.3.2 Trigger counters for the beam spectrometer . . . . . . . . . . . .
2.4 Superconducting Kaon Spectrometer . . . . . . . . . . . . . . . . . . . .
2.4.1 Tracking chambers for the SKS . . . . . . . . . . . . . . . . . . .
2.4.2 Trigger counters for the SKS . . . . . . . . . . . . . . . . . . . . .
2.5 Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.6 Data-acquisition system . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.7 Liquid hydrogen target . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.8 Data summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

23
23
25
27
29
31
34
35
36
39
40
43
44

3 Data Analysis
3.1 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Analysis of beam particles . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Beam particle identiﬁcation . . . . . . . . . . . . . . . . . . . . .
3.2.2 Beam track reconstruction . . . . . . . . . . . . . . . . . . . . . .
3.3 Analysis of scattered particles . . . . . . . . . . . . . . . . . . . . . . . .

45
45
46
46
46
50

iii

iv

CONTENTS
3.3.1 Scattered-particle track reconstruction . . . . . . . . . . . . . . .
3.3.2 Scattered-particle identiﬁcation . . . . . . . . . . . . . . . . . . .
Scattering angle and vertex reconstruction . . . . . . . . . . . . . . . . .
Calibration data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Momentum calibration and missing mass scale uncertainty . . . . . . . .
3.6.1 Energy loss correction . . . . . . . . . . . . . . . . . . . . . . . .
3.6.2 Momentum correction in SKS . . . . . . . . . . . . . . . . . . . .
3.6.3 Momentum calibration . . . . . . . . . . . . . . . . . . . . . . . .
3.6.4 Missing mass scale uncertainty . . . . . . . . . . . . . . . . . . . .
Momentum and missing mass resolution . . . . . . . . . . . . . . . . . .
3.7.1 Energy loss straggling . . . . . . . . . . . . . . . . . . . . . . . .
3.7.2 Scattering angle resolution . . . . . . . . . . . . . . . . . . . . . .
3.7.3 Momentum resolution . . . . . . . . . . . . . . . . . . . . . . . .
3.7.4 Missing mass resolution . . . . . . . . . . . . . . . . . . . . . . .
Cross section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.8.1 Eﬃciency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.8.2 Acceptance of SKS . . . . . . . . . . . . . . . . . . . . . . . . . .
3.8.3 Systematic uncertainty . . . . . . . . . . . . . . . . . . . . . . . .
Σ production cross section . . . . . . . . . . . . . . . . . . . . . . . . . .

50
51
56
59
61
61
61
63
66
67
68
68
70
70
71
71
78
80
81

4 Results
4.1 Missing mass spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Background processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 Upper limit of production cross section . . . . . . . . . . . . . . . . . . .

84
84
85
87

3.4
3.5
3.6

3.7

3.8

3.9

5 Discussion
94
5.1 Upper limit of the Θ+ width . . . . . . . . . . . . . . . . . . . . . . . . . 94
5.1.1 Theoretical calculation . . . . . . . . . . . . . . . . . . . . . . . . 94
5.1.2 Upper limit estimation . . . . . . . . . . . . . . . . . . . . . . . . 97
5.1.3 Discussion on the present upper limit . . . . . . . . . . . . . . . . 103
6 Conclusion

104

A AC eﬃciency

107

B Miscellaneous vertex analyses
109
B.1 Z-vertex resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
B.2 X-vertex resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
B.3 Vertex distribution diﬀerence between (π − , K − ) and (π − , π − ) events . . . 111
C Stability of magnetic ﬁeld
113
C.1 Field of the beam spectrometer . . . . . . . . . . . . . . . . . . . . . . . 113
C.2 Field of the SKS spectrometer . . . . . . . . . . . . . . . . . . . . . . . . 114
D Summary of Σ production cross section

115

E Additional study of background processes

118

Chapter 1
Introduction
1.1

Pentaquark Θ+

The strong interaction is described by quantum chromodynamics (QCD) as the fundamental theory. It has been tested quantitatively in hundreds of experiments at highmomentum transfer, where asymptotic freedom justiﬁes the use of perturbation theory.
Hadrons are clearly bound states of quarks held together by gluon-mediated interactions. However, we still fail to put our hands on a quantitative and predictive theory of
conﬁned states of quarks and gluons. Hadron spectroscopy is a laboratory in which ourunderstanding of the low-energy dynamics of quarks and gluons is tested.
The concept of “quark” as a fundamental particle was advocated just 50 years ago[1]. Since then, the constituent quark model is very successful in classiﬁcation of lightbaryons and mesons consisting of u, d, and s quarks. Mesons are assigned to quarkantiquark pairs (q q̄), and baryons are assigned to three-quark conﬁgurations (qqq). In
particular, the lowest baryon conﬁguration gives two irreducible representations of the
ﬂavor SU(3) symmetry: spin-1/2 octet 8 and spin-3/2 decuplet 10. It is reminded thatthe constituent quark model is a phenomenological model and not derived from the ﬁrst
principle of QCD; therefore, the existence of exotic states beyond its classiﬁcation is notprecluded. QCD requires only that hadrons are formed in color singlet and does not
limit the number of quarks. Multiquark hadrons, interpreted as the conﬁgurations ofmore than three quarks, e.g., “tetraquark (qq q̄ q̄)”, “pentaquark (qqqq q̄)”, and “dibaryon(qqqqqq)”, have been discussed ever since the appearance of the quark model [2, 3, 4, 5].
In the past decade, many charmonium-like and bottomonium-like resonances, so
called X, Y , and Z, have been observed in the B-factories and many other experiments[6]. They are diﬃcult to ﬁt in the conventional quark model, and thus are considered as
candidates of exotic hadrons, such as tetraquarks, meson molecules, and hybrid states.
Since most of these states are experimentally established, there is no doubt that exotics
do exist at least in the heavy ﬂavor sector.
Pentaquarks are deﬁned as particles with a valence structure of four quarks and one
antiquark. In a naive sense, since a pentaquark decays into a three-quark baryon anda quark-antiquark meson, it was expected to have a wide width [2, 5]; this would makethe experimental observation diﬃcult. After decades, however, a possible existence of apentaquark with a narrow width was suggested by Diakonov, Petrov, and Polyakov in1

2

CHAPTER 1. INTRODUCTION

1997 [7]. They predicted an exotic positive-strangeness baryon, later called Θ+ , having
spin-parity 1/2+ and isospin 0, with a light mass of about 1530 MeV/c2 and a widthof less than 15 MeV. The narrow width is a great advantage for experiments to detectthe Θ+ with a good signal-to-noise ratio. The Θ+ has a strangeness quantum number
S = +1 with its minimal quark conﬁguration of uudds̄; hence, it is manifestly exotic.
The problem whether the pentaquark with such a light mass and a narrow width reallyexists (or not) could be a good testbed for the current understanding of hadron physics.
The ﬁrst experimental evidence of the Θ+ was reported in 2003 by the LEPS Collaboration [8]. A sharp resonance decaying into K + n was observed in the γn → K + K − nreaction on 12 C at a mass of 1540 ± 10 MeV/c2 with a width smaller than 25 MeV.
The resonance has a strangeness +1 and its mass and width are consistent with theΘ+ predicted by Diakonov et al. Soon after the ﬁrst evidence was presented, several
experimental groups published supporting evidence for the Θ+ . The Θ+ has received
enthusiastic attention and numerous papers have been published [9, 10]. In a conference in 2003, Wilczek noted “Although the discoveries are striking, I don’t think they
are so peculiar as to require introducing new interaction or modifying QCD. . . On theother hand these discoveries do oﬀer us a golden opportunity to sharpen and expand ourunderstanding of QCD itself ” [11]. However, the evidences were followed by a numberof experiments with no evidence and the experimental situation became controversial.
In this thesis, a search for the Θ+ pentaquark via the π − p → K − X reaction conducted at J-PARC is presented. In the subsequent sections, a discussion about the Θ+
width based on K + d scattering data is given in Sec. 1.2, followed by theoretical andexperimental reviews in Secs. 1.3 and 1.4, respectively. The production mechanism ofthe Θ+ via meson-induced reactions is discussed in Sec. 1.5, which is relevant to thepresent experiment. Finally, a goal and outline of the present experiment is described inSec. 1.6.

1.2

Width of Θ+ from K +d scattering data

Since the pentaquark Θ+ has the same quark contents as the combination of a K + meson
together with a neutron, the K + d scattering is the most straightforward way to search
for the resonance. However, there is no clear evidence of the resonance in the region
around 1540 MeV from past K + d scattering data. A question why the Θ+ was missedin the past experiments is raised. The answer to the question probably lies, at least
partly, in the very small width of the Θ+ . If the step size of beam momenta was muchsparser than the width, the existence of the Θ+ might be passed over. Shortly after theexperimental evidence for the Θ+ appeared, consistency of the Θ+ with the past K + dscattering data was discussed vigorously in connection with the width of the Θ+ . Here,study in this direction is reviewed.
The K + N scatterings such as K + p and K + d scattering were measured mostly withbubble chambers in the 1960s and 1970s. Assuming that the mass of the Θ+ is 1540 MeV,
the momentum of K + on the resonance in the K + n scattering is 440 MeV/c. Such a low
momentum K + beam was provided by degrading an initial beam of higher momenta. The
resulting beam energy can have signiﬁcant momentum spread of typically 6% (FWHM).
Because there is no neutron target, the isospin I = 0 amplitude must be extracted from

1.3. THEORETICAL WORKS

3

the K + d scattering data, containing a mixture of I = 0 and I = 1 amplitudes. This canbe done only after correcting the data for the Fermi motion of the target nucleons andthe momentum spread of the K + beam. Owing to the diﬃculty of treatment of these
unfolding procedures, there was disagreement between the cross sections measured in
diﬀerent experiments. Hence, one must be careful when drawing any conclusions fromthe past database of K + d scattering.
One of the ﬁrst discussion using the past K + d scattering data was made by Nussinov[12]. If the Θ+ is narrow, it could escape detection if there is a gap in the database at
the resonant energy, but the deuteron Fermi motion will spread it out so that it should
be noticeable. Using these estimates and a cursory examination of the database, he
concludes that the width of the Θ+ must be less than 6 MeV for I = 0 and J P = 1/2+ .
Arndt, Strakovsky, and Workman reanalyzed the existing K + N data based on thephase shift analysis focusing on the energy region around 1540 MeV [13]. They checked
the change of χ2 in ﬁtting the database associated with additional resonances in the s, p
and d waves with some widths. They conclude that the Θ+ widths beyond the few-MeV
level are excluded.
Haidenbauer and Krein examined the K + N elastic cross section and the phase shift
in I = 0 and J P = 1/2+ partial wave using the Jülich KN meson-exchange model [14].
They conclude that there is no way to reconcile the existing KN cross section data withthe existence of the Θ+ with a width of 5 MeV or more. A similar method was applied
to the K + d → K 0 pp reaction by Sibirtsev et al. [15]. They conclude that the Θ+ width
is constrained to be less than 1 MeV.
Cahn and Trilling illustrated the extraction of the Θ+ width from the charge exchange
reaction cross section [16]. They deduced the width Γ = 0.9 ± 0.3 MeV from the DIANA
result reported in 2003 [55]. They also estimated the upper limit of the width of 1–4
MeV from the past K + d data.
Gibbs [17] showed a possible existence of a narrow resonance using the K + d total
cross section data measured by Bowen et al. [18]. On the basis of a weak scattering
approximation, and taking account of the Fermi motion in the deuteron, the total crosssection was calculated with a resonance with an assumed width and mass. An experimental bump structure was well reproduced by the assumption of a resonance at 1559±3
MeV with a width of 0.9 ± 0.3 MeV for the J P = 1/2+ case, as shown in Fig. 1.1.
As reviewed above, according to the reanalyses of the K + d scattering data, there isa consensus that the width should be less than a few MeV, if the Θ+ exists. The widthis quite narrower than those of ordinary strongly decaying hadrons, and the narrowness
is peculiar to the Θ+ .

1.3

Theoretical works

Theoretical studies for the Θ+ pentaquark are introduced in this section. A point of the
discussion is whether the pentaquark with a light mass and a narrow width could be
explained theoretically, i.e., what structure the pentaquark has. Since the structure ofa hadron is often reﬂect in its parity as well as spin, which parity and spin theoreticalmodels predict is also interesting.

4

CHAPTER 1. INTRODUCTION

FIG. 1.1: Total cross section of K + d scattering measured by Bowen et al. [18], together
with the ﬁtting results by Gibbs [17] using a weak scattering approximation for a p-wave
resonance. The dashed-dotted, solid, and dashed curves correspond to widths of 1.2, 0.9,
and 0.6 MeV, respectively. The dotted curve is the background ﬁt.

Naive insight into the narrowness of Θ+
The narrow width of the Θ+ is a challenge for any theoretical interpretation. Since
the mass of Θ+ is about 100 MeV above the KN threshold, the Θ+ decays into KN(pK 0 or nK + ) by the strong interaction. The Θ+ is unique in that its valence quark
conﬁguration (uudds̄) already contains all the quarks needed for the decay into KN .
Non-exotic hadrons can only couple to their decay channels by creating quark pairs; e.g.,Λ(1520) → K̄N needs creating a uū or dd¯ pair. The suppression of quark pair creation,
known as the OZI rule, is often invoked as an explanation for narrow widths. For the
narrowness of Θ+ , some other unknown mechanism would have to be responsible.
Conventional quark model
The constituent quark model is the most traditional way to understand hadron properties. Since quarks have positive parity and antiquarks have negative parity, ground statesof pentaquarks without orbital excitation would have negative parity: namely, 1/2− . Although the quark model contains some variations, in a naive quark model approach,
1/2− pentaquark states give the lowest mass. Haung, Zhang, Yu, and Zou calculatedthe Θ+ mass in the chiral SU(3) quark model, and found it 200–300 MeV higher thanthe experimental value [19]. Furthermore, it is obviously diﬃcult for the 1/2− state torealize the narrow width of Θ+ (without any novel mechanism) because it decays intoK(0− ) and N (1/2+ ) in s wave.
Chiral soliton model
The ﬁrst prediction of the light and narrow pentaquark was provided using the chiralsoliton model by Diakonov, Petrov, and Polyakov in 1997 [7]. The model was brieﬂyreviewed in [20]. The chiral soliton 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 ﬁeld
in the nucleon in which quarks move. Baryons are regarded as rotational states in the1.3. THEORETICAL WORKS

5

FIG. 1.2: Antidecuplet of baryons with J P = 1/2+ predicted by Diakonov et al. using the−−chiral soliton model [7]. The corners of this diagram are manifestly exotic: Θ+ , Ξ+
3/2 , Ξ3/2 .
Their quark content and the predicted masses are shown.

ordinary space and ﬂavor SU(3) space. The baryon octet (1/2+ ) and decuplet (3/2+ )states are well reproduced as the two lowest rotational states of the chiral solitons. The
next lowest is the antidecuplet with 1/2+ as shown in Fig. 1.2, where the corners of the
diagram are manifestly exotic. Diakonov et al. assumed the known nucleon resonanceN ∗ (1710, 1/2+ ) a member of the antidecuplet, and estimated the properties of the othermembers. The positive strangeness exotic baryon, later called Θ+ , was predicted at amass of about 1530 MeV with a width of 15 MeV or less. In their model, the narrowness
follows from a cancellation of diﬀerent contributions in the decay operator.
Diquark correlation
The models that are often called “correlated quark models” are a kind of extended
quark models introducing speciﬁc inter-quark correlations, called “diquark” correlations.
Various eﬀective quark interactions as well as phenomenological analyses predict thestrong correlation between quarks [21]; i.e., the color antitriplet 3̄c , ﬂavor antitriplet+
3̄f , and spin singlet with even parity: [qq]3̄c 3̄f 0 . This channel is favored by one-gluon
exchange.
Jaﬀe and Wilczek proposed a [ud][ud]s̄ picture, where two ud diquarks are coupledwith an s̄ antiquark [22]. To satisfy the total color singlet, two diquarks must combine
into 3c , which is the antisymmetric part of 3̄c ⊗ 3̄c ; therefore, the space wave functionof the two diquarks must be antisymmetric, i.e., negative space parity; the two diquarks
must have a relative angular momentum L = 1 at least. Combining with s̄, the Θ+
spin-parity of 1/2+ was predicted.
Karliner and Lipkin proposed a diquark-triquark model giving a [ud][uds̄] picture,
where a ud diquark are coupled with a uds̄ triquark in a relative p wave [23]. The uds̄triquark belongs to 3c , where the ud spins are parallel and each one is antiparallel to thes̄ antiquark. They also predicted the Θ+ spin-parity of 1/2+ .
In both the models above, the spin-parity of 1/2+ with ﬁnite relative angular momentum was predicted, which is signiﬁcantly diﬀerent from the naive quark model prediction

6

CHAPTER 1. INTRODUCTION

of 1/2− . Furthermore, in their pictures, the initial and ﬁnal states in the Θ+ → KN
decay have diﬀerent conﬁgurations in terms of the color, spin, and space; i.e., the overlapof the wave function between the initial and ﬁnal states is small. They suggested thatthe narrow width might be explained with the rearrangement of the color, spin, andspatial wave functions.
Lattice QCD calculation
If pentaquarks exist, such states must emerge directly from the ﬁrst principle, QCD;
practically through lattice QDC calculation. It is not so easy to deal with pentaquarks
rather than usual baryons or mesons in lattice QCD, because the qqqq q̄ state can be
decomposed into qqq and q q̄ even in the quenched approximation, in which quark paircreations and annihilations do not occur. Since the Θ+ mass is slightly above the threshold of KN , the presence of the KN scattering state complicates the exploration of the Θ+
pentaquark (see Ref. [24] for an early review). Several lattice calculations were publishedto search for the Θ+ in the quenched approximation. Some positive signals were reported
whereas negative results were also reported. The results are summarized in Table 1.1.
Notice that the positive results tend to favor the spin-parity 1/2− , which is against either
predictions from the chiral soliton model or the diquark approach. However, the results
are diverging and seem to be inconclusive so far.
TABLE 1.1: Summary of the results from the lattice QCD calculations searching for theΘ+ . The third column shows the examined spin-parities, which are lined in the case of no
signal obtained.

Author(s)Csikor et al.
SasakiChiu-Hsieh
Mathur et al.
Ishii et al.
Lasscock et al.
Takahashi et al.
Alexandrou-Tsapalis
Holland-Juge

1.4

SignalYes→No
Yes
Yes
No
No
No/Yes
Yes
(Yes)
No

Spin-parity
1/2+ , 1/2− → 1/2−
1/2+ , 1/2−
1/2+ , 1/2−
1/2+ , 1/2−
1/2+ , 1/2− , 3/2+ , 3/2−
1/2+ , 1/2− , 3/2+ , 3/2−
1/2+ , 1/2−
1/2+ , (1/2− )1/2−

Ref(s).
[25, 26]
[27]
[28]
[29]
[30, 31][32, 33]
[34]
[35]
[36]

Experimental review

After the ﬁst evidence of Θ+ was presented, considerable numbers of experimental results
were published. The experimental status of the Θ+ has a complicated history withvicissitudes. One can ﬁnd experimental and historical reviews by Hicks in Refs. [9, 10]
and by Danilov and Mizuk in Ref. [37], and also reviews of Particle Data Group, written
by Trilling in 2004 [38] and 2006 [39], and by Wohl in 2008 [40], after which no update isgiven. Here, I review the experiments classifying them under the production processes.

1.4. EXPERIMENTAL REVIEW

7TABLE 1.2: Summary of the photoproduction experiments for the Θ+ . The forth column
shows the experimental results for the mass and width in a unit of MeV in case of positive
results, or the upper limit in case of negative results.

Group

ReactionLEPS
SAPHIR
CLAS
CLAS
CLAS
CLAS
CLAS
LEPS
Amaryan et al.

γC → K K X
γp → K̄ 0 K + n
γd → K + K − p n
γp → π + K + K − nγp → K̄ 0 K + n/K̄ 0 K 0 p
γd → K + K − p n
γd → ΛK + n
γd → K + K − p n
γp → KS0 KL0 p

1.4.1

+

−

SignalResultRef(s).

Yes(Yes) 1
Yes 2
Yes
No
No
No
Yes
Yes

(Mass)(Width)1540 ± 10< 25(1540 ± 4 ± 2) (< 25)1542 ± 5< 211555 ± 10< 26
σ < 0.7 nb
σγn < 3 nb
σ < 5–25 nb
1524 ± 2 + 3
< 26
1543
< 14

[8]
[41]
[42]
[43]
[44, 45]
[46]
[47]
[48]
[49]

Low-energy photoproduction experiments

The photoproduction of the Θ+ has been intensively studied by the LEPS, SAPHIR and
CLAS Collaborations using photon beams around 1–5 GeV, as summarized in Table 1.2.
Most of the experiments used the photoproduction on a neuron or proton, i.e., γn →K − Θ+ , or γp → K̄ 0 Θ+ , where n stands for a neutron in a nucleus.
γn → K − Θ+
The LEPS Collaboration reported the ﬁrst experimental evidence for the Θ+ in the γC →K + K − X reaction in 2003 [8]. A sharp peak was observed at a mass of 1540 ± 10 MeV
with a width less than 25 MeV, which is compatible with the experimental resolution, as
shown in Fig. 1.3 (top left). LEPS reported the further evidence in the γd → K + K − p nreaction with improved statistics in 2009 [48]. Since they detected only the K + K − pair at
forward angles and expected a quasifree reaction on a neutron, a Fermi motion correction
was necessary. Figure 1.3 (top right) shows the Fermi-motion-corrected nK + invariant
mass spectrum, which shows a narrow peak at 1524 ± 2 + 3 MeV with a statisticalsigniﬁcance of 5.1σ. The cross section of the γn → K − Θ+ reaction was estimated to be
12 ± 2 nb/sr in the LEPS angular range.
An alternative interpretation for the LEPS result was proposed by Martı́nez Torresand Oset [50]. Using their theoretical model of the γd → K + K − p n reaction withoutthe Θ+ production, they suggested that the analysis method used in the experiment,
together with the chosen cut, might create an artiﬁcial broad peak in the nK + invariant
mass spectrum, and claimed that the observed peak is compatible with a statisticalﬂuctuation of the 2σ signiﬁcance.
The CLAS Collaboration also searched for the Θ+ in the γd → K + K − p n reaction
with high statistics data of 38 pb−1 , but observed no peak [46]. The upper limit of the
1
2

This SAPHIR result is inconsistent with the high-statistics CLAS result [44, 45] (see text.)
This earlier CLAS result was disproved by themselves with the 30 times higher statistics data [46].

8

CHAPTER 1. INTRODUCTION

40
35
30
25
20
15
10
5
0

35

2

150

Events / 20 MeV/c

Counts/5 MeV

40

100
50

30
25
20

1.5
2
+
2
M(nK ) (GeV/c )

15
10

0
1.4

1.5

1.6
1.7
MX (KS) [GeV]

5
0

1.4

1.6

1.8

2
+

2.2

2.4

2

M(nK ) (GeV/c )FIG. 1.3: Positive results from the photoproduction experiments. (Top left) Fermi-motioncorrected missing mass spectrum of the (γ, K − ) reaction for a signal sample (solid line) andevents from LH2 (dotted line) reported by the LEPS Collaboration in 2003 [8]. (Top right)
Fermi-motion-corrected nK + invariant mass spectrum reported by the LEPS Collaborationin 2009 [48]. (Bottom left) (γ, KS ) missing mass spectrum obtained by Amaryan et al.
with a cut −tΘ < 0.45 GeV2 , where tΘ represents a four momentum transfer [49]. (Bottom
right) nK + invariant mass spectrum in the γp → π + K + K − n reaction reported by the
CLAS Collaboration in 2004 [43]. The inset shows a diﬀerent cut condition.

cross section for the elementary γn → K − Θ+ reaction was estimated to be 3 nb. In
contrast to LEPS, since they required all the charged particles, K + K − p, the reaction
is not a simple quasifree reaction but the rescattering of the spectator proton shouldbe needed. Moreover, the discrepancy between the LEPS and CLAS results might be
attributed to the diﬀerent angular acceptances of these two experiments. The LEPS
spectrometer has the acceptance of θK − < 20◦ , whereas the CLAS spectrometer has
the acceptance of θK − > 20◦ . If the Θ+ production cross section has a strong angulardependence peaked forward, there is still a room to explain the positive result of LEPS.
Recently, a preliminary result from the LEPS Collaboration with improved statistics
of 2.6 times higher than the previous paper [48] was presented at a conference in 2012[51]. The same analysis did not show a strong narrow peak and resulted in decrease of
the signiﬁcance. However, an enhancement still remained in data enriching the quasifree
γn reaction on the basis of a new analysis. They continue data taking with an improved
setup optimized for the analysis.

1.4. EXPERIMENTAL REVIEW

9γp → K̄ 0 Θ+
The γp → K̄ 0 Θ+ reaction was studied by the SAPHIR [41] and CLAS [44, 45] Collaborations. There is an apparent contradiction in their results: SAPHIR found the evidenceof the Θ+ with the cross section of 300 nb [41] 3 , whereas CLAS found no evidence usingmuch higher statistics data of 70 pb−1 and estimated the cross section upper limit of 0.7
nb [45]. Because the quality of the CLAS data is much better than that of SAPHIR, it
is hard to believe the result reported by the SAPHIR Collaboration.
The cross section diﬀerence between the γn → K − Θ+ and γp → K̄ 0 Θ+ reactions wasstudied by Nam et al. using the eﬀective Lagrangian method [53]. They suggested thatthe Θ+ photoproduction from a proton could be strongly suppressed as compared withthat from a neutron assuming the Θ+ spin-parity of 3/2± , owing to a large contribution
from the contact term of γ K̄N Θ, which exists only in the γn → K − Θ+ reaction diagram.
They remarked that the CLAS result [44, 45] does not immediately lead to the absenceof Θ+ .
Recently, Amaryan et al. [49], a break-oﬀ group of the CLAS Collaboration, reported
an observation of a narrow peak in the missing mass of KS0 in the γp → pKS0 KL0 reaction
using the CLAS data, as shown in Fig. 1.3 (bottom left). Since the ϕ-meson photoproduction predominates in this photon energy, it was usually cut out by excluding the
K K̄ invariant mass near the ϕ mass; however, they did not apply the cut to utilize aninterference eﬀect. They claimed that the peak may be due to the interference between
the Θ+ and ϕ leading to the same ﬁnal state. On the other hand, the CLAS Collaboration itself was not convinced of the evidence [54]. Their primary concern is the lack ofjustiﬁcation for the kinematic cuts used in the analysis, without which the narrow peakdoes not appear. Amaryan et al. are indeed aware of the concern and remarked thenecessity of additional data to understand the details of the interference.
OthersThe CLAS Collaboration published the positive evidence for the Θ+ in the γp →π + K + K − n reaction using a relatively higher energy photon beam of 3–5.47 GeV early in
2004, as shown in Fig. 1.3 (bottom right) [43]. They suggested that the reaction might
be mediated through an N ∗ resonance decaying into K − Θ+ around 2.4 GeV, such as
γp → π + N ∗ → π + K − Θ+ . Note that, although the other early CLAS results were later
examined by the dedicated experiments with higher statistics data, the conﬁrmation ofthis result by high statistics data has not been performed yet.

1.4.2

Formation experiments

The formation reaction, K + n → Θ+ , which is a reverse reaction of the decay, is particularly important. In this reaction, the Θ+ width can be derived from the cross section,
as explained in [16]. The resonant cross section is determined entirely by the width of
the resonance, Γ, and its branching ratios Bi and Bf into the initial and ﬁnal channels
3

The reanalysis of SAPHIR is found in [52] leading the same result.

10

CHAPTER 1. INTRODUCTION

according to the Breit-Wigner form:
[

]
Γ2 /4
,
(m − m0 )2 + Γ2 /4(1.1)

2J + 14π= 68 mb,(2s1 + 1)(2s2 + 1) k 2(1.2)

σ(m) = Bi Bf σ0
where m0 is the resonance mass, and
σ0 ≡where J is the spin of the resonance, s1 and s2 are the spins of incident particles, andk is the breakup momentum at the resonance rest frame. For the K + n → Θ+ reaction,
σ0 is 68 mb assuming that the Θ+ mass is 1540 MeV and the spin J = 1/2. Then, thetotal cross section is calculated as∫ ∞πΓσtot =
σ(m)dm =Bi Bf σ0 = (27 mb/MeV) Γ,
(1.3)
2
−∞
where Bi = Bf = 1/2, which is appropriate for either isospin I = 0 or 1, was used.
The K + n → Θ+ formation reaction was investigated by the DIANA and Belle Collaborations, as summarized in Table 1.3. Both groups searched for the Θ+ as an intermediateresonance in the charge-exchange reaction K + n → Θ+ → KS0 p on nuclei.
The DIANA Collaboration reanalyzed the 1970’s xenon bubble chamber data irradiated by a 0.85-GeV/c K + beam, and found the evidence for the Θ+ produced in the
K + Xe → KS0 p Xe′ reaction [55, 56]. They observed a narrow peak in the pKS invariant
mass spectrum at 1538±2 MeV with a width consistent with the experimental resolution,
as shown in Fig. 1.4 (left). The intrinsic width of the Θ+ was estimated by comparing thesignal magnitude with the level of nonresonant charge-exchange background under the
peak. To obtain the original nonresonant background distribution prior to the rescattering of the K 0 and proton in nuclear medium, they used a Monte Carlo simulation using
the intranuclear cascade medel. They assumed that the bulk of produced Θ+ baryons
decay upon leaving the Xe nucleus because of its possible width of 1 MeV or less. The
Θ+ width was estimated to be 0.34 ± 0.10 MeV, where the error does not include the systematic uncertainties of the simulation procedure. This is currently the only information
about a ﬁnite experimental value for the Θ+ width.
The Belle Collaboration also searched for the Θ+ using kaon secondary interactionsin the materials of the Belle detector [57]. The kaons produced in e+ e− annihilation havequite low momenta peaking at 0.6 GeV/c. They found no evidence in the pKS invariant
mass spectrum shown in Fig. 1.4 (right). In the same manner as DIANA, comparing
with the nonresonant charge-exchange background yield, the upper limit of the Θ+ width
was estimated to be ΓΘ < 0.64 MeV at the 90% C.L. at a mass of 1539 MeV. Note thatthe limit does not contradict the DIANA result.

1.4.3

Experiments using high-energy beams

Following the low-energy experiments, many experimental results using high-energy
beams, e.g., 10–100 GeV or much higher, were reported one after another. To begin
with, the following three points should be noticed:

1.4. EXPERIMENTAL REVIEW

11TABLE 1.3: Summary of the formation experiments for the Θ+ . The forth column showsthe experimental results for the mass and width in a unit of MeV.

Group

Reaction

SignalDIANA K + Xe → KS0 p Xe′
Belle
K + A → KS0 p A′

Yes
No

ResultRef(s).
(Mass)(Width)1538 ± 2 0.34 ± 0.10 [55, 56]< 0.64[57]

FIG. 1.4: Results of the DIANA and Belle experiments. (Left) pKS invariant mass spectrum under a cut condition reported by the DIANA Collaboration [56]. (Right) Invariant
mass spectrum for secondary pKS0 pairs reported by the Belle Collaboration [57].

Fragmentation In the high-energy reaction in which quarks or partons rather thanhadrons are involved, hadrons are produced in fragmentation or “string breaking”
as the quark-antiquark separation. In order to form the Θ+ , there must be fourquarks and one antiquark localized in space with small relative volocity. It seems
to be unlikely to achieve such a situation in a naive sense. One should examine
closely wheter the reaction is sensitive to the Θ+ production from the viewpoint of
the reaction mechanism.
Strangeness tag Almost all the following experiments in this subsection measured
the pKS0 invariant mass spectra from inclusive production. Since the KS0 is not
an eigenstate of ﬂavors, one cannot distinguish the strangeness S = +1 or −1;
therefore, the invariant mass spectra include both Σ∗+ and possible Θ+ peaks. Since
there is no sharp Σ∗ resonance established in 1500-1600 MeV [58], it is practicallyregarded as the Θ+ if the sharp peak is observed.
Production ratio The production ratio of Θ+ to Λ(1520), RΛ∗ , is often used for anindicator of the cross section, because Λ(1520) is narrow (15.6 MeV) and easily
reconstructed, and the mass is close to that of the Θ+ . In the same manner, RΣ∗is also deﬁned as the production ratio of Θ+ to Σ(1385).
Table 1.4 shows a summary of the Θ+ search experiments using high-energy lepton beams
or decay processes.

12

CHAPTER 1. INTRODUCTIONTABLE 1.4: Summary of the Θ+ search experiments using high-energy lepton beams or
decay processes. The forth column shows the experimental results. B denotes a branchingratio for a corresponding decay producing Θ+ .

Group
νBC
HERMES
ZEUS
H1
BES
ALEPH
DELPHI
BaBar
Belle
BaBar
L3
FOCUS
NOMAD
BaBar

ReactionνA → KS0 p X
e+ d → KS0 p X
ep → eKS0 p X/eKS0 p̄ X
ep → eKS0 p X/eKS0 p̄ X
e+ e− → J/ψ → Θ+ Θ̄−e+ e− → Z → KS0 p X
e+ e− → Z → KS0 p X
e+ e− → q q̄/Υ(4S) → KS0 p X
B 0 → KS0 p p̄B 0 → KS0 p p̄γ ∗ γ ∗ → KS0 p X/KS0 p̄ X
γBeO → KS0 p X/KS0 p̄ X
νA → KS0 p X
e± Be → KS0 p X

Signal
Yes
Yes
Yes
No
No 4
No
No
No
No
No
No
No
No
No

ResultM = 1533 ± 5 MeV
M = 1528 ± 2.6 ± 2.1 MeV
M = 1521.5 ± 1.5+2.8−1.7 MeVσ < 30–90 pb
B < 1.1 × 10−5
B < 6.2 × 10−4
B < 5.1 × 10−4
B < 5.0 × 10−5 /1.8 × 10−4
B < 2.3 × 10−7
B < 2.0 × 10−7
σ < 1.8 nb
RΣ∗ < 2.3%
< 2.13 × 10−3 /ν interaction
not given

Ref.
[59]
[60]
[61]
[62]
[63]
[64]
[65]
[66]
[67]
[68]
[69]
[70]
[71]
[72]

In 2003, Asratyan et al., an ITEP group, analyzed past experimental data with big
bubble chambers (νBC) irradiated by 30–140 GeV neutrino beams, and observed a peakin the invariant mass of the pKS0 system at 1533 ± 5 MeV [59]. Three years later,
the NOMAD Collaboration reported no evidence in the νA interactions, and set an
upper limit of the Θ+ production rate as shown in Fig. 1.5 [71]. They claimed that the
production rate of ∼ 10−3 reported by Asratyan et al. is excluded for a large fraction of
the xF range, except for the region xF ≈ −1.
In 2004, the HERMES [60] and ZEUS [61] Collaborations reported the evidence of+Θ in the ed and ep collision data, respectively. It is noted that, in the ZEUS data,
they required the momentum transfer Q2 > 20 GeV2 , without which the peak was notobserved; no justiﬁcation is given on this criterion. Furthermore, the H1 Collaboration
reported no evidence in the same reaction for either Q2 region between 5 and 100 GeV2[62]. Later, in 2007, the BaBar Collaboration presented the result obtained from thee± Be → KS0 p X reaction using the events from the beam halo hitting the beryllium
beampipe [72]. The obtained pKS0 spectra were compared with the HERMES and ZEUS
results in Fig. 1.6. The high-statistics of the BaBar result shows smooth spectra withno hint of a Θ+ peak, and hence disagree with the previous two results. Note that thecenter-of-mass energy of 9.4 GeV and the Q2 region (∼0) of BaBar are almost the sameas those of HERMES but diﬀerent from those of ZEUS.
Table 1.5 shows a summary of the Θ+ search experiments using high-energy hadronbeams. The SVD Collaboration studied the pA → KS0 p X reaction using a 70-GeV
proton beam, and observed a peak at M = 1523 ± 2 ± 3 MeV for a region xF ≥ 0, as
shown in Fig. 1.7 [75]. The SPHINX Collaboration also studied the pA → K̄ 0 N KA
reaction using a 70-GeV proton beam, but found a null result [76]. It was claimed,
4

Azimov and Strakovsky suggest that this reaction is not sensitive enough to produce the Θ+ [73].

Production rate

1.4. EXPERIMENTAL REVIEW

13

Limits at 90% CL-2

10

M = 1.51 GeV/c2
M = 1.53 GeV/c2
M = 1.55 GeV/c2
Sensitivity

-3

10

-1

-0.5

0

0.5

1

xF

FIG. 1.5: Sensitivity and upper limits at 90% C.L. for Θ+ production rates in the νAinteractions as a function of xF , for masses of 1510, 1530, and 1550 MeV/c2 , reported by
the NOMAD Collaboration [71].

Normalization region

60

Normalization
region300
Candidates / (5 MeV/c )2

2

Candidates / (8 MeV/c )

50

40

30

20

candidates±

HERMES e D

10

0

1.450

−

BaBar

e Be

1.500

1.550
pKshort Mass

1171
227174

ECM

2

Q

200

±

ZEUS e p
100−

BaBar e Be

10.6 GeV ~0
9.4

1.600
2
(GeV/c )1.650

2

candidates

ECM

Q

14622

300 GeV>20 GeV

227174

9.4

~0

1.600
2
(GeV/c )

1.650

2

~0
1.700

0

1.450

1.500

1.550
pKshort Mass

1.700

FIG. 1.6: (Left) The HERMES pKS0 mass distribution [60] compared to the corresponding BaBar distribution [72] normalized to the HERMES data for the region above 1.58
GeV/c2 . (Right) The ZEUS pKS0 mass distribution [61] compared to the corresponding
BaBar distribution [72] normalized to the ZEUS data for the region below 1.48 GeV/c2 .
Both ﬁgures are taken from [72].

however, that the Θ+ was produced with very small xF at SVD, whereas SPHINX has
no acceptance in this region. Still, it is not clear how to reconcile the SVD positive resultwith the null result of the HERA-B Collaboration [77], which was obtained from the same
reaction with the same acceptance of xF but with a higher center-of-mass energy of 41.6
GeV instead of 11.5 GeV. The production ratio RΛ∗ = 8–12% estimated from the SVD
result is in marked disagreement with the HERA-B upper limit, RΛ∗ < 2.7%.
As described above, the production of Θ+ may be suppressed in high-energy reactions.
This was studied by Titov et al. [82] based on energy dependence of the Regge trajectories
and the scaling behavior of the hadronic amplitudes. They found distinct decreasingof the Θ+ production fraction in fragmentation at high energy, although there is nosuppression in the central rapidity region in inclusive reactions. They suggested that thethreshold region with the initial energy of a few GeV or less seems to be more favorable
for the Θ+ production.

14

CHAPTER 1. INTRODUCTIONTABLE 1.5: Summary of the Θ+ search experiments using high-energy hadron beams.
The forth column shows the experimental results.

Group
SVD
SPHINX
HERA-B
HyperCPPHENIX
CDF
WA89

ReactionpA → KS0 p X
pA → K̄ 0 N KA
pA → KS0 p X
p(π/K)Cu → KS0 p X
dAu → K − n̄Xpp̄ → KS0 p X/KS0 p̄ X
Σ− A → KS0 p X

Signal
Yes
No
No
No
No
No
No

ResultM = 1523 ± 2 ± 3 MeV
RΛ∗ < 2%RΛ∗ < 2.7%
< 0.3%/KS0 p candidate
not givenRΛ∗ < 3%< 1.8 µb/nucleon

Ref(s).
[74, 75]
[76]
[77]
[78]
[79]
[80]
[81]

N/10 MeV/c

2

SVD2

300

250

200

2

M=1523.6±3.1(stat.) MeV/c
σ=12.9±2.5(stat.) MeV/c2
Nevents=187

150

100

50

0

1450

1500

1550

1600

0

Meff(Κ p)

1650

1700

2

MeV/c

FIG. 1.7: pKS0 invariant mass spectrum for events with KS0 decaying outside a vertex
detector, reported by the SVD Collaboration [75].

1.4.4

Low-energy hadron-induced experiments

Experiments using low-energy hadron beams are a good probe to study the Θ+ . The
hadron-induced cross section ought to be rather larger than the photoproduction. Furthermore, hadron-induced reactions are complementary to the photo-induced ones interms of the Θ+ production mechanism in the low energy region. Comparing various
types of reactions, it is possible to discuss the Θ+ properties through the reaction mechanism. The experimental aspect is described in this subsection, and interpretation of theresults is given in Sec. 1.5. Table 1.6 shows a summary of the low-energy hadron-induced
experiments. Since the KEK-PS E522 and E559 experiments are particularly related tothe present experiment, they are reviewed in the following.
KEK-PS E522 experiment+−−
The E522 experiment [86] was performed to search for√ the Θ via the π p → K X
reaction with beam momenta of 1.87 and 1.92 GeV/c ( s = 2.10 and 2.12 GeV, respec5

This earlier COSY-TOF result was disproved by themselves with the 4–8 times higher statistics
data [84].

1.4. EXPERIMENTAL REVIEW

15TABLE 1.6: Summary of the low-energy hadron-induced experiments for the Θ+ . The
forth column shows the experimental results.

Group
COSY-TOF
COSY-TOF
COSY-ANKEKEK E522
KEK E559

Reaction
pp → KS0 p Σ+
pp → KS0 p Σ+
pp → π + KS0 p Λ
π−p → K −X
K +p → π+X

Signal
Yes 5
No
No
No
No

ResultRef.
M = 1530 ± 5 MeV [83]σ < 0.15 µb[84]
σ < 58 nb[85]
σ < 1.8, 3.9 µb[86]dσ/dΩ < 3.5 µb/sr [87]tively) at KEK-PS. Both the incident π − and outgoing K − were measured using theK2 beam line and the forward spectrometer, KURAMA. Since a scintillation ﬁber or abulk polyethylene was used as a target, the missing mass spectra included the contribution from the carbon nuclei. No clear peak was found in the missing mass spectrum
obtained at 1.87 GeV/c, while, in the spectrum obtained at 1.92 GeV/c, a bump wasobserved at 1530.6 MeV with a width compatible to the experimental resolution of 13.4
MeV (FWHM), as shown in Fig. 1.8 (left). The statistical signiﬁcance of this bump,however, is only 2.5–2.7σ, which is not suﬃcient to claim the bump as the evidence of
Θ+ . The upper limits of the diﬀerential cross section at scattering angles of 0–20◦ in thelaboratory frame were estimated to be 1.6 and 2.9 µb/sr at the 90% C.L. for the 1.87and 1.92-GeV/c data, respectively. Assuming that Θ+ is produced isotropically in thecenter-of-mass system, the upper limits of the total cross section were also estimated tobe 1.8 and 3.9 µb at the 90% C.L., respectively.
KEK-PS E559 experiment+++
The E559 experiment [87] was performed to search√ for the Θ via the K p → π X
reaction with a beam momentum of 1.2 GeV/c ( s = 1.89 GeV) at KEK-PS. Both theincident K + and outgoing π + were measured using the K6 beam line and the forward
spectrometer, Superconducting Kaon Spectrometer (SKS), leading to a good mass resolution of 2.4 MeV (FWHM). Since the low-momentum kaon beam was used, the missing
mass spectrum includes the background originating from the beam K + decay. As shownin Fig. 1.8 (right), no clear peak was observed in the missing mass spectrum. The upper
limit of the diﬀerential cross section averaged over 2–22◦ in the laboratory frame wasestimated to be 3.5 µb/sr at the 90% C.L.

1.4.5

Isospin of Θ+

If the Θ+ belongs to the antidecuplet as shown in Fig. 1.2, the isospin is 0 by deﬁnition.
Nevertheless, this should be conﬁrmed experimentally. If it was an isovector (I = 1), one
might expect to observe its isospin partners, Θ0 and Θ++ . The Θ++ was searched for in
the pK + decay channel, but no evidence was observed in the SAPHIR [41], HERMES[60], ZEUS [61], and CLAS [88] experiments, even though each reported positive evidencefor Θ+ . No observation was also reported in the DELPHI [65] and JLab Hall A [89]experiments. These results indicate that possibility of the isovector was excluded. The

16

CHAPTER 1. INTRODUCTIONKEK E559: K + p → π + X−

Counts/4MeV/c 2

KEK E522: π p → K X
Gaussian peak+cubic B.G.

700
600
500

(a) Fitting results

cubic B.G. only

χ2/nof = 16.5/28
2
M=1530.6 +2.2
-1.9 MeV/c2
Γ=9.8 +7.1
-3.4 MeV/c

σ2o-22o(µb/(sr MeV/c 2))

Double differential cross section spectrum

−

400

8
6
4
2

300

0
200

1.46 1.48 1.5 1.52 1.54 1.56 1.58 1.6 1.62 1.64
Missing Mass (GeV/c2)

100(b) Residual plots

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 )σ2o-22o(µb/sr)

Counts/4MeV/c 2

Differential cross section

100

4
3
2
1
0
-1
-2
-3

90% C.L. upper limit

1.51 1.515 1.52 1.525 1.53 1.535 1.54 1.545 1.55
Mass (GeV/c2)

FIG. 1.8: Results of the KEK-PS E522 and E559 experiments. (Left) (a) Missing mass
spectrum of the π − p → K − X reaction at 1.92 GeV/c obtained in the E522 experiment [86].
The solid line represents the ﬁtting result with third-order polynomial background and a
Gaussian peak. The red dashed line represents the ﬁtting result with only the background.
(b) Residual plot from the background function obtained from the ﬁtting with third-orderpolynomial background and a Gaussian peak. (Right) (Top) Missing mass spectrum of theK + p → π + X reaction at 1.2 GeV/c obtained in the E559 experiment [87]. The spectrum
was ﬁtted using a second-order polynomial function and a Gaussian peak with a ﬁxed
width of 2.4 MeV (FWHM). (Bottom) The upper limits of the diﬀerential cross section of
the K + p → π + Θ+ reaction averaged over 2◦ to 22◦ in the laboratory frame as a functionof the mass of Θ+ .

Θ+ is likely to be isoscalar (I = 0).

1.4.6

Other pentaquarks

If the Θ+ exists and is a member of the antidecuplet, other members of the antidecuplet should exist, and a charmed analog of Θ+ may exist. In 2004, a doubly strange−−
pentaquark Ξ−−), which is positioned at the bottom left corner of
3/2 (also denoted as Φ− −+ +the antidecuplet shown in Fig. 1.2, was observed at 1862
√ MeV in the Ξ π and Ξ̄ πinvariant mass spectra in proton-proton collisions at s = 17.2 GeV by the NA49 Collaboration [90]. An anticharmed pentaquark Θ0c (uuddc̄) was observed at√3099 MeV in
the D∗− p and D∗+ p̄ invariant mass spectra in electron-proton collisions at s = 300 and
320 GeV by the H1 Collaboration [91]. These evidences had encouraged the study ofpentaquarks more vigorously at that time. However, these evidences were not supported

1.4. EXPERIMENTAL REVIEW

17

by any other subsequent experiments; the Ξ−−
3/2 was not observed in the HERA-B [77],WA89 [92], ALEPH [64], HERMES [93], COMPASS [94], ZEUS [95], BaBar [66], E690[96], EXCHARM [97], CDF [98], DELPHI [65], H1 [99], FOCUS [100], and CLAS [101]experiments; the Θ0c was not observed in the ZEUS [102], ALEPH [64], CDF [80], BaBar[103], CHORUS [104], and DELPHI [65] experiments. At present, the evidence for either0Ξ−−
3/2 or Θc is hardly credible unless further evidences are reported.

1.4.7

Summary of experimental results

As described above, the experimental situation for the Θ+ pentaquark is controversial.
The followings are the current situation of Θ+ from an experimental point of view:• The mass of Θ+ reported in the experiments with positive evidence ranged from1520 to 1550 MeV/c2 . The Θ+ is generally denoted as Θ(1540)+ , or sometimes
Θ(1530)+ .
• The width of Θ+ measured in the experiments is usually limited by the experimental
resolution of 10–25 MeV. Only the DIANA Collaboration reported a ﬁnite widthof 0.34 ± 0.10 MeV estimated from the production cross section [56]. At least,
the width should be less than a few MeV from the reanalyses of the past K + dscattering data.
• Non-existence of the Θ++ resonance indicates that the isospin of Θ+ is 0.
• The spin and parity of Θ+ have not been determined yet experimentally.
One of the problems on the Θ+ is that the positive evidences were usually reportedwith limited statistics. The statistical signiﬁcance of the Θ+ peaks were questioned
due to uncertainty of the shape of the background under the peaks. Figure 1.9 shows asummary of early experiments reporting the Θ+ evidence, presented by Pochodzalla [105],
where the data were plotted with statistical error bars and without ﬁtted curves. He
suggested that obviously a common drawback of the individual observation is the limited
statistics and hence limited conﬁdence of the peaks. As described so far, some of these
positive results were later disproved by the higher statistics data by the collaboration
itself, or criticized by other experiments; the LEPS and DIANA Collaborations, however,conﬁrmed the evidence by further analysis using improved statistics data.
In addition, the problem of arbitrary selection criteria was pointed out by several
authors, e.g., [10, 37, 105]. Because of the low statistics, it is important to note thatany cuts applied during the search process can modify the statistical signiﬁcance of ana priori unknown peak, unless the cuts are justiﬁed with an independent data sample orMonte Carlo data.
Anyway, the solution that convinces everyone of the existence of Θ+ could be obtained
from conﬁrming the evidence by various independent experiments with high statistics.

18

CHAPTER 1. INTRODUCTION

FIG. 1.9: Summary of early experiments reporting the Θ+ evidence, presented without
ﬁtted curves, taken form [105].

1.5

Θ+ production via meson-induced reactions

On the basis of the previous experimental results, the production mechanism of the Θ+
via meson-induced reactions at low energy is discussed in this section. As described inSec. 1.4.4, the Θ+ was not observed in both the π − and K + induced reactions. Whatcan we learn from this ?
Theoretical calculations for the meson-induced Θ+ productions have been studied inRefs. [106, 107, 108, 109, 110, 111, 112, 113], where the authors adopted the eﬀective
interaction Lagrangian approach with several reaction mechanisms and diﬀerent frameworks. Figure 1.10 shows possible diagrams for the π − p → K − Θ+ and K + p → π + Θ+reactions at the tree level for the isosinglet Θ+ . For the π − p → K − Θ+ reaction, sand t-channel diagrams together with the contact term are allowed. Because I = 0 is
assumed for Θ, the u-channel is precluded, where an isospin partner Θ++ is needed as anintermediate state. In the s-channel diagram, only a neutron is considered as an intermediate state for simplicity. In the t-channel diagram, a K ∗0 vector meson is exchanged,
whereas a K 0 pseudoscalar meson exchange is forbidden due to the parity conservation
at the three-meson vertex. The diagrams for the K + p → π + Θ+ reaction are obtained
crossing the π and K.
In the theoretical calculations published so far [106, 107, 108, 109, 110, 111, 112, 113],
the authors considered all or part of diagrams in Fig. 1.10, adopted the pseudoscalar
and/or pseudovector coupling scheme for the Yukawa couplings, and often introduced
phenomenological form factors to reﬂect the ﬁnite size of hadrons. (See the recent paper[113] for detailed formalism.) The results can be diﬀerent depending on details of themodel employed; nevertheless, qualitative understanding of the experimental results isimportant. Although some of theoretical parameters can be determined from known
hadronic reactions (e.g., K ∗ → Kπ and πN scattering), the KN Θ, K ∗ N Θ and N πKΘ
couplings are unknown. Note that the KN Θ coupling constant, gKN Θ , is directly related

1.5. Θ+ PRODUCTION VIA MESON-INDUCED REACTIONS

19

FIG. 1.10: Diagrams for the π − p → K − Θ+ (a,b,c) and K + p → π + Θ+ (d,e,f) reactions at
the tree level for the isosinglet Θ+ .

to the width of Θ+ , ΓΘ .
Figure 1.11 (left) shows the diﬀerential cross sections of the K + p → π + Θ+ reaction√
at s = 2.4 GeV calculated by Oh, Kim, and Lee [109], taking account of the t- andu-channels for the spin-parity of 1/2+ . Their calculation is controlled by two coupling
constants, gKN Θ and gK ∗ N Θ . They assumed that gKN Θ = 1.0 which corresponds to ΓΘ =1.03 MeV. In case of hyperons (Y ), |gK ∗ N Y | is usually smaller than |gKN Y |; therefore, they
assumed the following three cases: gK ∗ N Θ = gKN Θ , gK ∗ N Θ = −gKN Θ , and gK ∗ N Θ = 0. If
the t-channel process exists (gK ∗ N Θ = ±gKN Θ ), the diﬀerential cross section would havea forward peak distribution as shown by the solid and dashed lines in Fig. 1.11 (left).
The calculated diﬀerential cross section averaged over 2◦ to 22◦ in the laboratory frame,σ̄2◦ -22◦ , is about 140 µb/sr in this case. The upper limit of 3.5 µb/sr obtained fromthe E559 experiment [87] is much smaller than this value. Thus, the t-channel process is
excluded by the E559 result; i.e., gK ∗ N Θ must be very small. If only the u-channel process
exists (gK ∗ N Θ = 0), the diﬀerential cross section shows a backward peak distribution asshown by the dashed-dotted line in Fig. 1.11 (left). In this case, σ̄2◦ -22◦ is almost 0 µb/sr.
Because the acceptance of E559 is limited to forward angles, it is not sensitive to theu-channel contribution.
The contribution of the contact term was studied by Hyodo and Hosaka [112]. The
N πKΘ coupling constant was determined from N ∗ decay into ππN channel, consistingof the ππ(I = 0, s wave)N and ππ(I = 1, p wave)N modes, referred to as “scalar” and“vector” types, respectively; therefore, two coupling constants g s and g v contribute to
the contact term. They calculated the cross sections of both the π − p → K − Θ+ andK + p → π + Θ+ reactions for the spin-parity of 1/2+ and 3/2− , taking account of thes- and u-channels as well as the contact term. Figure 1.11 (middle and right) shows
the calculated total cross sections for 1/2+ with g s = 1.59 and g v = −0.27. The s-

CHAPTER 1. INTRODUCTION

g
= +g
KNΘ
K*NΘ
g
= -g
KNΘ
K*NΘ
g
=0

70

120

K*NΘ

60

Theoretical calculation
σ 2o-22o = 141 ( µ b/sr) (g

= +g

)

σ 2o-22o = 135 ( µ b/sr) (g

= -g

)

K*NΘ

50

K*NΘ

40

σ 2o-22o ~ 0 ( µ b/sr) (g

K*NΘ

KNΘ

KNΘ

= 0)

Experiment30

σ 2o-22o ~ 3.5 ( µ b/sr) (Experiment)

2.5

π-p -> K-Θ+

80

s
v
Born
Total
w/o Born

2.0
σ [mb]

80

σ [µb]

dσ /d Ω ( µb/sr)

20

40

K+p -> π+Θ+

1.5
1.0
0.5

20
g
10
0
0

K*NΘ

20

=0

40

0
1600
60

80

100 120 140 160 180
θCM (degree)

2000 2400
s [MeV]

0.0
1600

2000 2400
s [MeV]

FIG. 1.11: (Left) Diﬀerential cross sections of the K + p → π + Θ+ reaction calculated by√
Oh, Kim, and Lee [109] at s = 2.4 GeV (the E559 experiment [87] was carried out at√
s = 1.9 GeV). The solid, dashed, and dashed-dotted lines represent gK ∗ N Θ = gKN Θ ,gK ∗ N Θ = −gKN Θ , and gK ∗ N Θ = 0, respectively. This ﬁgure is taken from [87]. (Middle
and right) Total cross sections of the π − p → K − Θ+ and K + p → π + Θ+ reactions calculatedby Hyodo and Hosaka [112] for 1/2+ with g s = 1.59 and g v = −0.27. “s” and “v” standfor the scalar and vector type amplitudes in the contact term, respectively (see text).

channel contribution (labeled “Born” in the ﬁgure) is negligibly small owing to the small
width assumed ΓΘ = 1 MeV in their calculation. As shown in Fig. 1.11 (middle), thetotal cross section of the π − p → K − Θ+ reaction is suppressed due to the destructive
interference between the scalar and vetor type amplitudes (labeled “s” and “v” in theﬁgure), which can help to explain the small cross section of < 3.9 µb obtained from theE522 experiment [86]. On the other hand, as shown in Fig. 1.11 (right), the total crosssection of the K + p → π + Θ+ reaction is enhanced due to the constructive interference
between the two amplitudes, which connot explain the small cross section of < 3.5 µb/sr
obtained from the E559 experiment [87]. The 3/2− case also shows a similar tentdency.
Thus, the possible solution is that both g s and g v are quite small.
In summary, the theoretical calculations described above suggest that the contributions of the t-channel process and contact term must be very small from the E522 andE559 results.

1.6

Present experiment: J-PARC E19

The experimental situation about the Θ+ is controversial, and therefore it is important
to conﬁrm the existence of the Θ+ in an unambiguous way. As described in Sec. 1.4.4, the
KEK-E522 Collaboration reported the bump structure at 1530 MeV in the π − p → K − X
reaction with an incident momentum of 1.92 GeV/c. Although the statistical signiﬁcancewas not suﬃcient to claim the evidence, it is suggestive of a possible signal of the Θ+ .
The signiﬁcance was limited by the poor mass resolution of 13.4 MeV (FWHM). We can
improve the resolution by an order of magnitude with a good spectrometer system.
Under the current situation, the present experimental search should satisfy the following requirements. (i) High-statistics data are indispensable in order not to be disturbed

1.6. PRESENT EXPERIMENT: J-PARC E19

Counts / (MeV/c2)

300

21

π- p → K- X
at 1.92 GeV/c

200

100

0
1.45

1.50

1.55

1.60

Missing Mass [GeV/c2]

FIG. 1.12: Missing mass spectrum of the π − p → K − X reaction at 1.92 GeV/c obtained
from the E19-2010 data [116].

by statistical ﬂuctuation. (ii) High resolution of less than a few MeV is desirable tomeasure the potentially narrow Θ+ .
The present experiment (J-PARC E19 [114]) was proposed to search for the Θ+
using the π − p → K − X reaction. It was timely to use high-intensity meson beams at
the recently constructed J-PARC facility [115]. We have constructed a high-resolution
spectrometer system in order to achieve a good mass resolution of 2 MeV (FWHM).
Since we used the missing mass technique with a liquid hydrogen target, we could avoid
corrections for the Fermi motion or rescattering eﬀect. An order of magnitude higher
sensitivity than the previous E522 experiment was expected.
As described in the previous section, the production mechanism of Θ+ in the π − p →K − Θ+ reaction was theoretically discussed on the basis of the KEK-E522 and E559
results. Knowing that the t-channel and contact term contributions are very small, thes-channel contribution is important in the π − p → K − Θ+ reaction. Since the s-channel
amplitude is related to the Θ+ decay width through the coupling constant gKN Θ (Fig. 1.10(a)), we are able to estimate the width, which is the most peculiar property of Θ+ , fromthe cross section measured in the experiment.
In 2010, the ﬁrst physics run of the E19 experiment was carried out at the J-PARC
K1.8 beam line using a beam momentum of 1.92 GeV/c in order to obtain a directcomparison with the E522 result. Figure 1.12 shows the missing mass spectrum obtained
from the 2010 data [116]. No peak structure corresponding to the Θ+ was observed. The
upper limit of the production cross section averaged over scattering angles of 2–15◦ wasestimated to be 0.26 µb/sr in a mass region of 1510–1550 MeV/c2 . This upper limit isan order of magnitude lower than the previous E522 experimental result of 2.9 µb/sr[86]. It was concluded that the bump structure observed in the E522 experiment was
not a sign of Θ+ (notably the E522 Collaboration did not claim so).
Comparing the above 2010 result with a theoretical calculation using the eﬀective
Lagrangian approach with the s-channel diagram [113], the upper limit of the Θ+ width
at the 90% C.L. was estimated to be 0.72 and 3.1 MeV for the spin-parity of 1/2+
and 1/2− , respectively. This upper limit of the width could not exclude the DIANA

22

CHAPTER 1. INTRODUCTION

FIG. 1.13: Total cross sections of the π − p → K − Θ+ reaction calculated by Hyodo, Hosaka,
and Oka [113] for J P = 1/2+ in units of ΓΘ /(1 MeV) [µb], considering only the s-channel
diagram. Each line represents a type of the coupling scheme and form factor (see text in√Sec. 5.1.1). Beam momenta of 1.92 and 2.01 GeV/c correspond to s = 2124 and 2164
MeV, respectively.

result of ΓΘ = 0.34 ± 0.10 MeV [56] 6 , which is the only result reporting a ﬁnite widthof Θ+ . Furthermore, it could not overcome even the upper limit of ΓΘ < 0.64 MeV
reported by the Belle Collaboration [57]. Since the statistical uncertainty dominated in
the determination of the upper limit in the 2010 data, 3 times more statistics are needed
to improve the upper limit to 1/2, if we continue the data-taking at the 1.92-GeV/cmomentum.
In theoretical calculations [108, 113], the cross section of the π − p → K − Θ+ reaction was predicted to increase with higher energy. Figure 1.13 shows the total crosssections of the π − p → K − Θ+ reaction calculated by Hyodo, Hosaka, and Oka [113] for
J P = 1/2+ , considering only the s-channel diagram. Each line represents a type of thecoupling scheme and form factor, details of√ which are described in Sec. 5.1.1. The beam
momentum of 1.92 GeV/c corresponds to s = 2124 MeV. The cross section is predicted
to increase except for the PS-Fc case. The maximum
momentum available at the K1.8√
beam line is 2 GeV/c, which corresponds to s = 2164 MeV. Thus, we determined toperform the experiment using a beam momentum of 2 GeV/c in order to challenge the
DIANA result. The data with diﬀerent momenta must be more useful than the datawith only increase of statistics.
The second physics run of the E19 experiment was carried out in 2012 using a beam
momentum of 2 GeV/c. The experimental setup was slightly improved to cover a wider
momentum acceptance, described in the next chapter. We expected to obtain more
stringent constraint on the existence of Θ+ .
In this thesis, the result of the 2012 data at 2 GeV/c is presented including detailsof the experimental apparatus and analysis procedures. Using both the 2010 and 2012
data together with a theoretical calculation, constraint on the Θ+ width is discussed.
6

The latest DIANA result before 2012 was ΓΘ = 0.39 ± 0.10 MeV [55].

Chapter 2
Experimental Apparatus
The experiment was performed at the K1.8 beam line in the J-PARC hadron facility witha high-resolution spectrometer system: the K1.8 beam spectrometer and the Superconducting Kaon Spectrometer (SKS) [117]. As the J-PARC E19 experiment, the previous
and present data were taken in 2010 and 2012 using pion beams of 1.92 and 2.01 GeV/c 1
momenta, respectively. The π − p → K − X reaction on a liquid hydrogen target was used
to search for the Θ+ pentaquark. Beam pions and outgoing kaons were identiﬁed andanalyzed by the beam spectrometer and SKS, respectively. In this chapter, details of theexperimental components are described.

2.1

J-PARC and hadron experimental facility

J-PARC (Japan Proton Accelerator Research Complex) [118] is a high intensity proton
accelerator facility which aims to pursue frontier in nuclear physics, particle physics,
material and life science, and nuclear technology, with the highest beam power in theworld. J-PARC consists of three accelerators: LINAC (Linear Accelerator), RCS (Rapid
Cycling Synchrotron), and MR (Main Ring). A bird’s-eye view of the entire facility isshown in Fig. 2.1.
A negative hydrogen ion, H− , was produced at an ion source and accelerated by
LINAC up to 181 MeV. The accelerated H− was converted to a proton (H+ ) and injected
to RCS, which accelerates the proton up to 3 GeV. Part of the protons were injected to
MR and accelerated up to 30 GeV. The primary proton beam was extracted with a slow
extraction scheme for a duration of 2.2 second in every 6 second; this duration of the beam
extraction is called a spill. Typical proton beam intensities were 3 × 1012 and 4 × 1012 perspill in 2010 and 2012, respectively. The extracted proton beams were transported to thehadron experimental facility and bombarded to a platinum production target (ϕ6 × 60mm). Produced particles such as pions and kaons were delivered to experimental areas
through secondary beam lines and utilized for experiments. A schematic view of thehadron experimental facility is shown in Fig. 2.2.

1

2.01 GeV/c is a momentum after an oﬄine calibration. The nominal momentum was 2.00 GeV/c.

23

24

CHAPTER 2. EXPERIMENTAL APPARATUS

FIG. 2.1: Entire view of J-PARC, taken from [118].

FIG. 2.2: Schematic view of the hadron experimental facility.

2.2. K1.8 BEAM LINE

25

FIG. 2.3: Schematic view of the K1.8 beam line.

2.2

K1.8 beam line

The K1.8 beam line is a general-purpose mass-separated beam line that can supply
various secondary hadron beams up to 2.0 GeV/c [119]. Figure 2.3 shows a schematic
view of the K1.8 beam line. The beam line consists of four dipole magnets (D1–D4),
thirteen quadrupole magnets (Q1–Q13), four sextupole magnets (S1–S4), three octupole
magnets (O1–O3), two electrostatic separators (ESS1 and ESS2) with four correction
magnets (CM1–CM4), and four slits (IF, MOM, MS1, and MS2). The total lengthof the beam line is about 46 m. Figure 2.4 shows the beam envelopes and dispersion
function calculated with the ﬁrst order ion optical parameters.
Secondary pions were produced at the production target located at the most upstreamof the beam line. The pion beam was separated by the electrostatic separators. As for anegative pion beam around 2 GeV/c, original contamination from kaons and antiprotons
is two orders of magnitude smaller than pions. The separators are especially importantfor kaon beams. After the momentum and mass selections, the pion beam was focusedon the experimental target. A typical beam size at the experimental target position was
10 (horizontal) × 5 (vertical) mm2 (rms). The derivatives of the horizontal (dx/dz) andvertical (dy/dz) directions were typically 0.010 and 0.003 (rms), respectively. The beams
were almost parallel to the nominal beam axis. In the present experiment, the central
beam momenta were set at 1.92 and 2.01 GeV/c in 2010 and 2012, respectively. A typicalmomentum spread was adjusted to be 1% (rms) by the momentum slit (MOM).

26

CHAPTER 2. EXPERIMENTAL APPARATUS

FIG. 2.4: Beam envelopes and dispersion function of the K1.8 beam line [119].

Time structure of the beam
In the present beam operation, a spike-like time structure on the extracted beam appeared. This structure arose from ﬂuctuations in the betatron tune, which were due tocurrent ripples of ∼10−4 of the MR magnet power supplies [120]. Figure 2.5 shows atypical instantaneous rate per 100 µs measured with a beam counter at the K1.8 beamline. The maximum instantaneous rate became up to 10–20 times as high as the mean
rate due to the spike structure. A quality of the extracted beam is represented by a spill
duty factor deﬁned as a ratio of the eﬀective beam time length to the extraction time of
2.2 s. The duty factor was 16–18% in the present operation in 2010 and 2012 2 .
In physics experiments using coincidence measurements, acceptable counting rates ofdetectors and data-acquisition system are generally limited by the instantaneous rate.
High multiplicity environment causes signal pileups, event overlaps, and dead time ofdetectors and data acquisition. In particular, the beam spike severely prevented a stable
operation of gas chambers in the present experiment. The average secondary beam
intensity in the 2010 run was adjusted to 1.0 × 106 per spill. In the 2012 run, we could
handle 1.7 × 106 per spill owing to improvements in the spill structure and a practicaloperation of gas chambers, details of which is described in Sec. 2.3.1.

2

The time structure was improved step by step, and the duty factor increased to ∼30% until 2013.

2.3. BEAM SPECTROMETER

27

FIG. 2.5: Typical instantaneous rate per 100 µs measured with a beam counter (BH1).
The blue line indicate the average rate of 106 per spill (2.2 s).

2.3

Beam spectrometer

Figure 2.6 shows a schematic view of the experimental setup at the 2012 run. The lastpart of the K1.8 beam line is used as a beam spectrometer. The beam spectrometercomprises a QQDQQ magnet system with four sets of wire chambers (BC1–BC4), a gas
Cherenkov counter (GC), and two sets of plastic scintillation counters (BH1 and BH2).
Details of each detector are described in the following subsections.
Beam tracks were measured by BC1–BC4 at the entrance and exit of the QQDQQ
magnets with a position resolution of 200–300 µm. Beam momenta were reconstructedparticle by particle with a resolution of 1 × 10−3 (FWHM). In order to minimize themultiple-scattering eﬀect on the momentum resolution, the beam spectrometer optics
was designed to realize point-to-point focus to the ﬁrst order. The magnetic ﬁeld of thedipole magnet (D4) was monitored during the experimental period by a high-precision
Hall probe [121]. Speciﬁcations of the beam spectrometer are summarized in Table 2.1.
TABLE 2.1: Speciﬁcations of the beam spectrometer.

Maximum momentum
Maximum ﬁeld (D4)
Bending angle
Central orbital radius (D4)Pole gap (D4)
Momentum resolution
Flight path (BH1–BH2)

2.0 GeV/c
1.67 T64◦
4.00 m19 cm∼ 1 × 10−3 (FWHM)
10.4 mCHAPTER 2. EXPERIMENTAL APPARATUS

LC
AC
SDCTOF
4
SDC
3

28

SKS

SDC2
SDC1

Target
0

BH2
BC4
BC3
Q13

3m

Q12

BH1

D4

Q10 Q11
BC2

BC1

GC

FIG. 2.6: Schematic view of the experimental setup at the 2012 run.

2.3. BEAM SPECTROMETER

29

TABLE 2.2: Speciﬁcations of the wire chambers. BC1 and BC2 are MWPCs, while theothers are drift chambers.

Name
BC1
BC2
BC3
BC4
SDC1
SDC2
SDC3
SDC4

2.3.1

Sensitive area
W × H (mm)256 × 100
256 × 100
192 × 100
240 × 150
192 × 100
400 × 150
2140 × 1140
2140 × 1140

Sense wire
pitch (mm)
1
1
3
5
3
5
20
20

Wire
conﬁg.
xvuxvuvuxvuxxx′ vv ′ uu′
vv ′ uu′ xx′
vv ′ uu′
vv ′ uu′ xx′
vxuvxuvxuvxuTilt angle
Resolution
x, u, v (deg) (µm in rms)
0, +15, −15300
0, +15, −15300
0, +15, −15
200
0, +15, −15
200
0, +15, −15
200
0, +15, −15
200
0, +30, −30
300
0, +30, −30
300

Tracking chambers for the beam spectrometer

Speciﬁcations of the tracking chambers for the beam spectrometer (BC1–BC4) are listed
in Table 2.2.
MWPCs (BC1 and BC2)
Detectors at the upstream part of the beam spectrometer are required to operate underhigh counting rates of 10–20 MHz. According to the past experience at the KEKPS K6 beam line, where wire chambers with 5 mm sense wire pitch had been used, adeterioration in the detection eﬃciency became serious with a counting rate over 200
kHz per wire [122, 123]. This situation requires wire chambers with the sense wire pitchof less than 1 mm for the K1.8 beam line. Therefore, multiwire proportional chambers(MWPCs) with 1 mm anode pitch were constructed for BC1 and BC2. Note that there
are practical diﬃculties in precisely stringing and soldering wires at a pitch below 1 mm.
A schematic view of the wire structure of the MWPC is shown in Fig. 2.7. Each of
BC1 and BC2 has 6 layers labeled like [xuvxuv], where x stands for a vertical-wire planeand u and v are ±15◦ -tilted wire planes. The sense wire is a gold-plated tungsten wire
alloyed with 3% rhenium with a diameter of 15 µm. The cathode planes are made of 12µm thick mylar ﬁlms coated with a 20 µm thick graphite paste to reduce the damage
from discharge. The gas mixture was Ar (76%) + iso-C4 H10 (20%) + methylal (4%)
at the atmospheric pressure. For the front-end readout electronics, an ampliﬁer-shaperdiscriminator chip (CXA3183Q TGC ASD [124]) was used. The timing information of
the MWPCs was digitized by an 100 MHz sampling MWPC encoder mounted on the
COPPER boards.
As described in Sec. 2.2, the spikes in the beam structure severely prevented a stable
operation of gas chambers. This eﬀect was the most serious for BC1 and BC2. In the2012 run, we adjusted the operational high voltage of the cathode planes to slightly
lower values of 2.43–2.47 kV, whereas the value applied in the 2010 run was 2.51 kV.
Figure 2.8 shows a eﬃciency curve for a layer of BC1. The detection eﬃciency becomes
lower by a few percent; however, BC1 and BC2 have a redundant conﬁguration of 12
layers. The low voltage operation had a merit because it let us handle an beam intensity

30

CHAPTER 2. EXPERIMENTAL APPARATUS

of 1.7 × 106 /spill, which is 1.7 times higher than that of the 2010 run.
ASD readout

track
Cathode
3 mm
Anode
1 mm

Cathodecell
ASD readout

FIG. 2.7: (Left) Cell structure of the MWPC (BC1 and BC2). (Right) Front view of ananode plane of the MWPC.

FIG. 2.8: Detection eﬃciency for a layer of the MWPC (BC1) as a function of high voltage
of cathode planes.

2.3. BEAM SPECTROMETER

31

Cathode plane
2 mm
dl1

Anode
Potential

Cathode plane
dl2

3 mm

Cathode plane

FIG. 2.9: Cell structure of the drift chamber BC3.

Drift chambers (BC3 and BC4)
In order to cope with several MHz counting rate at the downstream part of the beam
spectrometer, a drift chamber with a sense wire pitch of 3 mm was fabricated and used
as BC3. For BC4, a drift chamber with a sense wire pitch of 5 mm was recycled fromthe KEK-PS K6 beam line, because of a practical scheduling. Each drift chamber has 6
layers labeled like [xx′ uu′ vv ′ ], where x stands for a vertical-wire plane and u and v are±15◦ -tilted wire planes. In each pair plane, the sense wire position is shifted by a halfof the cell size in order to solve the left/right ambiguity. Figure 2.9 shows a schematic
view of the cell structure of BC3. For both BC3 and BC4, the sense wire is a gold-plated
tungsten wire alloyed with 3% rhenium with a diameter of 12.5 µm, and the ﬁeld wire
is a gold-plated copper-beryllium wire with a diameter of 75 µm. The cathode planesof BC3 are made of 12 µm thick mylar ﬁlms coated with a 20 µm thick graphite paste,
while the cathode planes of BC4 are made of 7.5 µm-thick kapton coated with 0.1 µm
thick aluminum and 0.0025 µm thick chromium. The gas mixture was Ar (76%) + isoC4 H10 (20%) + methylal (4%) at the atmospheric pressure. For the front-end readout
electronics, the same ASD as BC1 and BC2 was commonly used for BC3 and BC4. The
timing information of BC3 and BC4 was digitized by a multi-hit TDC (AMT-2 [125])
mounted on the TKO boards.

2.3.2

Trigger counters for the beam spectrometer

Speciﬁcations of the trigger counters for the beam spectrometer (BH1, BH2, and GC)
are listed in Table 2.3.
Beam hodoscope counters (BH1 and BH2)
The plastic scintillation hodoscope counters, BH1 and BH2, were used as trigger andtime-of-ﬂight counters. Beam particles were identiﬁed by the time of ﬂight between BH1and BH2 with a ﬂight path of 10.4 m and with a time resolution of 0.2 ns (rms).

32

CHAPTER 2. EXPERIMENTAL APPARATUS
TABLE 2.3: Speciﬁcations of the trigger counters.

Name
GC
BH1
BH2
TOF
AC
LC

Sensitive volume
W × H × T (mm)340 × 80 mirror , 290 gas
170 × 66 × 5145(133) × 60 × 52240 × 1000 × 30
2040 × 1200 × 113
2800 × 1400 × 40

Etc.

PMT

iso-C4 H10 , n = 1.002 (1.5 atm)
11 segments, BC420
7 segments, BC420
32 segments, BC410
Silica aerogel, n = 1.05
28 segments, Lucite, n = 1.49

R1250-03 (UV glass)H6524MOD
H6524MOD
H1949
R1584-02, Burle 8854
H1949, H6410

BH1 is a plastic scintillation counter located between GC and BC1. It is segmented
into 11 vertical pieces of 5 mm thick plastic scintillators to balance the counting rateof each segment. A schematic view of BH1 is shown in Fig. 2.10. Each segment isoverlapped with its adjacent segments by 1 mm to avoid a dead space. Photomultipliertubes (PMTs) are connected on both ends of each segment and a high voltage powerwith a three-stage booster was supplied.
BH2 is a plastic scintillation counter located 120 cm upstream of the target. It issegmented into 7 vertical pieces of 5 mm thick plastic scintillators. A schematic viewof BH2 is shown in Fig. 2.11. Each segment was overlapped with its adjacent segmentsby 2 mm in the 2010 run. Since BH2 is placed between the beam spectrometer and thescattered-particle spectrometer, it should be made as thin as possible to minimize theenergy loss straggling in the counter. Therefore, the segment conﬁguration of BH2 was
modiﬁed to no overlap before the 2012 run. PMTs are connected on both ends of eachsegment and a high voltage power with a three-stage booster was supplied. The BH2 hit
timing deﬁned the trigger timing and the time origin for any timing measurements.
Gas Cherenkov counter (GC)The gas Cherenkov counter, GC, was installed at the most upstream of the beam spectrometer to reject electrons/positrons in the momentum range above 1 GeV/c, where itis diﬃcult to separate pions from electrons by the time-of-ﬂight method. The Cherenkov
radiator is an isobutane gas of 1.5 atm, which corresponds to a refractive index n = 1.002.
A paraboloidal mirror is used as the reﬂector, which is made of aluminum evaporated ona borosilicate glass of 6 mm thickness. For the antioxidation of aluminum, the surface iscoated with MgF2 , which is transmissive to ultraviolet photons. The Cherenkov photons
are detected by a 5-inch PMT with a UV-transmissive window. Figure 2.12 shows aschematic view of GC. The measured number of photoelectrons was approximately 5
for electron beams of higher than 0.5 GeV/c. The detection eﬃciency was found to be
99.5%, which was enough to reject electrons contaminating 10–20% of the beam.

2.3. BEAM SPECTROMETER

Back

33

Side

Front
Y
Acrylic
Light Guide

Beam
t=5

X
66

Scintillater
BC420

Hamamatsu
H6524MOD

Beam
12

20

170

8
8
16

30

FIG. 2.10: Schematic view of the BH1 counter.

Back

Side

Front
Y
Acrylic
Light Guide

Beam

t=5

X
60

Scintillater
BC420

Hamamatsu
H6524MOD

Beam
20

133

15
15
30
FIG. 2.11: Schematic view of the BH2 counter. Notice that each segment was not overlapped in the 2012 run.

34

CHAPTER 2. EXPERIMENTAL APPARATUS

Hamamatsu
R1250-03 (UV glass)

200 mmyx

250 mmf340 mm

80 mm
Glass
t=6 mmMirror

290 mmAl
t=1 mmz

BeamAl
t=1 mmFIG. 2.12: Schematic view of the gas Cherenkov counter (GC).

2.4

Superconducting Kaon Spectrometer

The Superconducting Kaon Spectrometer (SKS) comprises a superconducting dipole
magnet with four sets of drift chambers (SDC1–SDC4) and three types of particleidentiﬁcation counters (TOF, AC, and LC), as shown in Fig. 2.6. A remarkable featureof the spectrometer is a simultaneous realization of both a good momentum resolutionof 2 × 10−3 (FWHM) and a large acceptance of 100 msr around 1 GeV/c. In addition,
it keeps the ﬂight path as short as 5 m, and has a powerful kaon identiﬁcation ability.
The SKS was originally designed and constructed for the study of Λ hypernuclei via
the (π + , K + ) reaction at the KEK K6 beam line [126]. The SKS magnet was moved to
the J-PARC K1.8 beam line. The detectors were upgraded to increase the momentum
acceptance and the high rate capability. Details of each detector are described in thefollowing subsections.
Particle trajectories are reconstructed particle by particle using hit positions of thedrift chambers together with a magnetic ﬁeld map. The pole gap and the open spacefrom SKS to SDC3 were occupied with helium bags to reduce multiple scattering eﬀects.
The magnet was excited at 2.5 T, and the ﬁeld at the central region was monitored during
the experimental period by an NMR probe [127]. The setup of SKS was slightly changed
between 2010 and 2012 as follows: (i) the incident angle to the magnet face was adjusted
from 30◦ to 15◦ ; (ii) the AC detector was replaced with a new larger-size detector,
while two small-size ACs were used in the 2010 run. Owing to these modiﬁcations, themomentum acceptance was changed from 0.75–1.0 GeV/c to 0.8–1.2 GeV/c, and the ﬂat
acceptance region increased. Speciﬁcations of the SKS spectrometer are summarized inTable 2.4.

2.4. SUPERCONDUCTING KAON SPECTROMETER

35

TABLE 2.4: Speciﬁcations of the SKS spectrometer.

Maximum ﬁeld
Pole gap
Momentum resolution
Momentum acceptanceSolid angle
Angular coverage
Flight path (Target–TOF)

2.5 T
49.75 cm
∼ 2 × 10−3 (FWHM)
0.8–1.2 (0.75–1.0) GeV/c
100 msr< 5◦ (vertical), ≲ 15◦ (horizontal)∼5m

Cathode (GND)
Potential (-450 V)
Potential (-350 V)

12 mm
Anode (~+2200 V)

Drift length

Potential (-450 V)

20 mm

FIG. 2.13: Cell structure of the drift chambers, SDC3 and SDC4.

2.4.1

Tracking chambers for the SKS

Speciﬁcations of the tracking chambers for the SKS (SDC1–SDC4) are listed in Table 2.2.
Drift chambers (SDC1 and SDC2)
The drift chambers, SDC1 and SDC2, were installed at the entrance of the SKS magnet.
Since they are exposed to the beam, they are required to have the high rate capability
at the same level as that of BC3 and BC4. SDC1 has 4 layers with a sense wire pitch of
3 mm, while SDC2 has 6 layers with a sense wire pitch of 5 mm. The structure of SDC1
is identical to that of BC3, and the structure of SDC2 is also similar to SDC1 except
for the wire spacing and the size of the eﬀective area. The gas mixture and readout
electronics were the same as those of BC3 and BC4.
Drift chambers (SDC3 and SDC4)
The drift chambers, SDC3 and SDC4, were installed at the exit of the SKS magnet. They
have a large eﬀective area of 2140 (horizontal) × 1140 (vertical) mm2 . Each chamber
has 6 layers labeled as [vxuvxu], where x stands for a vertical-wire plane and u and v are±30◦ -tilted wire planes. The sense wire pitch is 20 mm. Figure 2.13 shows a schematic
view of the cell structure. The sense wire is a gold-plated tungsten wire alloyed with 3%
rhenium with a diameter of 25 µm, and both the ﬁeld and cathode wires are a gold-plated

36

CHAPTER 2. EXPERIMENTAL APPARATUS

cFront viewc

Top view

ZTOF

30 mm

YTOF 70 mm

c

XTOF

1000 mm

c

O

Beam
Segment
Number 32 31 30 29

c

18 17 16 15

c

3 2 1

Scintillator
BC410
Acrylic Light Guide
Hamamatsu H1949

FIG. 2.14: Schematic view of the TOF counter.

copper-beryllium wire with a diameter of 80 µm. The gas mixture was Ar (50%) + C2 H6(50%) at the atmospheric pressure. After passing through a front-end ASD, the timing
information of SDC3 and SDC4 was digitized by a single-hit TDC module (TKO Dr.T
II).

2.4.2

Trigger counters for the SKS

Speciﬁcations of the trigger counters for the SKS are listed in Table 2.3.
Time-of-ﬂight counter (TOF)
The time-of-ﬂight counter, TOF, is a segmented plastic scintillation counter locatedat just the downstream of SDC4. TOF is horizontally segmented into 32 pieces ofscintillators with a volume of 70W × 1000H × 30T mm3 . Photomultiplier tubes (PMTs)
are connected on both ends of each segment. A schematic view of TOF is shown in
Fig. 2.14. A part of the segments (#1–10) installed at the high-momentum side were
not used in the present experiment, because they are out of acceptance needed for theΘ+ search. Scattered particles are identiﬁed by the time-of-ﬂight measurement between
TOF and BH2 in an oﬄine analysis with a typical time resolution of 0.2 ns (rms).
Aerogel Cherenkov counter (AC)The threshold-type silica aerogel Cherenkov counter, AC, was installed at just the downstream of TOF for pion veto at the trigger level. As shown in Fig. 2.15, pions with
momenta above a threshold of 0.44 GeV/c emit the Cherenkov radiation in silica aero-2.4. SUPERCONDUCTING KAON SPECTROMETER

37

Refractive index (= 1/ β )

1.6
1.5
1.4

Lucite

p
Water

1.3
1.2

K

π

1.1
1.0
0.9
0.2

Aerogel

e
0.4

0.6
0.8
1.0
Momentum [GeV/c]

1.2

1.4

FIG. 2.15: Threshold refractive index for the Cherenkov radiation as a function of theparticle momentum.

gels with a refractive index of 1.05. The sensitive volume of AC is 2040W × 1200H × 113T
mm3 . Figure 2.16 shows a schematic view of AC. For the uniform eﬃciency without
dead space over a large sensitive area, AC is not segmented but of a large one-box type.
The inner surfaces of the counter box are covered with aluminized mylar sheets. The
Cherenkov photons are reﬂected by a mirror behind the radiator, and detected by 5-inch
PMTs placed on both sides, which are sensitive to a single photon.
In the present experiment, the AC eﬃciency for pions was 98%, which deteriorated,locally due to support plates placed at Y = ±200 mm, and globally due to gaps of the
aerogel tiles (see Appendix A). In addition, since the horizontal size of the AC radiator
is smaller than that of TOF and LC, AC was inactive to the lowest momentum region,
which corresponds to the last two segments of TOF (#31, 32).
Lucite Cherenkov counter (LC)The threshold-type lucite Cherenkov counter, LC, was installed just the downstream of
AC. As shown in Fig. 2.15, protons with momenta below a threshold of 0.85 GeV/c
are insensitive to the Cherenkov radiation in lucite (acrylic) with a refractive index of
1.49. LC is horizontally segmented into 28 vertical pieces of lucite bars with a volumeof 100W × 1400H × 40T mm3 . PMTs are connected on both ends of each segment.
A schematic view of LC is shown in Fig. 2.17. In order to keep the uniform detection
eﬃciency for various incident angles, a wavelength shifter (bis-MBS) is mixed in the lucite
radiator by 10 ppm in weight, by which directional Cherenkov photons are diﬀused. Dueto the scintillating radiation of the wavelength shifter, LC is slightly sensitive to protons
even below the threshold. A part of the segments (#1–7) installed at the high-momentum
side were not used in the present experiment, because they are out of acceptance needed
for the Θ+ search.

38

CHAPTER 2. EXPERIMENTAL APPARATUS

FIG. 2.16: Schematic view of the AC counter.

c

Top view

ZLC

40 mm
100 mmFront view

XLC

c

1400 mm

c

YLC

O
Beam

Segment
Number 28 27 26 25

c

16 15 14 13

c

3

2

1

Lucite +bisMSB

Acrylic Light
Guide
Hamamatsu
H1949

FIG. 2.17: Schematic view of the LC counter.

2.5. TRIGGER

39

FIG. 2.18: (π, K) trigger logic diagram.

2.5

Trigger

The trigger system was constructed to select (π, K) events eﬃciently from a large background produced through various pion-induced reactions, such as (π, π) and (π, p) 3
in addition to muons from beam pion decay, whose cross sections are typically two or
three orders of magnitude larger than that of the (π, K) reaction. The trigger used only
fast signals from the scintillation counters and the Cherenkov counters with a minimum
trigger latency. The (π, K) trigger logic diagram is illustrated in Fig. 2.18.
The pion beam trigger was deﬁned by the coincidence between BH1 and BH2 together
with the anticoincidence of GC as
BEAM ≡ BH1 × BH2 × GC.
For the scattered kaon trigger, TOF, AC and LC were used to eliminate scattered pions
and protons as T OF × AC × LC. In addition, the matrix trigger (M T X), which isa coincidence matrix between the TOF and LC segments, was adopted to reject theparticles coming not from the target but from detector frames. As shown in Fig. 2.19,
particles passing through the SKS magnet make a correlation in hit segments between
TOF and LC, which appears from the lower left to the top right corner on the ﬁgure. The
open boxes represent kaon events identiﬁed by the SKS tracking, whereas entire triggered
events are shown in a dark scale. A locus on the top left corner originates from particles
generated by the beam hitting the SDC3 frame. Such events were rejected by the matrix
trigger, which accepted the region surrounded by the red lines. The trigger rate was
reduced to 1/2 using the matrix trigger. The matrix coincidence was implemented using
an FPGA module (TUL-8040 [128]). Then, the (π, K) trigger was deﬁned as
P IK ≡ BEAM × T OF × AC × LC × M T X.
Since the present experiment aimed at the π − p → K − X reaction, (π, p) events came into detection
only in calibration runs using the π ± p → K + Σ± reactions.
3

40

CHAPTER 2. EXPERIMENTAL APPARATUS

LC hit segment

25
20
15
10
5

10

15
20
25
TOF hit segment

30

FIG. 2.19: Hit segment correlation between TOF and LC taken with the (π, K) trigger
without the matrix trigger. Entire triggered events are shown in a dark scale, while theopen boxes represents kaon events identiﬁed by the SKS tracking. The red line indicatesthe region accepted by the matrix trigger.

In order to study ineﬃciency of the matrix trigger, the (π, K) trigger data without thematrix coincidence were simultaneously acquired at a 1/10 prescaled rate. A typicaltrigger rate for the π − p → K − X data was 600 per spill at a beam rate of 1.7 × 106 per
spill.

2.6

Data-acquisition system

For the data acquisition (DAQ) system of the K1.8 experimental area, we adopted a
new network-oriented readout module, KEK-VME/COPPER [129], as well as conventional readout systems such as VME, CAMAC, and TKO [130]. These diﬀerent DAQ
subsystems were integrated by a network-based DAQ software (HDDAQ) [131]. Today,
networking communication among the inter-subsystem has become the most common
method. Data from each subsystem are gathered by controllers having network interfaces
with the TCP/IP protocol. However, since the network is an asynchronous communication, the event identiﬁcation becomes an issue. Therefore, the master trigger module(MTM) and the receiver module (RM) were developed for the experiment [131]; the system distributes an event tag to each subsystem. The entire scheme of the DAQ system
is illustrated in Fig. 2.20.
MTM manages functions controlling the DAQ system such as “trigger”, “clear”,“busy”, and the event tag. These information are distributed via the Ethernet cablefrom MTM to RM of each subsystem. The trigger signal is used as a start/stop timingof TDC and a gate of ADC. The busy signals issued in the subsystems veto the next

2.6. DATA-ACQUISITION SYSTEM

41

trigger on MTM. The event tag is decoded in RMs and embedded in an event packet. The
tags embedded in the data structure are checked at the beginning of the data analysis.
After ﬁnishing the analog-to-degital conversion, the data are transferred to an event
builder.
HDDAQ is a network-based DAQ software consisting of several DAQ components, i.e.,
Front-end (FE), Event Builder (EB), Event Distributor (ED), and Recorder (RD). The
FE process is running on each front-end computer, while other components are runningon the control DAQ server. These components have two diﬀerent paths, namely, “datapath” and “message path”, with the TCP/IP protocol. The data path is a pathway
to individual detector data, while all components are controlled via the message path.
The FE process reads data from each readout electronics and transmits them to the EB
process. The EB process collects data fragments from FEs and builds an event packet
event by event. This packet is sent to the ED process, which distributes it to downstream
processes such as RD and online monitors. The RD process reads data from ED andstores them to storage devices with compression.

42

CHAPTER 2. EXPERIMENTAL APPARATUS

FIG. 2.20: Schematic diagram of the data-acquisition system.

2.7. LIQUID HYDROGEN TARGET

2.7

43

Liquid hydrogen target

We used a liquid hydrogen (LH2 ) target with a thickness of 0.85 g/cm2 . Figure 2.21
shows a schematic view of the target system. The hydrogen vessel size was 67.8 mm indiameter and 120 mm in length along the beam direction. The hydrogen vessel was madeof a 0.30-mm thick PET (polyethylene terephthalate) for the cylinder part, and a 0.25mm thick mylar for the end cap part. The windows of the target vacuum chamber weremade of a 0.25-mm thick mylar. The hydrogen target was cooled by a heat exchanger
and continuous ﬂow of cold helium gas from a liquid helium container. The stabilityof the pressures and temperature was kept by a feedback system of the He ﬂow, andmonitored during the experimental period. The density ﬂuctuation was found to be lessthan 3 × 10−5 . Speciﬁcations of the liquid hydrogen target are summarized in Table 2.5.
TABLE 2.5: Speciﬁcations of the liquid hydrogen target.

Vessel size
ϕ67.8 × 120 mm
Vessel material
PET (cylinder), Mylar (end cap)
Average thickness
0.30 mm (cylinder), 0.25 mm (end cap)
Target chamber
Aluminum: t = 3 mm, ϕ270 mm
Chamber window
Mylar: t = 0.25 mm
LH2 thickness
0.85 g/cm2 (0.0708 g/cm3 × 12 cm)
Density ﬂuctuation < 3 × 10−5

Target chamber

Target cellMylar
(t=0.25)

Mylar(t=0.25)
Mylar
0.25

PET ( f 67.8, t=0.3)

Mylar
Mylar
(t=0.25)
0.25

t=3
AlAl.
(t=3)

Mylar
(t=0.25)

FIG. 2.21: Schematic view of the liquid hydrogen target. All units are in mm.

44

CHAPTER 2. EXPERIMENTAL APPARATUS

2.8

Data summary

Table 2.6 shows the data summary of the E19 experiment taken in both the previous
and present runs in 2010 and 2012, respectively. For the Θ+ search data, the π − p →K − X reaction at 1.92 and 2.01 GeV/c were accumulated in the 2010 and 2012 runs,
respectively. In the present data, 8.1 × 1010 π − beams were irradiated on the liquidhydrogen target, which is almost the same amount as the previous data of 7.8 × 1010 .
Empty target data with the empty vessel instead of the liquid hydrogen target werealso taken in order to estimate a background contamination from surrounding materials
and the vertex cut eﬃciency. For the momentum calibration of the spectrometers, thefollowing two kinds of calibration data were used:Σ production data The outgoing kaon momenta in the π − p → K − Θ+ (1530) reaction at 2.01 GeV/c are around 1.0 GeV/c at forward angles. The kinamatics of theoutgoing kaons in the π − p → K + Σ− reaction at 1.46 GeV/c is similar to that inthe π − p → K − Θ+ (1530) reaction at 2.01 GeV/c (see Fig. 3.25 in detail). Therefore, the π − p → K + Σ− reaction at 1.46 GeV/c are useful for various calibration.
In the same manner, the π ± p → K + Σ± reactions at 1.38 GeV/c correspond tothe π − p → K − Θ+ (1530) reaction at 1.92 GeV/c. The validity of the analysis is
examined by using the missing-mass peak and the cross section of the Σ hyperons.
Beam-through data A low-momentum pion beam of 0.75–1.38 GeV/c can directly
pass through the both spectrometers. This kind of data is called π ± beam-throughdata. The data were acquired at several momentum settings between 0.75 and 1.38
GeV/c with both positively and negatively charged beams.
In the subsequent chapters, the analysis and result of the 2012 data are presented.
TABLE 2.6: Summary of the E19 experimental data. The 2010 and 2012 data represent
the previous and present data, respectively. The ﬁrst row is the Θ+ search data, while theothers are calibration data.

Reaction

Beam momentum Target Number of pions on target(GeV/c)2010 data
2012 data−−
10
π p→K X
1.92 / 2.01
LH2
7.8 × 10
8.1 × 1010
9
Empty run
1.92 / 2.01
empty 4.6 × 10
4.1 × 109π + p → K + Σ+
1.38
LH2
2.9 × 109
8.5 × 108π − p → K + Σ−
1.38
LH2
1.2 × 1010
3.8 × 109−
+ −π p→K Σ1.46
LH2—
8.7 × 109
π ± beam-through
0.75–1.38
empty
—
—

Chapter 3
Data Analysis
3.1

OutlineThe Θ+ was searched for in a missing mass spectrum of the π − p → K − X reaction. The
missing mass, MX , is calculated in the laboratory frame as follows:√
MX =(Eπ + mp − EK )2 − (p2π + p2K − 2pπ pK cos θ),(3.1)

where Eπ and pπ are the energy and momentum of a beam pion, respectively; EK and pK
are those of a scattered kaon; mp is the mass of a target proton; and θ is the scattering
angle. Thus, there are three kinematic variables to be measured: pπ , pK and θ.
The procedure of the missing mass reconstruction was as follows:
1. event selection by using counter information,
2. momentum reconstruction for beam and scattered particles,
3. particle identiﬁcation of kaons,
4. reconstruction of the scattering angle and the vertex point, and5. calculation of the missing mass.
Details of the procedure are described in Secs. 3.2, 3.3 and 3.4.
The calibration procedures applied in the present analysis are described in Secs. 3.6
and 3.7. Analyses on both the momentum scale calibration and the momentum resolution
are performed by using the dedicated calibration data: the Σ± production data and theπ ± beam-through data.
The method of the cross section calculation is described in Sec. 3.8. The cross section
is calculated with experimental eﬃciency and acceptance correction. The validity of themethod is examined through the Σ± production cross sections in Sec. 3.9.
45

46

CHAPTER 3. DATA ANALYSIS

3.2

Analysis of beam particles

3.2.1

Beam particle identiﬁcation

The beam particles were identiﬁed by using the time of ﬂight between BH1 and BH2
with a ﬂight length of 10.4 m. Figure 3.1 shows a typical time-of-ﬂight spectrum for a
2-GeV/c π − beam, where the π peak position was adjusted to be zero in the horizontal
axis. The same spectrum in a logarithmic scale is shown in the inset. The continuous
background around the peak was due to accidental hits on BH1 and BH2. Neither kaons(+1.0 ns) nor antiprotons (+3.5 ns) are seen because their production and survival rate
to the target position is two orders of magnitude smaller than that of pions. Furthermore,
the electrostatic separators could reject protons in case of π + beams. A contamination
rate of muons, which con not be separated from poions by the time-of-ﬂight method, aredescribed in Sec. 3.8.1. Electron contamination in the beam trigger was negligibly small
as described in Sec. 2.3.2. The time resolution of the time-of-ﬂight measurement is 0.2
ns (rms). The cut positions were set at ±1 ns with the eﬃciency of 96.8 %.
104

Counts / (0.05 ns)

Counts / (0.05 ns)

5000

π-

3

4000

π

-

3000

10

102
10
1
-5 -4 -3 -2 -1 0 1 2 3 4 5Beam TOF [ns]

2000
1000
0
-5

-4

-3

-2

-1 0
1
2
Beam TOF [ns]

3

4

5

FIG. 3.1: Time-of-ﬂight spectrum for a 2-GeV/c π − beam. The inset shows the same
spectrum in a logarithmic scale. The selected time window is indicated by the dashedlines.

3.2.2

Beam track reconstruction

The beam momentum was reconstructed from the BC1–4 data as follows. First, straightline tracks were deﬁned locally at the entrance and exit of the QQDQQ magnets by thelinear least-squares ﬁtting. In the MWPC (BC1 and BC2) tracking, hits on adjoining
wires within a proper timing of ±10 ns were made up as a cluster hit and the weightedmean position of the cluster was used. In the drift chamber (BC3 and BC4) tracking,the drift time was converted to the drift length and the pair-plane information wasused to solve the left/right ambiguity. Figure 3.2 shows typical χ2 distributions for the3.2. ANALYSIS OF BEAM PARTICLES

47

104

104
All tracks
Single track

103
CountsCounts

103
102

102

10

10

1

1

0

5

10

15
20
χ (BC1,2)

25

All tracks
Single track

30

0

2

5

10

15
20
χ (BC3,4)

25

30

2

FIG. 3.2: χ2 distributions of the local straight-line tracking of BC1 and BC2 (left), andBC3 and BC4 (right). The red histograms denote single track events. The dashed lines
indicate the χ2 cut positions.

local straight-line tracking. The red histograms represent single track events, while theblack histograms represent all tracks including multitrack events. The multitrack event
consists of a triggered (true) track and subsequent (false) tracks. For the drift chambers(Fig. 3.2 (right)), the single track events show a reasonable χ2 distribution, whereas
the χ2 distribution for multitrack events shows a bump structure around 20, because
the subsequent tracks do not have a proper drift time. Most of the subsequent tracks
were excluded by setting the cut position at χ2 = 10 without decreasing the tracking
eﬃciency.
Next, the straight-line tracks determined at the entrance and exit of the QQDQQ
magnets were connected using a transport matrix (third-order in horizontal and secondorder in vertical) calculated by orbit [132]:⃗ out = M(X⃗ in ),
X(3.2)⃗ in and X⃗ out are vectors that represent positions, directions and momentum (p)where X()
⃗ = x, dx , y, dy , p ; the local (x, y, z) coordinate was deﬁnedof the particle such as X
dz
dz
⃗ in and X⃗ out
as shown in Fig. 3.3. VI and VO stand for reference planes in which X
are deﬁned, respectively. The operator M denotes the transport matrix. The particle
trajectory was determined by minimizing the following χ2 value:

(
(
)2
)2 
24
12
∑
∑
⃗
⃗
1 
Pi − gi (Xout ) 
Pi − fi (Xin )χ2K1.8 ≡
+
Hi
(3.3)
Hi
n − 5 i=1
wi
wi
i=13
n =

24
∑

{

Hi ,

i=1

Hi =

1 if i-th plane has a hit,
0 if i-th plane has no hit

(3.4)
}
,

(3.5)

48

CHAPTER 3. DATA ANALYSIS

z
x

y

5m

VO

BH2
BC4
BC3

Q13
Q12

x

D4
z

y

VI
GC BH1BC1 BC2Q10 Q11

FIG. 3.3: Reference planes VI and VO in which the local coordinates are deﬁned. VI
is deﬁned at a 13-cm upstream of the entrance of Q10, while VO is deﬁned at a 13-cm
downstream of the exit of Q13.

where Pi and wi denote the hit position and resolution of the i-th plane in BCs, respectively. The calculated position by the transport matrix at the i-th plane is denoted by⃗ in ) or gi (X⃗ out ). The minimization was done for each combination of the straight-linefi (X⃗ in as parameters.
tracks by using minuit [133] with respect to X
2
Figure 3.4 (left) shows a typical χK1.8 distribution for a 2-GeV/c π − beam. Eventswith χ2 less than 30 were accepted as good tracks. Figure 3.4 (right) shows a momentum
distribution for a 2-GeV/c π − beam. The central momentum was found to be 2.01
GeV/c 1 and the momentum spread was 1% in rms. In the present analysis, events
including more than two beam tracks were discarded, which corresponds to 6% of thetotal events. Figure 3.5 shows a typical beam proﬁle at the target position in the Θ+
search data at 2 GeV/c. The beam was irradiated to the LH2 target with a typicaltargeting eﬃciency of 96%. Since 2 GeV/c is the maximum momentum of the K1.8
beam line, the horizontal proﬁle was skew toward right in the ﬁgure.

1

This value is the one obtained after applying the momentum scale calibration described in Sec. 3.6.3

3.2. ANALYSIS OF BEAM PARTICLES

49

5000
Counts / (MeV/c)

104

Counts

4000

103

3000

102

2000
1000

10
0

5 10 15 20 25 30 35 40 45 50
χ2(K1.8)

0
1.90

1.95
2.00
2.05
Beam Momentum [GeV/c]

2.10

FIG. 3.4: (Left) χ2K1.8 distribution of the K1.8 tracking for a 2-GeV/c beam. The dashedline indicates the cut position. (Right) Reconstructed beam momentum distribution for a
2-GeV/c beam.

Vertical position (y) [mm]

100

50

0

-50

-100
-100

-50
0
50
Horizontal position (x) [mm]100FIG. 3.5: Beam proﬁle at the target position in the Θ+ search data at 2 GeV/c. The(x, y, z) coordinate is deﬁned in the right-handed system with the z-axis as the nominal
beam direction. The beam proﬁle peaks at (x, y) = (7 mm, −2 mm) with (σx , σy ) =(11 mm, 4 mm). The horizontal proﬁle is skew toward right in this ﬁgure. The red circle
indicates the target vessel with a diameter of 67.8 mm.

50

CHAPTER 3. DATA ANALYSIS

104

102

102

10

10

1

1
0

0

All tracks
Single track

103
CountsCounts103

104

All tracks
Single track

5 10 15 20 25 30 35 40 45 50
χ2(SDC1,2)

5 10 15 20 25 30 35 40 45 50
χ2(SDC3,4)

FIG. 3.6: χ2 distributions of the local straight-line tracking of SDC1 and SDC2 (left), andSDC3 and SDC4 (right). The red histograms denote single track events. The dashed lines
indicate the χ2 cut positions.

3.3

Analysis of scattered particles

3.3.1

Scattered-particle track reconstruction

The momentum of a scattered particle was reconstructed from the SDC1–4 data as
follows. First, straight-line tracks were deﬁned locally at the entrance and exit of the
SKS magnet by the linear least-squares ﬁtting. The same local tracking method as forBC3 and BC4 was applied both for SDC1 and SDC2 and for SDC3 and SDC4. For
SDC3 and SDC4, all combinations of the left/right ambiguity were examined because
they do not have the pair-plane structure. Figure 3.6 shows typical χ2 distributions forthe local straight-line tracking. The red histograms denote single track events. In the χ2
distribution for the local tracking of SDC1 and SDC2 (Fig. 3.6 (left)), a bump around
30–40 caused by multitrack events was observed due to the same reason as for BC3 andBC4. Most of the subsequent tracks were excluded by setting the cut position at χ2 = 20
without decreasing the tracking eﬃciency. In the χ2 distribution for the local trackingof SDC3 and SDC4 (Fig. 3.6 (right)), multitrack events were rarely observed, because
the beam does not pass through the chambers. In addition to the χ2 cut, a position
matching between the hit segment of TOF and the local track of SDC3 and SDC4 waschecked.
Next, the momentum of the scattered particle was determined by reconstructing the
trajectory from the chamber hit positions. The trajectory was reconstructed with thefast Runge-Kutta method [134] using a magnetic ﬁeld map of SKS. The magnetic ﬁeld
map was calculated by ansys [135] using the ﬁnite element method. The trajectory andthe momentum were iteratively optimized by minimizing the following χ2 value:n
1 ∑2
χSKS ≡n − 5 i=1(

xtracking− xdata
i
i
wi

)2
,

(3.6)

3.3. ANALYSIS OF SCATTERED PARTICLES

51Counts

104

103

102

10
0

5

10 15 20 25 30 35 40 45 50
χ2(SKS)

FIG. 3.7: χ2SKS distribution of the SKS tracking for scattered proton events contaminating
the Σ− production data. The dashed line indicates the cut position.

where n is the number of the chamber planes with a hit; xtracking
and xdata
are the hitiipositions on the i-th hit plane in the tracking and the data, respectively; and wi is the
position resolution of the i-th hit plane. The ﬁtting parameters were the momentum (p),the horizontal (x) and vertical (y) positions and their derivatives (dx/dz, dy/dz) at thetarget position. The convergence criterion in the iteration was δχ2 = (χ2k+1 − χ2k )/χ2k <2 × 10−4 , where χ2k is the tracking χ2 for the k-th iteration.
Figure 3.7 shows a typical χ2SKS distribution for scattered proton events in the calibration data. Events with χ2 less than 30 were accepted as good tracks. The tracking
eﬃciency is discussed in Sec. 3.8.1.

3.3.2

Scattered-particle identiﬁcation

After the SKS tracking, the mass of a scattered particles, Mscat , was calculated as
Mscat =

p√1 − β 2,β(3.7)

where β is the velocity of a scattered particle obtained from the time-of-ﬂight and theﬂight path length between BH2 and TOF; and p is the momentum obtained from the
SKS tracking. In the (π, K) trigger events, a main source of background in scatteredparticles were fast protons which ﬁred LC and pions which were not vetoed by AC due
2) distributions in the Θ+
to its ineﬃciency. Figure 3.8 shows typical squared-mass (Mscat
search data and the Σ+ production data. Negatively charged particles are detected in theΘ+ search data, while positively charged particles are detected in the Σ production data.
The kaon cut region was determined in order to reduce contamination from other particles
without decreasing the eﬃciency described below. The kaon cut region is indicated in2< 0.40 (GeV/c2 )2 .
the spectra: 0.15 < Mscat

52

CHAPTER 3. DATA ANALYSIS

2500
2000

π-

Counts

-

K

1500
1000
500
0
-0.2

0

0.2

0.4

0.6

0.8

1

0.8

1.0

2 2

Squared Mass [(GeV/c ) ]
1200

p

1000

Counts

800
600
400

π+

K+

200
0
-0.2

0.0

0.2

0.4

0.6
2 2

Squared Mass [(GeV/c ) ]FIG. 3.8: Squared mass distribution for scattered particles in the Θ+ search data (top)and the Σ+ production data (bottom). A momentum range of 0.9–1.1 GeV/c is selectedin the top ﬁgure. The vertex cut and the scattering angle selection of 2–15◦ have been
applied in both ﬁgures. The dashed lines indicate the kaon selection gate.

3.3. ANALYSIS OF SCATTERED PARTICLES

53

Kaon identiﬁcation and pion contamination
In the squared-mass distribution, a peak for each particle has a tail ascribed to the time
walk eﬀect of TOF and time lags among the TOF segments. Figure 3.9 shows a masssquared distribution in a logarithmic scale. In order to estimate the kaon identiﬁcationeﬃciency, two types of assumptions were considered:(a) Assume that the low-mass tail of the kaon peak is subjected to the Gaussian
distribution. This may slightly underestimate the total amount of kaons, since a
low-mass tail tends to be longer than the Gaussian distribution.
(b) Assume that the low-mass tail shape of the kaon peak is the same as that of thehigh-mass tail. This may slightly overestimate the total amount of kaons, since a
low-mass tail tends to be shorter than a high-mass tail.
A result of the peak ﬁttings for pions and kaons by using the Gaussian function is shown2
in Fig. 3.9. The kaon identiﬁcation eﬃciency for 0.15 < Mscat< 0.40 (GeV/c2 )2 was
calculated according to the assumption (a) or (b). The mean value between the resultsfrom (a) and (b) was adopted, and the diﬀerence of the two results was attributed to thesystematic uncertainty. In order to estimate the pion contamination fraction in the kaon
region, the high-mass tail of the pion peak was ﬁtted by using the exponential function
as shown in Fig. 3.9. The systematic uncertainty was estimated from the ﬁtting range
dependence.
Moreover, the squared-mass distribution depends on the momentum as shown in
Fig. 3.10. The mass resolution deteriorates with increase of the momenta. Figure 3.11
shows the kaon identiﬁcation eﬃciency and the pion contamination fraction estimatedfor some momentum ranges. With the increase of the momenta, the eﬃciency decreases
whereas the contamination increases. The high contamination fraction in the momenta
of 0.8–0.9 GeV/c is caused by the large pion contribution due to a trigger bias shown in
Fig. 3.10. The Θ+ search region in the missing mass is 1500–1560 MeV/c2 which corresponds to the kaon momentum range of 0.9–1.1 GeV/c. In this momentum range, thekaon identiﬁcation eﬃciency was estimated to be 95.5±2.0 % and the pion contamination
fraction was 1.9 ± 1.0 %.

54

CHAPTER 3. DATA ANALYSISCounts

103
102

10

1
-0.2

-0.1

0.0
0.1
0.2
0.3
0.4
2 2
Squared Mass [(GeV/c ) ]

0.5

0.6

FIG. 3.9: Squared mass distribution for scattered particles with ﬁtting results used for theeﬃciency evaluation. The distribution is taken from the Θ+ search data in a momentum
range of 0.9–1.1 GeV/c. The red and green Gaussian functions were obtained by ﬁtting thepion and kaon peaks, respectively. The blue exponential function was obtained by ﬁtting
the high-mass tail of the pion peak. The dashed lines indicate the kaon selection gate.

1.4

Momentum [GeV/c]

1.3
1.2
1.1
1.0
0.9
0.8
-0.2

-0.1

0.0 0.1 0.2 0.3 0.4
Squared Mass [(GeV/c2)2]

0.5

0.6

FIG. 3.10: Two-dimensional plot of the squared mass versus the momentum for scatteredparticles in the Θ+ search data. The large contribution of pions around 0.8 GeV/c isattributed to a trigger bias due to the AC inactive region. The red lines indicate the kaon
selection gate.

55

1.00

0.20

0.95

0.15

0.90

0.10

0.85

0.05

0.80

0.8

0.9
1.0
1.1
Momentum [GeV/c]

1.2

Pion contamination

PID efficiency

3.3. ANALYSIS OF SCATTERED PARTICLES

0.00

FIG. 3.11: Kaon identiﬁcation eﬃciency and pion contamination fraction for each momentum range. The black circles denote the kaon identiﬁcation eﬃciency (left axis), while theblue crosses denote the pion contamination fraction in the kaon region (right axis). The
vertical error bars denote the systematic uncertainty described in the text.

56

CHAPTER 3. DATA ANALYSIS

3000

2500

2500

2000

2000
CountsCounts

1500

1500

1000

1000
500

500
0
-30

-20 -100
10
20
30
Horizontal angle difference [mrad]

0-30-20 -100
1020
Vertical angle difference [mrad]

30

FIG. 3.12: Distributions of the horizontal (left) and vertical (right) angle diﬀerence between
the beam track and the SKS track at the target position in the 1.1-GeV/c π − beam-through
data.

3.4

Scattering angle and vertex reconstruction

The scattering angle and the reaction vertex were reconstructed from two tracks: thelocal straight-line track obtained from BC3 and BC4 hit positions and the track obtained
from the momentum reconstruction in SKS. The relative geometry between the beam
and SKS spectrometers was adjusted by using the beam-through data. Figure 3.12 shows
distributions of the horizontal and vertical angle diﬀerence between the two tracks at thetarget position in the 1.1-GeV/c π − beam-through data. The horizontal and verticalangular resolutions were estimated to be 2.2 and 2.7 mrad in rms, respectively. The
vertical resolution was worse than the horizontal one because of the wire conﬁgurationof the drift chambers.
The reaction vertex point was deﬁned as the closest point between the two tracks.
In the present analysis, the forward scattering angle less than 2◦ was excluded becauseof the following two reasons:• The z-vertex resolution rapidly deteriorates with decrease of the scattering angles.
The target image could not recognize in events with the scattering angle less than2◦ ; see Appendix B.1 in detail.
• Large contribution of muons which originated from beam pion decay around thetarget region was observed in the forward scattering angle region as shown in
Fig. 3.13. These muons which passed through the AC veto contaminated the(π, K) trigger data.
Figure 3.14 shows the vertex distributions along the z-axis (beam direction) and ther-axis (radial direction). The histograms of LH2 target data are overlaid with those of theempty target data normalized by the beam ﬂux. In order to accumulate a large numberof events, (π − , π − ) scattering events were used instead of (π − , K − ) reaction events in theboth histograms. In the z-vertex distribution, contributions from the mylar windows ofScattering angle [deg]3.4. SCATTERING ANGLE AND VERTEX RECONSTRUCTION

57

20
18
16
14
12
10
8
6
4
2
0
-800 -600 -400 -200 0
200z-vertex [mm]

400

600

800

FIG. 3.13: Two-dimensional plot of the z-vertex versus the scattering angle in the Θ+
search data. The large contribution of muons which originated from beam pion decay wasobserved in the small scattering angle region.

the target vessel (z = ±60 mm) and the vacuum chamber (z = ±135 mm) are clearlyseen in the empty target data. The bump around 280 mm is due to SDC1. In ther-vertex distribution, contribution from the side surface of the target vessel (r = 33.9mm) are seen. The vertex cuts of −60 < z < 60 mm and r < 30 mm were applied inorder to exclude the contamination from the surrounding materials without decreasing
reaction events at the LH2 .

Vertex cut eﬃciency and contamination fraction
Figure 3.15 shows the vertex cut eﬃciency and the contamination fraction, which strongly
depend on the scattering angle because the z-vertex resolution deteriorates with decreaseof the scattering angles; therefore, they were calculated angle by angle. A net contribution from the LH2 was obtained by subtracting the empty target data from the LH2
target data as shown in Fig. 3.14. The vertex cut eﬃciency averaged over 2-15◦ was
84.8% with a typical statistical uncertainty of 1.0% in each angle. The contaminationfrom the surrounding materials was obtained from the remaining events in the empty target data after applying the vertex cut. The contamination fraction averaged over 2–15◦
was found to be 3%. It should be reminded that the present value was estimated by using
the (π − , π − ) events. The contamination fraction for the (π − , K − ) events may be slightly
smaller than that of the (π − , π − ) events, because of a diﬀerence of these two reactions
between a proton and nucleus target (see Appendix B.3). Hence, the contamination
fraction for the (π − , K − ) events was found to be less than 3%.

58

CHAPTER 3. DATA ANALYSIS

7000

Beam direction

6000

LH2 target
Empty target

Counts

5000
4000
3000
2000
1000
0
-400

-300 -200

-100

0

100

200

300

400

z-vertex [mm]4000

LH2 target
Empty target

Counts

3000
2000
1000
0

0

10

20

30

40

50

60

Vertex-R [mm]FIG. 3.14: Vertex distribution along (top) the z-axis, beam direction, and (bottom) the
r-axis, radial direction. The open histograms show the LH2 target data. The red hatchedhistograms show the empty target data normalized by the beam ﬂux. The subtraction ofthese histograms represents a net contribution from LH2 . (π − , π − ) events of scattering
angles from 2◦ to 15◦ are selected in the both histograms. In the top ﬁgure, events withr < 30 mm are plotted, while, in the bottom ﬁgure, events with −60 < z < 60 mm areplotted. The blue dashed lines indicate the vertex cut positions.

59

1.0

0.1

0.9

0.08

0.8

0.06

0.7

0.04

0.6

0.02

0.5

2

4

6
8
10
12
Scattering Angle [deg]14

16

Contamination

Vertex cut efficiency

3.5. CALIBRATION DATA

0FIG. 3.15: Vertex cut eﬃciency and contamination fraction for each scattering angle. The
black circles denote the vertex cut eﬃciency (left axis), while the blue crosses denote thecontamination fraction (right axis). The vertical error bars denote the statistical uncertainty. The values at 16◦ stand for the values for scattering angles beyond 15◦ .

3.5

Calibration data

As described in Sec. 2.8, several calibration data were taken in addition to the Θ+
search data. The validity of the missing-mass reconstruction was examined by using
the π ± p → K + Σ± reactions. Figure 3.16 shows the missing mass spectra obtained inthree data sets of the Σ production reactions: (a) π + p → K + Σ+ at 1.38 GeV/c, (b)π − p → K + Σ− at 1.38 GeV/c, and (c) π − p → K + Σ− at 1.46 GeV/c. The Σ± peaks
were correctly reconstructed with low background. The peak positions are used for the
momentum calibration described in Sec. 3.6. The peak widths, which represent themissing-mass resolution for the Σ hyperons, are used for the estimation of the missingmass resolution for the Θ+ , described in Sec. 3.7.
In the present experiment, the beam-through data were taken with three momentum
settings, i.e., 0.9, 1.1, and 1.38 GeV/c, with both positively and negatively charged
beams and with the empty target. In the beam-through data, the momentum diﬀerence,
pdiﬀ , was deﬁned as
pdiﬀ ≡ pB − pS ,(3.8)
where pB and pS denote the momenta obtained by the beam and SKS spectrometer,
respectively. Figure 3.17 shows a distribution of the momentum diﬀerence in the π +beam-through data at 1.1 GeV/c. The tail of the distribution is ascribed to the energyloss straggling in the BH2 counter. In the same manner as the above Σ data, the peak
positions are used for the momentum calibration, while the peak widths are used for theestimation of the missing-mass resolution for the Θ+ .

60

CHAPTER 3. DATA ANALYSIS

6050(a) π+ p → K+ X at 1.38 GeV/c
Σ+

40
30
20
10
0

14 (b) π- p → K+ X at 1.38 GeV/c
σ2-15° [µb/sr/(0.5MeV/c2)]

σ2-15° [µb/sr/(0.5MeV/c2)]

70

12
10

Σ

-

8
6
4
2
0
1.185 1.190 1.195 1.200 1.205
Missing Mass [GeV/c2]

1.180 1.185 1.190 1.195 1.200
Missing Mass [GeV/c2]

σ2-15° [µb/sr/(0.5MeV/c2)]+
10 (c) π p → K X at 1.46 GeV/c

8

Σ

-

6
4
2
0
1.185 1.190 1.195 1.200 1.205
Missing Mass [GeV/c2]

FIG. 3.16: Missing mass spectra of the π ± p → K + X reactions for the Σ± production.
The ordinates represent the diﬀerential cross section averaged over the scattering angles of
2–15◦ in the laboratory frame. The quoted errors are statistical. (These plots were madeafter applying the momentum calibration described in Sec. 3.6.)

3.6. MOMENTUM CALIBRATION AND MISSING MASS SCALE UNCERTAINTY612500
π+ beam-throughat 1.1 GeV/c

Counts

2000
1500
1000
500
0
-10

-5
p

diff

0
5
= p - p [MeV/c]
B

10

15

S

FIG. 3.17: Distribution of the momentum diﬀerence between the beam and SKS spectrometers, deﬁned as pdiﬀ ≡ pB − pS (see text), in the π + beam-through data at 1.1 GeV/cbefore the momentum calibration. The energy loss in the BH2 counter was subtracted
from pB .

3.6

Momentum calibration and missing mass scale
uncertainty

The absolute scales of the momenta and missing mass are discussed in this section. Thereis no calibration peak in the Θ+ search data, because the π − p → K − X reaction is an
exotic production channel. Therefore, the absolute scale of the momenta were calibrated
by using the Σ± production data and the π ± beam-through data. In this experiment, it isimportant to determine the mass of Θ+ correctly, if the peak is observed. The uncertaintyof the missing mass scale for the π − p → K − Θ+ reaction was ﬁnally estimated with themomentum scale uncertainty.

3.6.1

Energy loss correction

The energy loss in the LH2 target and the BH2 counter was evaluated according to theBethe-Bloch formula. The liquid hydrogen of a 12-cm length and the plastic scintillatiorof a 0.5-cm length were taken into account. The correction was applied to the beam-pionand scattered-kaon momenta event by event considering the reaction vertex point.

3.6.2

Momentum correction in SKS

Figure 3.18 (a,b) show correlation plots between an accuracy of the momentum versus theincident angle to SKS in the π − p → K + Σ− reaction. The accuracy of the momentum wasdeﬁned by pSKS − pkine , where pSKS is the kaon momentum measured with SKS, and pkine
is the kaon momentum calculated from the incident pion momentum and the scattering

kine

-p
SKS

p
0.1

0.2

0.3

kine

[MeV/c]

0.0
dx/dz

SKS

12
10 (c)
8
6
4
2
0
-2
-4
-6
-8
-0.3 -0.2-0.1

pcorr - p

kine

-p
SKS

p
[MeV/c]kine
SKS

pcorr - p

12
10 (a)
8
6
4
2
0
-2
-4
-6
-8
-0.3 -0.2[MeV/c]CHAPTER 3. DATA ANALYSIS[MeV/c]

62

-0.1

0.0
dx/dz

0.1

0.2

0.3

12
10
8
6
4
2
0
-2
-4
-6
-8

12
10
8
6
4
2
0
-2
-4
-6
-8

(b)

-0.10

-0.05

0.00
dy/dz

0.05

0.10

-0.05

0.00
dy/dz

0.05

0.10

(d)

-0.10

FIG. 3.18: Correlation between the accuracy of the momentum versus the incident angle
to SKS in the π − p → K + Σ− reaction. The left panels (a,c) show the correlation to thehorizontal angle dx/dz before (a) and after (c) the correction, while the right panels (b,d)
show the correlation to the vertical angle dy/dz before (b) and after (d) the correction.
The ordinates are pSKS − pkine , where pSKS is the kaon momentum measured with SKS,
and pkine is the kaon momentum calculated from the incident pion momentum and thescattering angle according to the kinematics of the π − p → K + Σ− reaction.

3.6. MOMENTUM CALIBRATION AND MISSING MASS SCALE UNCERTAINTY63
TABLE 3.1: Mass/Momentum diﬀerence in each calibration data. pB and pS are thecorrmomenta obtained by the beam and SKS spectrometer, respectively. Mdiﬀ (pdiﬀ ) and Mdiﬀ
(pcorrdiﬀ ) are the mass (momentum) diﬀerences before and after the calibration, respectively.

Data+
π p → K + Σ+
π − p → K + Σ−
π − p → K + Σ−Data
π + B.T.
π − B.T.
π + B.T.
π − B.T.
π + B.T.
π − B.T.

pB [GeV/c]
1.38
1.38
1.46
pB [GeV/c]
0.90
0.90
1.10
1.10
1.38
1.38

pS [GeV/c]
0.92
0.90
0.99
pS [GeV/c]
0.90
0.90
1.10
1.10
1.38
1.38

corr
Mdiﬀ [MeV/c2 ] Mdiﬀ
[MeV/c2 ]-3.20 ± 0.07
-0.75
-1.63 ± 0.05
-1.07
-1.32 ± 0.04
-0.20
pdiﬀ [MeV/c]
pcorr
diﬀ [MeV/c]
0.91 ± 0.06
-0.20
3.04 ± 0.06
-0.85
0.39 ± 0.10
1.21
3.74 ± 0.07
1.79
-3.17 ± 0.06
0.48
0.40 ± 0.08
1.28

angle according to the kinematics of the π − p → K + Σ− reaction. The abscissas are (a)the horizontal angle dx/dz or (b) the vertical angle dy/dz. A correlation was observed
especially in the region of dx/dz > 0.1, which corresponds to the inner tracks in SKS.
The correlation seems to be attributed to the inaccuracy of the calculated magnetic ﬁeldof SKS.
The correlation was corrected by using a forth-order polynomial function. The correction was applied to both dx/dz and dy/dz. Figure 3.18 (c,d) show the correlation
plots after applying the correction 2 . By this correction, the missing mass resolution forΣ− was improved by 10%. The correlation scheme was examined in three kinds of theΣ production data. The correlation curve of the Σ+ data at 1.38 GeV/c was similar
to that of the Σ− data at 1.38 GeV/c due to the same reaction kinematics. Since thekaon momentum region for the Θ+ (1530) production at 2.01 GeV/c is almost the sameas that for the Σ− production at 1.46 GeV/c as shown in Fig. 3.25, the same correction
function determined by the Σ− at 1.46 GeV/c was applied to the Θ+ search data.

3.6.3

Momentum calibration

The initial scales of the momenta were reconstructed by the beam and SKS spectrometers
based on the magnetic-ﬁeld values monitored by the Hall probe and the NMR probe,
respectively. Then, the energy loss correction in the LH2 target and the BH2 counter
was applied as described in Sec. 3.6.1. The Σ production data provided information
on a mass diﬀerence, Mdiﬀ , between the reconstructed mass and the known Σ mass,i.e., 1189.37 ± 0.07 MeV/c2 for Σ+ and 1197.449 ± 0.030 MeV/c2 for Σ− [58]. On theother hand, the momentum diﬀerence, pdiﬀ , deﬁned in Eq. (3.8) was obtained from eachbeam-through event.
Table 3.1 shows the mass/momentum diﬀerence in each calibration data. Mdiﬀ andpdiﬀ represent the peak value in the distribution. The error of Mdiﬀ was derived from2

The zero-th order coeﬃcient of the function was not used for the correction because it corresponds
to the absolute momentum scale which should be calibrated later in Sec. 3.6.3.

64

CHAPTER 3. DATA ANALYSIS

the quadratic sum of the known Σ mass uncertainty [58] and the uncertainty of a peakﬁtting in the missing mass spectra, while the error of pdiﬀ was from the uncertainty ofa peak ﬁtting in the pdiﬀ distributions. These mass and momentum diﬀerences must be
zero, if the absolute scales of both the beam and scattered-particle momenta are correct.
Thus, the momentum scale calibration was done so as to reduce the mass and momentum
diﬀerences simultaneously.
To compare Mdiﬀ equivalently with pdiﬀ , Mdiﬀ was divided by the kinematical factor,
∂M
or ∂M
:
∂pB
∂pS
∂M
1
=
[βB (mp − ES ) + pS cos θ] ,
∂pB
M
∂M
1
= − [βS (mp + EB ) − pB cos θ] .
∂pS
M

(3.9)
(3.10)

These are derived from Eq. (3.1) where the subscripts π and K should be replaced by B
and S which represent the beam and scattered particle, respectively; and β is the velocity∂Mof each particle. In the present Σ production reactions, ∂pand ∂Mare 0.68 and -0.57,∂pS
B
respectively, in the forward angle. Mdiﬀ divided by the kinematical factor is compatible
with pdiﬀ .
∂M
pdiﬀ and Mdiﬀ /( ∂p) are plotted in Fig. 3.19 (a) as a function of the beam momentumB) are plotted in Fig. 3.19 (b) as a function of the scatteredpB , while −pdiﬀ and Mdiﬀ /( ∂M∂pS
particle momentum pS . In Fig. 3.19 (a,b), one can see a common shift of 2–3 MeV/c
between the opposite-charge with the same momentum, namely, three pairs of the π ±beam-through data (blue open or green solid triangles) and a pair of the π ± p → K + Σ±data at 1.38 GeV/c (red open or magenta solid circles). The shift is due to the opposite
polarity setting of the beam spectrometer, because the shift was observed even in Mdiﬀ sof the π ± p → K + Σ± data at 1.38 GeV/c where only the charge of the beam was diﬀerent.
In order to minimize the shifts observed in four pairs of the data with the opposite beam
charge, a polarity oﬀset parameter, z, was introduced as
pB → p′B ≡ pB ± z (double sign corresponds to the beam charge.),z = 1.39 ± 0.03 MeV/c.

(3.11)(3.12)

Figure 3.19 (c,d) show the mass/momentum diﬀerences after applying the polarity oﬀset.
The shifts were reduced within 0.9 MeV/c.
Figure 3.19 (c) and (d) give a dependence of the mass/momentum diﬀerence on
the beam momentum pB and scattered-particle momentum pS , respectively. A negative
correlation in terms of pB is seen in Fig. 3.19 (c), whereas no clear correlation in termsof pS is seen in Fig. 3.19 (d). This negative correlation corresponds to a linearity of thereconstructed beam momentum. Since the Hall probe was set at 75-mm upside of thecentral plane of the D4 magnet, the measured ﬁeld value could deviate from the central
ﬁeld value which should be used in the transport calculation. This deviation could cause
the linear correlation for pB . Therefore, a linear correction for p′B was introduced asp′B → p′′B ≡ ap′B + b,
a = 1.0100 ± 0.0001,
b = −11.56 ± 0.13 MeV/c,(3.13)(3.14)(3.15)

3.6. MOMENTUM CALIBRATION AND MISSING MASS SCALE UNCERTAINTY65

or Mdiff /( ∂M/∂p ) [MeV/c]

6(a) Before calibration
4

S

2
0
(π-, K +) Σ

(π+, K +) Σ+(π , π ) B.T.

-6
0.8

-

diff

-

-4

-

(π+, π+) B.T.

0.9

1.0

(b) Before calibration
4
2
0
-2
-4

-p

-2

p

diff

B

or Mdiff /( ∂M/∂p ) [MeV/c]

6

1.1 1.2 1.3
p [GeV/c]

1.4

-6
0.8

1.5

0.9

1.0

B

or Mdiff /( ∂M/∂p ) [MeV/c]

4

S

2
0
-2

(d) After polarity offset correction
4
2
0
-2
-4

0.9

1.0

1.1 1.2 1.3
p [GeV/c]

1.4

-6
0.8

1.5

0.9

1.0

B

1.4

1.5

(e) After beam linear correction
4

S

2
0
-2

diff

-4

(f) After beam linear correction
4
2
0
-2
-4

p

-p

B

1.1 1.2 1.3
pS [GeV/c]

6
or Mdiff /( ∂M/∂p ) [MeV/c]

6
or Mdiff /( ∂M/∂p ) [MeV/c]

1.5

-p

diff

-4
-6
0.8

diff

1.4

6

(c) After polarity offset correction

p

diff

B

or Mdiff /( ∂M/∂p ) [MeV/c]

6

1.1 1.2 1.3
pS [GeV/c]

-6
0.8

0.9

1.0

1.1 1.2 1.3
p [GeV/c]
B

1.4

1.5

-6
0.8

0.9

1.0

1.1 1.2 1.3
pS [GeV/c]

1.4

1.5

FIG. 3.19: Plots of the mass/momentum diﬀerence through the momentum calibration.
∂M
The left-side panels (a,c,e) show pdiﬀ or Mdiﬀ /( ∂p) versus pB , while the right-side panels
B∂M(b,d,f) show −pdiﬀ or Mdiﬀ /( ∂pS ) versus pS . The top panels (a,b) are the plots before themomentum calibration, the middle panels (c,d) are the plots after applying the polarity
oﬀset correction, and the bottom panels (e,f) are the plots after applying the beam linear
correction. The red open circles are from the Σ− data, the magenta solid circle is from theΣ+ data, the blue open triangles are from the π − beam-through data, and the green solid
triangles are from the π + beam-through data.

66

CHAPTER 3. DATA ANALYSIS

where a and b are the correction parameters determined by minimizing the mass andmomentum diﬀerences. Figure 3.19 (e,f) show the mass/momentum diﬀerence after applying the beam linear correction, which is also tabulated in the last column of Table 3.1.
The diﬀerences were reduced between -2 and 2 MeV/c.
We regarded the remaining diﬀerences as a systematic uncertainty of the momentum
scale. In the momentum calibration above, no correction was applied for pS ; in otherwords, we regarded the momentum reconstructed by the SKS as the reference of the
momentum scale. Therefore, the beam spectrometer was calibrated with SKS. The
absolute scale uncertainty of the beam momentum is expected to be the same as that of
the scattered-particle momentum. Assuming that the uncertainty is simply proportional
to the momentum,
δpB
δpS
=
≡ ε.
(3.16)pB
pS
ε was estimated to be 0.12% from the maximum remaining diﬀerence obtained in the
1.1-GeV/c π − beam-through data.

3.6.4

Missing mass scale uncertainty

In the momentum calibration, we applied the polarity-oﬀset and linear correction for the
beam momentum, i.e.,pB → p′′B ≡ a(pB ± z) + b,
(3.17)
where the double sign corresponds to the beam charge. The π − beam momentum of 2.01
GeV/c was corrected by +7.1 ± 0.1 MeV/c according to Eq. (3.17). The uncertaintyof 0.1 MeV/c was propagated from the errors of a, b, and z 3 , which correspond to theuncertainties of the correction itself. Considering the kinematics of the π − p → K − Θ+reaction at 2.01 GeV/c, the absolute scale of the missing mass was corrected by +3.8±0.1
MeV/c2 for the Θ+ (1530) production. The uncertainty of 0.1 MeV/c2 was propagatedfrom the above uncertainty of 0.1 MeV/c.
In addition to the uncertainty of the correction itself (0.1 MeV/c2 ), the systematic
uncertainty of the momentum scale (ε = 0.12%) discussed above, should be taken into
account. Considering the kinematics of the π − p → K − Θ+ reaction at 2.01 GeV/c,the systematic uncertainty of the missing mass scale was estimated to be 1.3 MeV/c2 ,propagating from the momentum scale uncertainty of 0.12%.
Hence, summing up 0.1 and 1.3 MeV/c2 , overall uncertainty of the missing mass scalefor Θ+ was found to be 1.4 MeV/c2 .

3The covariance between a and b (−1.39 × 10−5 ) was also taken into account.

3.7. MOMENTUM AND MISSING MASS RESOLUTION

3.7

67

Momentum and missing mass resolution

The resolutions of the momenta and missing mass are discussed in this section. As
described in the previous section, there is no calibration peak in the Θ+ search data,
because the π − p → K − X reaction is an exotic production channel. Therefore, theresolution of the momenta was evaluated by using the Σ± production data and the π ±beam-through data. In this experiment, it is important to estimate the missing mass
resolution for the π − p → K − Θ+ reaction.
In a reaction B + p → S + X, where B and S denote a beam and scattered particles,
respectively, the missing mass of X is calculated in the laboratory frame as follows:√(3.18)
M = (EB + mp − ES )2 − (p2B + p2S − 2pB pS cos θ),
where EB and pB are the energy and momentum of a beam particle, respectively; ES
and pS are those of a scattered particle; mp is the mass of a target proton; and θ is thescattering angle. The mass resolution ∆M is derived from the momentum resolution of
the beam and scattered particles, ∆pB and ∆pS , the scattering angle resolution ∆θ, and∆Estrag which stands for a contribution from the energy-loss straggling to the missing
mass resolution. It can be expressed in the following equations 4 :
(
)2
(
)2
(
)2
∂M
∂M
∂M
2
2
2
2
∆M =
∆pB +
∆pS +
∆θ2 + ∆Estrag,(3.19)
∂pB
∂pS
∂θ
∂M
1
=
[βB (mp − ES ) + pS cos θ] ,(3.20)∂pB
M∂M
1= − [βS (mp + EB ) − pB cos θ] ,(3.21)∂pS
M∂M
1= − pB pS sin θ,(3.22)∂θM
where β represents the velocity of each particle. The covariance terms in Eq. (3.19)
were ignored in this analysis. Since pB and pS were obtained by independent spectrometers, they are not correlated. The correlation between the scattering angle θ and each
momentum was neglected assuming that their contribution to the overall resolution islimited.
In the following subsections, the contributions of ∆pB , ∆pS , ∆θ, and ∆Estrag are
estimated step by step, and then, the missing mass resolution for the π − p → K − Θ+reaction is ﬁnally estimated.

4

The scattering angle term was negligibly small in previous hypernulcear experiments using SKS
because of the large target mass M ; however, the term is not negligible in hadron production reactions.

68

3.7.1

CHAPTER 3. DATA ANALYSIS

Energy loss straggling

The energy loss distribution in materials of moderate thickness is expressed by theLandau-Vavilov distribution. The FWHM of the distribution is approximately expressedas [58]
FWHM ≃ 4ξ,ξ ≡ 2πNA re2 me(3.23)
Z ρx,
A β2(3.24)

where NA is the Avogadro’s number, re the classical electron radius, me the electron
mass, Z and A the atomic number and atomic mass of the material, β the particle
velocity, and ρx the mass thickness. ∆Estrag denotes the contribution from the energyloss straggling in the LH2 target and the BH2 counter to the missing mass resolution.
The liquid hydrogen of a 12-cm length and the plastic scintillatior of a 0.5-cm length
were considered. ∆Estrag was calculated to be 0.39 MeV (FWHM) for the Θ+ production
reaction at 2 GeV/c. The dependence on the reaction vertex point in the target was lessthan 0.01 MeV.

3.7.2

Scattering angle resolution

The missing mass resolution for Σ at the scattering angles of 2-15◦ was obtained byﬁtting the peaks of the Σ hyperons shown in Fig. 3.16. The missing mass peaks tend
to have the Landau tail in the high-mass side due to the energy-loss straggling. Since
the tails are not so signiﬁcant as shown in Fig. 3.16, the Gaussian distribution was usedin the ﬁtting. Table 3.2 shows the obtained missing mass resolution. The systematic
uncertainty of ±0.1 MeV was estimated from the ﬁtting range dependence.
As can be seen in Eq. (3.19–3.22), the missing mass resolution depends on the scattering angle θ. At the forward angles of 2–15◦ , the θ-dependence predominantly comesfrom the sin θ term in Eq. (3.22). Therefore, ∆M can be expressed as a function of θ:√∆M (θ) =a0 + a1 sin2 θ,(3.25)
(
)2
(
)2
∂M
∂M
2
a0 ≡
∆p2B +∆p2S + ∆Estrag,(3.26)
∂pB
∂pS
)2
(p p
B S
∆θ .
(3.27)a1 ≡M
Figure 3.20 shows the scattering angle dependence of the missing mass resolution inthe Σ− production data at 1.46 GeV/c. The data were well ﬁtted by Eq. (3.25) with theθ-independent parameters a0 and a1 ; here, we neglected a slight θ-dependence of pS , andassumed that ∆pS and ∆θ are independent of θ. The scattering angle resolution ∆θ wasfound from a1 to be 5.7 ± 0.8 mrad (FWHM). The value was consistent with the othertwo set of the Σ data. In addition, since a0 is equivalent to ∆M 2 (0◦ ), the missing mass
resolution at 0◦ , ∆M (0◦ ), was found to be 1.89 ± 0.07 MeV (FWHM).

3.7. MOMENTUM AND MISSING MASS RESOLUTION

69

TABLE 3.2: Missing mass resolution for Σ, ∆M2-15◦ , at scattering angles of 2-15◦ (upper
table) and the resolution for the momentum diﬀerence, ∆pdiﬀ , in the beam-through data
(lower table). ∆M2-15◦ and ∆pdiﬀ are shown in FWHM. For the errors of ∆M2-15◦ , the ﬁrst
one is statistical and the second one is systematic uncertainty estimated from the ﬁtting
range dependence. For the errors of ∆pdiﬀ , the statistical error is negligibly small and thequoted error is estimated from the ﬁtting range dependence.

Data
π p → K + Σ+
π − p → K + Σ−
π − p → K + Σ−Data+
π B.T.
π − B.T.
π + B.T.
π − B.T.
π + B.T.
π − B.T.

pB [GeV/c]∆M2-15◦ [MeV]
1.38
2.12 ± 0.06 ± 0.1
1.38
2.24 ± 0.10 ± 0.1
1.46
2.21 ± 0.05 ± 0.1
pB [GeV/c]∆pdiﬀ [MeV/c]
0.90
2.22 ± 0.12
0.90
2.18 ± 0.12
1.10
2.69 ± 0.12
1.10
2.65 ± 0.12
1.38
4.11 ± 0.12
1.38
4.00 ± 0.12

0

6
8
10
12
Scattering angle [deg]Missing mass resolution [MeV]

+

2.6
2.4
2.2
2.0
1.8
2

4

14

16

FIG. 3.20: Scattering angle dependence of the missing mass resolution in the Σ− production
data at 1.46 GeV/c. The data were ﬁtted by Eq. (3.25) with the θ-independent parametersa0 and a1 .

70

3.7.3

CHAPTER 3. DATA ANALYSIS

Momentum resolution

The stability of the magnetic ﬁeld of both spectrometers was monitored during the experiment (see Appendix C). The long-term ﬂuctuation of the beam and SKS spectrometerﬁeld was less than 2.4 × 10−4 and 9.6 × 10−5 , respectively, which were neglected in the
momentum resolution estimation.
In order to obtain ∆pB and ∆pS , Eq. (3.19) in the Σ production data is used. In
addition, from the pdiﬀ (= pB − pS ) distribution obtained from the beam-through data as
shown in Fig. 3.17, the width of the distribution ∆pdiﬀ is also used. ∆pdiﬀ is composedof the momentum resolutions of the beam and SKS spectrometers and the energy-loss
straggling eﬀect in BH2 (∆pstrag ). It is written as∆p2diﬀ = ∆p2B + ∆p2S + ∆p2strag ,(3.28)

where ∆pstrag was calculated in the same way as for ∆Estrag . Table 3.2 shows ∆pdiﬀ
obtained from each beam-through data. Since ∆pdiﬀ s in three pairs of the beam-throughdata with the same momentum but with the opposite charge were consistent within
the errors, it was found that the momentum resolution does not depend on the magnet
polarity.
Assuming that the momentum resolution is simply proportional to the momentum,∆pB /pB and ∆pS /pS were derived by solving the quadratic equations (3.19) and (3.28).
Considering the consistency of pS with the Θ+ production reaction, the Σ− data at 1.46
GeV/c were used for Eq. (3.19) and the beam-through data at 1.1 GeV/c were used for
Eq. (3.28). The resolution of the beam spectrometer was calculated to be ∆pB /pB =(1.4 ± 0.2) × 10−3 and that of the SKS spectrometer was ∆pS /pS = (2.0 ± 0.2) × 10−3 in
FWHM.

3.7.4

Missing mass resolution

Using ∆pB , ∆pS , ∆θ and ∆Estrag obtained above and considering the kinematics forthe Θ+ production, the missing mass resolution expected for the Θ+ was derived asa function of the scattering angle, ∆MΘ (θ), which is shown in Fig. 3.21 with a blacksolid line with an yellow 1σ error band. The contributions from each component arealso shown in the ﬁgure. As for the Θ+ missing mass resolution, the beam momentum
resolution was dominant in the small angle region because of the high beam momentumof 2 GeV/c, whereas the scattering angle resolution was dominant in the large angle
region.
In order to utilize in the following analysis, we needed the mass resolution averaged
over 2–15◦ , which was evaluated to be 2.13 ± 0.15 MeV (FWHM) with a simulation assuming the isotropic angular distribution for the Θ+ (1530) production. The uncertainty
was estimated from the upper and lower error bands of ∆MΘ (θ). The dependence on
diﬀerent angular distributions, e.g., forward or backward peaked distributions such as
1±cos θ, was examined and found to be less than 0.1 MeV, because the present experi2
mental acceptance was limited to the forward angles of 2-15◦ . The Θ+ mass dependence
was also examined between 1500 and 1550 MeV/c2 , and found to be negligible (< 0.002
MeV).

3.8. CROSS SECTION

Missing mass resolution [MeV]

3.0
2.5
2.0

71

Total: ∆M∆(Beam)∆(Scat)∆(Angle)∆(Strag)-π- p → K Θ+ at 2.01 GeV/c

1.5
1.0
0.5
0.0
0

2

4

6
8
10
12
Scattering angle [deg]1416

FIG. 3.21: Scattering angle dependence of the missing mass resolution for the Θ+ production at 2.01 GeV/c. The black solid line indicates ∆MΘ (θ) and the yellow area
represents the 1σ error band. The four contributions in Eq. (3.19) are also shown:∂M∂M∆pB (green), ∆(Scat) ≡ ∂M∆(Beam) ≡ ∂p
∂pS ∆pS (blue), ∆(Angle) ≡ ∂θ ∆θ (red) and
B∆(Strag) ≡ ∆Estrag (cyan).

3.8

Cross section

The cross section of the πp → KX reaction was calculated from the experimental yields
as
dσ
A
NK
1
=
·
·
,
(3.29)dΩ(ρx) NA Nbeam εexp dΩwhere A is the atomic mass of target Hydrogen, ρx the target mass thickness, NA the
Avogadro’s number, Nbeam the scaler counts of the beam trigger, NK the number of (π, K)
events, εexp the total experimental eﬃciency and dΩ the solid angle of SKS. Table 3.3
is a list of the experimental eﬃciency factors which consists of the beam normalization,
detection eﬃciency, analysis eﬃciency and other factors. Some factors depend on various
experimental conditions, e.g., beam intensity, scattering angle, and momentum, which are
discussed in the next subsection. The acceptance of SKS estimated by a MC simulation
is described in the following subsection.

3.8.1

Eﬃciency

The eﬃciency factors were evaluated for both the Θ+ search data and the Σ production
data. Hereinafter, representative values for the Θ+ search data are mentioned and quoted
errors are statistical one unless otherwise noted.
5

A representative value in case of a 1-GeV/c momentum and a 5-m path length.

72

CHAPTER 3. DATA ANALYSISTABLE 3.3: List of the experimental eﬃciency factors. Typical values in the Θ+ searchdata are shown.

Eﬃciency
Beam normalization factor
BC1,2 eﬃciency
BC3,4 eﬃciency
Beam spectrometer tracking eﬃciency
Single track ratio
SDC1,2 eﬃciency
SDC3,4 eﬃciency
SKS tracking eﬃciency
TOF eﬃciency
LC eﬃciency
AC overkill factor
PID eﬃciency for kaon
Vertex cut eﬃciency
Kaon decay factor
K − absorption factor
Data acquisition eﬃciency
Matrix trigger eﬃciency
Total eﬃciency

Typical value [%]90.2 ± 1.985.0 ± 0.5
99.1 ± 0.3
98.2 ± 0.3
94.3 ± 0.3
97.4 ± 0.2
94.6 ± 1.1
97.0 ± 0.8
99.6 ± 2.5
97.5 ± 2.4
91.8 ± 2.1
95.5 ± 2.0
84.8 ± 1.0
48.3 ± 0.4 5
91.1 ± 1.2
76.9 ± 0.5
98.6 ± 1.4
15.1 ± 0.9(1) Beam normalization factor
The beam normalization factor represents a fraction of the eﬀective pion number out ofNbeam . It was estimated to be 90.2±1.9 %, taking into account the following components:
Muon contamination Electrons (or positrons) in the beam were rejected by GC
at trigger level. However muons, which are decay products of pions, can not be
separated from pions. The muon contamination rate was estimated to be 3.0 ±2.0 % by a MC simulation using decay-turtle [136]. In the simulation, theproperties of the magnets, slits and separators in the K1.8 beam line were taken
into account. Note that most of muons which reached the experimental target wereoriginated from the pion decay in the beam spectrometer magnets. The quoted
error represents the systematic uncertainty in the simulation, which was estimatedas follows; in previous experiments at KEK-PS [137, 138], the muon contamination
rate was measured with a high-pressure Freon-gas Cherenkov counter and agreed
with a decay-turtle simulation within 2%.
Accidental coincidence The accidental coincidence rate between BH1 and BH2
was estimated to be 3.2 ± 0.3 % by using time-of-ﬂight spectra in the beam trigger
as described in Sec. 3.2.1.
Beam proﬁle The beam tracks which did not pass through the target volume were
excluded from the number of beams. A typical targeting eﬃciency was 96.1±0.3 %as shown in Fig. 3.5.

3.8. CROSS SECTION

73(2) BC1·2 and BC3·4 tracking eﬃciency
The eﬃciency of the beam local tracking was estimated using pion beam particles deﬁned
with BH1 and BH2 in the beam trigger data. The BC1·2 and BC3·4 tracking eﬃciencies
are the total eﬃciency including the analysis eﬃciency to ﬁnd a local straight-line trackat the entrance and exit of the QQDQQ magnets, which were found to be typically
85.0 ± 0.5 % and 99.1 ± 0.3 %, respectively. As was mentioned in Sec. 2.2, due to thebeam ripples, the maximum instantaneous rate came up to 10–20 times as high as themean rate. Since these high-multiplicity events consumed enormous processing time in
the track ﬁnding, events including more than 105 track candidates were discarded in thepresent analysis. The BC1·2 tracking eﬃciency depended on the beam intensity andthe number of active layers, and was evaluated run by run, whereas the BC3·4 tracking
eﬃciency was stable within the error.
(3) Beam spectrometer tracking eﬃciency and single track ratio
The beam spectrometer tracking eﬃciency is the analysis eﬃciency to reconstruct aparticle trajectory in the beam spectrometer after determining the local straight-line
tracks in both the BC1·2 and BC3·4 tracking. A typical eﬃciency was found to be
98.2 ± 0.3 %. In the present analysis, events including more than two beam tracks werediscarded. A typical single track ratio was 94.3 ± 0.3 %.
(4) SDC1·2 tracking eﬃciency
The SDC1·2 tracking eﬃciency is the total eﬃciency including the analysis eﬃciency
to ﬁnd a local straight-line track at the entrance of the SKS magnet. It was estimatedby using the beam trigger data. Tracks which should pass through the eﬀective area of
SDC1 and SDC2 were deﬁned by the beam track determined by BC3 and BC4. The
beam absorption between BC4 and SDC1 was ignored. The eﬃciency was found to be
97.4±0.2 %. In this procedure, the incident beam angles to SDC1 and SDC2 were almost
less than 2◦ . We assumed that the eﬃciency was the same for large incident angles.
(5) SDC3·4 tracking eﬃciency
The SDC3·4 tracking eﬃciency is the total eﬃciency including the analysis eﬃciency toﬁnd a local straight-line track at the exit of the SKS magnet. It was estimated by using
scattered proton events in the data set of the π ± p → K + Σ± reactions, since protons arefree from decay in ﬁght. Figure 3.22 shows a scatter plot of the horizontal scattering
angle determined by SDC1 and SDC2 versus the inverse time-of-ﬂight between TOF andBH2 taken from the Σ− production data. The scattered proton events were selected asshown in the ﬁgure. The eﬃciency estimated in the Σ− production data was 98.2±0.2 %.
Figure 3.23 shows the SDC3·4 tracking eﬃciency as a function of the horizontal track
positions at TOF. The position dependence was found to be within 0.5%. As for the Σ+
production data, the chamber hit rate was higher than that of Σ− data because of the
decay product of the beam particle, and therefore the eﬃciency decreased by 2%. Taking
account of the rate dependence, the eﬃciency for the Θ+ search data was estimated tobe 94.6 ± 1.1 %.

74

CHAPTER 3. DATA ANALYSIS

0.075

π

0.070
1 / TOF [/ns]

0.065

K

0.060

p

0.055
0.050
0.045
0.040
0.035
-0.4

-0.3

-0.2 -0.1
0
0.1 0.2 0.3
Horizontal incident angle (dx/dz)

0.4

FIG. 3.22: Scatter plot of horizontal scattering angle versus inverse time-of-ﬂight between
TOF and BH2 in the Σ− production data. The loci for pions, kaons and protons are seen.
The red lines indicate the proton selection gate.

SDC3,4 tracking efficiency

1.00
0.98
0.96
0.94
0.92
0.90
0.88

-400 -200 0 200 400 600 800 1000 1200
Horizontal position at TOF [mm]FIG. 3.23: SDC3·4 tracking eﬃciency for each horizontal track position at TOF in theΣ− production data. Each point corresponds to a segment of TOF. The quoted errors are
statistical.

3.8. CROSS SECTION75

SKS tracking efficiency

1.00
0.95
0.90
0.85
0.80
0.75
0.70

0

2

4

6
8 10 12 14
Scattering angle [deg]

16

18

20

FIG. 3.24: SKS tracking eﬃciency for each scattering angle. The dashed lines indicate theangle region adopted in the present analysis. The quoted errors are statistical.

(6) SKS tracking eﬃciency
The SKS tracking eﬃciency is the analysis eﬃciency to reconstruct a particle trajectoryin the SKS spectrometer after determining the local straight-line tracks in both the
SDC1·2 and SDC3·4 tracking. It was estimated by using the scattered proton events inthe data set of the π ± p → K + Σ± reactions, since protons are free from decay in ﬁght.
Since the eﬃciency depends on the incident angle to SKS, it was estimated angle byangle as shown in Fig. 3.24. For the forward angles of less than 2◦ , it was diﬃcult toestimate the proper eﬃciency since beam-related products contaminated the scatteredproton events. The eﬃciency decrease in the large angle region was due to an inaccuracyof the magnetic ﬁeld calculation in the fringing regions 6 . Events with the scattering
angles more than 15◦ were not used in the present analysis. A typical eﬃciency for 2–15◦
was 97.0 ± 0.8 %.
(7) TOF and LC eﬃciency
The detection eﬃciency of TOF was estimated by using controlled trigger data (BEAM× LC) where hits of the TOF counter were not required. Scattered pion events wereselected by reconstructing a particle trajectory in SKS, because the number of kaon
events was too small to use for this analysis. Events which should be detected in TOF
were deﬁned by the particle trajectory and the LC hit segment. The eﬃciency was foundto be 99.6 ± 2.5 %. The dependence on the momentum and incident angle was within
the error in the 0.8–1.2 GeV/c and 0–20◦ ranges, respectively. The result was assumed
to be the same for kaons because of a small energy-loss diﬀerence between a pion and akaon in a momentum range of 0.8–1.2 GeV/c.
6

In the region near the pole edge and the coil of the SKS magnet, the calculated ﬁeld value deviatedfrom the measured value in 10−2 , whereas the deviation was within 10−3 in the central region [139].

76

CHAPTER 3. DATA ANALYSIS

The detection eﬃciency of LC was similarly estimated to be 97.5 ± 2.4 % by using
controlled trigger data (BEAM × TOF) where hits of the LC counter were not required.
Events which should be detected in LC were deﬁned by the particle trajectory and the
TOF hit segment. The pion absorption in AC (∼2%) was ignored. The dependence on
the momentum and the incident angle was within the error. The result was assumed
to be the same for kaons, because the discriminator threshold of LC was set to be low
enough.
(8) AC overkill factor
The kaon overkill by AC occurred by the following reasons:Accidental veto The accidental veto rate, facc , was calculated as
facc =

RAC × Wcoin,
Fduty(3.30)

where RAC is the single rate of AC, Wcoin = 30 ± 5 ns is the coincidence widthof AC in the (π, K) trigger, and Fduty = 0.18 is the beam duty factor describedin Sec. 2.2. In the Θ+ search data, the single rate of AC was 200 kHz due tomuons originated from the beam pion decay. Therefore, the accidental veto rate
was calculated to be 3.3 ± 0.6 %.
δ-ray induced The overkill rate induced by the δ-ray was estimated by using controlled trigger data (BEAM × TOF × LC) mixed in the Σ− production data, where
the accidental veto rate was negligible (0.4%) since the single rate of AC was 20
kHz. Scattered proton events which should not ﬁre AC were used, because thenumber of kaon events was too small to use for this analysis. The tracks whichshould pass through the AC eﬀective area were deﬁned by the particle trajectorywith the hits of TOF and LC. The overkill rate was found to be 4.9 ± 2.0 % in
the momentum range of 0.8–1.1 GeV/c. The uncertainty was estimated from themomentum dependence. The result was assumed to be the same for kaons.
Consequently, summing up the above two factors, the kaon overkill rate by AC wasestimated to be 8.2 ± 2.1 %.
(9) Kaon decay factor
Since the βγcτ of a 1-GeV/c kaon is 7.5 m, about a half of the kaons produced in thetarget decay before they reach the detectors. The kaon decay events before passing
through SDC4 were rejected by the SKS track reconstruction process. The kaon survival
rate to SDC4 (εsurv ) was calculated event by event using the momentum (p) and theﬂight path length from the vertex point to SDC4 (L) as)(
Lm,(3.31)
εsurv = exp −pcτwhere m and τ denote the mass and the life time of the kaon, respectively. A representative value was 51.4 ± 0.4 % in case of p = 1 GeV/c and L = 5 m. The uncertainty was
mainly ascribed to that of L which was estimated from the thickness of SDC4 of 6 cm.

3.8. CROSS SECTION

77

TABLE 3.4: Materials along the ﬂight path in the SKS spectrometer.

Material
LH2 target
TOF
AC (aerogel)AC (Al frame)
He
Air
Total

Length [cm]
12.0
3.0
11.3
0.6
∼300
∼200

Density [g/cm3 ] Thickness [g/cm2 ]0.0709
0.85
1.06
3.18
0.20
2.26
2.70
1.62
0.0001790.05
0.00129
0.26
8.22

Furthermore, a part of kaons which decayed after passing through SDC4 ﬁred ACor escaped from the detector acceptance. The probability of these leakages from the(π, K) trigger was evaluated to be 6.1 ± 0.4 % by a MC simulation. The uncertainty wasestimated from the momentum dependence between 0.9 and 1.1 GeV/c.
Consequently, a typical kaon decay correction factor was 48.3 ± 0.4 % in case of a
1-GeV/c momentum and a 5-m path length.
(10) Kaon absorption factor
Some of the kaons produced in the target are absorbed by materials along the ﬂight pathin the spectrometer, which are listed in Table 3.4.
First, a simple calculation is given: the absorption rate fabs was estimated as∑
KA NA (ρx)iKN
fabs =σinel≈ σinelNA (ρx) ,(3.32)Ai
i
KA
KN
where σinel
and σinel
denote the K-induced inelastic cross sections for a nucleus A anda nucleon N , respectively; NA is the Avogadro’s number, ρx the thickness of materials,
KA
A the atomic mass, and i represents an index of the materials; here, we assumed σinel≈
KN−+
A σinel . The K N and K N inelastic cross sections around 1 GeV/c are approximately
20 and 3 mb, respectively [58]. Therefore, the absorption rates for K − and K + were
found to be 10% and 1.5%, respectively.
Next, the absorption rate was evaluated by using a MC simulation based on Geant4[140] including the realistic materials and hadronic reactions. The K − absorption rate
was found to be 8.9 ± 1.2 %. The uncertainty was estimated from the momentum
dependence between 0.9 and 1.1 GeV/c. The K + absorption rate was found to be
2.7 ± 0.7 %. These values are in good agreement with those of the simple calculation.
We adopted the simulated values as the absorption rates.

(11) Data-acquisition eﬃciency
The data-acquisition eﬃciency, caused by the dead time of the data-acquisition system,
was obtained as a ratio of the number of events accepted by the data-acquisition system
to that of the triggered events. Since the eﬃciency depends on the trigger rate, it wasestimated rate by rate. A typical eﬃciency was 76.9 ± 0.5 % at a trigger rate of 600 per
2.2-s spill. The uncertainty was estimated from the time ﬂuctuation.

78

CHAPTER 3. DATA ANALYSIS(12) Matrix trigger eﬃciency
In the Θ+ search data, the prescaled (π, K) trigger data without the matrix coincidence
trigger was also taken with the prescale factor of 10. The matrix trigger eﬃciency wasdeﬁned as a ratio of the number of (π, K) events with the matrix trigger to that without
the matrix trigger. It was estimated to be 98.6 ± 1.4 %. Since the dependence on the
scattering angle and the scattered-particle momentum was within the error, the matrix
trigger made no bias on the missing mass spectrum.
Summary of eﬃciencies
Summarizing the eﬃciency factors described above with the PID eﬃciency for a kaon
(Sec. 3.3.2) and the vertex cut eﬃciency (Sec. 3.4), the overall eﬃciency factor was
calculated event by event. A typical eﬃciency was estimated to be 15.1%. A typicaluncertainty of 0.9% was obtained by summing up all the uncertainties in quadrature assuming no correlation among the eﬃciencies. Hence, the relative systematic uncertainty
caused by the eﬃciency correction was estimated to be 0.9/15.1 = 6% for the Θ+ searchdata.
The relative systematic uncertainty for the Σ± production data was similarly estimated to be 5%. Since the kaon momentum in the Σ production reaction is withina narrow range around 0.9 or 1.0 GeV/c, the uncertainty due to the kaon momentum
dependence was smaller than that of the Θ+ search data.

3.8.2

Acceptance of SKS

The acceptance of SKS was estimated with a MC simulation as a function of the momentum pSKS and the angle θSKS which was deﬁned as the incident angle to SDC1 7 . In thesimulation, realistic distributions of the beam proﬁle and the reaction vertex point weretaken into account, and the acceptance was averaged over the distribution. Note that theacceptance evaluated in this simulation is a geometrical one; the eﬀect of the detector
eﬃciencies, particle decay and absorption are taken into account as the eﬃciency factor.
Particles were generated uniformly in a phase space deﬁned by pSKS and θSKS : from(pSKS − 21 ∆p) to (pSKS + 12 ∆p) and from cos(θSKS + 12 ∆θ) to cos(θSKS − 12 ∆θ), where thestep sizes were deﬁned as ∆p = 5 MeV/c and ∆θ = 0.25◦ . The particle generation was
uniform in azimuthal angle from 0 to 2π. The acceptance was calculated as a ratio of
the number of the detected events (Ndet ) to that of the generated events (Ngen ). Hence,the solid angle was calculated as∫ θ+ 1 ∆θ
2dΩ(pSKS , θSKS ) = 2π
θ− 12 ∆θd cos θ ×

Ndet (pSKS , θSKS ).
Ngen (pSKS , θSKS )(3.33)

This process was carried out step by step for pSKS and θSKS .
Figure 3.25 shows the acceptance of SKS as a function of pSKS and θSKS . The full
acceptance was conﬁrmed in the region of the momenta of 0.8–1.2 GeV/c and the angles
less than 5◦ . The angular acceptance was limited by the vertical gap of the SKS magnet.
7

θSKS is almost the same as the scattering angle and does not depend on the beam direction.

79

Momentum p

SKS[GeV/c]

1.4
1.3
1.2
1.1
1.0
0.9
0.8
0

2

4

6

8 10 12 14 16 18 20
Angle θSKS [deg]

1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0

Acceptance3.8. CROSS SECTION

FIG. 3.25: Acceptance of SKS as a function of the momentum (pSKS ) and the incident
angle (θSKS ) in the Θ+ search data. The magnetic ﬁeld was set at 2.5 T. A part of the
TOF (#1–10) and LC (#1–7) segments installed at the high-momentum side were not usedin the present experiment. The black solid, dashed, and dashed-dotted lines indicate thekinematics of the π − p → K − Θ+ reaction at 2.01 GeV/c assuming the Θ+ masses of 1530,
1500, and 1560 MeV/c2 , respectively. The gray dashed and dashed-dotted lines indicate
the kinematics of the π − p → K + Σ− reaction at 1.46 and 1.38 GeV/c, respectively.

In Fig. 3.25, the band extended toward the lower right is attributed to the outer tracks
in SKS, while the band extended toward the upper right is attributed to the inner tracks
in SKS. 8 A kinematical line corresponding to the π − p → K − Θ+ reaction at 2.01 GeV/cis also indicated with black lines in the ﬁgure, assuming the Θ+ mass of 1500 (dashed),
1530 (solid), or 1560 (dashed-dotted) MeV/c2 . The present experimental acceptance wellcovers the Θ+ mass range of 1500-1560 MeV/c2 .
Figure 3.26 (top) shows the acceptance projected onto the θSKS at the momentumof 1.0 GeV/c. In the present analysis, events with the scattering angle more than 15◦
were not used because of the small acceptance. Figure 3.26 (bottom) shows the solid
angle of SKS as a function of the momentum for the angle range from 0◦ to 15◦ . The
momentum acceptance was almost ﬂat in the momentum range from 0.9 to 1.1 GeV/c,
which corresponds to the Θ+ missing mass region of 1500-1560 MeV/c2 .
The uncertainty of the acceptance was estimated from the statistical error in thesimulation, which was controlled within typically 1%.

8

The inner (outer) track corresponds to the events scattered to left (right) at the target in Fig. 2.6.

80

CHAPTER 3. DATA ANALYSIS

1.0

p = 1.0 GeV/c
Acceptance

0.8
0.6
0.4
0.2
0.0

0

2

4

6

8 10 12 14
Angle θSKS [deg]

16

18

20

100
°

0 < θ < 15

Solid angle [msr]

80
60
40
20
0
0.7

0.8

0.9
1.0
1.1
1.2
Momentum p [GeV/c]

1.3

1.4

SKS

FIG. 3.26: (Top) Acceptance of SKS as a function of the incident angle (θSKS ) for the
momentum of 1.0 GeV/c in the Θ+ search data. (Bottom) Solid angle of SKS as a functionof the momentum for the incident angle range from 0◦ to 15◦ in the Θ+ search data. The
condition is the same as that for Fig. 3.25.

3.8.3

Systematic uncertainty

The systematic uncertainty of the cross section is summarized in Table 3.5, which was
obtained from the uncertainty of the experimental eﬃciency and that of the SKS acceptance, described above. The uncertainties for the Θ+ search data and the Σ± production
data were estimated to be 7% and 6%, respectively.
TABLE 3.5: Systematic uncertainty of the cross section. ε and Ω denote the overall
eﬃciency and the solid angle of SKS, respectively.

Data
π − p → K − Θ+
π ± p → K + Σ±∆ε/ε [%]
6
5∆Ω/Ω [%]
1
1

Total [%]
76

3.9. Σ PRODUCTION CROSS SECTION

3.9

81

Σ production cross section

The validity of the cross section was examined by using the π ± p → K + Σ± reactions.
Table 3.6 shows the cross sections for the three data sets of the π ± p → K + Σ± reactions
obtained in the present experiment. The cross section averaged over scattering angles of
2–15◦ in the laboratory frame are deﬁned as∫ 15◦ ( dσ )dΩ◦σ̄2-15◦ ≡ 2 ∫ 15◦dΩ.
(3.34)dΩ◦2
The systematic errors are from the uncertainty of the eﬃciency and acceptance describedin Sec. 3.8.3.
Figure 3.27 shows the diﬀerential cross sections of the π + p → K + Σ+ reaction at 1.38
GeV/c, while Figure 3.28 shows the diﬀerential cross sections of the π − p → K + Σ− reaction at 1.38 and 1.46 GeV/c. The present data are indicated by the black solid circles 9 .
The cross sections reported in the previous 2010 data [116, 139] and other previous experiments [141, 142, 143] are also shown. The present data are in reasonable agreementwith both the 2010 data and the other previous experimental data. Furthermore, theE19 data provided the Σ production cross section at forward angles more precisely thanany previous experimental data.
TABLE 3.6: Forward production cross sections averaged over the scattering angles of 2–15◦
in the laboratory frame (σ̄2-15◦ ) for the π ± p → K + Σ± reactions obtained in the E19-2012
data. The ﬁrst and second errors of the cross section denote the statistical and systematic
uncertainties, respectively.

Reactionπ + p → K + Σ+
π − p → K + Σ−
π − p → K + Σ−9pπ [GeV/c]
σ̄2-15◦ [µb/sr]
1.38
274.8 ± 8.1 ± 17.6
1.38
51.5 ± 2.1 ± 3.0
1.46
40.4 ± 0.8 ± 2.4

The diﬀerential cross sections in the c.m. frame are presented in Appendix D.

82

CHAPTER 3. DATA ANALYSIS

700
E19 2012 data

600dσ/dΩLab [µb/sr]

E19 2010 data

500

Candlin et al. (1983)

400
300
200
100
0

π+ p → K+ Σ+ at 1.38 GeV/c
0

2

4

6
8 10 12 14 16
Scattering Angle (Lab) [deg]1820

FIG. 3.27: Diﬀerential cross sections for the π + p → K + Σ+ reaction at 1.38 GeV/c. The
black solid circles are the present E19-2012 data at 1.38 GeV/c. The red open circles are
the E19-2010 data at 1.375 GeV/c [116, 139]. The blue crosses are the data from Candlin
et al. [141] at 1.377 GeV/c, converted from the c.m. frame to the laboratory one. The
quoted errors are statistical only. The present data are tabulated in Table D.1.

3.9. Σ PRODUCTION CROSS SECTION

120

83

E19 2012 data, 1.38 GeV/cdσ/dΩLab [µb/sr]

E19 2010 data, 1.389 GeV/c

100

Good et al., 1.325 GeV/c
Good et al., 1.275 GeV/c80

Dahl et al., 1.500 GeV/c

60
40
20
0

π- p → K+ Σ
0

2

4

-

6
8 10 12 14 16
Scattering Angle (Lab) [deg]1820

dσ/dΩLab [µb/sr]

90
80

E19 2012 data, 1.46 GeV/c70

Dahl et al., 1.500 GeV/c

60
50
40
30
20
π- p → K+ Σ

10
0

0

2

4

-

6
8 10 12 14 16
Scattering Angle (Lab) [deg]1820

FIG. 3.28: Diﬀerential cross sections for the π − p → K + Σ− reaction. (Top) The blacksolid circles are the present E19-2012 data at 1.38 GeV/c. The red open circles are theE19-2010 data at 1.389 GeV/c [139]. The blue crosses and the green open squares are
the data from Good et al. [142] at 1.325 and 1.275 GeV/c, respectively. The cyan open
triangles are the data from Dahl et al. [143] at 1.500 GeV/c. (Bottom) The black solid
circles are the present E19-2012 data at 1.46 GeV/c. The cyan open circles are the sameas those of the top ﬁgure. The quoted errors are statistical only. The present data aretabulated in Table D.1.

Chapter 4
Results
4.1

Missing mass spectrum

The missing mass spectrum of the π − p → K − X reaction at a beam momentum of 2.01
GeV/c at scattering angles of 2◦ to 15◦ in the laboratory frame is shown in Fig. 4.1. The
spectrum has no distinct structure, and no clear peak was observed. Comparing withthe previous 2010 data shown in Fig. 1.12, the missing mass acceptance became wider
owing to the improved experimental setup as described in Sec. 2.4.

-

Counts / (MeV/c2)500

π- p → K X at 2.01 GeV/c

400
300
200
100
0

1.45

1.50
1.55
Missing Mass [GeV/c2]

1.60

FIG. 4.1: Missing mass spectrum of the π − p → K − X reaction at 2.01 GeV/c at scattering
angles of 2◦ to 15◦ . The quoted errors are statistical.

844.2. BACKGROUND PROCESSES

4.2

85

Background processes

The background events remaining in the missing mass spectrum of the π − p → K − X
reaction shown in Fig. 4.1 are discussed in this section. The scattered pion contamination,
which is due to the misidentiﬁcation of outgoing kaons with pions, was estimated to be
1.9% in a central missing mass region of 1500–1560 MeV/c2 , as described in Sec. 3.3.2.
The background events from materials surrounding the LH2 target were estimated to beless than 3%, as described in Sec. 3.4. Since these background components are controlled
within small fractions, the remaining background events ought to originate from physicalbackground processes.
In the π − p → K − X reaction, several physical background processes are associatedwith the Θ+ production. The π − p → K̄KN reaction at a beam momentum of 1.8–2.2
GeV/c was reported by Dahl et al. [144] using a hydrogen bubble chamber. In thismomentum region around 2 GeV/c, the main physical processes are the following threereactions:π − p → ϕ n → K − K + n,π − p → Λ(1520) K 0 → K − K 0 p,
π − p → K − K + n or K − K 0 p (nonresonant).

(4.1)
(4.2)
(4.3)

Since other higher excited Λ∗ and Σ∗ resonances were not observed in [144], we assumed
the cross section of these resonances is small and neglected the contributions. 1
The background event should include a K − in the three-body ﬁnal state detectedin the spectrometer acceptance. Since the SKS is a single-arm spectrometer which isdedicated to the high-resolution measurement of K − , we could not detect the otherparticles in the ﬁnal state. The missing mass spectrum of the π − p → K − X reaction
includes the reﬂections of the ϕ and Λ(1520) productions together with the nonresonant
components.
The background distribution should be reproduced by a MC simulation taking account of the three reactions (4.1–4.3). The cross sections and angular distributions of
the reactions (4.1) and (4.2) were taken from previous experiments [144, 145]. The total
cross section of the π − p → ϕn reaction was measured to be 30.0 ± 8.0 and 21 ± 7 µb
for incident momenta of 1.8–2.2 [144] and 2.0 GeV/c [145], respectively. The weightedaverage of these values, 25 ± 5 µb, was used for the simulation. The isotropic angular
distribution of both the production and decay of ϕ was used in the simulation as reported
in [144, 145]. The total cross section of the π − p → Λ(1520)K 0 → N K̄K 0 reaction wasmeasured to be 20.8 ± 5.0 µb for an incident momentum of 1.8–2.2 GeV/c [144]. According to [144], the angular distributions of the production and the decay of Λ(1520) wereθ
and 13 + cos2 θ, respectively. Since there was noused in the simulation such as 1−cos
2reliable information on the nonresonant cross sections, the amplitude of the nonresonant
productions were normalized to the present experimental data. Because of the same
spectrum shape of the nonresonant K − K + n and K − K 0 p, these spectra are represented
by an uniﬁed spectrum as nonresonant K̄KN , hereafter.
Figure 4.2 shows simulated missing mass spectra of the π − p → K − X reaction forthe background processes together with the present experimental data. The nonresonant
1

The Λ∗ and Σ∗ contributions are reconsidered in Appendix E.

86

CHAPTER 4. RESULTSCounts / (MeV/c2)

500
400

E19 data (2012)
Simulation sum
Nonresonant KKN-

π- p → K X at 2.01 GeV/cφn0Λ(1520) K

300
200
100
0

1.45

1.50
1.55
Missing Mass [GeV/c2]

1.60

FIG. 4.2: Missing mass spectrum of the π − p → K − X reaction at 2.01 GeV/c. The experimental data are indicated by the black points with statistical errors. The red histogram
represents the total background shape obtained by the MC simulation including three processes: nonresonant K̄KN (blue dashed), ϕ-intermediated K − K + n (green dotted) andΛ(1520)-intermediated K − K 0 p (magenta dashed-dotted). The scale of the nonresonant
components was normalized to the experimental data.

K̄KN production is dominant in the present reaction. In the missing mass spectra, thelow-mass edges (1.43 GeV/c2 for nonresonant and 1.50 GeV/c2 for ϕ and Λ(1520)) arerestricted from the maximum K − momenta kinematically allowed in the reactions, while
the high-mass edge at 1.61 GeV/c2 is from the minimum K − momentum accepted in SKS.
Note that the background spectra do not make any sharp structure in the missing mass
spectrum. Therefore, we can represent the background shape with a smooth function
such as polynomial functions, especially in a central missing mass region of 1500–1560
MeV/c2 .

4.3. UPPER LIMIT OF PRODUCTION CROSS SECTION

σ2-15° [µb/(sr (MeV/c2))]

1.0

87

-

π- p → K X at 2.01 GeV/c

0.8
0.6
0.4
0.2
0.0

1.45

1.50
1.55
Missing Mass [GeV/c2]

1.60

FIG. 4.3: Missing mass spectrum of the π − p → K − X reaction at 2.01 GeV/c. The ordinate
represents the diﬀerential cross section averaged over 2–15◦ in the laboratory frame. The
quoted errors are statistical only.

4.3

Upper limit of production cross section

Figure 4.3 shows the missing mass spectrum of the π − p → K − X reaction at 2.01 GeV/cafter the experimental eﬃciency and acceptance correction. The ordinate represents thediﬀerential cross section averaged over 2◦ to 15◦ in the laboratory frame (as deﬁned in
Eq. (3.34)). The missing mass spectrum for each angle region at 2◦ intervals is also
shown in Fig. 4.4. Since the eﬃciency and acceptance are almost ﬂat except for theacceptance edges as described in Sec. 3.8, the spectrum shape does not change so muchand still has no distinct structure. In particular, as shown in Sec. 3.8.2, the momentum
acceptance of SKS is ﬂat in a range of 0.9–1.1 GeV/c, which corresponds to a missing
mass range of 1500–1560 MeV/c2 . The mass of Θ+ reported in experiments with positive
evidence ranged from 1520 to 1550 MeV/c2 . Thus, we evaluated the upper limit of theΘ+ production cross section in a mass region of 1500–1560 MeV/c2 .
As shown in Fig. 4.5 (top), the spectrum was ﬁtted with a background plus signal
function. The background function is a second-order polynomial function deﬁned in a
mass range of 1495–1565 MeV/c2 . The signal function is a Gaussian distribution with
a ﬁxed width of 2.13 MeV (FWHM), which is the experimental resolution evaluated inSec. 3.7.4. The natural width for the Θ+ was ignored in the ﬁtting, because the Θ+
must have very small width. In the ﬁgure, the error bar at each point indicates only the

88

CHAPTER 4. RESULTS

1.0

0.5

1.0

0.5

1.45
1.50
1.55
1.60
Missing Mass [GeV/c2]

1.0

0.5

1.45
1.50
1.55
1.60
Missing Mass [GeV/c2]

1.5

10-12°
1.0

0.5

0.0

6-8°

0.0

1.45
1.50
1.55
1.60
Missing Mass [GeV/c2]

1.5

8-10°

σ10-12° [µb/(sr (MeV/c2))]σ8-10° [µb/(sr (MeV/c2))]

0.5

0.0

1.45
1.50
1.55
1.60
Missing Mass [GeV/c2]

1.5

0.0

1.0

1.45
1.50
1.55
1.60
Missing Mass [GeV/c2]

σ12-14° [µb/(sr (MeV/c2))]

0.0

1.5

4-6°

σ6-8° [µb/(sr (MeV/c2))]

1.5

2-4°

σ4-6° [µb/(sr (MeV/c2))]

σ2-4° [µb/(sr (MeV/c2))]

1.5

12-14°
1.0

0.5

0.0

1.45
1.50
1.55
1.60
Missing Mass [GeV/c2]

σ14-16° [µb/(sr (MeV/c2))]

1.5

14-16°
1.0

0.5

0.0

1.45
1.50
1.55
1.60
Missing Mass [GeV/c2]

FIG. 4.4: Missing mass spectrum of the π − p → K − X reaction at 2.01 GeV/c for eachangle region. The ordinate represents the diﬀerential cross section averaged over the angle
region at 2◦ intervals in the laboratory frame. The quoted errors are statistical only.

4.3. UPPER LIMIT OF PRODUCTION CROSS SECTION

σ2-15° [µ b/(sr (MeV/c2))]

1.0

89

-

π- p → K X at 2.01 GeV/c

0.8
0.6
0.4
0.2
0.0

0.3

χ2 / ndf = 66.5 / 67
M = 1.537 GeV/c2 (fixed)
Γexp = 2.13 MeV (fixed)
Area = 0.171 ± 0.083 µ b/sr
1.50

1.51

1.52
1.53
1.54
Missing Mass [GeV/c2]

90% C.L. upper limit

1.55

1.56

-

π- p → K Θ+ at 2.01 GeV/c

σ2-15° [µ b/sr]

0.2
0.1
0.0
-0.1
-0.2
-0.3

1.50

1.51

1.52
1.53
1.54
Mass [GeV/c2]

1.55

1.56

FIG. 4.5: (Top) Missing mass spectrum of the π − p → K − X reaction at 2.01 GeV/c in themass region of the Θ+ search. The quoted errors of the data are statistical. A ﬁtting resultat the mass of 1537 MeV/c2 is also shown. The ﬁtting function (red solid) is a second-orderpolynomial (green dashed) with a Gaussian peak (blue dotted) whose width is ﬁxed at theexperimental resolution of 2.13 MeV. (Bottom) Allowed signal yields for each mass. The
error bars denote the statistical uncertainty. The red line indicates the upper limit at the
90% C.L.

90

CHAPTER 4. RESULTS

statistical uncertainty. The systematic uncertainty, which came from the eﬃciency andacceptance correction, is almost common within a local mass range of a few MeV/c2 . The
systematic uncertainty is discussed later. Hence, the ﬁtting result provides an estimationof the eﬀect only from statistical ﬂuctuation.
The ﬁtting was carried out for every assumed peak position from 1500 to 1560 MeV/c2
with 1-MeV step. The cross section was calculated from the area of the signal function.
The results are plotted with black points as a function of masses in Fig. 4.5 (bottom). In
the conﬁdence level estimation, we assumed a Gaussian distribution where an unphysicalregion corresponding to negative cross section was excluded; i.e., the upper limit at the
90% C.L., xup , was obtained from
∫ xup
G(x; µ, σ)dx
∫0 ∞= 0.9,
(4.4)
G(x;
µ,
σ)dx
0
where G(x; µ, σ) is a Gaussian function with a mean µ and a standard deviation σ, whichcorrespond to the obtained cross section and the uncertainty. The upper limit at the 90%
C.L. was obtained as a function of masses as shown with a red line in Fig. 4.5 (bottom).
The upper limit was found to be at most 0.28 µb/sr in the mass region of 1500–1560
MeV/c2 .
Systematic uncertainty
The systematic uncertainties on the upper limit of the cross section are discussed here.
The following components can be a source of the uncertainty;• The systematic uncertainty of the eﬃciency and acceptance correction was discussed in Sec. 3.8.3. The upper limit of the cross section is aﬀected by this uncertainty of 7% over the mass region of 1500-1560 MeV/c2 .
• The width of the signal Gaussian peak was ﬁxed to the missing-mass resolution of
2.13 MeV (FWHM) in the above ﬁtting. As described in Sec. 3.7.4, the uncertaintyof the missing-mass resolution was estimated to be ±0.15 MeV. The dependence of
the upper limit on the missing-mass resolution was examined as shown in Fig. 4.6(top). The uncertainty of ±0.15 MeV corresponds to deviations of ±0.012 µb/sr
at the maximum upper limit of 0.28 µb/sr, as shown in red and blue solid lines
in the ﬁgure. Therefore, the missing-mass resolution uncertainty has at most 4%
inﬂuence upon the upper limit.
• The uncertainty due to the background shape was examined by applying a thirdorder polynomial function instead of the second-order one as shown in Fig. 4.6(bottom). The diﬀerence was less than 0.005 µb/sr and found to be negligibly
small. This means that it is reasonable enough to use the second-order polynomial
function as the background shape.
Considering the above three kinds of uncertainties, the systematic uncertainty on theupper limit of the cross section was found to be controlled within 10%. This means thatthe present upper limit is predominantly determined by the statistics of the experimental
data.

4.3. UPPER LIMIT OF PRODUCTION CROSS SECTION

Upper Limit [µb/sr]

0.4∆M + 0.5 MeV∆M + 0.15 MeV∆M (= 2.13 MeV)
∆M - 0.15 MeV∆M - 0.5 MeV

0.3

0.2

0.1

0.0

1.50

1.51

1.52
1.53
1.54
2
Mass [GeV/c ]

1.55

1.56

1.55

1.56

BG = 2nd order pol.

0.3
Upper Limit [µb/sr]

91

BG = 3rd order pol.

0.2

0.1

0.0

1.50

1.51

1.52
1.53
1.54
2
Mass [GeV/c ]FIG. 4.6: (Top) Dependence of the upper limit on the missing-mass resolution. The blacksolid line is the upper limit obtained with the expected missing mass resolution (∆M = 2.13
MeV). The red and blue solid lines correspond to the upper limits with 1σ-deviated mass
resolutions (±0.15 MeV). The red and blue dashed lines correspond to the upper limits
with ∆M ± 0.5 MeV. (Bottom) Dependence of the upper limit on the background function.
The black solid line is the upper limit obtained with the second-order polynomial function,
while the red dashed line is that of the third-order one.

92

CHAPTER 4. RESULTSΓΘ = 1.0 MeV
ΓΘ = 0.5 MeV
ΓΘ = 0.1 MeV
ΓΘ = 0 MeV

Upper Limit [µb/sr]

0.4
0.3
0.2
0.1
0.0

1.50

1.51

1.52
1.53
1.54
2
Mass [GeV/c ]

1.55

1.56

FIG. 4.7: Θ+ -width dependence of the upper limit. The solid lines represent the upper
limits with assumed Θ+ widths of 0 (black), 0.1 (red), 0.5 (green), and 1.0 (blue) MeV.

Dependence on the Θ+ width
The natural width of Θ+ was ignored in the above ﬁtting, because the Θ+ must havevery small width. The dependence of the upper limit on the natural width of Θ+ isdiscussed here. The width of Θ+ was implemented with the Breit-Wigner distribution
convoluted by the Gaussian with the experimental resolution of 2.13 MeV (FWHM). The
signal function in the ﬁtting was replaced with the Breit-Wigner distribution smearedby the Gaussian. Figure 4.7 shows the upper limits with assumed widths of 0–1.0 MeV.
The upper limit rises by 0.10 µb/sr at most, if the Θ+ width is 1 MeV.
Summary of the 2012 and 2010 data
The present upper limit obtained in the 2012 data at an incident momentum of 2.01
GeV/c was compared with that of the 2010 data at 1.92 GeV/c. For the 2010 data,
the upper limit was reevaluated with an updated missing-mass resolution of 1.72 MeV[146], which was previously estimated as 1.44 MeV [139] 2 . The upper limits obtainedin the 2012 and 2010 data are shown in Fig. 4.8 with black solid and red dashed lines,
respectively, in case of the Θ+ natural width of 0 MeV. The available mass range of
1500–1560 MeV/c2 in the 2012 data is wider than that of 1510–1550 MeV/c2 in the 2010
data, owing to the improved experimental acceptance. The upper limits in the both data
are on the same level and less than 0.28 µb/sr. This is attributed to almost the same
The missing-mass resolution of 1.44 MeV was estimated by assuming ∆pB /pB = 5.2×10−4 (FWHM),
which was calculated by the ﬁrst-order transport matrix with a tracker position resolution of 0.2 mm
and by ﬂuctuation of the magnetic ﬁeld. We found that this underestimated the resolution of the beam
spectrometer.
24.3. UPPER LIMIT OF PRODUCTION CROSS SECTION

pπ = 2.01 GeV/cpπ = 1.92 GeV/c

0.3
Upper Limit [µb/sr]

93

0.2

0.1

0.0

1.50

1.51

1.52
1.53
1.54
Mass [GeV/c2]

1.55

1.56

FIG. 4.8: Comparison of the upper limits in the 2012 and 2010 data. The black solid (reddashed) line indicates the upper limit in the 2012 (2010) data with the incident momentumof 2.01 (1.92) GeV/c using the missing mass resolution of 2.13 (1.72) MeV. The diﬀerenceof the mass range is due to the diﬀerence of the missing mass acceptance.

statistics of the both data, and the resolution diﬀerence of 2.13 versus 1.72 MeV does
not have much inﬂuence.

Chapter 5
Discussion
5.1

Upper limit of the Θ+ width

The narrowness of the width is the most peculiar property to the Θ+ pentaquark. It isa big issue for any theoretical models to interpret the narrow width in a viewpoint of
the internal structure of the hadron. The width of Θ+ should be less than a few MeV atleast on the basis of past K + d scattering data, and the Belle Collaboration obtained theupper limit of 0.64 MeV [57]. Only the DIANA Collaboration claims a ﬁnite value of0.34 ± 0.10 MeV [56], which is extraordinarily small as the width for strongly decaying
hadrons.
As described in Sec. 1.5, the production mechanism of Θ+ in the π − p → K − Θ+reaction was studied in several theoretical calculations using the eﬀective Lagrangian
approach as shown in Fig. 1.10 (a,b,c). They suggest that the contributions of thet-channel process and contact term must be very small from the KEK E522 and E559
results. Therefore, the s-channel contribution is important in the π − p → K − Θ+ reaction.
Since the s-channel amplitude is related to the Θ+ decay width through the coupling
constant gKN Θ , we are able to estimate the width from the cross section measured in
the experiment. From the present null result, the upper limit of the Θ+ width can bederived.
In this section, we evaluate the upper limit of the Θ+ width using both the 2010
and 2012 data together with a theoretical calculation. The theoretical framework is
described in the next subsection. Using the theoretical prescription, the upper limit of
the width is estimated in the subsequent subsection. Finally, we discuss the obtained
result comparing with other experimental results.

5.1.1

Theoretical calculation

Several theoretical groups discussed the production mechanism of Θ+ in the π − p →K − Θ+ reaction using the eﬀective Lagrangian approach, which was described in Sec. 1.5.
Recently, Hyodo, Hosaka, and Oka have published a comprehensive calculation [113],
which can be directly compared to our experimental result. They considered only the
nucleon pole term which corresponds to the s-channel diagram in the π − p → K − Θ+reaction as shown in Fig. 5.1. Their calculation was performed for the isosinglet Θ+ with94

5.1. UPPER LIMIT OF THE Θ+ WIDTH

95

FIG. 5.1: s-channel diagram for the π − p → K − Θ+ reaction.

the spin-parity J P = 1/2± and 3/2± cases.
In the 3/2± cases, the width corresponding to the upper limit of the previous experiment [87] becomes much smaller than 1 MeV in their calculation, which is too narrow
to be understood as a strongly decaying hadron. Therefore, the 3/2± cases are highly
disfavored in their calculation. Hence, only the 1/2± cases are discussed in the following.
To evaluate the diagram in Fig. 5.1, the Yukawa couplings for the KN Θ and πN N
vertices are needed for the eﬀective interaction Lagrangian. They introduced two schemes
for the Yukawa couplings, namely pseudoscalar (PS) and pseudovector (PV) schemes.
For the πN N coupling, the former and latter correspond to the linear and nonlinear
representations of the chiral symmetry, respectively. The diﬀerence of results in the two
schemes are regarded as a theoretical uncertainty. The interaction Lagrangians in the
PS scheme are given by
1/2±

1/2±

LKN Θ = gKN Θ Θ̄ΓKN + h.c.,
LπN N = igπN N N̄ γ5 πN,

(5.1)
(5.2)

where Γ = 1 for the negative parity case and Γ = iγ5 for the positive parity case. The
KN Θ coupling constant is determined by the Θ+ decay width ΓΘ as√±
2πmΘ ΓΘ
1/2
gKN Θ =,
(5.3)
q(EN ∓ mN )where mΘ and mN are the mass of the Θ+ and√the nucleon, respectively; q is the momentum of K or N in the Θ+ decay; and EN = q 2 + m2N . The interaction Lagrangiansin the PV scheme are the derivative couplings:
1/2±−igA∗±
Θ̄γµ Γ∂ µ KN + h.c.,2fgA=N̄ γµ γ5 ∂ µ πN,
2f

LKN Θ =

(5.4)

LπN N

(5.5)

where f is the meson decay constant, and gA is the axial coupling constant of the nucleon.
The transition axial coupling constant, gA∗ , for the Θ+ → N is related to the gKN Θ
through the generalized Goldberger-Treiman relation as [147]gA∗± =

2f
1/2±
gKN Θ .
mΘ ± mN(5.6)

The theoretical constants were determined based on known hadron reactions except for
the unknown KN Θ coupling constant. Their calculation adopted standard values such
as gπN N = 13.5, f = 93 MeV, and gA = 1.25.

96

CHAPTER 5. DISCUSSION

1.0

0.06
1/2+

PV, Fc0.05
dσ/dΩ [µb/sr]

dσ/dΩ [µb/sr]

0.8
0.6
0.4
0.2
0.0
-1

0.04

1/2-

PV, FsPS, FcPS, Fs

0.03
0.02
0.01

-0.5

0
cos θCM

0.5

1

0.00
-1

-0.5

0
cos θCM

0.5

1

FIG. 5.2: Diﬀerential cross sections of the π − p → K − Θ+ reaction calculated by Hyodo,
Hosaka, and Oka [113, 148] at an incident momentum of 2.0 GeV/c, the Θ+ mass of 1540
MeV, and the Θ+ width of 1 MeV for the spin-parity of 1/2+ (left) and 1/2− (right). Eachline indicates the diﬀerent theoretical treatments: pseudoscalar (PS) or pseudovector (PV)couplings, and static (Fs ) or covariant (Fc ) types of form factors (see text).

In addition, they introduced a phenomenological form factor, which reﬂects the ﬁnite
size of the hadrons, in each vertex. They examined two types of from factors, namely
the static (Fs ) and covariant (Fc ) type form factors. The diﬀerence of results in the twoform factors are also regarded as a theoretical uncertainty. The static form factor is thethree momentum monopole type, deﬁned as
Fs =

Λ2s
,
Λ2s + |k|2

(5.7)

where k is the incident pion momentum in the c.m. frame, and Λs denotes a cutoﬀ value.
The covariant form factor is often used in photoproduction processes, deﬁned as
Fc =

Λ4c
,
Λ4c + (s − m2N )2(5.8)

where s is the squared total energy, and Λc denotes a cutoﬀ value. The cutoﬀ values
were determined based on known hyperon production reactions as Λs = 0.5 GeV andΛc = 1.8 GeV.
According to this prescription, the total cross section of the π − p → K − Θ+ reaction
was calculated as shown in Fig. 1.13. The calculated diﬀerential cross sections are shownin Fig. 5.2 at an incident momentum of 2.0 GeV/c for J P = 1/2± assuming ΓΘ = 1
MeV. One can see that the cross section for 1/2+ is larger than that for 1/2− as a generaltendency. This can be understood by a parity dependence of the coupling constant shownin Eq. (5.3); the coupling constant for 1/2+ is larger than that for 1/2− for ΓΘ being
ﬁxed. This is essentially attributed to the partial wave of the Θ+ → KN decay. Θ+5.1. UPPER LIMIT OF THE Θ+ WIDTH

97

decays in s(p)-wave in 1/2− (1/2+ ) case. In general, a decay width is suppressed in ahigher partial wave for the coupling constant being ﬁxed.
Since the amplitude for the s-channel diagram is proportional to the KN Θ coupling
constant, the cross section (σΘ ) is simply proportional to the width of Θ+ :
dσΘ
2
∝ gKN
Θ ∝ ΓΘ ,dΩ(5.9)

Thus, the cross section is written asdσΘ= kC,F (pπ , mΘ ) ΓΘ ,dΩ

(5.10)

where the coeﬃcient k is obtained in each coupling scheme (C), PS or PV, and form
factor (F ), Fs or Fc . k is a function of the incident momentum pπ and the Θ+ mass mΘ .
The diﬀerential cross section was calculated at the incident momenta of 1.92 and 2.00
GeV/c and at the Θ+ masses between 1510 and 1550 MeV/c2 at 10 MeV/c2 intervals.

5.1.2

Upper limit estimation

From the E19 experimental results, two structureless missing-mass spectra at the incident momenta of 1.92 and 2.01 GeV/c were obtained. The upper limit of the Θ+
width was estimated by using the two spectra comparing with the theoretical calculation described above including the incident momentum dependence of the cross section.
This incident momentum dependence provides an useful information in addition to theincreased statistics, when we estimate the upper limit of the width by a simultaneousﬁtting of the 2010 and 2012 data.
For a direct comparison with the experimental data, the diﬀerential cross section averaged over the scattering angles of 2-15◦ in the laboratory frame was calculated according
to the above calculation. The calculated coeﬃcient k in Eq. (5.10) for each momentum
and mass was an input of the following ﬁtting. As shown in Fig. 5.3, both experimental data of 1.92 and 2.01 GeV/c were simultaneously ﬁtted with respect to a common
width parameter ΓΘ . The top panel shows the 2010 data at 1.92 GeV/c, while the bottom panel shows the 2012 data at 2.01 GeV/c. A signal function is the Breit-Wigner
distribution convoluted by a Gaussian distribution. The Breit-Wigner width represents
the parameter ΓΘ , which is common for each data. The Gaussian width represents theexperimental resolutions, which were ﬁxed at 1.72 and 2.13 MeV (FWHM) for the 1.92and 2.01-GeV/c data, respectively. The signal cross section for each data is a functionof the common parameter ΓΘ , as given in Eq. (5.10). We allowed both positive andnegative cross sections in ﬁtting the spectra. In case of the negative cross section, thesignal function was a Gaussian with the experimental resolution and negative height. A
background function is a second-order polynomial function deﬁned in a mass range of
1500-1560 MeV/c2 , whose coeﬃcients are independently determined in each data.
Considering the narrower mass range of the 2010 data, the search range was determined as 1510–1550 MeV/c2 . The ﬁtting was carried out for every assumed peak
position from 1510 to 1550 MeV/c2 with 1-MeV step. Figure 5.4 (top) shows the ﬁtting
result of the Θ+ width for J P = 1/2+ , the PV scheme and the Fc form factor case,

98

CHAPTER 5. DISCUSSION

σ2-15° [µb/(sr (MeV/c2))]

1.0
0.8

χ2 / ndf = 122.7 / 115
M = 1.537 GeV/c2 (fixed)ΓΘ = 0.17 +0.14-0.13 MeV

1/2+, PV, Fc

0.6
0.4
0.2

Γexp1 = 1.72 MeV (fixed)
Area = 0.069 +0.057-0.052 µb/sr

pπ = 1.92 GeV/c

Γexp2 = 2.13 MeV (fixed)
Area = 0.079 +0.065-0.059 µb/sr

pπ = 2.01 GeV/c

σ2-15° [µb/(sr (MeV/c2))]

0.0

0.8
0.6
0.4
0.2
0.0
1.50

1.51

1.52
1.53
1.54
Missing Mass [GeV/c2]

1.55

1.56

FIG. 5.3: Missing mass spectra of the π − p → K − X reaction at 1.92 (top) and 2.01 GeV/c(bottom) in the mass region of the Θ+ width ﬁtting. The quoted errors of the data arestatistical. The ﬁtting was simultaneously applied to the both spectra with respect to acommon width parameter ΓΘ . A ﬁtting result at the mass of 1537 MeV/c2 for J P = 1/2+ ,the PV scheme and the Fc form factor case is shown. The ﬁtting function (red solid) is
deﬁned as second-order polynomials (green dashed) with the Breit-Wigner peak convoluted
by a Gaussian (blue dotted) whose width is ﬁxed at the experimental resolution of 1.72 or
2.13 MeV.

5.1. UPPER LIMIT OF THE Θ+ WIDTH

Decay Width [MeV]

0.4

90% C.L. upper limit99

for 1/2+, PV, Fc

0.2
0.0
-0.2
-0.4
1.51

1.52

Decay Width [MeV]3

1.53
Mass [GeV/c2]

1.54

1.55

for 1/2-, PS, Fc

2
1
0
-1
-2

1.51

1.52

1.53
Mass [GeV/c2]

1.54

1.55

FIG. 5.4: Results of the Θ+ width ﬁtting for J P = 1/2+ , the PV scheme and the Fc form
factor case (top), and for J P = 1/2− , the PS scheme and the Fc form factor case (bottom).
The black points with symmetric error bars are the obtained widths with approximate
errors estimated by the parabolic assumption, while the green asymmetric error bars denotethe 1σ errors estimated in an accurate way. The red line indicates the upper limit at the
90% C.L. based on the approximate errors.

100

CHAPTER 5. DISCUSSION

while Fig. 5.4 (bottom) shows the ﬁtting result for J P = 1/2− , the PS scheme and theFc form factor case. Since the ﬁtting is nonlinear due to the constraint of Eq. (5.10),
the estimated errors of the ﬁtting are asymmetric as shown with green error bars in theﬁgure. This asymmetry is enhanced when the ﬁtting result of the width become larger.
It is not negligible especially outside a range around 1530 or 1540 MeV/c2 in the 1/2−
case. However, in the 1/2+ case and in the mass region around 1530 and 1540 MeV/c2
for the 1/2− case, the deviation from the approximate errors estimated by the parabolic
assumption 1 , which is symmetric as shown with black error bars in the ﬁgure, is small:< 0.013 MeV for the 1/2+ case, and < 0.15 MeV for the 1/2− case. Therefore, the upper
limit at the 90% C.L. was simply estimated by using the approximate errors in the samemanner as described in Sec. 4.3, excluding an unphysical region of negative width.
The above procedure was carried out for every case of the spin-parity (1/2± ), coupling
scheme (PS or PV) and form factor (Fs or Fc ). Figure 5.5 shows the obtained upper
limits on the Θ+ width for each theoretical scheme and spin-parity. The width upper
limit curves are placed in reverse order to the cross sections shown in Fig. 5.2, where thewidth is being ﬁxed. Since the diﬀerence among each scheme is a theoretical uncertainty,
we took the most conservative one, where the result gives the largest upper limit. In
the 1/2+ case (Fig. 5.5 (top)), the PV scheme with the Fc form factor gives the largest
upper limits. The upper limits of the width are less than 0.36 MeV in almost the entire
mass region of 1510–1550 MeV/c2 . The 1/2− case (Fig. 5.5 (bottom)) shows relatively
larger widths than the 1/2+ case. This can be understood by the relation between thewidth and the cross section (Eq. (5.3)) described in Sec. 5.1.1. Equation (5.3) allows thewidth to become larger keeping a small cross section especially in the 1/2− case. The
PS scheme with the Fc form factor gives the largest upper limits in the 1/2− case. The
upper limits of the width are less than 1.9 MeV in the mass region around 1530 or 1540
MeV/c2 , whereas the sensitivity is not suﬃcient outside this region.
Systematic uncertainty
The systematic uncertainties on the upper limit of the width caused by the spectrum
ﬁtting was examined. The missing mass has a systematic uncertainty due to the massscale calibration. As described in Sec. 3.6.4, the missing mass scale uncertainty wasestimated to be 1.4 MeV for the 2.01-GeV/c data. The corresponding value for the
1.92-GeV/c data is 1.7 MeV [116, 139]. These values were assumed to be independent,
because the 2010 and 2012 run are independent experiments. The missing mass scales
were shifted by δm1 and δm2 in the 1.92- and 2.01-GeV/c data, respectively. Figure 5.6
shows the upper limits of the width when the mass scale was shifted by ±1.5 MeV. The+−
upper limits could vary by ±30% and +10−30 % in the 1/2 and 1/2 cases, respectively.

1

The approximate error is estimated by using the curvature at the minimum of the χ2 function andassuming a parabolic shape [133].

5.1. UPPER LIMIT OF THE Θ+ WIDTH

101

0.6

Decay Width [MeV]

0.5
0.4

PV, FcPV, FsPS, FcPS, FsDIANA

90% C.L. upper limit for 1/2+

0.3
0.2
0.1
0.0

1.51

1.52

1.53

1.54

1.55
2

3.0
Decay Width [MeV]for 1/22.5
2.0
1.5
1.0
0.5
0.0

1.51

1.52

1.53
Mass [GeV/c2]

1.54

1.55

FIG. 5.5: Upper limits at the 90% C.L. on the Θ+ decay width for the spin-parity of 1/2+
(top) and 1/2− (bottom) case. Each line indicates the diﬀerent theoretical treatments:
pseudoscalar (PS) or pseudovector (PV) couplings, and static (Fs ) or covariant (Fc ) typesof form factors. The DIANA result [56] is also indicated by the open square (magenta).

102

CHAPTER 5. DISCUSSION

Decay Width [MeV]

0.6

δm1,2 = 0 MeV
δm1 = +1.5 MeV

0.5

for 1/2+, PV, Fc

δm1 = -1.5 MeV
δm2 = +1.5 MeV

0.4

δm2 = -1.5 MeV

0.3
0.2
0.1
0.0

1.51

1.52

1.53
Mass [GeV/c2]

1.54

1.55

3.0
Decay Width [MeV]for 1/2-, PS, Fc
2.5
2.0
1.5
1.0
0.5
0.0

1.51

1.52

1.53
Mass [GeV/c2]

1.54

1.55

FIG. 5.6: Investigation of the systematic uncertainty of the upper limit of the Θ+ widthfrom the missing mass scale uncertainties. The top ﬁgure shows the 1/2+ case with the PV
scheme and the Fc form factor, while the bottom ﬁgure the 1/2− case with the PS schemeand the Fc form factor. Shifts for the missing mass scales, δm1 and δm2 , were introducedin the 1.92- and 2.01-GeV/c data, respectively. The black solid line represents the no-shiftcase. The red dashed and dotted lines represent δm1 = ±1.5 MeV, while the blue dashedand dotted lines represent δm2 = ±1.5 MeV.

5.1. UPPER LIMIT OF THE Θ+ WIDTH

5.1.3

103

Discussion on the present upper limit

As described above, the upper limits of the Θ+ width at the 90% C.L. were estimatedto be 0.36 and 1.9 MeV for the spin-parity of 1/2+ and 1/2− , respectively. The upper
limits were improved to about 1/2 from the previous limits of 0.72 and 3.1 MeV for 1/2+
and 1/2− , respectively, obtained with the 2010 data [116]. The 2010 and 2012 data havealmost the same statistics, but diﬀerent incident momenta. It was conﬁrmed that theincident momentum dependence of the cross section in the theoretical calculation was
more eﬀective to improve the upper limit of the width.
The present upper limit depends on the parity of Θ+ . It is natural for the 1/2− state
to have a larger upper limit of the width, because the 1/2− state is an s-wave resonance.
This is a reason why the negative parity state is disfavored from a theoretical point ofview, as described in Sec. 1.3. The width of 1.9 MeV is quite narrow as for an s-wave
resonance. However, the widths reported in the DIANA and Belle experiments do notdepend on the parity, and smaller than 1.9 MeV. If the Θ+ is really a 1/2− state withsuch a narrow width, the production cross section can be below our sensitivity on thebasis of the above theoretical calculation. The present measurement is not sensitive tothe 1/2− state with a very narrow width, although such a state is diﬃcult to understandtheoretically.
We discuss the spin-parity of 1/2+ case, next. The present upper limit of 0.36 MeV
is much smaller than a few MeV constrained from the past K + d scattering data [13, 14,
16, 15, 17], described in Sec. 1.2. It is also more stringent than the upper limit from theBelle Collaboration, e.g., < 0.64 MeV at 1539 MeV/c2 [57]. The latest DIANA result
is indicated with a magenta square in Fig. 5.5; they claimed that the Θ+ was observed
at 1538 ± 2 MeV/c2 and the width is 0.34 ± 0.10 MeV [56]. The present upper limit
at the 90% C.L. for the PV-Fc case are comparable to their value. Considering that
we adopted the most conservative case in the four variation, the consistency between
our result and DIANA is subtle, but the present result does not completely contradictthe DIANA claim. Since the present upper limit is predominantly determined by thestatistics of the experimental data, several times more statistics are needed to exclude
the DIANA result.

Chapter 6
Conclusion
Study of exotic hadrons, which cannot be interpreted as ordinary three-quark baryons
or quark-antiquark mesons, would oﬀer us a good opportunity to investigate low-energy
quark dyanmics. The pentaquark Θ+ has a strangeness quantum number S = +1 with its
minimal quark conﬁguration of uudds̄. The distinct features of the Θ+ are a light mass ofabout 1540 MeV and a narrow width of a few MeV or less. If such an exotic pentaquark
exits, it is quite interesting from a viewpoint of the hadron structure. Many experiments
searched for the Θ+ so far, but the experimental situation was still controversial. For
further investigation, a high-statistics and high-resolution experiment has been required.
The diﬀerential cross section of the π − p → K − X reaction was measured in forward
scattering angles to search for the Θ+ pentaquark with the missing-mass technique.
The experiment was performed in 2012 using a beam momentum of 2.01 GeV/c at
the K1.8 beam line in the J-PARC hadron facility. A liquid hydrogen target with athickness of 0.85 g/cm2 was exposed to 8.1 × 1010 π − beams with a typical intensity of
1.7 × 106 per 2.2-second spill. We constructed a high-resolution spectrometer system.
The beam pions were measured with the beam spectrometer with a momentum resolutionof 1 × 10−3 (FWHM). The outgoing kaons were identiﬁed with the SKS spectrometerwith a momentum resolution of 2×10−3 (FWHM). We measured the missing mass of theπ − p → K − X reaction at forward scattering angles of 2–15◦ in the laboratory frame. The
missing-mass resolution for the Θ+ was estimated to be 2.13±0.15 MeV (FWHM). Usingthe Σ± production data and the beam-through data, the absolute scale of the missing
mass for the Θ+ production data was calibrated with an uncertainty of 1.4 MeV/c2 .
Thus, it was demonstrated that we are able to observe a sharp missing-mass peak anddetermine the mass and, possibly, width with a good precision, if the Θ+ is produced.
The cross section was calculated by correcting the data for the experimental eﬃciency
and acceptance with an uncertainty of 7%. The measured diﬀerential cross sections ofthe π ± p → K + Σ± reactions were in good agreement with the past experimental data.
No sharp peak structure was observed in the missing-mass spectrum of the π − p →K − X reaction. The missing-mass acceptance was wider than the previous 2010 dataowing to the improved experimental setup. The upper limit on the Θ+ production
cross section averaged over scattering angles from 2◦ to 15◦ in the laboratory frame wasobtained as a function of the Θ+ mass, and found to be less than 0.28 µb/sr at the 90%
C.L. in a mass region of 1500–1560 MeV/c2 . Note that we assumed the intrinsic width of
104

105
Θ+ is negligibly smaller than the experimental resolution. If the width of Θ+ is 1 MeV,
the above upper limit rises by 0.10 µb/sr. The systematic uncertainty of the upper limit
was controlled within 10%. Hence, the present upper limit is predominantly determinedby the statistical uncertainty. The present upper limit is as small as the previous 2010
result of 0.28 µb/sr. This is attributed to almost the same statistics of the data.
The narrowness of the width is the most peculiar property to the Θ+ pentaquark. The
mechanism of the π − p → K − Θ+ reaction was theoretically discussed using the KEKE522 and E559 results. Knowing that the t-channel and contact term contributions arevery small, the s-channel contribution is important in the π − p → K − Θ+ reaction. Since
the s-channel amplitude is related to the Θ+ decay width through the KN Θ coupling
constant, we can estimate the upper limit of the width from the cross section measured
in the experiment. Using both the 2010 and 2012 data together with a theoretical
calculation using the eﬀective Lagrangian approach, the upper limit of the Θ+ width
was estimated as a function of the Θ+ mass. Considering the theoretical uncertainty, we
adopted the most conservative theoretical scheme that gives the largest upper limit. The
upper limits of the width were estimated to be 0.36 and 1.9 MeV for the Θ+ spin-parityof 1/2+ and 1/2− , respectively. The upper limits of the width were improved by halfof the previous limits of 0.72 and 3.1 MeV for 1/2+ and 1/2− , respectively, obtained in
the 2010 data [116]. The present upper limit of the width is not sensitive enough to the
1/2− state with a very narrow width in this theoretical model. For the 1/2+ case, thepresent limit is more stringent than the upper limit of 0.64 MeV reported from the Belle
Collaboration [57]. The present limit is comparable to the width of 0.34 ± 0.10 MeV
reported by the DIANA Collaboration [56]. The consistency is subtle but the present
result does not completely contradict the DIANA claim.

Acknowledgements
I would like to express my sincere gratitude to my supervisor, Prof. Tomofumi Nagae. He
guided me to an exciting world of the experimental hadronic physics. He always encouraged me and let me have invaluable experience in detector development and experiments
at many places. I learned an attitude of physicists from him.
I am deeply indebted to Prof. Megumi Naruki, who is the spokesperson of the JPARC E19 experiment. She gave me an opportunity to join the experiment and write
this doctoral thesis.
I would like to express my thanks to Dr. Masayuki Niiyama and Dr. Hiroyuki Fujioka
for useful discussions and advice. They often helped me when I was in trouble. I was
deeply impressed with their sharp insight into analysis and physics.
I would like to address my thanks to all the members of the J-PARC E19 Collaboration. In particular, I am grateful to Dr. Kotaro Shirotori and Dr. Tomonori Takahashi,
who are my colleagues from the construction phase of the K1.8 experimental area. They
always led me and gave me a lot of advice. I acknowledge Mr. S. Adachi, Mr. H. Ekawa,
Mr. S. Hayakawa, Dr. R. Honda, Mr. Y. Ichikawa, Ms. R. Iwasaki, Mr. S. Kanatsuki,
Dr. R. Kiuchi, Ms. M. Sato, Dr. H. Sugimura, Dr. M. Ukai, Mr. T. O. Yamamoto,
Mr. S. B. Yang, and Mr. Y. Yonemoto for their outstanding eﬀorts in construction of
the experimental setup. I spent an enjoyable time at J-PARC thanks to their warm hospitality. Dr. K. Miwa, Prof. A. Sakaguchi, Prof. T. Takahashi, and Prof. K. Tanida gaveme helpful advice based on their profound knowledge and experience. I also acknowledge
Dr. M. Agnello, Dr. K. Aoki, Prof. B. Bassalleck, Dr. E. Botta, Dr. S. Bufalino, Dr. A. Feliciello, Dr. K. Hosomi, Dr. Y. Igarashi, Prof. K. Imai, Mr. N. Ishibashi, Prof. S. Ishimoto,Prof. K. Itahashi, Dr. M. J. Kim, Prof. T. Koike, Prof. V. V. Kulikov, Prof. S. Marcello,
Mr. Y. Matsumoto, Mr. K. Matsuoka, Prof. H. Noumi, Mr. Y. Nozawa, Mr. R. Ota,
Dr. S. Suzuki, Prof. H. Takahashi, Prof. H. Tamura, Mr. T. Tanaka, Dr. A. O. Tokiyasu,
Ms. N. Tomida, Mr. K. Yagi, and Mr. K. Yoshida. The experiment could not be carriedout without their great contributions. It is my great pleasure to work with them.
I would like to express my thanks to Dr. Tetsuo Hyodo for helpful discussions about
the experimental results from a theoretical point of view. He kindly provided us atheoretical calculation without which we could not extract the constraint of the width.
I would like to thank members of the Experimental Nuclear and Hadronic Physics
Laboratory, Kyoto University. I love the spirit of academic freedom. I was happy tospent my graduate-school life in this laboratory.
Last but not least, I express my deep appreciation to my parents for their continuous
supports and encouragements.

106Appendix A
AC eﬃciency
The eﬃciency of the AC counter is described in this appendix. AC was replaced witha new large-size detector with a sensitive area of 2040W × 1200H mm2 before the 2012
run. The speciﬁcation of the new AC counter is found in Sec. 2.4.2. AC is required tohave a good eﬃciency of ∼99.9% for pion veto at the trigger level.
The AC eﬃciency was estimated for pions with 0.8–1.2 GeV/c in the 2012 data. The
position dependence of the eﬃciency is shown in Fig. A.1, where apparent eﬃciency
drops are observed. In the horizontal position dependence, the drop at X > 1000 mm is
ascribed to an edge of the silica aerogel radiator. In the vertical position dependence, thedrops at Y = ±200 mm are ascribed to 2-mm thick aluminum plates which support thestack of aerogel tiles. The 2-mm thick regions are insensitive to the Cherenkov radiation.
Note that, since SKS is a horizontally bending magnet, the X-position is related tothe particle momentum, whereas the Y -position is not related to the momentum. The
momentum dependence of the AC eﬃciency is shown in Fig. A.2, where signiﬁcantdependence is not observed. The eﬃciency drops at the Y positions does not aﬀect
the missing mass distribution. In addition, kaons are well discriminated from pions in
the oﬄine analysis using particle trajectories and time of ﬂight, as described in Sec. 3.3.2.
The ineﬃciency of AC is not a problem of the oﬄine analysis but of the trigger.
The AC eﬃciency was 98–99% even except for the local eﬃciency drops. This might
be attributed to gaps among the aerogel tiles. After this experiment, the support plates
were removed, and the aerogel tiles were stacked up again. The eﬃciency was improved
to 99.7% in a subsequent experiment [149].

107

108

APPENDIX A. AC EFFICIENCY

0.95

0.95
Efficiency

1.00

Efficiency

1.00

0.90

0.90

0.85

0.80

0.85

-500
0
500
1000
Horizontal position (X) [mm]0.80-600 -400 -200 0 200 400 600
Vertical position (Y) [mm]FIG. A.1: Position dependence of the AC eﬃciency. (Left) Horizontal position (X) dependence for an interval of 60 mm. (Right) Vertical position (Y ) dependence for an intervalof 40 mm.

1.00

Efficiency

0.95

0.90

0.85

0.80

0.8

0.9
1.0
1.1 1.2
Momentum [GeV/c]

1.3

FIG. A.2: Momentum dependence of the AC eﬃciency for an interval of 20 MeV/c.

Appendix B
Miscellaneous vertex analyses
The analysis of the vertex reconstruction was described in Sec. 3.4. Miscellaneous vertex
analyses which were not included in the main text are given in this appendix.

B.1

Z-vertex resolution

The (beam direction) z-vertex resolution was estimated using the empty target data
where the scattering events at the target vessel and the vacuum chamber windows wereobserved. Both the end caps of the vessel and the chamber windows were made of a 0.25mm thick mylar, which were positioned at z = ±60 and ±135 mm. Figure B.1 shows thez-vertex distributions for diﬀerent scattering angle regions in the empty target data. One
can see that the z-vertex resolution deteriorates with decrease of the scattering angles.
The target image could not recognize in events with the scattering angle less than 2◦ .
Contribution from the four mylar windows are clearly identiﬁed in events with the large
scattering angle. The z-vertex resolution was estimated to be 10–20 mm (σ) for the
scattering angles from 2◦ to 15◦ .

B.2

X-vertex resolution

The (horizontal) x-vertex resolution was estimated in the same manner as for the zvertex resolution. The target vessel was a cylinder with a 33.9-mm radius and the sidesurface was made of a 0.3-mm thick PET. Figure B.2 shows the x-vertex distribution in
the empty target data. To observe contribution from the side surface clearly, the z-vertex
from -50 mm to 50 mm were selected. The x-vertex resolution was estimated to be 2
mm (σ) for the scattering angles from 2◦ to 15◦ . 1
1

The (vertical) y-vertex resolution could not be estimated since the beam proﬁle at the target was ahorizontally oblate shape and the beam hit neither the upside nor downside of the vessel.

109

110

APPENDIX B. MISCELLANEOUS VERTEX ANALYSES

25°(a) θ < 2

70

20

50

CountsCounts

60

40
30
20

°

(b) 2 < θ < 5

15
10
5

10
0
-300 -200 -1000100
z-vertex [mm]0-300 -200 -1000100
z-vertex [mm]300°(c) 5 < θ < 10

30

25

25

20

20

CountsCounts

30

200

15

10

5

5
200

300

300

200

300

°

(d) 10 < θ < 15

15

10

0
-300 -200 -1000100
z-vertex [mm]200

0-300 -200 -1000100
z-vertex [mm]FIG. B.1: Z-vertex distributions in the empty target data. The scattering angle θ isselected as (a) θ < 2◦ , (b) 2 < θ < 5◦ , (c) 5 < θ < 10◦ , or (d) 10 < θ < 15◦ . The mylar
windows were positioned at z = ±60 and ±135 mm.

B.3. VERTEX DISTRIBUTION DIFFERENCE BETWEEN (π − , K − ) AND (π − , π − ) EVENTS111

20

Counts15
10
50-50 -40 -30 -20 -10 0 10 20 30 40 50
x-vertex [mm]FIG. B.2: X-vertex distribution in the empty target data. Events with the scattering
angles of 2–15◦ and the z-vertex from -50 mm to 50 mm are selected. The target vessel
had a cylindrical shape with a 33.9-mm radius.

B.3

Vertex distribution diﬀerence between (π −, K −)and (π −, π −) events

As for the (π − , K − ) reaction from a proton at 2 GeV/c, the following processes are
known:
π − p → ϕ n → K − K + n,π − p → Λ(1520) K 0 → K − K 0 p,
π − p → K − K + n or K − K 0 p (nonresonant).

(B.1)
(B.2)
(B.3)

As for the (π − , K − ) reaction from a neutron at 2 GeV/c, only one process is possible:
π − n → K − K 0 n (nonresonant).

(B.4)

Hence, the cross section of the (π − , K − ) reaction from a neutron is expected to be smaller
than that from a proton. On the other hand, the cross section of the (π − , π − ) reaction
from a neutron is the same as that from a proton.
The z-vertex distribution for the (π − , K − ) events was compared to that for the(π − , π − ) events in Fig. B.3. The histogram for the (π − , π − ) events was normalized by the
number of contribution from the LH2 . The mylar window are composed by Hydrogen,
Carbon and Oxygen; therefore, the (π − , K − ) events from the mylar window are smaller
than the (π − , π − ) events. This is the reason why the contamination fraction estimatedby using (π − , π − ) events in Sec. 3.4 are slightly larger than that of (π − , K − ) events.

112

APPENDIX B. MISCELLANEOUS VERTEX ANALYSES

3000

-

(π-, K )(π-, π-)Counts

2500
2000
1500
1000
500
0
-300

-200

-100
0
100
z-vertex [mm]

200

300

FIG. B.3: Comparison of z-vertex distributions between (π − , K − ) and (π − , π − ) events.
The black histogram shows a z-vertex distribution for (π − , K − ) events, while the redhistogram shows that for (π − , π − ) events normalized by the number of contribution fromthe LH2 (−60 < z < 60 mm). Enhancements around the mylar window positions are seenin the (π − , π − ) events.

Appendix C
Stability of magnetic ﬁeld
C.1

Field of the beam spectrometer

The magnetic ﬁeld of the D4 magnet was monitored by the Hall probe with the precisionof 0.01% [121]. The probe was set at 75-mm upside of the central plane of the D4 magnet.
The ﬁeld was recorded every 1 sec during the experiment. Figure C.1 shows the magnetic
ﬁeld of the D4 magnet in the Θ+ search data. The gradual ﬂuctuation in the long-term
period may be attributed to the stability of the power supply. The spikes were coincident
with temporary shutdowns of the D3 and D2 magnets to enter the experimental area;
therefore, they have no problem since the data acquisition was stopped at that time.
The stability of the magnetic ﬁeld was found to be within 2.4 × 10−4 in the whole ofthe period, which is small enough comparing with the beam momentum resolution. The
stability in the calibration data was also investigated and found to be better than thatof the Θ+ search data.

1.6714

D4 Field [T]1.6713
1.6712
1.6711
1.67101.6709

0

50

100

150
200
Run Time [sec]

250

300

FIG. C.1: Magnetic ﬁeld of the D4 magnet in the Θ+ search data.

113

×103
350

114

C.2

APPENDIX C. STABILITY OF MAGNETIC FIELD

Field of the SKS spectrometer

The magnetic ﬁeld of the SKS magnet was monitored by the NMR probe with theprecision of 1 µT [127]. The probe was set on the bottom pole of the magnet. The ﬁeld
was recorded every 1 sec during the experiment. Figure C.2 shows the magnetic ﬁeld of
the SKS magnet in the Θ+ search data. The gradual ﬂuctuation in the long-term period
may be attributed to the stability of the power supply. The sudden ﬂuctuations of ±0.1
mT in 1 sec may be caused by the readout electronics of the probe. The stability ofthe magnetic ﬁeld was found to be within 9.6 × 10−5 in the whole of the period, whichis small enough comparing with the momentum resolution for scattered particles. The
stability in the calibration data was also investigated and found to be better than thatof the Θ+ search data.
2.4875SKS Field [T]2.48742.48732.48722.48712.4870

0

50

100

150
200
Run Time [sec]

250

300

FIG. C.2: Magnetic ﬁeld of the SKS magnet in the Θ+ search data.

×103
350

Appendix D
Summary of Σ production crosssectionThe Σ± production cross sections were presented in Sec. 3.9. In this appendix, the crosssections are tabulated and the cross sections in the center-of-mass (c.m.) frame arepresented for convenience of other use.
Table D.1 shows the diﬀerential cross sections in the laboratory frame which wereplotted in Fig. 3.27 or 3.28. Figure D.1 and Table D.2 show the diﬀerential cross sectionsin the c.m. frame. It should be noticed that the present Σ production cross sections
have the systematic uncertainty of 6% described in Sec. 3.8.3.
TABLE D.1: Diﬀerential cross sections in the laboratory frame for π + p → K + Σ+ at 1.38
GeV/c, π − p → K + Σ− at 1.38 GeV/c and 1.46 GeV/c obtained in the E19-2012 data. The
quoted cross sections were derived from the average between θLab ±1 deg and are presented
in a unit of µb/sr. The errors are statistical only. The data points are plotted in Fig. 3.27
or 3.28.

θLab [deg]
3
5
7
9
11
13
15

Σ+ at 1.38 GeV/c Σ− at 1.38 GeV/c Σ− at 1.46 GeV/c
dσ/dΩ
error
dσ/dΩ
error
dσ/dΩ
error
601.
32.
95.7
7.4
74.7
3.1
452.
22.
83.3
5.5
63.8
2.2
464.
23.
69.8
5.2
62.3
2.3
289.
19.
60.4
5.0
47.0
2.0
199.
17.
39.9
4.8
38.0
1.9
143.
17.
37.5
5.2
20.4
1.5
139.
18.
29.9
4.9
18.0
1.8

115

116

APPENDIX D. SUMMARY OF Σ PRODUCTION CROSS SECTION9080dσ/dΩCM [µb/sr]

7060

π+ p → K+ Σ+ at 1.38 GeV/c
E19 2012 data
Candlin et al. (1983)

50
40
30
20
10

dσ/dΩCM [µb/sr]

0
0.70

0.75

0.80 0.85 0.90
cos θ (CM)

0.95

1.00

20
E19 2012 data, 1.38 GeV/c
18
E19 2012 data, 1.46 GeV/c
Good et al., 1.325 GeV/c
16
Good et al., 1.275 GeV/c
Dahl et al., 1.500 GeV/c
14
12
10
8
6
4
2
π- p → K+ Σ
00.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00
cos θ (CM)FIG. D.1: (Top) Diﬀerential cross sections in the c.m. frame for the π + p → K + Σ+ reaction.
The black solid circles are the present E19-2012 data at 1.38 GeV/c. The blue crosses are
the data from Candlin et al. [141] at 1.377 GeV/c. (Bottom) Diﬀerential cross sectionsin the c.m. frame for the π − p → K + Σ− reaction. The black solid circles and the graysolid squares are the present E19-2012 data at 1.38 and 1.46 GeV/c, respectively. The
blue crosses and the green open squares are the data from Good et al. [142] at 1.325 and1.275 GeV/c, respectively. The cyan open triangles are the data from Dahl et al. [143] at
1.500 GeV/c. The scattering angle is deﬁned as the one between the outgoing kaon andthe incoming pion. The quoted errors are statistical only. The present data are tabulated
in Table D.2.

117

TABLE D.2: Diﬀerential cross sections in the c.m. frame for π + p → K + Σ+ at 1.38 GeV/c,
π − p → K + Σ− at 1.38 GeV/c and 1.46 GeV/c obtained in the E19-2012 data. The quoted
cross sections were derived from the average between cos θcm ± 0.025 and are presented ina unit of µb/sr. The errors are statistical only. The data points are plotted in Fig. D.1.

cos θcm
0.975
0.925
0.875
0.825
0.775

Σ+ at 1.38 GeV/c Σ− at 1.38 GeV/c Σ− at 1.46 GeV/c
dσ/dΩ
error
dσ/dΩ
error
dσ/dΩ
error
77.6
2.4
12.75
0.56
10.50
0.24
51.4
2.6
9.56
0.66
8.35
0.29
33.3
2.9
6.64
0.77
4.98
0.27
25.1
3.2
5.95
0.88
3.79
0.32
19.2
3.2
5.97
1.05
2.77
0.35

Appendix E
Additional study of backgroundprocesses
The background processes associated with the Θ+ production in the π − p → K − X reaction were discussed in Sec. 4.2, where only the three reactions (4.1–4.3) were considered.
In this appendix, other higher excited Λ∗ and Σ∗ resonances, which were neglected in
the main text, are reconsidered.
In addition to the reactions (4.1–4.3), following reactions potentially contribute to
the background:
π − p → Y ∗− K + → K − K + n,π − p → Y ∗0 K 0 → K − K 0 p,

(E.1)
(E.2)

where Y ∗ represents Λ∗ or Σ∗ resonances above the K̄N threshold except for Λ(1520).
The beam momentum of 2.01 GeV/c in the present experiment corresponds to the totalc.m. energy of 2164 MeV, which is near the production threshold of Λ(1600, 1670, 1690)
and Σ(1660, 1670). These Y ∗ resonances are summarized in Table E.1.
Figure E.1 shows simulated missing mass spectra of the π − p → K − X reaction for the
background reactions (E.1, E.2). Since the angular distributions of the production anddecay of the Y ∗ s are not known, an isotropic distribution was assumed in the simulation.
The Y ∗ resonances contribute to the relatively low mass region. The Λ(1670, 1690) andΣ(1660, 1670) contributions make similar spectrum shapes.
TABLE E.1: Λ∗ and Σ∗ resonances which potentially contribute to the background [58].
Unestablished resonances with a status of * or ** are neglected 1 .

ParticleΛ(1600)Σ(1660)Λ(1670)Σ(1670)Λ(1690)
1

JP
1/2+
1/2+
1/2−
3/2−
3/2−

Γ [MeV]
150
100
35
60
60

Status
***
***
****
****
****

Σ(1480, 1560, 1580, 1620) are reported as resonances with * or ** status in [58].

118

119

Counts / (MeV/c2) [arbitrary]

500
Simulation-

π- p → K X
Λ(1600) K
0Λ(1670) K
Λ(1690) K0
00Σ (1660) K00Σ (1670) K
0

400
300
200
100
0

1.45

1.50
1.55
Missing Mass [GeV/c2]

1.60

FIG. E.1: Simulated missing mass spectra of the π − p → K − X reaction for the backgroundreactions (E.1, E.2). The angular distributions of the production and decay of all the Y ∗ s
are assumed to be isotropic. The production cross section of all the Y ∗ s are assumed to be
the same.

These Y ∗ resonances were not observed in Ref. [144]. Considering that ϕ and Λ(1520)
were clearly identiﬁed in their data, the Y ∗ resonances are expected to have smaller
cross sections than ϕ or Λ(1520). Figure E.2 shows simulated missing mass spectra ofthe π − p → K − X reaction including the Λ(1600) and Λ(1670) contributions in addition to (4.1–4.3). The Λ(1670) represents an uniﬁed contribution of Λ(1670, 1690) andΣ(1660, 1670) because of the similar spectrum shapes. Both cross sections of Λ(1600)
and Λ(1670) were assumed to be a half of Λ(1520) and the scale of the nonresonant
K̄KN was normalized to the experimental data. The overall spectrum shape are inbetter agreement with the present data than Fig. 4.2, owing to the Y ∗ contributions to
the low mass region.
As discussed above, the Y ∗ contributions have a possibility to reproduce the spectrum
shape better. However, as long as the cross sections and the angular distributions for
the Y ∗ s are not known, we can not make a deﬁnite statement from the present data.
Finally, it should be noted that the reproducibility of the overall spectrum shape is notdirectly related to the conclusion, because polynomial functions in 1500–1560 MeV/c2
were used as the background shape in the upper limit estimation.

120

APPENDIX E. ADDITIONAL STUDY OF BACKGROUND PROCESSESCounts / (MeV/c2)

500
400

E19 data (2012)
Simulation sum
Nonresonant KKNφnΛ (1520) K0Λ (1600) K00Λ (1670) K-

π- p → K X at 2.01 GeV/c

300
200
100
0

1.45

1.50
1.55
Missing Mass [GeV/c2]

1.60

FIG. E.2: Missing mass spectrum of the π − p → K − X reaction at 2.01 GeV/c. The experimental data are indicated by the black points with statistical errors. The red histogram represents the total background shape obtained by the MC simulation including ﬁve processes:
nonresonant K̄KN (blue dashed), ϕ (green dotted), Λ(1520) (magenta dashed-dotted),Λ(1600) (cyan dashed-two-dotted) and Λ(1670) (orange dashed-three-dotted). Both crosssections of Λ(1600) and Λ(1670) were assumed to be a half of Λ(1520). The scale of thenonresonant components was normalized to the experimental data.

Bibliography[1] M. Gell-Mann, Phys. Lett. 8, 214 (1964).
[2] R. L. Jaﬀe, Proceedings of Topical Conference on Baryon Resonances, Oxford, July
1976, SLAC-PUB-1774.
[3] R. L. Jaﬀe, Phys. Rev. D 15, 267 (1977); 281 (1977).
[4] R. L. Jaﬀe, Phys. Rev. Lett. 38, 195 (1977); 617(E) (1977).
[5] D. Strottman, Phys. Rev. D 20, 748 (1979).
[6] S. Godfrey and S. L. Olsen, Ann. Rev. Nucl. Part. Sci. 58, 51 (2008).
[7] D. Diakonov, V. Petrov, and M. Polyakov, Z. Phys. A 359, 305 (1997).
[8] T. Nakano et al. (LEPS Collaboration), Phys. Rev. Lett. 91, 012002 (2003).
[9] K. H. Hicks, Prog. Part. Nucl. Phys. 55, 647 (2005).
[10] K. H. Hicks, Eur. Phys. J. H 37, 1 (2012).
[11] R. Jaﬀe and F. Wilczek, Eur. Phys. J. C 33, s38 (2004).
[12] S. Nussinov, arXiv:hep-ph/0307357.
[13] R. A. Arndt, I. I. Strakovsky, and R. L. Workman, Phys. Rev. C 68, 042201(R)(2003); 69, 019901(E) (2004).
[14] J. Haidenbauer and G. Krein, Phys. Rev. C 68, 052201(R) (2003).
[15] A. Sibirtsev, J. Haidenbauer, S. Krewald, and Ulf-G. Meißner, Phys. Lett. B 599,
230 (2004).
[16] R. N. Cahn and G. H. Trilling, Phys. Rev. D 69, 011501(R) (2004).
[17] W. R. Gibbs, Phys. Rev. C 70, 045208 (2004).
[18] T. Bowen et al., Phys. Rev. D 2, 2599 (1970).
[19] F. Huang, Z. Y. Zhang, Y. W. Yu, and B. S. Zou, Phys. Lett. B 586, 69 (2004).
[20] K. Goeke, H.-C. Kim, M. Praszalowicz, and G.-S. Yang, Prog. Part. Nucl. Phys.
55, 350 (2005).
121

122

BIBLIOGRAPHY[21] R. L. Jaﬀe, Phys. Rep. 409, 1 (2005).
[22] R. Jaﬀe and F. Wilczek, Phys. Rev. Lett. 91, 232003 (2003).
[23] M. Karliner and H. J. Lipkin, Phys. Lett. B 575, 249 (2003).
[24] S. Sasaki, Nucl. Phys. B (Proc. Suppl.) 140, 127 (2005).
[25] F. Csikor, Z. Fodor, S. D. Katz, and T. G. Kovács, J. High Energy Phys. 11, 070(2003).
[26] F. Csikor, Z. Fodor, S. D. Katz, T. G. Kovács, and B. C. Tóth, Phys. Rev. D 73,
034506 (2006).
[27] S. Sasaki, Phys. Rev. Lett. 93, 152001 (2004).
[28] T.-W. Chiu and T.-H. Hsieh, Phys. Rev. D 72, 034505 (2005).
[29] N. Mathur et al., Phys. Rev. D 70, 074508 (2004).
[30] N. Ishii, T. Doi, H. Iida, M. Oka, F. Okiharu, and H. Suganuma, Phys. Rev. D 71,
034001 (2005).
[31] N. Ishii, T. Doi, Y. Nemoto, M. Oka, and H. Suganuma, Phys. Rev. D 72, 074503(2005).
[32] B. G. Lasscock et al., Phys. Rev. D 72, 014502 (2005).
[33] B. G. Lasscock et al., Phys. Rev. D 72, 074507 (2005).
[34] T. T. Takahashi, T. Umeda, T. Onogi, and T. Kunihiro, Phys. Rev. D 71, 114509(2005).
[35] C. Alexandrou and A. Tsapalis, Phys. Rev. D 73, 014507 (2006).
[36] K. Holland and K. J. Juge (BGR Collaboration), Phys. Rev. D 73, 074505 (2006).
[37] M. V. Danilov and R. V. Mizuk, Phys. Atom. Nucl. 71, 605 (2008).
[38] S. Eidelman et al. (Particle Data Group), Phys. Lett. B 592, 1 (2004).
[39] W.-M. Yao et al. (Particle Data Group), J. Phys. G 33, 1 (2006).
[40] C. Amsler et al. (Particle Data Group), Phys. Lett. B 667, 1 (2008).
[41] J. Barth et al. (SAPHIR Collaboration), Phys. Lett. B 572, 127 (2003).
[42] S. Stepanyan et al. (CLAS Collaboration), Phys. Rev. Lett. 91, 252001 (2003).
[43] V. Kubarovsky et al. (CLAS Collaboration), Phys. Rev. Lett. 92, 032001 (2004).
[44] M. Battaglieri et al. (CLAS Collaboration), Phys. Rev. Lett. 96, 042001 (2006).

BIBLIOGRAPHY

123[45] R. De Vita et al. (CLAS Collaboration), Phys. Rev. D 74, 032001 (2006).
[46] B. McKinnon et al. (CLAS Collaboration), Phys. Rev. Lett. 96, 212001 (2006).
[47] S. Niccolai et al. (CLAS Collaboration), Phys. Rev. Lett. 97, 032001 (2006).
[48] T. Nakano et al. (LEPS Collaboration), Phys. Rev. C 79, 025210 (2009).
[49] M. J. Amaryan et al., Phys. Rev. C 85, 035209 (2012).
[50] A. Martı́nez Torres and E. Oset, Phys. Rev. Lett. 105, 092001 (2010); Phys. Rev.
C 81, 055202 (2010).
[51] Y. Kato (LEPS Collaboration), Few-Body Syst. 54, 1245 (2013).
[52] M. Ostrick, Prog. Part. Nucl. Phys. 55, 337 (2005).
[53] S.-I. Nam, A. Hosaka, and H.-C. Kim, Phys. Lett. B 633, 483 (2006).
[54] M. Anghinolﬁ et al., Phys. Rev. C 86, 069801 (2012).
[55] V. V. Barmin et al. (DIANA Collaboration), Phys. Atom. Nucl. 66, 1715 (2003);
70, 35 (2007); 73, 1168 (2010).
[56] V. V. Barmin et al. (DIANA Collaboration), Phys. Rev. C 89, 045204 (2014).
[57] R. Mizuk et al. (Belle Collaboration), Phys. Lett. B 632, 173 (2006).
[58] J. Beringer et al. (Particle Data Group), Phys. Rev. D 86, 010001 (2012).
[59] A. E. Asratyan, A. G. Dolgolenko, and M. A. Kubantsev, Phys. Atom. Nucl. 67,
682 (2004).
[60] A. Airapetian et al. (HERMES Collaboration), Phys. Lett. B 585, 213 (2004).
[61] S. Chekanov et al. (ZEUS Collaboration), Phys. Lett. B 591, 7 (2004).
[62] A. Aktas et al. (H1 Collaboration), Phys. Lett. B 639, 202 (2006).
[63] J. Z. Bai et al. (BES Collaboration), Phys. Rev. D 70, 012004 (2004).
[64] S. Schael et al. (ALEPH Collaboration), Phys. Lett. B 599, 1 (2004).
[65] J. Abdallah et al. (DELPHI Collaboration), Phys. Lett. B 653, 151 (2007).
[66] B. Aubert et al. (BaBar Collaboration), Phys. Rev. Lett. 95, 042002 (2005).
[67] M.-Z. Wang et al. (Belle Collaboration), Phys. Lett. B 617, 141 (2005).
[68] B. Aubert et al. (BaBar Collaboration), Phys. Rev. D 76, 092004 (2007).
[69] P. Achard et al. (L3 Collaboration), Eur. Phys. J. C 49, 395 (2007).
[70] J. M. Link et al. (FOCUS Collaboration), Phys. Lett. B 639, 604 (2006).

124

BIBLIOGRAPHY[71] O. Samoylov et al. (NOMAD Collaboration), Eur. Phys. J. C 49, 499 (2007).
[72] K. Götzen (BaBar Collaboration), Nucl. Phys. B (Proc. Suppl.) 164, 117 (2007).
[73] Ya. I. Azimov and I. I. Strakovsky, Phys. Rev. C 70, 035210 (2004).
[74] A. N. Aleev et al. (SVD Collaboration), Phys. Atom. Nucl. 68, 974 (2005).
[75] A. Aleev et al. (SVD Collaboration), arXiv:hep-ex/0509033.
[76] Yu. M. Antipov et al. (SPHINX Collaboration), Eur. Phys. J. A A21, 455 (2004).
[77] I. Abt et al. (HERA-B Collaboration), Phys. Rev. Lett 93, 212003 (2004).
[78] M. J. Longo et al. (HyperCP Collaboration), Phys. Rev. D 70, 111101(R) (2004).
[79] C. Pinkenburg et al. (PHENIX Collaboration), J. Phys. G 30, S1201 (2004).
[80] D. O. Litvintsev et al. (CDF Collaboration), Nucl. Phys. B (Proc. Suppl.) 142, 374(2005).
[81] M. I. Adamovich et al. (WA89 Collaboration), Phys. Rev. C 72, 055201 (2005).
[82] A. I. Titov, A. Hosaka, S. Daté, and Y. Ohashi, Phys. Rev. C 70, 042202(R) (2004).
[83] M. Abdel-Bary et al. (COSY-TOF Collaboration), Phys. Lett. B 595, 127 (2004).
[84] M. Abdel-Bary et al. (COSY-TOF Collaboration), Phys. Lett. B 649, 252 (2007).
[85] M. Nekipelov et al. (COSY-ANKE Collaboration), J. Phys. G 34, 627 (2007).
[86] K. Miwa et al. (KEK-PS E522 Collaboration), Phys. Lett. B 635, 72 (2006).
[87] K. Miwa et al. (KEK-PS E559 Collaboration), Phys. Rev. C 77, 045203 (2008).
[88] V. Kubarovsky et al. (CLAS Collaboration), Phys. Rev. Lett. 97, 102001 (2006).
[89] Y. Qiang et al. (Jeﬀerson Lab Hall A Collaboration), Phys. Rev. C 75, 055208(2007).
[90] C. Alt et al. (NA49 Collaboration), Phys. Rev. Lett. 92, 042003 (2004).
[91] A. Aktas et al. (H1 Collaboration), Phys. Lett. B 588, 17 (2004).
[92] M. I. Adamovich et al. (WA89 Collaboration), Phys. Rev. C 70, 022201(R) (2004).
[93] A. Airapetian et al. (HERMES Collaboration), Phys. Rev. D 71, 032004 (2005).
[94] E. S. Ageev et al. (COMPASS Collaboration), Eur. Phys. J. C 41, 469 (2005).
[95] S. Chekanov et al. (ZEUS Collaboration), Phys. Lett. B 610, 212 (2005).
[96] D. C. Christian et al. (FNAL E690 Collaboration), Phys. Rev. Lett. 95, 152001(2005).

BIBLIOGRAPHY

125[97] A. N. Aleev et al. (EXCHARM Collaboration), Phys. Atom. Nucl. 70, 1527 (2007).
[98] A. Abulencia et al. (CDF Collaboration), Phys. Rev. D 75, 032003 (2007).
[99] A. Aktas et al. (H1 Collaboration), Eur. Phys. J. C 52, 507 (2007).
[100] J. M. Link et al. (FOCUS Collaboration), Phys. Lett. B 661, 14 (2008).
[101] H. Egiyan et al. (CLAS Collaboration), Phys. Rev. C 85, 015205 (2012).
[102] S. Chekanov et al. (ZEUS Collaboration), Eur. Phys. J. C 38, 29 (2004).
[103] B. Aubert et al. (BaBar Collaboration), Phys. Rev. D 73, 091101 (2006).
[104] G. De Lellis et al. (CHORUS Collaboration), Nucl. Phys. B 763, 268 (2007).
[105] J. Pochodzalla, arXiv:hep-ex/0406077 (Talk presented at the 2nd PANDA Physics
Workshop, Frascati, March 2004).
[106] W. Liu and C. M. Ko, Phys. Rev. C 68, 045203 (2003).
[107] T. Hyodo, A. Hosaka, and E. Oset, Phys. Lett. B 579, 290 (2004).
[108] Y. Oh, H. Kim, and S. H. Lee, Phys. Rev. D 69, 014009 (2004).
[109] Y. Oh, H. Kim, and S. H. Lee, Phys. Rev. D 69, 074016 (2004).
[110] C. M. Ko and W. Liu, arXiv:nucl-th/0410068 (Proceedings of PENTAQUARK04).
[111] P. Ko, J. Lee, T. Lee, and J.-H. Park, Phys. Lett. B 611, 87 (2005).
[112] T. Hyodo and A. Hosaka, Phys. Rev. C 72, 055202 (2005).
[113] T. Hyodo, A. Hosaka, and M. Oka, Prog. Theor. Phys. 128, 523 (2012).
[114] M. Naruki et al., J-PARC Proposal E19 (2006), http://j-parc.jp/researcher/
Hadron/en/pac_0606/pdf/p19-Naruki.pdf.
[115] Prog. Theor. Exp. Phys. 2012, Issue 2 “Special Issue: Particle and Nuclear Physics
at J-PARC,” edited by T. Nagae.
[116] K. Shirotori et al. (J-PARC E19 Collaboration), Phys. Rev. Lett. 109, 132002(2012).
[117] T. Takahashi et al., Prog. Theor. Exp. Phys. 2012, 02B010 (2012).
[118] S. Nagamiya, Prog. Theor. Exp. Phys. 2012, 02B001 (2012).
[119] K. Agari et al., Prog. Theor. Exp. Phys. 2012, 02B009 (2012).
[120] T. Koseki et al., Prog. Theor. Exp. Phys. 2012, 02B004 (2012).

126

BIBLIOGRAPHY[121] Digital
Teslameter
151(DTM-151),
Group3
Technology,//www.group3technology.com/index.php/products/product/
digital-teslameter-151.

http:[122] T. Hasegawa, Ph.D. thesis, University of Tokyo, INS-IM-15 (1994).
[123] H. Hotchi, Ph.D. thesis, University of Tokyo, KEK Report 2000-3 (2000).
[124] O. Sasaki and M. Yoshida, IEEE Trans. Nucl. Sci., 46, 1871 (1999).
[125] Y. Arai, Nucl. Instrum. Meth. A 453, 365 (2000).
[126] T. Fukuda et al., Nucl. Instrum. Methods A 361, 485 (1995).
[127] EFM-3000AX, Echo Electronics, http://echo-denshi.co.jp/nmr_magnetic.
htm.
[128] Tohoku Universal Logic~takahasi/TUL-8040/.

Module,http://lambda.phys.tohoku.ac.jp/[129] Y. Igarashi et al., IEEE Trans. Nucl. Sci., 52, 2866 (2005).
[130] KEK Data Acquisition Development Working Group, KEK Report 85-10 (1985).
[131] Y. Igarashi et al., IEEE Trans. Nucl. Sci., 57, 618 (2010).
[132] S. Morinobu (private communication).
[133] F. James, “MINUIT—Function minimization and error analysis”, CERN-D506(1994).
[134] J. Myrheim and L. Bugge, Nucl. Instrum. Meth. 160, 43 (1979).
[135] ANSYS, http://www.ansys.com.
[136] K. L. Brown and Ch. Iselin, CERN 74-2 (1974); U. Rohrer, Compendium of Decay
Turtle Enhancements, PSI.
[137] K. Aoki et al., Phys. Rev. C 76, 024610 (2007).
[138] T. Takahashi et al., Phys. Rev. C 51, 2542 (1995).
[139] K. Shirotori, Ph.D. thesis, Tohoku University (2011).
[140] S. Agostinelli et al., Nucl. Instrum. Meth. A 506, 250 (2003); J Allison et al., IEEE
Trans. Nucl. Sci. 53, 270 (2006).
[141] D.J. Candlin et al., Nucl. Phys. B 226, 1 (1983).
[142] M. L. Good and R. R. Koﬂer, Phys. Rev. 183, 1142 (1969).
[143] O. I. Dahl et al., Phys. Rev. 163, 1430 (1967).

BIBLIOGRAPHY[144] O. I. Dahl et al., Phys. Rev. 163, 1377 (1967).
[145] H. Courant et al., Phys. Rev. D 16, 1 (1977).
[146] T. N. Takahashi, Ph.D. thesis, University of Tokyo (2014).
[147] S.-I. Nam, A. Hosaka, and H.-C. Kim, Phys. Lett. B 579, 43 (2004).
[148] T. Hyodo (private communication).
[149] R. Ota, Master Thesis (in Japanese), Osaka University (2013).

127