Search for η ′-nucleus bound statesfrom 12C(γ, p) reaction
with simultaneous detection of decay products

Natsuki Tomida
A dissertation submitted in partial fulfillment of the requirements
for the degree of Doctor of Science
Department of Physics, Kyoto University
June, 2020

Abstractη ′ (958) meson has large mass compared with π, K and η mesons because of the axial vector anomaly term in the quantum chromodynamics (QCD) Lagrangian. It is called UA (1)anomaly and the eﬀect of the UA (1) anomaly might be weaken in a dense matter. A large
mass reduction of η ′ meson in nuclear medium is expected in several model calculations. If
the η ′ mass is reduced in a nucleus, the η ′ meson and the nucleus can form a bound state. We
searched for the η ′ -nucleus bound states via missing mass spectroscopy of the 12 C(γ, p) reaction. The experiment was carried out in the LEPS2 beam line at SPring-8 using photon beamwith the energy of 1.3–2.4 GeV. Produced particles were measured using the BGOegg detector system. Missing-mass spectroscopy around η ′ -mass suﬀers from numerous backgroundarising from multiple light-meson productions. Thereby, we tagged an η-proton pair, whichis expected to be emitted in the η ′ N → ηN absorption process of a bound η ′ in a nucleus.
Namely, we investigated the γ + 12 C → p + (η + p) + X reaction. This is the first missing
mass spectroscopy around the η ′ production threshold in coincidence with decay products.
Although multi pion backgrounds were suppressed by tagging an (η + p) pair, background
events from the γ + 12 C → p + η + 11 B and γ + 12 C → p + (η + π 0 ) + 11 B reactions werestill observed. We optimized kinematical selection criteria of the (η + p) pair to reduce thosebackgrounds and to enhance signals from the η ′ -nucleus bound states. After the kinematicalselections, no events were observed in the kinematical region of bound states. The experimental upper limit of the production cross section of the η ′ -bound nuclei with an (η + p)
ηpemission in the η-p opening angle of cos θlab
< −0.9, was obtained to be 2.2 nb/sr at the′
90% confidence level. In addition to the η absorption process, the missing mass spectrumof the η ′ escape reaction, γ + 12 C → p + η ′ + X, was also measured for the first time. Bymeasuring the missing mass spectrum of the η ′ escape process, we evaluated the production
rate of η ′ mesons around the kinematical region of the η ′ -nucleus bound states. The obtained
experimental upper limit of the (η + p) coincidence cross section was compared with thetheoretical cross sections with diﬀerent η ′ -nucleus potential parameters, as a function of the
branching fraction of the η ′ N → ηN absorption process. The uncertainty of the absolutevalue of the theoretical cross section was suppressed with the measured cross section of theη ′ escape process. Our result indicates a small branching fraction of the η ′ N → ηN process
and/or a shallow η ′ -nucleus potential.

Contents
1 Introduction
1.1 The η ′ (958) meson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.1 Light pseudoscalar mesons . . . . . . . . . . . . . . . . . . . . . . . .
1.1.2 Mass of octet mesons . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.3 Mass of an η ′ meson . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 The η ′ -nucleus bound state . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.1 η ′ mass modification in a finite nucleus . . . . . . . . . . . . . . . . .
1.2.2 η ′ -nucleus potential . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 Theoretical predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4 Past experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.5 Present experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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2 Experimental setup
2.1 SPring-8/LEPS2 facility . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.1 LEPS2 beam line . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.2 Laser system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.3 Backward Compton scattering . . . . . . . . . . . . . . . . . . . . . .
2.1.4 Transmission rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Target . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Detector in LEPS2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.1 Tagging counter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.2 UpVeto counter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.3 BGOegg calorimeter . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.4 Inner Plastic Scintillator . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.5 Drift Chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.6 Resistive Plate Chamber . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.7 RF signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5 Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.6 Data summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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3 Event reconstruction
3.1 Photon beam energy measurement . . . . . . . . . . . . . . . . . . . . . . .
3.1.1 Tagger track reconstruction . . . . . . . . . . . . . . . . . . . . . . .
3.1.2 Photon energy determination . . . . . . . . . . . . . . . . . . . . . .
3.2 Reaction timing reference . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Measurement of decay products . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 BGOegg clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.2 Leak cluster . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.3 Photon energy and polar angle resolution . . . . . . . . . . . . . . . .
3.3.4 Proton kinetic energy and polar angle resolution . . . . . . . . . . . .
3.4 Charge identification of decay products . . . . . . . . . . . . . . . . . . . . .
3.4.1 IPS energy deposit and hit timing correction . . . . . . . . . . . . . .
3.4.2 Charge identification . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5 Forward going-particle detection . . . . . . . . . . . . . . . . . . . . . . . . .
3.6 Forward-going proton momentum measurement . . . . . . . . . . . . . . . .
3.6.1 Hit strip selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6.2 Timing calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6.3 Evaluation of forward proton momentum . . . . . . . . . . . . . . . .

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4 Event selection
4.1 Outline of the event selection . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Recoil electron track . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 In-beam e+ e− veto . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4 Decay particle identification . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4.1 Identification of gammas . . . . . . . . . . . . . . . . . . . . . . . . .
4.4.2 Identification of η and η ′ mesons . . . . . . . . . . . . . . . . . . . . .
4.4.3 Identification of side-going protons . . . . . . . . . . . . . . . . . . .
4.5 Treatment of additional hit . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.6 Forward-going particle selection . . . . . . . . . . . . . . . . . . . . . . . . .
4.6.1 Clean track selection . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.6.2 e+ e− event suppression . . . . . . . . . . . . . . . . . . . . . . . . . .
4.6.3 Energy conservation . . . . . . . . . . . . . . . . . . . . . . . . . . .

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5 The η ′ -nucleus search
5.1 Obtained data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Outline of the kinematical selection . . . . . . . . . . . . . . . . . . . . . . .
5.3 Background source and feature . . . . . . . . . . . . . . . . . . . . . . . . .
5.4 Expected signal kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.1 Characteristics of signal . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.2 QMD simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.3 Survival probability . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5 Cut optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5.1 Opening angle cut . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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5.5.2 Missing energy cut . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.5.3 η and ps polar angle cut . . . . . . . . . . . . . . . . . . . . . . . . .
Expected signal and background yields after the kinematical selection . . . .
Experimental result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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6 Luminosity, acceptance and eﬃciency for the cross section measurement
6.1 The (η + ps ) measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1.1 Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1.2 The number of photons weighted with the RPC acceptance and theDAQ eﬃciency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1.3 Number density of the target . . . . . . . . . . . . . . . . . . . . . .
6.1.4 Acceptance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1.5 Detector eﬃciencies . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1.6 Filling mode correction factor . . . . . . . . . . . . . . . . . . . . . .
6.1.7 Pion contamination to the forward particle . . . . . . . . . . . . . . .
6.1.8 Branching fraction of η → 2γ mode . . . . . . . . . . . . . . . . . . .
6.1.9 Systematic error . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2 The η ′ escape measurement . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.1 Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.2 The η ′ acceptance . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.3 The η ′ angle region . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.4 Systematic error . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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7 Experimental results and discussion
7.1 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.1.1 Upper limit of the production cross section of the η ′ -nucleus boundstate with (η + ps ) emission . . . . . . . . . . . . . . . . . . . . . . .
7.1.2 Cross section of the η ′ escape process . . . . . . . . . . . . . . . . . .
7.2 Estimation of the η ′ -nucleus potential V0 . . . . . . . . . . . . . . . . . . . .
7.2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2.2 Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2.3 Calculation procedure . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2.4 Normalization factor of the theoretical cross section . . . . . . . . . .
7.2.5 Cross section of the (η + ps ) coincidence reaction . . . . . . . . . . .
7.2.6 Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.3 Comparison with theoretical expectations and past experimental results . . .

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8 Summary and prospects

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A Filling pattern of the SPring-8 storage ring98

B Detector module101

C Photon beam energy calibration

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5.6
5.7

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D Timing selection criteria
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D.1 Selection of gammas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
D.2 Selection of protons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
E QMD model calculation
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E.1 Basic description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
E.2 Signal simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
E.3 Detector acceptance and resolution . . . . . . . . . . . . . . . . . . . . . . . 110
F Detector acceptance and eﬃciency
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F.1 Systematic uncertainty of the acceptance . . . . . . . . . . . . . . . . . . . . 111
F.1.1 Acceptance for (η + ps ) . . . . . . . . . . . . . . . . . . . . . . . . . . 111
F.1.2 Acceptance for pf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
F.2 Eﬃciency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
F.2.1 Tagger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
F.2.2 UpVeto over veto rate . . . . . . . . . . . . . . . . . . . . . . . . . . 114
F.2.3 DC track reconstruction eﬃciency . . . . . . . . . . . . . . . . . . . . 114
F.2.4 RPC reconstruction eﬃciency . . . . . . . . . . . . . . . . . . . . . . 114
F.3 Transmission rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
G Theoretical estimation of the cross section
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G.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
G.2 Nuclear response function R(Eex ) . . . . . . . . . . . . . . . . . . . . . . . . 117
G.3 Fermi averaging method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
G.3.1 Formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
G.3.2 Nucleon momentum distribution . . . . . . . . . . . . . . . . . . . . . 120
G.3.3 Elementary cross section in the CM system . . . . . . . . . . . . . . . 120
G.3.4 Elementary cross section in the laboratory system . . . . . . . . . . . 121
G.3.5 Numerical result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
G.4 Inclusion of the detector resolution . . . . . . . . . . . . . . . . . . . . . . . 122
G.4.1 The detector resolutions . . . . . . . . . . . . . . . . . . . . . . . . . 122
G.4.2 The treatment above Eex − E0 = 50 MeV . . . . . . . . . . . . . . . . 123
G.4.3 Excitation energy spectra . . . . . . . . . . . . . . . . . . . . . . . . 124
G.5 Eγ dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
G.6 Expected cross section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
G.7 pf polar angle dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
H The measurement of the η ′ escape process130
H.1 Definition of the excitation energy . . . . . . . . . . . . . . . . . . . . . . . . 130
H.2 Eγ dependence of the cross section . . . . . . . . . . . . . . . . . . . . . . . 131
H.3 Comparison with the measurement by CBELSA/TAPS . . . . . . . . . . . . 131
Bibliography

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Chapter 1
Introduction
η ′ (958) meson could be an interesting probe to investigate the origin of hadron masses ina finite density because a large mass reduction of η ′ (958) meson is expected at the normal
nuclear density. If there is a large mass reduction in such environment, the η ′ meson and anucleus form a bound state. We looked for the η ′ -nucleus bound state from the missing mass
spectrum of the 12 C(γ, p) reaction around the η ′ production threshold. In this section, we
describe the details of the origin of pseudoscalar meson mass spectra, the theoretical models
expecting η ′ mass shift in a finite density, past experiments to examine η ′ -nucleus potential,
and the aim of the present experiment.

1.1

The η ′(958) meson

1.1.1

Light pseudoscalar mesons

η ′ (958) meson is meson with the mass of 957.78 MeV/c2 , composed of u, d, s quarks andtheir antiquarks. Its spin-parity is J P = 0− . Mesons having J P = 0− are called pseudoscalarmesons. In the constituent quark model, the light three quarks and their antiquarks generate
octet and singlet pseudoscalar mesons as shown in Fig.1.1. In Fig.1.1, the constituent quarksof each meson are also shown. The horizontal and vertical axes of Fig.1.1 are the third
component of isospin, I3 , and hypercharge, Y , respectively. u and d quarks have I3 = +1/2,
and d and u quarks have I3 = −1/2. s quark has Y = −1 and s quark has Y = +1. The π 0meson is composed of uu and dd as1|π 0 ⟩ = √ (|uu⟩ − |dd⟩),
2

1

(1.1)

The η and η ′ mesons are mixed states of the octet η8 and singlet η0 mesons, which aredescribed as follows:|η⟩ = cos θ |η8 ⟩ − sin θ |η0 ⟩ ,|η ′ ⟩ = sin θ |η8 ⟩ + cos θ |η0 ⟩ ,1|η8 ⟩ = √ (|uu⟩ + |dd⟩ − 2 |ss⟩),
61|η0 ⟩ = √ (|uu⟩ + |dd⟩ + |ss⟩),
3

(1.2)
(1.3)
(1.4)
(1.5)

where θ = −11.5◦ is the mixing angle of η8 and η0 [1]. Because θ is small, we can assume
that |η⟩ ≈ |η8 ⟩ and |η ′ ⟩ ≈ |η0 ⟩. The mass of η meson is 547.85 MeV/c2 . The main decay
modes of η ′ and η mesons are shown in Table.1.1 and 1.2. The η ′ → γγ and η → γγ decay
processes were measured in the present experiment.

Figure 1.1: The pseudoscalar mesons composed of u, d, s quarks and their antiquarks.

Table 1.1: Main decay modes of η ′ meson [1]. Table 1.2: Main decay modes of η meson [1].
modebranching fraction
meson branching fractionπ+π−η(42.6 ± 0.7)%
γγ(39.41 ± 0.20)%0+ −0ρ γ(π π γ)(28.9 ± 0.5)%
3π(32.68 ± 0.23)%
π0π0η(22.8 ± 0.8)%π+π−π0(22.92 ± 0.28)%+ −γγ(2.22 ± 0.08)%
π π γ(4.22 ± 0.08)%2

1.1.2Mass of octet mesons

In Table.1.3 and 1.4, we summarize the masses of pseudoscalar and vector (J P = 1− ) mesons
composed of u, d and s quarks and their anti-quarks. As can be seen, the mass diﬀerences ofoctet pseudoscalar mesons are large compared with vector mesons. The light masses of octetmesons are considered to be attributed to the spontaneous breaking of chiral symmetry inthe quantum chromodynamics (QCD). The chirality operator γ 5 is defined asγ 5 ≡ iγ 0 γ 1 γ 2 γ 3(1.6)

where γ 0 , γ 1 , γ 2 and γ 3 are gamma matrices. The eigenstates of chirality of qurarks are qL
and qR , which satisfies
γ 5 qL (x) = −qL (x),γ 5 qR (x) = qR (x),q(x) = qL (x) + qR (x).

(1.7)
(1.8)
(1.9)

By using qL (x) and qR (x), the QCD Lagrangian for 3 flavors (u, d, s) is described as
L = q L (x)iγ µ Dµ qL (x) + q R (x)iγ µ Dµ qR (x)1− q L (x)M qR (x) − q R (x)M qL (x) − Tr[Gµν (x)Gµν (x)],2(1.10)
uL (x)qL (x) =  dL (x)  ,sL (x)uR (x)qR (x) =  dR (x)  ,sR (x)
M = diag(mu , md , ms ).

Table 1.3: Mass of pseudoscalar mesons [1].
meson mass [MeV/c2 ]
π0134.97±π139.57
K±
493.6800K ,K497.61
η
547.86′
η957.783(1.11)(1.12)(1.13)

Table 1.4: Mass of vector mesons [1].
mesonmass [MeV/c2 ]
ρ
775.3
K ∗±
891.7
∗0
K ∗0 , K
895.6
ω
782.7
ϕ
1019.5

The first and second terms in Eq.(1.10) are kinetic terms, and third and fourth terms are massterms. When M → 0, the Lagrangian is invariant under a SU (3)L × SU (3)R transformation:
λa), UL ∈ SU (3)L ,2
aa λqR → UR qR , UR = exp(iθR), UR ∈ SU (3)R .
2
qL → UL qL , UL = exp(iθLa(1.14)(1.15)

where λa ’s are Gell-Mann matrices. This transformation is called chiral transformation, andthus the QCD Lagrangian has chiral symmetry in the limit of M → 0.
Although the QCD Lagrangian has the chiral symmetry in the massless limit, the groundstate of the QCD breaks the chiral symmetry. This is called the breaking of the chiralsymmetry. We can see it in the following equations. The Noether currents for the chiralsymmetry are described as follows:λaqL (x),
2λa= q R (x)γ µ qR (x),2

JLaµ = q L (x)γ µ(1.16)

JRaµ(1.17)The vector and axial vector currents, V aµ and Aaµ , are described as follows:
λa
q(x),
2
λa
= JRaµ − JLaµ = q(x)γ µ γ 5 q(x).
2

V aµ = JRaµ + JLaµ = q(x)γ µ(1.18)

Aaµ(1.19)

Then, the vector and axil vector conserved charges, QaV and QaA , are expressed as:
∫
∫
λa
a
3
a0
QV =
d xV = d3 xq(x)γ µ q(x),
2
∫
∫
λa
QaA =
d3 xAa0 = d3 xq(x)γ µ γ 5 q(x).
2(1.20)(1.21)

Next, we consider an equal time commutation relation of the axial vector conserved charge
QaA and a pseudoscalar operator ϕb ;
λb
q(x),
2
[QaA , ϕb ] = δ ab q(x)q(x).
ϕb ≡ q(x)γ 5(1.22)(1.23)The expectation value for a vacuum is⟨0|[QaA , ϕb ]|0⟩ = δ ab ⟨q(x)q(x)⟩ .

(1.24)⟨q(x)q(x)⟩ is called quark condensate and ⟨q(x)q(x)⟩ ̸= 0 in a QCD vacuum. This means thatthe vacuum has non zero axial vector current QaA , and the chiral symmetry is spontaneously
broken in the QCD vacuum.
4

From the Nambu-Goldstone theorem, there are massless particles when a symmetry is
spontaneously broken [2]. The massless particles are called Nambu-Goldstone (NG) bosons.
The octet mesons are NG bosons associated with the spontaneous breaking of the chiral symmetry. Because quarks have finite masses, the chiral symmetry is an approximate symmetry
in the QCD. Thereby, the octet mesons are not massless but their masses are small. Kaonsare heavier than pions because an s quark mass is larger than u, d quarks.

1.1.3

Mass of an η ′ meson

The η ′ meson could be the ninth NG boson but it is not. As can be seen in Table.1.3, the η ′mass is extremely large compared with other pseudoscalar mesons. It is explained with theanomaly of the axial vector current, namely UA (1) anomaly. It appears in the divergence ofthe singlet axial vector current, A0µ (x), as
A0µ (x) =∑q f (x)γ µ γ 5 qf (x),(1.25)f∂ µ A0µ = 2i∑m f q f γ 5 qf −f

Nf g 2 a aµν
G G̃ ,
16π 2 µν(1.26)

where f is flavor of quarks and Gaµν G̃aµν is a color sum of gluon. The last term does notvanish even quark masses are 0 and thus the axial vector current does not conserve. Becauseof this UA (1) anomaly, the singlet η 0 and thus η ′ has large masses.

1.2

The η ′-nucleus bound state

1.2.1

η ′ mass modification in a finite nucleus

As described in section 1.1.2, the chiral symmetry breaking is associated with finite quark
condensate ⟨qq⟩ in vacuum. The quark condensate is considered to decrease in finite baryon
density [3]. Therefore, partial restoration of the chiral symmetry breaking is expected in a
nucleus, where density is high. As described in Refs.[4, 5], the eﬀect of the UA (1) anomaly
to the η0 mass appears under existence of the chiral symmetry breaking. Thus, the UA (1)anomaly eﬀect might be weakened together with the partial restoration of the chiral symmetry. If it is weakened, the η ′ mass can decrease in a nucleus. As described in section 1.3,
a large mass reduction of 80–150 MeV at a normal nuclear density is expected by model
calculations. Thereby, the η ′ meson is a good probe to examine hadron masses at high density. The decay width of the η ′ meson can also change in a nucleus due to the absorption ofan η ′ meson by nucleons. Although there is no theoretical expectation of the change of thewidth in a nucleus, a small absorption width of 7–19 MeV is derived from the experimental
measurement by the CBELSA/TAPS collaboration (see section 1.4).

5

1.2.2

η ′ -nucleus potential

According to Refs.[6, 7], the mass reduction of an η ′ meson in a nucleus can be translated as
an attractive potential between the η ′ meson and the nucleus. The optical potential of theη ′ -nucleus system can be described as [6, 7]
U (r) = (V0 + iW0 ) ×
V0 = ∆m(ρ0 ),Γ(ρ0 )
W0 = −
,
2

ρ(r)
,
ρ0

(1.27)(1.28)(1.29)

where ρ(r) is the nuclear density distribution, ρ0 is the normal nuclear density, and ∆m(ρ0 )and Γ(ρ0 ) are the mass shift and width of the η ′ meson at ρ = ρ0 , respectively. The realpart of the potential V0 corresponds to the mass shift in the nucleus. ∆m(ρ0 ) is defined as∆m(ρ0 ) = m(ρ0 ) − m0 , where m0 is the mass in a vacuum. When ∆m(ρ0 ) is negative, thepotential is attractive, and when it is positive, the potential is repulsive. If V0 is deep enoughto have a binding energy, the η ′ meson and the nucleus form a bound state [8]. The imaginary
part of the potential W0 corresponds to an absorption width of η ′ meson in the nucleus. If W0
is too large, η ′ mesons are immediately absorbed by nucleons and an η ′ -nucleus bound statecannot be formed. Thereby, W0 needs to be small to form a bound state. As described in
section 1.4, the CBELSA/TAPS collaboration derived W0 = −(13 ± 3(stat) ± 3(syst)) MeV[9]. It is small enough to have bound states when there is a large mass shift of V0 = ∆m(ρ0 ) =−80 ∼ −150 MeV. In the present experiment, we examine the real part of the η ′ -nucleus
potential V0 .

1.3

Theoretical predictions

The amount of mass shift in a nucleus, or the depth of the η ′ -nucleus potential is estimatedusing diﬀerent models. The expectation of each model is shown in this section.
NJL model
In the Nambu-Jona-Lasinio (NJL) model [10, 11], the UA (1) anomaly is taken into accountthrough the Kobayashi-Maskawa-’t Hooft interaction [12, 13]. Costa et al. and Nagahiro
et al. examined the mass of an η ′ meson in a finite density using the NJL model [7, 14].
The strength of the UA (1) anomaly term in a vacuum is described using a parameter, gD .
gD was adjusted to reproduce the observed π, K, η ′ masses and π decay constant [15]. They
calculated the π, η and η ′ masses as a function of density ρ, considering several cases of thedensity dependence of gD : (a) gD (ρ) = gD , (b) gD (ρ) = 0, and (c) gD (ρ) = gD exp(−(ρ/ρ0 )2 ).
Their calculation results are shown in Fig.1.2. They suggested the mass reduction of η ′ meson∆m(ρ0 ) = −150 MeV at ρ = ρ0 in the case (a). The case (b) corresponds to the calculation
without the UA (1) anomaly eﬀect, and the masses of η and η ′ at ρ = 0 are not reproduced.
In the case (c), a larger mass reduction ∆m(ρ0 ) = −300 MeV for η ′ and η mesons at ρ = ρ06

is expected. The η-nucleus bound states were searched for with 12 C and 27 Al targets by the
JINR and COSY-GEM collaborations, respectively, and there are only indications of shallow
bound states [16, 17]. Thereby the density dependence of the case (c) is nonpreferred.

Figure 1.2: The expected mass shift of π, η and η ′ using the NJL model [7]. See the text forthe diﬀerence of (a)–(c).

Linear sigma model
Sakai and Jido evaluated ∆m(ρ) by using the linear sigma model [18]. The fundamental
degree of freedom in the linear sigma model is a hadron, and therefore the model can include
nucleon fields straightforwardly. The Lagrangian of the model contains a term represents theUA (1) anomaly, which corresponds to the Kobayashi-Maskawa-’t Hooft term. The strengthparameter of this term (B) is determined from decay constants and masses of π, K, andmasses of u, d quarks. The spontaneous breaking of the chiral symmetry is described withσ condensate as an order parameter. Their calculation result is shown in Fig.1.3. They
extracted ∆m(ρ0 = 0.17 fm−3 ) = −80 MeV for the η ′ meson without considering density dependence of the parameter B. Larger mass reduction is possible if there is density dependenceof the B parameter.
QMC model
Bass and Thomas calculated η ′ mass at ρ = ρ0 by using the Quark-Meson Coupling (QMC)
model [19]. They evaluated the η ′ mass in nuclear matter by solving for an MIT Bag Diracequations in nuclear medium. Mass reduction ∆m(ρ0 ) = −37 MeV is expected by theirmodel calculation. The UA (1) anomaly is not taken into account in the QMC model.

7Figure 1.3: The expected mass shift of π, η and η ′ using the linear sigma model [18].
Chiral unitary approach
Nagahiro et. al. evaluated the η ′ -nucleus potential, (V0 , W0 ), within a chiral unitary approach [8]. They estimated (V0 , W0 ) for several η ′ N scattering length values. However, later
they pointed out in Ref.[20] that there was problems of one of parameters, which is called“subtraction constant”, used for the calculation in Ref.[8]. Diﬀerent subtraction constants
should be used for η and η ′ mesons but they used the same values in Ref.[8]. In addition,
they also pointed out there was a problem of a calculation method of the potential in Ref.[8].
Thus, the expectation in Ref.[8] is not reliable and an updated result is desired.

1.4

Past experiments

Experimental information of the η ′ -nucleus potential is poor. As of now, only the η-PRiME/
Super-FRS Collaboration and the CBELSA/TAPS collaboration gave experimental results onthe η ′ -nucleus potential. Their results are summarized in this section. Indirect measurementof the mass modification of η ′ mesons in heavy ion collision is also reviewed.
The η-PRiME/Super-FRS Collaboration
A straight-forward method of accessing (V0 , W0 ) is missing-mass spectroscopy around theη ′ -nucleus system. The peak position and width of the η ′ -nucleus bound state are directly
correlated with V0 and W0 , respectively. However, the missing-mass spectroscopy around η ′bound states suﬀers from numerous backgrounds arising from multiple production of mesons

8having smaller mass than an η ′ meson. The η-PRiME/Super-FRS Collaboration firstly measured the missing mass spectrum near the η ′ -meson production threshold in p +12 C → d + X
reactions [21, 22]. They used a very high energy resolution spectrometer of σ = 2.5±0.1 MeV,
and aimed to measure narrow peaks of bound states above background. The measured excitation energy spectrum of the η ′ +11 C system Eex , relative to the production threshold E0

Figure 1.4: The measured excitation energy spectrum Eex − E0 . The figure is from Ref.[21].

Figure 1.5: The obtained upper limit of (V0 , W0 ) by the η-PRiME/Super-FRS Collaboration[21]. The numbers indicate the normalization factor of the theoretical cross section.
9

is shown in Fig.1.4. It is an inclusive spectrum and production of η ′ meson is not tagged.
Although the cross sections of background events were as expected, no signals indicating
a bound state were observed above backgrounds. An upper limit of (V0 , W0 ) was obtained
depending on the normalization factor of the theoretical cross section calculated in the framework of a distorted wave impulse approximation (DWIA) as shown in Fig.1.5 [23, 24]. Thelines in Fig.1.5 show the upper limit of (V0 , W0 ) with diﬀerent normalization factors. Although DWIA calculations nicely describe the spectral shape of bound states such as hyper
nuclei and pionic atoms, there is uncertainty in the absolute value of the cross sections andthus normalization factors are needed [25–30]. Furthermore, their theoretical cross section
has an uncertainty of a factor of 2 coming from the unknown elementary cross section of the
pn → η ′ d reaction. Their is no experimental measurement of the pn → η ′ d reaction, and theyused estimated value for the input of the DWIA calculation. Thus, large ambiguity comingfrom the normalization of the theoretical calculation exists in the upper limit of (V0 , W0 )obtained by the η-PRiME/Super-FRS Collaboration.
The CBELSA/TAPS Collaboration
The CBELSA/TAPS Collaboration evaluated both V0 and W0 . For the evaluation of V0 ,they precisely measured η ′ mesons escaping from nuclei in the photoproduction process andcompared the kinematical distributions with those in a collision model [31] in diﬀerent V0
cases. In Ref.[32], they compared the beam energy dependence and the η ′ momentum dependence of the cross section of the γ + 12 C → η ′ + X reaction as shown in Fig.1.6. Fromthe comparison, they deduced V0 = −(37 ± 10(stat) ± 10(syst)) MeV. In Ref.[33], they performed the same analysis as in Ref.[32] for the γ + 93 Nb → η ′ + X reaction, and deduced
V0 = −(41 ± 10(stat) ± 15(syst)) MeV. The weighted average of V0 measured in Ref.[32] and[33] is V0 = −(39 ± 7(stat) ± 15(syst)) MeV. In Ref.[34], they measured γ + 12 C → η ′ + p + X
reaction. By measuring protons in the forward angle, they selected events with low η ′ kinetic
energy of ∼ 150 MeV. They can identify protons but they can not measure the momentumof protons, and thus they can not study the missing mass of the 12 C(γ, p) reaction. From thecomparison of the beam energy dependence and the η ′ kinetic energy dependence of the crosssections with those in the collision model, they deduced V0 = −(44±16(stat)±15(syst)) MeV.
It is consistent with the measurements in Ref.[32] and [33] for the larger average η ′ momentumof ∼ 1.1 GeV/c. The consistency of V0 evaluated in diﬀerent measurements is a strong pointof their results. However, the collision model has not been calibrated for established boundstates, such as hypernuclei and pionic atoms. Therefore, there could be some systematic
errors. In addition, there are some questionable points in their cross section measurement as
indicated in Appendix H.3.
They estimated W0 from the measurement of the γ + A → η ′ + A′ reaction with 12 C and93
Nb targets [9]. They derived W0 = −(13±3(stat)±3(syst)) MeV from the mass number (A)dependence of the production cross sections. The A dependence of the cross section is called“transparency ratio”. Large (small) transparency ratio indicates small (large) absorption
rate of the produced hadron in nuclei. The transparency measurement is widely used forevaluating W0 [35–38]. Thereby, their obtained W0 is much reliable compared with V0 .
10Figure 1.6: (a) The beam energy dependence of the total cross sections and (b) the η ′momentum distributions of the γ + 12 C → η ′ + X reaction measured by the CBELSA/TAPS
Collaboration [32]. The circles show the experimental values and lines show the calculation
results with the collision model.
Heavy ion collision
The weakening of the UA (1) anomaly eﬀect is also expected in a hot matter [39]. T. Csörgő
√
et al. claimed that the η ′ mass is reduced at least 200 GeV/c2 in sN N = 200 GeV Au+Au
collisions from the analysis of charged pion Bose-Einstein correlation data taken by the
PHENIX and STAR Collaborations [40–42]. In thermal models, the production cross sectionof light mesons are exponentially suppressed by the mass. Thus, if the η ′ mass is reduced in
medium, the η ′ yield can be increased. η ′ mesons can decay via η ′ → η +π + π − → (π 0 π + π − )+π + π − . The transverse mass (mT ) of charged pions from this decay process is small. Since η ′mesons mostly decay in halo region of the collision, we may see enhancement (reduction) of
charged pion yield at low transverse mass in the halo (core) region when the η ′ yield increases.
T. Csörgő et al. examined the transverse mass dependence of the eﬀective intercept parameterof the two-pion Bose-Einstein correlation function, λ∗ . λ∗ is given by the ratio of the numberπππof events in the core and (core+halo) regions as λ∗ = [Ncore/(Ncore+ Nhalo)]2 . The measured
intercept parameter λ∗ (mT ) relative to λ∗max = λ∗ (mT = 0.7 GeV/c2 ) is shown in Fig.1.7.
They compared it with theoretical calculations with diﬀerence η ′ mass cases and claimed thatthe η ′ mass is reduced at least 200 GeV/c2 , at the 90% confidence level.

11Figure 1.7: The transverse mass dependence of the ratio of λ∗ /λ∗max measured by the
PHENIX and STAR Collaborations and theoretical calculations with diﬀerence η ′ mass cases
in medium.

1.5

Present experiment

To search for η ′ -nucleus bound states and evaluate the η ′ -nucleus potential, we carried out
missing mass spectroscopy of the 12 C(γ, p) reaction at the LEPS2 beam line of SPring-8.
By using photon beam of 1.3–2.4 GeV and detecting protons in extremely forward angles of0.9◦ − 6.8◦ in the laboratory frame, we investigated the missing mass spectrum in a small
momentum transfer kinematics, where η ′ -nucleus bound states are likely to be produced.
The photon energy dependence of the momentum transfer of the γ + p → η ′ + p reaction
is shown in Fig.1.8. In order to suppress background events from (multi) meson production
reactions, such as the γ + 12 C → p + ππ + X, γ + 12 C → p + πππ + X, γ + 12 C → p +ω + X, and γ + 12 C → p + πη + X reactions, possible decay products from the η ′ -nucleus
system were simultaneously measured for the first time, in coincidence with the missing mass
spectroscopy. More specifically, we investigated the following two processes; the η ′ absorption
process (Eq.(1.30)) and the η ′ escape (quasi-free η ′ production) process (Eq.(1.31)):
γ + 12 C → pf + η ′ ⊗ 11 B↱ ′
η + p → η + ps .

(1.30a)(1.30b)γ + 12 C → pf + η ′ + 11 B↱ ′
η → 2γ.

(1.31a)(1.31b)Here, η ′ ⊗ 11 B represents a biparticle state of an η ′ meson and an 11 B nucleus. The forwardgoing proton, pf , is used for the missing-mass spectroscopy. The side-going proton, ps , is12

emitted in the η ′ N → ηN reaction, which is one of the most promising absorption processes for an η ′ meson bound in a nucleus [8, 43]. The η ′ meson bound to a nucleus hardly
escapes from the nucleus and thus decays via an absorption process by a nucleon(s) in nucleus. Thereby, the η ′ -nucleus bound state was searched for from the reaction in Eq.(1.30).
As discussed in the previous section on the past experiment by the η-PRiME/Super-FRS
Collaboration, there is uncertainty of the production cross section of the η ′ oﬀ nuclei. By
measuring the missing mass spectrum of the η ′ escape process in Eq.(1.31), we evaluate theη ′ production rate around the η ′ production threshold, which is important to confirm that η ′mesons are actually produced and to evaluate the normalization factor of the absolute valueof the theoretical cross sections.
The (η+ps ) pair was detected with an electromagnetic calorimeter, BGOegg, which covers
the polar angle of 28.5◦ − 138.5◦ . By tagging an (η + ps ) pair, multi-pion backgrounds werestrongly suppressed. Remaining backgrounds are mainly from the γ + 12 C → pf + η + 11 B
and γ + 12 C → pf + (η + π 0 ) + 11 B reactions. In these events, an η is produced in the
primary reaction, and another proton, ps is kicked out by either a primary η, π 0 or pf . We
removed those background events by selecting the kinematical region which is characteristic
for signal events. The missing mass resolution of our detector system is 13–30 MeV/c2 ,which is not good enough to observe individual peaks of bound states. Thereby, we searched
for events around the production threshold in a very low background condition.
) Then, the(production cross section of the η ′ -bound nuclei emitting an (η + ps ) pair,

the production threshold were evaluated. (The (η + ps ) coincidence cross section

dσ
dΩpf

dσ
dΩpf

η+ps

, aroundexp)η+ps
can be compared with theoretical crossexp

Figure 1.8: The photon energy dependence of the momentum transfer of the γ + p → η ′ + p
reaction in the forward proton polar angle of 0.9◦ − 6.8◦ .
13

(sections,

dσ
dΩpf

)η+ps
, expected in diﬀerent V0 values. For this purpose, we calculated thetheoryexpected excitation energy of the η ′ +11 B system Eex , relative to the production thresholdE0 in the framework of a DWIA. DWIA calculations are widely used for describing boundstates such as hyper nuclei and pionic atoms [25–30]. This is the advantage to the resultsfrom the CBELSA/TAPS Collaboration, whose reliability on the theoretical cross section is
not established. Typical calculation results within in the DWIA are shown in Fig.1.9. The
spectra are decomposed to the η ′ absorption process and η ′ escape processes as
(

dσ
dΩpf

)γ+12 C→p+η′ ⊗11 B ()η′ esc ()η′ absdσ
dσ=+.
dΩpf theory dΩpf theory
theory(1.32)

In general, DWIA calculations nicely reproduce spectral shapes of both the bound statesand quasi-free processes, but hardly reproduce their absolute cross sections [25–30]. The
normalization factor F of the DWIA calculation was introduced as()η′ esc /()η′ escdσ
dσ
F =.
(1.33)dΩpf expdΩpf theory(
where,dσdΩpf)η′ esc

(
and

exp

dσ
dΩpf

)η′ escare the the experimental and theoretical cross sections oftheorythe η ′ escape process, respectively. As summarized in section 1.4, the η-PRiME/Super-FRS
Collaboration also used the DWIA calculation to evaluate V0 and W0 from a comparison of()η′ escthe experimental and theoretical cross sections. However, they did not measure dΩdσpfexp

and did not evaluate F , and thus there is large uncertainty of their upper limit of V0 and

Figure 1.9: The excitation spectra calculated within the DWIA in the cases of V0 = −100and −20 MeV, W0 = −12 MeV, θp = 6◦ and photon beam energy = 2.05 GeV.
14

W0 . Our advantage is that we can confirm that η ′ mesons are actually produced and theuncertainty of the absolute value of the theoretical cross section is reduced by measuring
the η ′ escape process. The theoretical production cross section of the η ′ bound states with
(η + ps ) emission can be described with the cross section of the η ′ absorption process as
(

dσ
dΩpf

)η+ps

(
=F×

theorydσdΩpf)η′ abs
ηps× Brη′ N →ηN × Psrv.

(1.34)

theoryHere, Brη′ N →ηN is the unknown branching fraction of the η ′ N → ηN process in all the η ′ηpsabsorption process and Psrv
is the probability that an (η + ps ) pair is emitted from a nucleus
ηpsafter final interactions of the (η + N ) pair in the residual nucleus. Psrv
can be estimated froma simulation and existing experimental data. If we observe an enough number of (η + ps )
(
)η+ps
(
)η+ps
events, we can estimate Brη′ N →ηN from the comparison of dΩdσpand dΩdσp
in
f
f
exp
theory()η+ps
Eex − E0 > 0 MeV. If not, dΩdσpdepends on unknown Brη′ N →ηN . Within the DWIA,
ftheorywe calculated the excitation spectra for η ′ angular momenta up to lη′ = 6, which is large
enough to have convergence for Eex − E0 ≲ 50 MeV [23, 44]. As can be seen in Fg.1.9,
the η ′ escape process contributes only in Eex − E0 > 0 MeV. Thereby, we evaluate F from)η′ esc()η′ esc(dσ
dσandwhich are integrated over 0 MeV < Eex − E0 < 50 MeV. After
dΩpf
dΩpf
exp
theory
)η+ps
(
)η+ps
(
and dΩdσp
normalizing the theoretical cross sections with F , we compared dΩdσpfin −50 MeV < Eex − E0 < 50 MeV.

15

exp

f

theoryChapter 2
Experimental setup
The experiment was carried out in the LEPS2 beam line at SPring-8. A photon beam
was produced by means of backward Compton scattering (BCS) of UV laser from 8 GeVelectrons in the SPring-8 storage ring. Photon beam energy was evaluated by measuring
recoil electrons with the tagging counter. The photon beam was transferred to the LEPS2
experimental building and hit a carbon target. Produced particles were measured by the
BGOegg detector system. The details of the experimental set up is described in this chapter.

2.1

SPring-8/LEPS2 facility

2.1.1

LEPS2 beam line

Figure 2.1 shows the accelerator system of SPring-8 [45]. 100 mA electrons with energiesof 8 GeV are stored in the storage ring. The electrons are in packets whose frequency is508.58 MHz. The beam lines of SPring-8 are shown in Fig.2.2. There are 62 beam lines andfour beam lines are in 30 m long straight sectors. The LEPS2 beam line locates in BL31LEP,
which is one of the four long sectors. The former LEPS beam line locates in BL33LEP.
The electron emittance of long sectors is small compared with ordinary ones, indeed, theaverage electron emittance in the X direction in BL31LEP is 14 µrad, whereas it is 58 µradin BL33LEP. The small emittance of BL31LEP enables us to keep small BCS photon beam
size after transferring to the LEPS2 experimental building located 125 m downstream fromthe collision point. By constructing the experimental building outside of the storage ringbuilding, we installed large detector system covering large acceptance.

2.1.2

Laser system

We used four laser system called TL, BL, TR and BR. They are UV lasers with a wavelengthof 355 nm, and substantial output power of each laser was 11, 10, 8 and 8 W, respectively.
The details of lasers are summarized in Table.2.1. Figure 2.3 shows the laser injection system.
The four UV lasers are shown with blue color. The laser is introduced to the vacuum chamber
16Figure 2.1: SPring-8 accelerators [45].

Figure 2.2: The beam line map of SPring-8 [45].

17Table 2.1: The details of lasers.
Name
TL
BL
TR
BR
Laser type
Paladin Advanced 355-16000 Paladin Advanced 355-8000
Default output power
>16 W
>8 W
Substantial output power 11 W
10 W
8W
8W
Wavelength
355 nmRepetition rate
80±1 MHz
Beam divergence
480 µrad550 µradFigure 2.3: The laser injection system of the LEPS2 beam line. The 6th mirror locates above
the 5th mirror and they are overlapped in the figure.

of the storage ring using and expander, six mirrors and one prisms. The expander was tuned
to focus the laser at the collision point. The 5th mirrors are on micro-stepping motors,
and the angles of 5th mirror were tuned during the data taking to obtain high BCS rate.
The laser is almost 100% linearly polarized. Orientation of polarization of the laser wascontrolled by a half-wave plate. The 1-4th mirrors have higher reflectivity for verticallypolarized photons than for horizontally polarized photons, and 5-6th mirrors have higher
reflectivity for horizontally polarized photons than for vertically polarized photons. In total,
the vertically polarized photons give ∼ 10% higher beam intensity than the horizontally18polarized photon. Therefore, we used vertically polarized lasers in almost all the experimental
period.

2.1.3

Backward Compton scattering

Figure 2.4 shows a schematic drawing of a backward Compton scattering (BCS) in the laboratory frame. Energy of the BCS photon, Eγ is calculated as [46]Eγ = k1 − β cos θ1.
k1 − β cos θ2 + (1 − cos(θ1 − θ2 ))
Ee

(2.1)

Here, Ee = 7.975 ± 0.003 GeV is incoming electron energy [47], β is velocity of the electron,and k = 3.49 eV is energy of a laser photon with a wave length of 355 nm. The angles between
an incident electron and, a laser and BCS photon is defined as θ1 and θ2 , respectively. Below,
we assume β ≃ 1, θ1 ≃ 180◦ and θ2 ≃ 0◦ . Then, Eq.(2.1) can be rewritten asEγ =4Ee2 k,m2e + 4Ee k + θ22 γ 2 m2e(2.2)

where me = 0.511 MeV/c2 is electron mass. The maximum BCS photon energy Eγmax is
obtained at θ2 = 0◦ :4E 2 k= 2.385 GeV.
(2.3)
Eγmax = 2 e
me + 4Ee k

Figure 2.4: A schematic drawing of a backward Compton scattering.

19

The Eγ dependence of a diﬀerential cross section can be described as [48]
dσ
dEγ

=

2πre2 a(χ + 1 + cos2 α),
Eγmax

m2e
,
m2e + 4Ee k(Eγ /Eγmax )2 (1 − a)2χ =,1 − (Eγ /Eγmax )(1 − a)Eγmax − Eγ (1 + a)cos α =.
Eγmax − Eγ (1 − a)
a =

(2.4)
(2.5)
(2.6)
(2.7)

(dσ/dEγ ) [b/GeV]In Fig.2.5, the Eγ dependence of the cross section of the BCS process is shown.

0.3

0.25

0.2

0.15

0.1

0.05

0
0

0.5

1

1.5

2

2.5
Eγ [GeV]Figure 2.5: The Eγ dependence of the cross section of a BCS process.

2.1.4

Transmission rate

In Table.2.2, materials located between the collision point and the target are summarized.
Conversion rate of the γ rays to e+ e− pairs at each material is also shown. As shown in
Fig.2.3, there is an X-ray absorber at the exit of the ultrahigh vacuum chamber. The e+ e−pairs generated in the absorber are swept out by a dipole magnet. After the magnet, theγ-rays are transferred to the LEPS2 experimental building through a medium vacuum pipe.
In total, 22.8% of the γ rays are converted to e+ e− pairs before arriving at the target.

20

Table 2.2: The materials located between the collision point and the target.
Material
Vacuum window 1
X-ray absorber
Air 1
Vacuum window 2
Vacuum window 3
UpVeto counter
Air 2
Total

2.2

Al
W
Air
Kapton+Aramid
Kapton+Aramid
Polystyrene
Air

Radiation
Thickness
Conversion rate
length LR (cm)t (cm)
1 − exp(−( 79 )( LtR )) (%)
8.90
0.20
1.7
0.35
0.10
19.9
30390
170
0.43
28.6
0.01250.03
28.6
0.0175
0.05
41.3
0.30
0.56
30390
310
0.79
22.8

TargetA carbon target used for the experiment is shown in Fig.2.6(a). The thickness is 20.0 mm
and the density is 1.73 g/cm3 . A measurement error for density×thickness is less than 1%.
The target holder was made with a 10-mm thick polystyrene form and a 0.125-mm thickkapton foil. They are shown in Fig.2.6(b)(c).

Figure 2.6: (a) A picture of the carbon target. (b)(c) Pictures of the target holder.

21

2.3

Detector in LEPS2

We measured the γ + 12 C → pf + (η + ps ) + X reaction to search for the η ′ -nucleus boundstate. Here, pf is the forward-going proton and ps is the side-going proton. We also measured
γ + 12 C → pf + η ′ + X reactions to evaluate the production rate of η ′ meson. The photon
beam energy was evaluated by measuring a recoil electron with a tagging counter locatednear the storage ring. Figure 2.7 shows the experimental set up in the LEPS2 building.
Events in which an incident photon were converted to an e+ e− pair when it was transmitted
to the experimental hall was excluded using an UpVeto counter. The energy of pf wasmeasured with Time-Of-Flight (TOF) technique using a resistive plate chamber (RPC) TOF
wall. There is the LEPS2 solenoid magnet between the target and the RPC wall, and theacceptance for pf is limited with the hole of the solenoid to be polar angle less than 7.0◦ . The
start timing of TOF is determined from RF signal of the SPring-8 storage ring. The η andη ′ mesons were identified from the invariant mass of 2γs with the BGOegg electromagnetic
calorimeter. Particle identification of ps was carried out with the energy deposit in the innerplastic scintillators (IPS) and BGOegg. A drift chamber was used to ensure that there is nocharged particle other than pf in the forward region which is not covered by the BGOegg.
Details of each detector are described in the following sections. The coordinates of theexperimental set up are defined as shown in Fig.2.7.

Figure 2.7: A schematic drawing of the detector set up in LEPS2.

22

2.3.1

Tagging counter

Installation area
In Fig.2.8(a), schematic drawing of the SPring-8 storage ring around the LEPS2 beam line
is shown. The BCS photon is produced upstream of the 31B1 bending magnet. The recoil
electrons are bent by the 31B1 magnet to diﬀerent directions depending on their momentum.
The track position of the recoil electron is measured by the 80-mm wide tagging countermade of plastic scintillators. The tagging counter (or tagger) locates at the side of the CR1C
chamber downstream of the 31B1 magnet. Figure 2.8(b) shows a schematic drawing of the
CR1C chamber. The tagging counter locates in the hatched region. The tagging counterdetects electrons coming out from a slit of a tungsten shield shown in Fig.2.8(b)(c). In the

Figure 2.8: (a) A schematic drawing of the LEPS2 beam line. (b) A schematic drawing of
the CR1C chamber. (c) A picture of the tungsten shields.
23

CR1C chamber, there is a crotch absorber. The crotch absorber reflects synchrotron radiation
X-rays generated at the 31BL magnet to bottom side to avoid damage on the chamber wall.
As can be seen in Fig.2.8(b), the slit for recoil electrons locates downstream side of the crotch
absorber whereas it locates upstream in the former LEPS beam line. In downstream side of
the crotch absorber, we can place the tagging counter closer to the 8 GeV electron orbit. The
lower limit of tagged photon energy of the tagging counter is 1.28 GeV. It is small comparedto the one of 1.5 GeV in the LEPS beam line. Note that the η ′ production threshold for a
proton at rest is 1.447 GeV. On the other hand, because the slit locates downstream side of
the crotch absorber, X-rays from the absorber are also emitted from the slit and give damage
to the tagging counter. Thereby, the tagging counter was designed to be in the hatchedregion in Fig.2.8(b) where X-rays do not directly hit the counter.
The detector design
A schematic drawing and picture of the tagging counter are shown in Fig.2.9. The tagging
counter consists of two layers of fiber scintillators (tagger-fiber) and pairs of plastic scintillators (tagger-PL). The fiber scintillators are used to measure the recoil electron hit position
and the plastic scintillators are used to generate a trigger signal for data acquisition. The
fiber scintillator is made of a Kuraray SCSF-78 with a cross section of 1.0 × 1.0 mm2 [49].
Each fiber layer consists of 80 fiber bundles, and each fiber bundle is made of 6 fibers in series.
The bundles are placed 1.02 mm-step, in which 0.02 mm for glue. Cladding thickness of thefiber is 0.02 mm, and thus there is (0.02(glue) + 0.02 × 2(cladding))/1.02 = 5.9% ineﬃcientarea per bundle. We placed the backward bundles so that the center of fibers are 0.5 mm
shifted from the one of forward bundles to cover the ineﬃcient region. At the other end, the6 fibers are bundled in round shape and connected to a single channel of a 4×4 channels

Figure 2.9: A schematic drawing and a picture of the tagging counter. Note that top andbottom of the drawing is opposite with Fig.2.8(b).

24photo multiple tube, HAMAMATSU MA-PMT, H6568-200MOD. The plastic scintillator oftagger PL is 4 mm (thick) × 8 mm (wide) × 10 mm (height) ELJEN EJ-200. Neighboring pairs of scintillators are overlapped by 1 mm. The plastic scintillator is connected to a
HAMAMATSU PMT, R9880U-210, with a light guide.

2.3.2

UpVeto counter

The UpVeto counter was installed upstream of the target and used to exclude events in whichphoton beam is converted to an e+ e− pair before arriving at the target. It was also used todetect charged particles going to backward from the target. Figure 2.10 shows a picture of
the UpVeto counter. The UpVeto counter is made of a plastic scintillator with 3 mm (thick)× 620 mm (wide) × 620 mm (height). It is connected to a HAMAMATSU fine mesh PMT,
H6614-70mod, with a light guide.

Figure 2.10: A picture of the UpVeto counter.

2.3.3

BGOegg calorimeter

Figure 2.11 shows a schematic drawing of the BGOegg calorimeter. It consists of 1,320
Bi12 GeO20 (BGO) crystals. There is no support frame between crystals, and thus there isno dead area. Figure 2.12 shows the cross section of the BGOegg calorimeter. There are 22
layers of the BGO crystals and the polar angle from 24◦ to 144◦ is covered. Each layer consistsof 60 crystals and covers 360◦ azimuthal angle. The shape of the crystals are diﬀerent layer
by layer. The length of the crystals is 220 mm which corresponds to 20 radiation length. The
25

Figure 2.11: A schematic drawing of the BGOegg. The crystals are shown with reddish
purple color. The PMTs are shown in black.
x/y
H11334 (R11265)

B
07 B
06 B
05
B
04
03B
02B
01B
00B
00F
01F
02F
03F
04
05 F
06 F
07 F
F

420

H6524 (R4125)

w2 h

L

08
B

200

w1
F
08 9F F
0 0
1 1F
1
12F

R
photon beam

−200

+400
targetz

Figure 2.12: The cross section of the BGOegg.

detailed proprieties of the BGOegg are summarized in Ref.[50]. The crystals of layer 1–4 and21,22 are read with HAMAMATSU H6524 PMTs. The crystals of layer 5–20 are read with
HAMAMATSU H11334 PMTs. The light yield of BGOegg strongly depends on temperature.
26

Therefore, we installed BGOegg in a thermostatic booth and kept the temperature at 25.0 C◦ .

2.3.4

Inner Plastic Scintillator

Figure 2.13(a)(b) shows schematic drawings of a cross section and front view of the innerplastic scintillators (IPS). The IPS consists of 30 ELJEN EJ-212 plastic scintillators with asize of 453 mm × 26 mm × 5 mm. The neighboring scintillators are overlapped as shownin Fig.2.13(b). The upstream side of the scintillators are connected to HAMAMATSU multipixel photon counters (MPPCs) S12572-050P. Eﬀective photosensitive area of the MPPC is
3 mm × 3 mm. Five MPPCs are connected to a plastic scintillator. Signals from MPPCs
were amplified using LeCroy 612A NIM modules.

Figure 2.13: A schematic drawing of the IPS (a) from side (b) from upstream. The cylindricaldrift chamber (CDC) was installed but it was not used for the analysis.

2.3.5

Drift Chamber

Figure 2.14 shows a schematic drawing of the drift chamber (DC). The DC was originallydeveloped to be used in the LEPS2 solenoid magnet, and thus its frame is a round shape. It
located 1.6 m downstream from the target. Wire planes are in a hexagonal shape as shown in
red-dashed lines in Fig.2.14. The diameter of the inscribed circle of the hexagon is 1300 mm
and the diameter of sensitive area is 1280 mm. The sensitive area corresponds to the polar
angle from the target center of 21◦ . Apexes of the hexagon corresponds to the polar angleof 24◦ . There are 6 planes named X, X, U, U’, V and V’, in order from upstream. There
are 80 wires in a plane. The wires of X, X’ planes are aligned horizontally. The wires of U,
U’ planes are +60◦ relative to X, X’ wires, and wires of V, V’ planes are -60◦ relative to X,
X’ wires. They are summarized in Table.2.3. Figure 2.15 shows a schematic drawing of across section of a plane. The cell size is 16 mm. Cathode layers are made of 25 µm-thick27

aluminized Mylar. Sense wires are made of gold-plated tungsten (Au-W) whose diameter is
30 µm. Potential wires are made of gold-plated beryllium copper (Au-BeCu) whose diameteris 80 µm. One side of a wire is connected to a Repic RPA-181 preamp card. The gas mixture
was 50% Ar and 50% ethane.

Figure 2.14: A schematic drawing of the DC. The sensitive area is shown by red-dashed lines.

Figure 2.15: The cross section of the DC plane.

2.3.6

Resistive Plate Chamber

Figure 2.16 shows a schematic drawing of the resistive plate chamber (RPC) wall. An RPC
is a gas chamber consists of multi layers of glasses. The cross section of the RPC chamber
28

Table 2.3: The angles of the DC wire planes.
Plane angle
X
0◦
X’
0◦
U
+60◦
U’
+60◦
V
−60◦
V’
−60◦

is shown in Fig.2.17. The width of gas gap is 260 µm and there are 10 gaps in an RPC.
There are 8 readout strips in a chamber. The strip is 1,000 mm (height) × 25.5 mm (wide)
and the gap between strips is 0.5 mm. Amplifiers are connected at the both ends of the
strips. The gas mixture is 90% R134a, 5% SF6 and 5% butane. The wall consists of 32
RPC chambers. The neighboring chambers in the X direction are overlapped with a few
mm. The RPCs in top row and bottom row are overlap by 70–80 mm. In total, an area of
3,280 mm (X) × 1,930 mm (Y ) is covered with 256 readout strips. The Z-position of the
RPC module is defined at the middle of 10 gaps and it is 12,456 mm (upstream layer of the
top row), 12,496 mm (downstream layer of the top row), 12,596 mm (upstream layer of thebottom row), and 12,636 mm (downstream layer of the bottom row). The polar angle is 4.4◦

Figure 2.16: A schematic drawing of the RPC wall.

29

at X = 0 mm and 7.4◦ at X = 1, 640 mm. The acceptance is limited to the polar angle lessthan 7.0◦ because of the LEPS2 solenoid magnet as explained in the beginning of section 2.3.
The details of the RPCs are described in Refs.[51, 52].

Figure 2.17: The cross section of an RPC.

2.3.7

RF signal

The electrons in SPring-8 are in bunches whose interval is 1.966 ns. There are 2436 packets
in total but not all packets are used to fill electron bunches. There are several bunch fillingmodes as summarized in Appendix A and the bunch width varies 14–18 ps depending on thefilling modes and bunch currents. By using RF signal from the SPring-8, we can determine
the start timing of the TOF with the resolution of the bunch width. The jitter of the RF
signal is ∼4 ps at the LEPS2 experimental hall. Because the RF signal is high frequent, weneed to prescale the signal to read it by a time-to-digital converter (TDC). Figure 2.18 showsa schematic drawing of the pre-scale system. We prescaled the RF signal using a 508 MHz
synchronous universal counter (SUC) [53] with a factor of 1/84. The 1/84 signal is used
to determine the TOF. We also prescaled the RF signal with a factor of 1/2436. Because
the interval of the 1/2436 signal is 4.8 µs, we used delay lines so that the 1/2436 signal isrecorded in a TDC measurement range. The time resolution of delayed signal is not goodenough to be used for TOF measurement. The 1/2436 signal is used to examine events in a
specific bunch.

2.4

Electronics

In Table.2.4, the number of channels and the readout electronics used for each detector are
summarized. We measured signal charge with analog-to-digital converter (ADC) modules
and signal timing with TDC modules. We measured both charge and timing of signals fromthe tagger-PL, UpVeto, BGOegg, IPS and RPC. We measured only timing of signals of the30

Figure 2.18: A schematic drawing of the RF prescale system.

Table 2.4: The modules used for each detector.
Detector
number of channels ADC
TDC
Tagger-PL
24 VME V792
VME V1190
Tagger-fiber
160 —VME V1190
UpVeto1 VME V792
VME V1290N
BGOegg1320 FERA 4300B VME V1190
IPS
30 VME V792
VME V1290A
DC
480 —
LeCroy 3377
RPC
256 FERA 4300B VME V1290ARF
5 —VME V1290A/N

tagger-fiber and DC. For the RPC, we summed up signals from neighboring strips for ADC,
and took “or” of two signals from neighboring chambers for TDC, as shown in Fig.2.19. We
utilized CAEN VME V792 ADC for the tagger-PL, UpVeto and IPS, and LeCroy FERA
(Fast Encoding and Readout ADC) 4300B for the BGOegg and RPC. For the tagger-PL,
tagger-fiber and BGOegg, we utilized CAEN VME V1190 TDC with 100 ps bin size. For
the UpVeto, IPS, RPC and RF, we utilized CAEN VME V1290 TDC with 25 ps bin size.
We utilized LeCroy 3377 with 500 ps bin size for the DC. There is integral nonlinearity inthe measurement with VME V1290. The nonlinearity was corrected by oﬄine analysis. The
details of power supply, preamplifier and discriminators used for each detector are summarizedin Appendix B.

31

Figure 2.19: A schematic drawing of AND and OR of the readout lines for the RPC.

Figure 2.20: The trigger logic.

2.5

Trigger

Trigger signals for data acquisition were required that two tagger-PLs in pair have hits andmore than one crystal of BGOegg have hits. A schematic drawing of the trigger logic isshown in Fig.2.20. For the tagger, we used a multi-purpose logic module (MPLM4) [54] andgenerated a trigger signal when both of pair PLs were fired. For the BGOegg, a GeV-γ 139
32

module were used for generating trigger signals [55]. The LeCroy 4413 discriminator module
used for BGOegg has a current sum output. It gives a signal proportional to the number ofchannels which exceed the threshold. The output signal is −50 mV/hit channel. The GeV-γ
139 module sums up signals from all the discriminators. Trigger signal is generated when thesum signal exceeds ∼ −75 mV, which corresponds to two-crystals hit. Matching timing hits
are required for the tagger signal and the BGOegg signal. With this trigger condition, allreactions which have at least two photons in the final state are recorded. In addition to theγ + 12 C → pf + (η + ps ) + X and γ + 12 C → pf + η ′ + X reactions, which we are interested in,
we also analyzed γ + 12 C → pf + η + X and γ + 12 C → pf + (η + π 0 ) + X reactions to study
backgrounds, and γ + 12 C → π 0 + X, γ + 12 C → p + 2π 0 + X and γ + 12 C → p + ω + X reactions
to study detector performance, using the same data set. Here, pf is a proton detected with
the RPC, and ps and p are protons detected with BGOegg. The π 0 → 2γ, η → 2γ, η ′ → 2γ
and ω → π 0 γ → 3γ decays were used to identify each meson.

2.6

Data summary

The experiment was carried out from April to July in 2015. The total number of incident
photons at the target was 8.5×1013 . Data which had a problem in a detector were carefully
searched for and excluded from the analysis. The data used for the analysis was 72% of thetotal amount. We also took data with a liquid hydrogen target from November in 2014 to
February in 2015. The liquid hydrogen target data is used for calibrations and eﬃciency
measurements of several detectors.

33

Chapter 3
Event reconstruction
We searched for the η ′ -bound states in the excitation energy spectrum of the γ + 12 C →pf + (η + ps ) + X reaction. We also measured the γ + 12 C → pf + η ′ + X reaction to examine
the production rate of η ′ . The energy of gamma beam was evaluated with the tagger. The
momentum of pf was measured with the RPC. The consistency of the hit position of pf at
the DC and RPC was required. The identification and energy measurement of η, ps and η ′were carried out with BGOegg and IPS. In this chapter, event reconstruction method foreach particle is described.

3.1

Photon beam energy measurement

The photon beam energy was evaluated photon by photon by measuring the momentum ofa recoil electron after backward Compton scattering. The tagger locates downstream of abending magnet in the electron storage ring of SPring-8, and the momentum of the recoil
electron can be evaluated from the track position. In this section, we describe the algorithmof the tagger track reconstruction and the evaluation of the photon beam energy.

3.1.1

Tagger track reconstruction

The track of recoil electrons was reconstructed in the following procedure. A schematic
drawing of the tagger with an example of an electron track is shown in Fig.3.1.
1. Search for PL pairs, which both of them fired.
2. Search for fiber clusters in front of the fired PL pair.
3. Reconstruct an electron track from fiber clusters.
When there were clusters in both of two fiber layers, a tagger track was reconstructed fromboth of clusters. Since there are some dead regions in each fiber layer, events which haveclusters only in one of the two fiber layers were also accepted. In this case, we need totake care cross talks in the MA-PMTs, which consists of 4×4 channels. Cross talks in the34

MA-PMTs create a fake cluster only in the front or backward fiber near the true cluster. To
suppress the cross talk events, clusters satisfying following conditions were excluded from thetracking.
• There is no pair cluster in the another layer.
• There is another track having clusters in both fiber layers.
• The diﬀerence of the smallest fiber number of the two clusters in the same layer is lessthan 6.
An example of a fake cluster is also shown in Fig.3.1. The intrinsic eﬃciency of the tagger-PL
was (98.8 ± 1.2)%. The reconstruction eﬃciency of the track of recoil electrons depends on
event selection criteria. See section 4.2 and Appendix F.2.1 for details.

Figure 3.1: (a) A schematic drawing of the tagger and an example of an electron track. (b) A
schematic drawing of the MA-PMT of the front fiber. Indicated numbers are fiber numbers.
Fired channels are shown with red color. Channel 8 is fired with a cross talk from channel 4.

3.1.2

Photon energy determination

A schematic drawing of the recoil electron tracks and the tagger is shown in Fig.3.2. There isa direct relation between the energy of recoil electron Ee′ and the X position of fiber clustersof the electron track. The energy of photon beam Eγ is described as Eγ = Ee − Ee′ , where
Ee = 7.975 GeV is the energy of electrons in the SPring-8 storage ring. Therefore, there
is a direct relation between Eγ and the fiber cluster X hit position. We evaluated Eγ as afunction of mean fiber number of the front (xf ) and back fiber (xf ) clusters, respectively.
We used the γp → 2π 0 p, γp → π 0 p and γp → ηp reactions with the liquid hydrogen target
data. The details of the evaluation of photon energy function are described in Appendix C.
We evaluated the function for front (Eγf ) and backward (Eγb ) fiber layer, respectively as
Eγf = 1250.7 + 34.912×xf − 0.27172×x2f + 5.4498×10−3 ×x3f − 7.7346×10−5 ×x4f [MeV] (3.1)
Eγb = 1266.0 + 34.486×xb − 0.25291×x2b + 4.9325×10−3 ×x3b − 7.2442×10−5 ×x4b [MeV] (3.2)
35Here, xf and xb are the mean fiber number of the front and back fiber clusters, respectively.
When a track contained both of forward and backward layer clusters, the photon beam energy
Eγ was obtained as
Eγ = (Eγf + Eγb )/2.

(3.3)

Otherwise, Eγ was obtained as
Eγ = EγforEγ = Eγb .

(3.4)

The photon energy function evaluated from diﬀerent reactions were consistent. The photon
energy resolution was 12.0±0.7 MeV (see Appendix C).

Figure 3.2: A schematic drawing of recoil electron tracks and the tagger.

3.2

Reaction timing reference

The timing of the RF signal of the SPring-8 storage ring was used as a reference of thereaction timing. The timing of the RF signal is synchronized with the timing of backward
Compton scattering, and thus it is also synchronized with the reaction timing at the target.
Because the RF signal was prescaled to 1/84, the RF signal timing was recorded with an
ambiguity of 1.966 × n nsec, where 1.966 ns is the electron bunch interval in the SPring-8
storage ring, and n = 0 to 83. We derived n from the time diﬀerence the tagger PL hit
and the prescaled RF signal. The distribution of the time diﬀerence TT ag − TRF is shownin Fig.3.3(a). 1.966 × n nsec was subtracted from the prescaled RF timing, when the RF
signal is used for the reference timing of all detectors, the tagger, UpVeto, BGOegg, IPS,36

DC and RPC. The distribution TT ag − TRF after subtraction of 1.966 × n nsec is shown in
Fig.3.3(b). The misidentification probability of n was 1%. It was taken into account to thetagger reconstruction eﬃciency (see Appendix F.2.1).

Figure 3.3: The time diﬀerence between the tagger PL hit and the RF signal. (a) The raw
prescaled RF signal. (b) After subtraction of 1.966 × n nsec.

3.3

Measurement of decay products

The energy and emission angle of η, η ′ and ps were measured with BGOegg. We measured
γ’s from the η → 2γ and η ′ → 2γ decay modes. We describe clustering algorithm of the
BGOegg crystals in this section.

3.3.1

BGOegg clustering

When BGOegg crystals have hits, they were clustered as follows. A schematic drawing of
the clustering algorithm is shown in Fig.3.4.
• A clustering is carried out when a crystal has a TDC hit (blue crystals).
• The eight neighboring crystals around the hit crystal are included to the cluster (green
crystals).
• If one of the eight neighboring crystal has a TDC hit, eight crystals around the hitcrystal are included to the cluster (cluster A in Fig.3.4).
Cluster information is defined as follows.
37• Core crystal : the crystal which has the largest energy in a cluster.
• Hit timing : the hit timing of the core crystal.
• Energy : the summation of the energy deposit in all crystals in the cluster.
• Hit position : the weighted average of all crystal positions in the cluster with the weightof energy deposit in each crystal.
The emission angle was determined form the cluster hit position assuming that the particle
is from the center of the target. When a crystal belonged to n clusters like an example inFig.3.4 (n = 2), 1/n of the energy of the crystal was used when we added up the crystal

Figure 3.4: A schematic drawing of the BGOegg clustering.

Figure 3.5: The η mass peak position as a function of η momentum.

38

energy to obtain the cluster energy. The hit timings were calibrated so that the hit timingof γ rays relative to the RF signal, Tγ − TRF , to be 0 ns. The energy was calibrated every
about 10 runs so that the invariant mass of η mesons to be the PDG value. The η peak
position as a function of η momentum is shown in Fig.3.5. Events in which a core crystalof a cluster is in the first (layer 1) or last layer (layer 22) of BGOegg are excluded from theanalysis. In such events, there can be energy leak to out side of BGOegg and the energy ofdetected particles can not be correctly measured. The polar angle coverage of BGOegg after
removing most outer layers is 29.5–138.5◦ .
The photon energy resolution of BGOegg crystal measured with positron beam at 19 C◦
was(σE /E)2 = (0.63%)2 + ((1.15 ± 0.04)%)/(E/GeV) + ((0.42 ± 0.03)%)/(E/GeV)2 ,(3.5)

i.e, (1.38 ± 0.05)% for 1-GeV positrons. The position resolution isσr /mm = (3.07 ± 0.03)(E/GeV)−0.202±0.008(3.6)

for 1-GeV positrons. We can measure photons from η and η ′ in any energy.

3.3.2

Leak cluster

Cluster A and B in Fig.3.4 are counted as diﬀerent clusters even if they are induced fromone gamma ray. We call such an associated cluster as a “leak cluster”. Leak clusters havesmall energy and slow hit timing. Figure 3.6 shows cluster energy vs timing, and distance

Figure 3.6: Distributions of candidates of leak clusters of the γ + 12 C → pf + (η + ps ) + X
data. (a) Cluster energy vs hit timing, (b) distances from gamma clusters.

39

from gamma clusters of candidates of leak clusters. A cluster is assumed as a leak cluster
when the following conditions are satisfied.
• Cluster energy is less than 60 MeV.
• Cluster hit timing relative to the RF signal, Tcls − TRF > 3 ns.
• There is a gamma cluster in the distance less than 140 mm.
The cut criteria are shown in Fig.3.6. Leak clusters were excluded when we count the numberof clusters. We found that 11.0% of the γ + 12 C → pf + (η + ps ) + X data have (a) leakcluster(s).

3.3.3

Photon energy and polar angle resolution

Although the energy and position resolutions of BGOegg crystal are describes as in Eqs.(3.5)
and (3.6), the actual experimental resolutions were worse than Eqs.(3.5) and (3.6) because
there is uncertainty of the reaction vertex position. The actual photon energy and polar
angle resolutions were estimated using a Monte Carlo simulation, implementing a realistic
vertex distribution. The energy and polar angle resolutions are in the range of 5–35 MeV
and 1–3◦ , respectively, which depends on the BGOegg cluster energy and hit layer. As an
example, the resolutions of layer 14 are shown in Fig.3.7. The kinetic energy and polar angle
resolutions of η meson are quadratic sum of each photon resolution.

Figure 3.7: The photon energy and polar angle resolutions of the BGOegg layer 14. The
black line in the left figure is the resolution when the vertex position is known.

40

3.3.4

Proton kinetic energy and polar angle resolution

The proton kinetic energy was evaluated from the cluster energy. Because there are energy
losses in the target and the IPS, the cluster energy is not equal to the proton kinetic energy.
The relation between proton kinetic energy and cluster energy were evaluated using theγp → ηp reactions with the liquid hydrogen target. We carried out kinematical fitting
assuming that proton energy is an unmeasured variable. The calculated predicted proton
kinetic energy every cluster energy of 50 MeV as shown in Fig.3.8(a). We fitted the black
points with a cubic function and obtained the following relation:
Tp = 33.704 + 0.75332 × eCls + 8.6131 × 10−4 × eCls2 − 1.1902 × 10−6 × eCls3 [MeV], (3.7)
where eCls is the cluster energy of a proton. The proton kinetic energy resolution is shown in
Fig.3.8(b) as a function of the cluster energy. Side-going protons with kinetic energy greaterthan 450 MeV penetrate BGOegg and do not deposit all the energy in BGOegg. Thus, above
functions are valid up to 450 MeV. We note that the maximum proton kinetic energy formthe η ′ N → ηN reaction is 250 MeV. The polar angle resolution of proton was estimated in
the similar way as photon. The angler resolution for layer 14 is shown in Fig.3.9. The polar
angle resoltion is in the range of 2–4◦ , depending on the proton energy and polar angle.

Figure 3.8: (a) The relation between the predicted proton kinetic energy and the BGOegg
cluster energy of the γp → ηp reaction. (b) The proton kinetic energy resolution as a functionof the BGOegg cluster energy.

41

Figure 3.9: The proton polar angle resolution of the BGOegg layer 14 estimated using a MC
simulation.

3.4

Charge identification of decay products

The charge identification of particles creating BGOegg clusters were carried out using the
IPS. In addition, side-going protons were identified from the correlation of the energy depositin the IPS and the BGOegg cluster energy. The particle identification of protons are describedin section 4.4.3. In this section, we describe the calibration method of the energy depositand hit timing of the IPS, and the criteria of the charge identification.

3.4.1

IPS energy deposit and hit timing correction

Energy deposit in the IPS depends on the hit position because the IPS thickness which aparticle pass depends on its polar angle. In addition, the IPS signal timing depends on
the hit position because signals from scintillators are read at a single end. Thereby, energy
deposit and hit timing of the IPS are corrected event by event depending on the emission
polar angle of measured with BGOegg. The energy deposit in the IPS is corrected to be 1.0
in all the polar angle region when the corresponding BGOegg cluster energy is in a certain
region: 185–245 MeV. The signal timing is also corrected so that the hit timing of the IPS
relative to the RF signal, TIP S − TRF , for the events of this energy region to be 0 ns in all
the polar angle region.

3.4.2

Charge identification

When there is a cluster in BGOegg, we investigate IPSs in front of the core crystal. A cluster
is identified as “charged cluster” created from a charged particle when the energy deposit in
the IPS is greater than 0.8 in the calibrated unit. The cut criteria were determined using theγp → π 0 p reaction with liquid hydrogen target, in which both the proton and two gammas
from the π 0 were detected with BGOegg. The energy deposit in the IPS of clusters of protons
and gammas is shown in Fig.3.10. There are events that a gamma converted to e+ e− in an
IPS and created an IPS hit. By requiring some energy deposit in the IPS, we could reduce42the charge misidentification rate of gamma clusters. If the energy deposit in the IPS is lessthan 0.8, the cluster was identified as a “neutral cluster” created from a neutral particle.
The charge misidentification rate of protons and gammas were (1.4 ± 0.1)% and (5.5 ± 1.4)%,
respectively. They were taken into account to the acceptance.

Figure 3.10: The energy deposit distribution in the IPS of protons and gammas of the
γp → π 0 p data.

3.5

Forward going-particle detection

We used the DC to ensure that there is only forward-going proton, pf , in the forward region
in the polar angle less that 25◦ , which is not covered by BGOegg. We also required that the
track of pf measured with the DC and the pf hit position at the RPC is consistent. The t0
and xt calibrations were carried out every cycle of the SPring-8 storage ring (about every
100 runs). The DC tracking was carried out with the following conditions:• Carry out the tracking assuming that a track starts from the center of the target.
• Carry out the tracking for all the combination of hit wires.
• The left-right ambiguity is solved by selecting the larger chi-square side.
• When there are more than one track which use a common wire, select the track which
has the largest chi-square probability.
• Count as diﬀerent tracks when there is no common wire used for the tracking.
43

Figure 3.11: A schematic drawing of the DC tracking of a mock data. Green points show
fired wires. Blue, black and red lines show the tracking results. The chi-square probabilityof each track is shown with Pχ2 .

Figure 3.12: The chi-square probability distribution of the DC tracks of pf in the γ + 12 C →pf + (η + ps ) + X data.

44• Count as a track only when the chi-square probability of the track is greater than 0.01.
In Fig.3.11, a schematic drawing of the tracking method of a mock data is shown. The fired
wires are shown with green color. There are two clusters of hit wires. In the right cluster,
two wires had a hit in the U plane. The black line is the tracking using the U6 wire andthe red one is the U7 wire. We choose the red tracking because its chi-square probability
is larger. The particle created the left cluster was not from the target but the tracking iscarried out assuming that it is from the target. Thus, the chi-square probability of the blue
track is small. We exclude the blue track when we count the number of tracks because its
chi-square probability is less than 0.01. In summary, the number of tracks of the mock datais one, and we use the red track for the analysis. The chi-square probability distribution of
the DC tracks of pf without the chi-square probability cut of the γ + 12 C → pf + (η + ps ) + X
data is shown in Fig.3.12. The position resolution of the DC is σ = 290 − 330 µm, dependingon the layer. The reconstruction eﬃciency of tracks with DC is (98.2 ± 0.4)% (see Appendix
F.2.3).

3.6

Forward-going proton momentum measurement

The momentum of pf , used for the missing mass analysis, was measured from the time-offlight (TOF) from the target to the RPC. In this section, the algorithm to select hit readout
strip and the measurement of the particle energy are described.

3.6.1

Hit strip selection

As described in section 2.4, we added RPC signals from two neighboring strips for the ADC
measurement and two strips from neighbor chambers for the TDC measurement. In addition, there were cross-talks in neighboring strips of a hit strip. Thereby, we constructed analgorithm to select the hit strip. In Fig.3.13, a mock data sample for the strip selection isshown. The hit strip is strip 3 of the chamber 1A. The strips sharing a read out channel are
shown in the same color. The hit strip has larger charge and faster timing hit than cross-talk
strips. We selected the hit strip when it satisfies the following condition.

Figure 3.13: A mock data for the hit strip selection of the RPC. The hit strip is strip 3 ofchamber 1A.

45

1. The pair-strips have the largest charge among the 16 strips in the neighboring two
chambers.
2. There are TDC hits in all the readout of the pair strips.
3. Faster hit timing than the other pair-strip.
In Fig.3.13, we show one example value for each strip. In the real analysis, data of both the
top-end and bottom-end of the strip was used. As described in section 2.3.6, the top-row
RPC and bottom-row RPC overlap 70–80 mm. When two strips have hits in the overlapped
area in a close timing, the two hits were assumed to be a single hit and the hit timing of
the top-row RPC, which located upstream, was used for the analysis. The reconstruction
eﬃciency of the RPC hit was (95.9 ± 2.3)% (see Appendix F.2.4).

3.6.2

Timing calibration

We carried out the timing calibration so that the hit timing of the RPC relative to the RF
signal, TRP C − TRF , of the e+ e− events to be 0 ns. The velocity of fast e+ e− is very close
to the speed of light. The time-walk distribution depends on the Y hit position. Thus,
slewing corrections were carried out depending on Y . The resulting time resolution of TOF
measurement was 60 − 90 ps, which also depends on the hit position of the Y direction of
the readout strip [52].

3.6.3

Evaluation of forward proton momentum

We evaluated the momentum of pf from the TOF and flight length calculated from the RPC
hit position. The velocity of β of the forward-going particle was obtained as
β=

L
v
,
= L
c
( c + TRP C − TRF )c(3.8)

where c is the speed of light and L is the flight length. Lc is the time of flight from the target to
the RPC at the speed of light. We obtained the hit position in X direction√ from the positionof the hit strip. Thus, the position resolution of X direction was 26/ 12 = 7.5 mm. We
evaluated the hit position in Y direction from the timing diﬀerence of signals from top-end
and bottom-endof a strip. The position resolution of Y direction was 16 mm. L is obtained√2
as L = X + Y 2 + Z 2 , where Z is defined chamber by chamber, which is described in
section 2.3.6. The momentum of particle was obtained assuming that the particle is a protonwith a mass of mp = 938.27 MeV as
p = mp βγ × closs ,
1
,
γ = √
1 − β2(3.9)(3.10)

where, closs is the correction factor for the momentum loss in the target and air. We evaluatedcloss by calculating the energy deposit in each material with 1 mm step for a straight track46

from the target to the RPC. A two-dimensional plot of the momentum distribution of pf andthe photon beam energy of the γ + 12 C → pf + (η + ps ) + X data is shown in Fig.3.14. Abovethe red line, proton momenta exceed the photon beam energy and thus the events there areunphysical. The events above the red lines are mostly pions. They are contaminated sinceparticle identification of forward-going particles was not performed. They were excluded in
the event selection described in section 4.6.3. The energy resolution varies from a few MeV
to ∼ 30 MeV depending on the momentum of pf . The energy resolution of pf in the γp → η ′ preaction is shown in Fig.3.15 as a function of the photon beam energy.

Figure 3.14: The momentum distributionof pf vs photon beam energy of the γ +12
C → pf + (η + ps ) + X data. The unphysical events above the red line are pions.

Figure 3.15: The energy resolution of pf
in the γp → η ′ p reaction as a functionof the photon beam energy.

47

Chapter 4
Event selection
We searched for a signal of the η ′ bound states from the excitation energy spectra of 12 C(γ, p)in the the γ + 12 C → pf + (η + ps ) + X reaction. Here, pf is a forward-going proton detectedwith the RPC and ps is a proton detected with BGOegg. In addition, we measured theγ + 12 C → pf + η ′ + X reaction to evaluate the production rate of η ′ . In this chapter, thedetails of the events selection of above two reactions are described.

4.1

Outline of the event selection

Most of event selection criteria are common for the measurements of the γ + 12 C → pf + (η +ps ) + X and γ + 12 C → pf + η ′ + X reactions. We measured the photon beam energy with thetagger by measuring the position of recoil electron tracks. We required a single recoil electron
track from an electron bunch in the tagger. Events having multi-tracks in the tagger were
excluded from the analysis because we can not discriminate the beam photon which invoked
the reactions above. We required that there is no hit in the UpVeto to exclude events inwhich a photon beam was converted to e+ e− when it was transmitted to the experimental
hall. We measured the momentum of pf with the time-of-flight (TOF) by assuming theparticle is a proton. The start timing of TOF was determined with the RF signal and theflight time was measured with the RPC. We did not carry out the particle-identificationof forward-going particles. Most of forward-going pion events give extremely large energy
which does not conserve the total energy when the energy is calculated assuming a proton
mass. Such events were excluded with the missing energy cut and the pion contamination
to the signal region of the excitation energy spectrum is small (see section 6.1.7). We usedmatching hit positions of pf at the DC and RPC. Only the selection criteria of BGOegg andthe IPS are diﬀerent for the (η + ps ) and η ′ tag analyses. We required that two photons andone proton were detected at BGOegg for the (η + ps ) tag data, and only two photons weredetected at BGOegg for the η ′ tag data. The η and η ′ mesons were identified from their two
gamma invariant mass. The side-going ps was identified with the energy deposit and the hit
timing in the IPS and BGOegg. In order to suppress events with (an) additional particle(s),we required that there is no other hit in BGOegg, and only a single hit was observed at the48

DC and RPC. In summary, we required the following conditions.
(1) Single recoil electron track in the tagger.
(2) No charged particle detected with the UpVeto.
(3) Single track at the DC.
(4) Single fired strip on the RPC.
(5) Matching hit positions at the DC and RPC.
(6-1) An η meson and one proton are observed at BGOegg ((η + ps ) analysis).
(6-2) An η ′ meson are observed at BGOegg (η ′ analysis).
For the γ + 12 C → pf + (η + ps ) + X analysis, we required that the events satisfies (1)–(5) and(6-1). For the γ + 12 C → pf + η ′ + X analysis, we required that the events satisfies (1)–(5) and(6-2). Details of the event selection of each detector are described in the following sections.

4.2

Recoil electron track

To select the certain tagger track corresponding to the beam photon which had the reactionin the target, events satisfying one of the following conditions we used for the analysis.
• The number of reconstructed tracks.
• The number of tracks is one after requiring the time diﬀerence between the averagetiming of PL hits and the average timing of first and second fastest neutral BGOegg
clusters is within ±1.0 ns.
When the fiber cluster size is large, we cannot measure the photon beam energy correctly.
Thereby, the following conditions were also required.
• If there are fiber clusters in both fiber layers, the number of fibers in both clusters is
less than 4.
• If there is only a single cluster in one of the fiber layers, the number of fibers in thecluster is less than 3.
The photon energy resolution with above conditions is 12.0±0.7 MeV (see Appendix C). The
tagger reconstruction eﬃciency was (89.9 ± 0.8)% with the above conditions (see Appendix
F.2.1).

49

4.3

In-beam e+e− veto

Events in which a photon beam converts to an e+ e− pair when the beam is transported to
the LEPS2 experimental building were excluded by using the UpVeto. The cut criteria were
determined from the single bunch events of the H-mode filling pattern. (See Appendix A
for the detail of the filling pattern.) Events were selected by using the 1/2436 prescaled RF
signal. The single bunch locates 1487 nsec away from other electron bunches. Thereby, there
is no event contamination from events in neighboring electron bunches. Figure 4.1(a) shows
the signal timing of the UpVeto relative to the RF signal, TU pV eto − TRF . TU pV eto − TRF , isexpressed in an unit of σ and 1σ varies 1.0–1.5 ns depending on run. Two-dimensional plot
of TU pV eto − TRF and the energy deposit in the UpVeto is shown in Fig.4.1(b). The eventsat around TU pV eto − TRF = 0σ are e+ e− pairs from the beam conversion. There is a slow
component after the main peak. It is considered to be scattered charged particles from thetarget to backward. Because we require that there is no produced particles other than thepf +(η +ps ) or pf +η ′ , we excluded events which have the slow hit at the UpVeto. In addition,
there is TDC dead time of ∼ 20 ns. Thereby, the following conditions were required for the
UpVeto.
• No TDC hit in |TU pV eto − TRF | < 30σ.
• Charge deposit smaller than the one of minimum ionization particle.
The selected are are shown with green square in Fig.4.1(b).

Figure 4.1: (a) TU pV eto − TRF distribution (b) TU pV eto − TRF vs energy deposit distributionof the single bunch events. The events in the green area were used for the analysis.

50

4.4

Decay particle identification

The (η + ps ) pair in the γ + 12 C → pf + (η + ps ) + X reaction and the η ′ meson in theγ + 12 C → pf + η ′ + X reaction were measured at BGOegg and the IPS. We identified η and η ′mesons from the invariant mass of two gammas. The gammas ware identified from the IPS
charge identification and the cluster hit timing. ps was identified from the energy deposit in
the IPS and BGOegg, and the hit timing of the IPS and BGOegg. We describe details ofparticle identification of decay products in this section.

4.4.1

Identification of gammas

For selecting gamma, neural clusters identified with the IPS as described 3.4.2 were selected.
Neutral clusters are from gammas or neutrons. Neutron takes larger time-of-flight from thetarget to BGOegg. Thus, we selected gammas by selecting fast timing events as shown in
Fig.4.2. Details of the timing selection criterial is described in Appendix D.

Figure 4.2: A scatter plot of the energy deposit and hit timing of neutral clusters in the (2neutral + 1 charged + 1 RPC hit) data sample. The selection criteria are shown with blacklines.

4.4.2

Identification of η and η ′ mesons

Figure 4.3 shows the two gamma invariant mass distributions around η and η ′ masses of theγ + 12 C → pf + (η + ps ) + X and γ + 12 C → pf + η ′ + X data sample, respectively. They
are fitted with Gaussian+polynomial functions as shown in Fig.4.4. The peak positions of ηand η ′ are (547.2 ± 0.3) MeV/c2 and (956.4 ± 1.5) MeV/c2 , respectively. The PDG values
are mη = 547.9 MeV/c2 and mη′ = 957.8 MeV/c2 . Thus, photon energy and polar angle
are calibrated well within the invariant mass resolution of 1 MeV. Events with the invariant51

Figure 4.3: The two gamma invariant mass distributions of (a) the γ + 12 C → pf +(η +ps )+Xand (b) the γ + 12 C → pf + η ′ + X data sample. Missing energy cut which is explained in thesection 4.6.3 is applied for the γ + 12 C → pf + η ′ + X data sample. The selection criteria areshown with blue-dashed lines.

Figure 4.4: The two gamma invariant mass distributions of (a) the γ + 12 C → pf +(η +ps )+Xand (b) the γ + 12 C → pf + η ′ + X data sample, fitted with Gaussian+polynomial functions.

52

mass within ±2.5σ and ±4.0σ from the peak were selected, for the (η + ps ) and η ′ tag events,
respectively. The selection criteria are shown with blue dashed lines in Fig.4.3.

4.4.3

Identification of side-going protons

Side-going protons, ps , were identified from the energy deposit in the IPS and BGOegg, andthe hit timing of the IPS and BGOegg. The details of the timing selection are describedin Appendix D. In this section, the selection criteria with the energy deposit are described.
Figure 4.5(a) shows a scatter plot of the energy deposit in the IPS and BGOegg of the charged
cluster in the γ + 12 C → pf + (η + ps ) + X data sample, before identifying side-protons. When
more than one IPS have hits, we selected the IPS which has the largest energy deposit. We
calculated expected energy deposit in the IPS in the case of a proton from the kinetic energy
measured with BGOegg using a table of PSTAR by NIST [56]. Figure 4.5(b) shows a scatterplot of the diﬀerence of the energy deposit in the IPS and the expected energy deposit, andthe BGOegg cluster energy. The region in which the diﬀerence is −3σ ∼ +4σ were selected.
Looser selection criteria were used for positive side because the IPS gain was unstable andpeak shift up to +0.5σ was observed in some experimental periods. We carried out particle
identification of charged particles only when the cluster energy is less than 250 MeV because
the expected maximum energy deposit of ps in the signal η ′ + p → η + ps reaction is less than
250 MeV. We discarded events in which the charged cluster energy is greater than 250 MeV
in the further analysis.

Figure 4.5: A scatter plot of the energy deposit in the IPS and BGOegg of the pf + (η + 1
charged particle) data sample. The selection criteria are shown with red lines.

53

4.5

Treatment of additional hit

We measured the γ + 12 C → pf + (η + ps ) + X and γ + 12 C → pf + η ′ + X reactions. (η + ps )and η ′ were measured with BGOegg, and pf was detected with the DC and RPC. In order to
exclude events with (an) additional particle(s), events in which other particles were detected
at BGOegg, the DC and RPC were excluded from the analysis. On the other hand, events inwhich the IPS has a hit without corresponding BGOegg cluster ware accepted. Protons whichhave kinetic energy smaller than ∼50 MeV stop in the IPS and are not detected with BGOegg.
Because the residual nucleus after emitting two protons (pf and ps ) is unstable, low energy
protons can be emitted when the unstable nucleus decays. In the γ + 12 C → pf + (η + ps ) + X
data sample, 27% of events have (an) IPS hit(s) without a BGOegg cluster. We accepted
those events with such very low energy activity.

4.6

Forward-going particle selection

Because we do not perform particle identification of forward-going particles, there are contamination of e+ e− and pions to forward-going pf . To remove e+ e− and pions, we applied
several cuts. We also required the matching hit positions of pf at the DC and RPC.

4.6.1

Clean track selection

To ensure that pf comes straight from the target, we required that the expected hit position of
the RPC from the DC tracking and the actual particle hit position at the RPC are consistent.
The selection criteria are shown in Fig.4.6 together with the pf + (η + ps ) data. The criteria
was determined from the γp → ηpf data with the liquid hydrogen target after the event
selection using a kinematical fitting, in which all events are in these criteria.

4.6.2

e+ e− event suppression

In the forward region near the beam axis, there are e+ e− showers coming from the conversionof photon beam. Most of the e+ e− can be remove by requiring the particle velocity β is lessthan 0.98. However, e+ e− from diﬀerent electron bunch of the SPring-8 storage ring cannot be
excluded with the β cut. Because e+ e− are √concentrated around the beam axis, we excluded22
events in RRP C < 200 mm, where RRP C = XRP
C + YRP C , and XRP C and YRP C are the X
and Y hit position measured with the RPC. We also excluded events in RRP C > 1500 mm,
where the particle path is close to the wall of the solenoid magnet. The selected area is shownpf< 6.8◦ .
in Fig.4.7. After the RRP C selection, the RPC coverage for pf is 0.9◦ < θlab

4.6.3

Energy conservation

Since we do not perform the particle identification of forward-going particles, the momentumof the forward-going proton pf was calculated from TOF assuming the proton mass. In mostcases, when the forward-going particle was a pion, the event gives extremely large momentum
54Figure 4.6: The diﬀerence of the expected and actual hit positions of pf at the RPC for thepf + (η + ps ) data. The selection criteria are shown with black lines.

Figure 4.7: (a) XRP C vs YRP C distribution (b) RRP C distribution of the γ + 12 C → pf + (η +ps ) + X data. The selection criteial RRP C > 200 mm and RRP C < 1500 mm are indicatedwith blue lines.

of pf which breaks the energy conservation rule. To suppress pion events, we applied missingηps pfenergy cut. The missing energy in the γ + 12 C → pf + (η + ps ) + X reaction, Emissis defined
as
ηp p

s f
Emiss
= Eγ + M12 C − M11 B − Eγ1 − Eγ2 − Eps − Epf .

55

(4.1)

The variables are defined as follows:• Eγ : the photon beam energy,• M12 C : the mass of a 12 C nucleus,• M11 B : the mass of a 11 B nucleus,• Eγ1 , Eγ2 : the neutral cluster energies,• Eps : the side proton kinetic energy + proton mass,• Epf : the forward proton total energy.
ηp p

s f
The distribution of Emissof the γ + 12 C → pf + (η + ps ) + X data is shown in Fig.4.8.
Negative missing energy indicates that the total energy after the interaction exceeds theinitial energy, and thus they are unphysical events coming from that a pion was assumed as
ηps pfa proton. Because of Fermi motion, there are physical events down to Emiss= −150 MeV.
ηps pfTherefore, events in Emiss< −150 MeV were excluded to suppress pion events.

ηp p

s f
Figure 4.8: The missing energy Emiss
distribution of the pf + (η + ps ) data. The selection
criterion is shown with a black line.

η′ pf
The missing energy in the γ + 12 C → pf + η ′ + X reaction, Emissis defined as

η′ p

f
Emiss
= Eγ + M12 C − M11 B − Eγ1 − Eγ2 − Epf .

η′ p

η ′ pf(4.2)

f
In addition to Emiss> −150 MeV, Emiss < 150 MeV is required for the η ′ tag data to exclude
events with additional particles, such as γ + 12 C → pf + η ′ π + X reaction, and combinatorial
multi meson background events, such as γ + 12 C → pf + ππ + X reaction. The selection
criteria are shown in Fig.4.9.

56

η′ p

f
Figure 4.9: The missing energy Emiss
distribution of the η ′ tag data. The selection criteria
are shown with black lines.

57

Chapter 5
The η ′-nucleus search
To search for the (η + ps ) events from the η ′ -nucleus bound state, the kinematical selection
was applied for the (η + ps ) pair. The optimization of the kinematical selection and theexperimental results of the η ′ -nucleus search are described in this chapter. Note that angles,
energies are given in the laboratory frame in this thesis if not specified.

5.1

Obtained data

In Fig.5.1 and Fig.5.2 the excitation energy of the η ′ +11 B system Eex , relative to the η ′production threshold E0 , of the γ + 12 C → pf + (η + ps ) + X and the γ + 12 C → pf + η ′ + X
data, are shown respectively. For the γ + 12 C → pf + (η + ps ) + X reaction, the excitationenergy is defined as
Eex − E0η′

= M M (12 C(γ, pf )) − M11 B − Mη′ ,(5.1)

where M M (12 C(γ, pf )) is the missing mass in the γ +12 C → p + X reaction, and M11 B andMη′ represent a mass of an 11 B and an η ′ meson, respectively. For the γ + 12 C → pf + η ′ + X
reaction, the following definition was used:Eex − E0γγ = M M (12 C(γ, pf )) − M11 B − Mγγ .

(5.2)

Here, we replace Mη′ in Eq.(5.1) with the invariant mass of two gammas, Mγγ . By using
Mγγ , we can cancel the Mγγ dependence of the Eex − E0 distribution and we can use sideband events of Mγγ for the background evaluation. Details are described in Appendix H. In
Fig.5.2, we observed a clean spectrum of the η ′ escape process, rising from the η ′ production
threshold. On the other hand, in Fig.5.1, we observed a large number of background events
rising below the η ′ production threshold. Huge (multi) meson background events in theγ +12 C → pf + X reaction, such as the γ + 12 C → pf + ππ + X, γ + 12 C → pf + πππ + X,
γ + 12 C → pf + ω + X, and γ + 12 C → pf + πη + X reactions, were suppressed by tagging an(η + ps ) pair, and thus remaining events are background events associating with an η and aside-going proton. To suppress reaming background events, a kinematical selection of (η +ps )was carried out. The details of the kinematical selection and results after the kinematicalselection are described in the following section.
58

Figure 5.1: The excitation energy spectrum of the γ + 12 C → pf + (η + ps ) + X data without
any kinematical selection cuts for η and ps .

Figure 5.2: The excitation energy distribution of the γ + 12 C → pf + η ′ + X reaction (a) in−600 MeV < Eex − E0γγ < 600 MeV and (b) in −100 MeV < Eex − E0γγ < 100 MeV. Redline shows the η ′ tag events in −4σ < Mγγ < +4σ and blue and green lines show side band
events in −8σ < Mγγ < −4σ and +4σ < Mγγ < +8σ, respectively.

59

5.2

Outline of the kinematical selection

Most of events in Fig.5.1 come from background reactions, γ + 12 C → pf + η + 11 B andγ + 12 C → pf + (η + π 0 ) + 11 B, where an η meson is produced in a primary reaction anda side-going proton, ps is kicked out by either a primary η, π 0 or pf . To suppress thosebackground events, we determined kinematical selection criteria of the (η + ps ) pair. The(η + ps ) pair from the bound η ′ meson is considered to be emitted in a close to back-to-backrelation, with an isotropic polar angle distribution in the laboratory frame. On the other
hand, η and ps from the background reactions are emitted in the forward direction in the

Figure 5.3: The polar angle and kinetic energy distribution of η and ps . (a)(c) The γ + 12 C →pf + (η + ps ) + X data in all Eex − E0 region, and (b)(d) the QMD signal simulation in−50 MeV < Eex − E0 < 50 MeV. The kinematical selection criteria are shown with blacklines.

60

laboratory frame because they are Lorentz-boosted as seen in Fig.5.3(a) and (c), in which thepolar angle and kinetic energy distribution of η and ps of the γ + 12 C → pf + (η + ps ) + X data
are shown. In addition, there is an undetected π 0 in the case of the γ+12 C → pf +(η+π 0 )+11 B
background reaction. The opening angle distribution and the missing energy distribution ofthe γ + 12 C → pf + (η + ps ) + X data are shown in Fig.5.4(a) and (c). When there isan undetected pion, the missing energy is greater than mπ0 = 135 MeV. We determinedkinematical cuts selecting back-to-back (η + ps ) pairs, backward-going ps and η, and eventswith no additional produced particle to enhance signals. The selection criteria are shown

Figure 5.4: The η − ps opening angle and missing energy distribution. (a)(c) The γ + 12 C →pf + (η + ps ) + X data in all Eex − E0 region, and (b)(d) the QMD signal simulation in−50 MeV < Eex − E0 < 50 MeV. The kienmatical selection criteria are shown with blacklines.

61

with black lines.
Even an (η + ps ) pair from the η ′ absorption is originally emitted back-to-back, the η andps interact in a nucleus and possibly loose their energy and/or change their direction. We
examined the kinematical distribution of the (η + ps ) after the interaction simulated with
the QMD model calculation is shown in Fig.5.3(b) and (d). The kinematical distributionsof η and ps simulated with the QMD model calculation are shown in Fig.5.3(b)(d) and
Fig.5.4(b)(d). The kinematics of background events are examined using the experimental
data of the γ + 12 C → pf + η + X and γ + 12 C → pf + (η + π 0 ) + X reactions. We
optimized the kinematical selection criteria using the side band of the excitationenergy of′the γ + 12 C → pf + (η + ps ) + X data, requiring 100 MeV < |Eex − E0η | < 200 MeV
ηpsand η − ps opening angle cos θlab
< −0.9. We used the QMD signal simulation and theγ + 12 C → pf + η + X and γ + 12 C → pf + (η + π 0 ) + X data as references of the cut
optimization. We describe details of the background sources, expected signal kinematics,
and optimization of kinematical selection criteria in the following sections.

5.3

Background source and feature

We searched for the signals in the following reaction:
γ + 12 C → pf + η ′ ⊗ 11 B↱ ′
η + p → η + ps .

(5.3a)(5.3b)On the other hand, we found that most of the background events are from the following
reactions:γ + 12 C → pf + η + 11 B↱
η + p → η + ps ,or pf + p → pf + ps .

(5.4a)(5.4b)(5.4c)

γ + 12 C → pf + η + π 0 + 11 B↱
η + p → η + ps ,or pf + p → pf + ps ,or π 0 + p → π 0 + ps ,or π 0 + p + n → ps + n.

(5.5a)(5.5b)(5.5c)(5.5d)(5.5e)

γ + 12 C → pf + η + π − + 11 C↱ −π + p + p → ps + n.

(5.6a)(5.6b)In all the background reactions, an η meson is produced in the primary reaction, and ps
is kicked out by one of the particles produced in the primary reaction. In the single ηbackground reaction (5.3), the particles in the final state are the same as the signal reaction62

(5.2). In the ηπ background reactions (5.4) and (5.5), there is an undetected π 0 (reactions(5.4b, 5.4c, 5.4d)) or n (reactions (5.4e, 5.5b)). The γ’s from π 0 and n escape from themeasurements when they fly to the holes of BGOegg at θ < 24◦ and θ > 144◦ . In addition,
because the detection eﬃciency for n of BGOegg is low, n can escape from the measurement
even if it is emitted to 24◦ < θ < 144◦ when it does not react with BGOegg. On the other
hand, reactions with an additional charged particle can not be background reactions because
all the solid angle is covered with BGOegg, the UpVeto and the DC. Events which had an
additional hit in BGOegg, a hit in the UpVeto or an additional track other than pf in theDC, are excluded in the event selection. Thereby, in the case of ηπ − production, only the twonucleon absorption process of the reaction (5.5b), which emits an n, can be a background.
We examined those background reactions using the γ + 12 C → pf + η + X and γ + 12 C →pf +(η +π 0 )+X data, in which only an η meson or the ηπ 0 mesons were detected in BGOegg,
respectively. To exclude events with an additional undetected particle, we selected region|Emiss | < 150 MeV. Here, we define
ηp

f
Emiss
= Eγ + M12 C − M11 B − Eη − Epf ,ηπ 0 pEmiss f = Eγ + M12 C − M11 B − Eη − Eπ0 − Epf ,

(5.7)
(5.8)

for the η and ηπ 0 data, respectively. Except the case that the secondary ps is kicked out
by pf (reaction (5.3c) and (5.4c)), the excitation energy is independent from the secondary
reaction. In Fig.5.5, we show the excitation energy distributions of the η, ηπ 0 and (η +ps ) tag
data. The distribution of the ηπ 0 tag data shows similar distribution as the (η + ps ) tag data.
For the η tag data, we require that the η kinetic energy is greater than 100 MeV. It is becausethat the η needs to have a certain kinetic energy, Tη to have the secondary reaction (5.3b)with ps kinetic energy large enough (≳ 50 MeV) to penetrate the IPS and to be detected

Figure 5.5: The excitation energy spectra of the (a) η, (b) ηπ 0 and (c) (η + ps ) tag data.
(a) The dashed line shows the distribution without Tη > 100 MeV requirement and the solidline with Tη > 100 MeV.

63

with BGOegg. The distributions without and with the requirement of Tη > 100 MeV areshown in Fig.5.5(a). The distribution with the requirement of Tη > 100 MeV starts to rise at
Eex − E0 = −350 MeV, which is similar to the distribution of the (η + ps ) tag data. We usedthe γ + 12 C → pf + η + X and γ + 12 C → pf + (η + π 0 ) + X data, to estimate the distributionof the background after the kinematical selection.

5.4

Expected signal kinematics

5.4.1

Characteristics of signal

When an η ′ meson is bound to a nucleus, its momentum is transferred to the nucleus andthus the η ′ meson is considered to be at rest in the laboratory frame. Therefore, the (η + N )pair from the η ′ N → ηN absorption process is emitted in a close to back-to-back relation,with an isotropic polar angle distribution, within the fluctuation coming from the Fermi
momentum of the nucleon. This is the unique feature of the (η + N ) pair from bound η ′absorption. However, the emitted η meson and nucleon interact with the nucleus and loose
their energy and/or change their direction, or even be absorbed by the nucleon. We examinedthe eﬀect of the final state interactions in the nucleus using a quantum molecular dynamics(QMD) model calculation. In Fig.5.6, the kinematical distributions of η and ps simulatedwith the QMD calculation are shown. In Fig.5.6, distributions without and with final stateinteractions are shown with blue and red lines, respectively. Protons with kinetic energy
smaller than 50 MeV is mainly from the decay of 11 B nucleus. Events with Tps < 50 MeV
are removed in Fig.5.6(a)(b)(c).

5.4.2

QMD simulation

To examine the η − ps opening angle distribution after the interactions and to evaluate theprobability that an (η + ps ) pair is emitted back-to-back after the interactions, we simulated
the interaction of the η meson and nucleon with nucleons in the nucleus using a QMD
model calculation. QMD calculations are widely used for the simulations of nucleus-nucleus
collisions and hadron productions in nuclei [57, 58]. We used the same parameters as inRef.[58], which well reproduce the angular and momentum dependence of diﬀerential crosssections of η photoproduction from carbon. In the simulation, we firstly injected a photon
to a 12 C nucleus. We changed the energy and angle of the forward going proton pf toreproduce the kinematics of diﬀerent Eex − E0 cases. Then, the remaining momentum after
the forward proton emission was shared with the residual 11 B nucleus. The remaining energy
was transferred to one of a nucleon in the 11 B nucleus and produced a hypothetical N ∗ statewith a mass of η ′ +nucleon, which immediately decays to an η and a nucleon. The polar
angle distribution of the η and nucleon is assumed to be isotropic. Because the momentum
was shared with the nucleus, the N ∗ momentum is the order of Fermi motion. The excitednucleon was chosen randomly, thus both the N ∗ → ηp and N ∗ → ηn processes are included
with the weight of 5:6, which is the ratio of the number of p and n in the 11 B nucleus. We areinterested in the case that an (η + p) pair, not an (η + n) pair, which is emitted back-to-back64

Figure 5.6: Kinematical distributions of the (η + ps ) pair of the QMD simulation in−50 MeV < Eex − E0 < 50 MeV, without (blue) and with (red) final state interaction.
Detector resolution and acceptance are not included in these figures. The selection criteriaof the survival sample are shown with black lines.

after the interactions. The details of the QMD simulation are described in Appendix E. The
detector acceptance and resolutions were implemented to the simulation.

5.4.3

Survival probability

There are cases that the η meson or nucleon is absorbed by a nucleon when they interact, andis not emitted to outside of the nucleus. Even the case that both the η meson and nucleon
are emitted, they may loose feature of the kinematics specified for the signal if they loose
their energy or change their direction after the interaction in a nucleus. Figure 5.6 shows the
kinematical distributions of the (η + ps ) pair in the QMD simulation when both the η and ps
are emitted outside of the nucleus. The yield decreases when the final state interactions are65

implemented and some events loose original kinematical information. We can not distinguishsuch events from the background reactions anymore. We are interested in only events whichkeep the original features of signal kinematics. Thus, we defined the events which satisfy thefollowing conditions as a “survival sample” after interactions:• there are an η meson and a proton in the final state,
ηps• opening angle : cos θlab
< −0.7,
ηp p

s f• missing energy : Emiss= Eγ + M12 C − M11 B − Eη − Eps − Epf < 150 MeV,

• ps kinetic energy : Tps > 50 MeV.
Here, E and M indicate the total energy and the mass of each particle, respectively. The
selection criteria are shown with black lines in Fig.5.6. Tps > 50 MeV is needed because
there are a lot of low energy protons from the decay of residual nuclei as shown in Fig.5.6(c).
We should note that the ps kinetic energy cut, Tps > 50 MeV is naturally included in theexperimental data because only protons with kinetic energy greater than about 50 MeV canpenetrate the IPS and can be detected with BGOegg (see section 4.5). We used the survival
sample for estimating the expected signal yield and optimizing the kinematical selection
criteria.
We evaluated a survival probability, which is the fraction of the survival sample after theinteractions. We used the QMD simulation with the kinematics corresponding to −10 MeV <Eex − E0 < 10 MeV. In the case that the initial reaction is N ∗ → ηp, the fraction of thesurvival sample is 32.5%. In the case that the initial reaction is N ∗ → ηn, we can observean (η + ps ) pair when a neutron kicked out a proton. The fraction of the survival sampleof the N ∗ → ηn case is 2.6%. In total, the fraction of survival events was 16.0% of the all
the generated events. In the analysis, we optimized the kinematical selection criteria to theηpsηpsopening angle cos θlab
< −0.9. The survival probability Psrv
that an (η + ps ) pair is emitted
ηps
ηps
ηps
in cos θlab < −0.9 (instead of cos θlab < −0.7) is Psrv = 25.2% for the η ′ p → ηp case andηpsηps= 12.1%. The obtained= 1.2% for the η ′ n → ηn case. Total survival probability is Psrv
Psrv
ηps
′
Psrv for the η p → ηp is consistent with the measured transparency of carbon nuclei for η
ηpswhen we estimate the(∼ 44% [59]) and protons (∼ 60% [60–62]). We took into account Psrv
expected yield.

5.5

Cut optimization

In this section, the optimization of kinematical cut is described. For optimization of the cut
criteria, we used the the side band of the interested excitation energy region of the (η + ps )tag data, η, ηπ 0 tag data, and the QMD survival sample. We determined kinematical cuts
selecting back-to-back (η + ps ) pairs, backward-going ps and η, and events with no additional
produced particles to improve the S/N ratio. The selection criteria are as follows:ηps< −0.9,(a) the η-ps opening angle : cos θlab

66

′

Table 5.1: Number of the events of the (η + ps ) coincidence data in 100 MeV < |Eex − E0η | <300 MeV, and the expected number of signal events for the case of V0 = −100 MeV, after
applying each kinematical selection cut.
′Eex − E0η region [MeV][−300, [−200,
expected signal−200] −100][−50, 50]
no cuts
67
188(58.4 ± 14.7) × Brη′ N →ηNηps(a):cos θlab
< −0.91126(43.8 ± 11.0) × Brη′ N →ηNηps pf(a), (b):|Emiss | < 150 MeV
1124(43.8 ± 11.0) × Brη′ N →ηNps(a), (b), (c):cos θlab < 0.5
918(35.7 ± 9.0) × Brη′ N →ηNη<0
4
1(13.1 ± 3.3) × Brη′ N →ηN(a), (b), (c), (d):cos θlab

[100, [200,200] 300]
507
438
24
18
9
4
9
4
0
0

ηp p

s f
(b) missing energy : Emiss= Eγ + M12 C − M11 B − Eη − Eps − Epf < 150 MeV,

ps(c) the ps polar angle : cos θlab
< 0.5,
η(d) the η polar angle : cos θlab
< 0.
′

The number of events of the γ + 12 C → pf + (η + ps ) + X data in 100 MeV < |Eex − E0η | <300 MeV after each kinematical selection are summarized in Table.5.1. The numbers of
expected signals for the case of V0 = −100 MeV are also shown as a function of the unknown
branching fraction of the η ′ N → ηN process, Brη′ N →ηN . The details of the calculation of the
expected number of signals are described in section 7.2 and Appendix G.
For optimizing cut criteria, we used the side band′ of the interested excitation energy
region of the (η + ps ) tag data, 100 MeV < |Eex − E0η | < 200 MeV. The excitation energy
distribution
is shown in Fig.5.1. Since kinematical distributionsof η and ps depend onη′η′
Eex − E0 , we did not use events in 200 MeV < |Eex − E0 | for optimizing cut criteria. For
optimizing the η − ps opening angle cut, we used the (η + ps ) data satisfying the following
condition:′• excitation energy : 100 MeV < |Eex − E0η | < 200 MeV.
For optimizing other kinematical cut criteria, we used the (η+ps ) data satisfying the following
conditions:′• excitation energy : 100 MeV < |Eex − E0η | < 200 MeV,ηps• η − ps opening angle : cos θlab
< −0.9.
ηps< −0.9 because the polar angler distributions of η mesons and proWe required cos θlab
tons strongly depends on the opening angle criteria. We call the samples satisfying above
conditions as the “(η + ps ) side band sample”.
psη
The resolutions of θlaband θlab
are in the range of 1.4–4.2◦ and 1.4–5.7◦ , respectively,
ηps
depending on the particle kinetic energy and polar angle. The resolution of θlab
is a quadratic

67

ηp p

s f
ps
η
sum of the resolutions of θlaband θlab. The resolution of Emissis a quadratic sum of theresolutions of Eγ , Eη , Eps and Epf . It is in the range of 15–40 MeV depending on the energyof η, ps and pf . Eγ and BGOegg cluster energy are calibrated so that Emiss to be 0 MeV in
the case of proton target. Those resolutions are implemented in the QMD simulation.
The details of the optimization of each cut criterion are described in the following sections.

5.5.1

Opening angle cut

First, we determined the criterion of η − ps opening angle cut. Figure 5.7 shows the η − ps
opening angle distribution of the QMD survival sample and the (η + ps ) side band data. Theηpssurvival sample is concentrated in cos θlab
< −0.9. On the other hand, the distribution of
ηpsthe side band data is flat. Thereby, we determined the cut condition to cos θlab
< −0.9.
As shown in Table.5.1, the opening angle cut suppress background events to 6.6%. The
acceptance for the QMD survival event is 75.8%.

Figure 5.7: The opening angle distributions of the (η + ps ) side band data in 100 MeV <′|Eex − E0η | < 200 MeV, and the QMD survival sample.

5.5.2

Missing energy cut

Figure 5.8 shows the missing energy distribution of the QMD survival sample (requiring
ηps pfTη > 150 MeV instead of Emiss< 150 MeV) and the (η + ps ) side band data. The missing′
12
energy distribution of the γ + C → pf + η ′ + X data in the region of Eex − E0η < 150 MeV

68

is also shown. Here, the missing energies are defined as follows:
ηp p

s f
(QMD, (η + ps ) data) Emiss= Eγ + M12 C − M11 B − Eη − Eps − Epf ,η ′ pf(η ′ ) Emiss= Eγ + M12 C − M11 B − Eη′ − Epf ,(5.9)(5.10)

for the QMD, (η + ps ) data and η ′ tag data, respectively. All distributions show the peak at
Emiss = 0 MeV, which corresponds to events that no other undetected particle was produced.
Because the shell structure of the nucleon is not included to the QMD simulation, it is diﬃcult
to evaluate the distribution of the tail of the missing energy with the QMD. Thereby, we set
ηps pfa safe missing energy cut criterion as |Emiss| <150 MeV. As shown in Table.5.1, this cutη′suppress the background events in Eex − E0 > 100 MeV to 31%, where an additional pionis more likely to be produced. The QMD signal acceptance is more than 99.9%. Note that
this cut can suppress the background reactions (5.4b, 5.4c, 5.4d), in which a missing energy
larger than the π 0 mass (Mπ0 = 135 MeV) is expected. The background reactions (5.4e,5.5b) survive this cut when the neutron kinetic energy Tn is smaller than ∼ 150 MeV.

Figure 5.8: The missing energy distributions of the (η + ps ) side band data, the η ′ tag data,
and the QMD survival sample.

5.5.3

η and ps polar angle cut

As can be seen in Fig.5.3(a)(c), there are less backgrounds in the η and ps backward polar
ηpsangle region than forward region. However, because of the selection criterion of cos θlab<
−0.9, we can not select the region where both the η meson and ps are emitted to backward
direction. We optimized the selection criteria of the η and ps polar angles simultaneously
ηps< −0.9.
because there is a correlation between η and ps polar angles when we require cos θlab
ηps
The number of events in each polar angle region, cos θlab and cos θlab , are summarized inpsTable.5.2. The expected signal yields for the case of V0 = −100 MeV
in each cos θlaband√
ηcos θlabregions are summarized in Table.5.3. We obtain the best S/ N ratio when we select
69

√
ps
η
the region of [cos θlab
< 0.5 and cos θlab< 0] ((13.2 × Brη′ N →ηN )/ 1). Thus, we determinedpsηthe η and ps polar angle cut to be [cos θlab
< 0.5 and cos θlab
< 0]. The signal acceptancepsη
with the cut of [cos θlab < 0.5 and cos θlab < 0] is 30.0%. As can be seen in Table.5.1, thebackground events are reduced to 10.4% with the polar angle cuts.
psη
Table 5.2: The number of background events in each cos θlaband cos θlabregion. The number′′ηof events in −200 MeV < Eex − E0 < −100 MeV and 100 MeV < Eex − E0η < 200 MeV isshown before and after slash, respectively. The selected region with the kinematical cut isshown with thick letters.
ηηηη<–0.5 –0.5<cos θlab
<0 0<cos θlab
<0.5 0.5<cos θlab<1
–1<cos θlabps
0.5<cos θlab <1
4/0
2/0
0/0
0/0
ps
0<cos θlab <0.5
0/0
1/0
1/0
0/0
ps
–0.5<cos θlab <0
0/0
0/0
6/4
4/2
ps
–1<cos θlab
<–0.5
0/0
0/0
2/0
4/3

′

Table 5.3: The expected signal yield in −50 MeV < Eex − E0η < 50 MeV for the case ofηpsand cos θlabregion. The selected region with the kinematical
V0 = −100 MeV in each cos θlabcut is shown with thick letters.
ηηηη–1<cos θlab<–0.5 –0.5<cos θlab
<0 0<cos θlab
<0.5 0.5<cos θlab<1
ps
0.5<cos θlab <1
5.6×Brη′ N →ηN
2.7×Brη′ N →ηN
0
0
ps
<0.5
0<cos θlab
1.3×Brη′ N →ηN 9.7×Brη′ N →ηN 3.6×Brη′ N →ηN0ps–0.5<cos θlab <00
2.2×Brη′ N →ηN 9.6×Brη′ N →ηN 2.7×Brη′ N →ηN
ps–1<cos θlab <–0.500
2.2×Brη′ N →ηN 5.0×Brη′ N →ηN

5.6

Expected signal and background yields after the
kinematical selection′

The numbers of background events in 100 MeV < |Eex −E0η | < 300 MeV and expected signal′
yields −50 MeV < Eex − E0η < 50 MeV after each kinematical selection are summarized inTable.5.1. With all the kinematical selection, the background events are reduced to 0.4%,
while
23% of the signal events is preserved.
The background events remained only in Eex −η′η′E0 < −100 MeV. In the small Eex − E0 region, the missing energy and the kinetic energiesof η and ps are small and those events are hardly removed with′ kinematical selections.
The remained numbers of events are 4 in −300 MeV < Eex − E0η < −200 MeV and 1 in′
−200 MeV < Eex − E0η < −100 MeV. Figure 5.9 shows the excitation energy distributionηη
of the single η, ηπ 0 and (η + ps ) tag sample with no cos θlabcut (black), cos θlab
< 0.5 (blue)ηηpsand cos θlab
< 0 (red). We require cos θlab
< −0.9 for the (η + ps ) tag data but do not
70

ηp p

s f
require |Emiss| <150 MeV to increase statistics. An identical or smaller background level in′′−100 MeV < Eex − E0η < 100 MeV as −200 MeV < Eex − E0η < −100 MeV is indicated for′ηthe case of cos θlab
< 0. Thereby, the expected background level in −50 MeV < Eex − E0η <50 MeV is 1±1 events or less after the kinematical selection. On the other hand, the expected
number of signal events is (13.1 ± 3.3) × Brη′ N →ηN . If Brη′ N →ηN is the order of a few tenth%, we can observe signals above backgrounds.

Figure 5.9: The excitation energy distributions of the single η, ηπ 0 and (η + ps ) tag dataηwith diﬀerent cos θlab
cut criteria.

5.7

Experimental result

In Fig.5.10, we′ show a two dimensional plot of each variable used for the kinematical selection
and Eex − E0η of the γ + 12 C → pf + (η + ps ) + X data. The black dots show the events
without any kinematical selection and blue circles show events after kinematical selections
except for the kinematical selection with the variable used in the vertical axis. The redrectangles indicate the regions to search for the signals. There is no event satisfying all thecut conditions, therefore, we do not observe (η + ps ) events from bound-η ′ absorption via the′η ′ N → ηN process. The events observed in Eex − E0η < −50 MeV are considered to be fromthe γ + 12 C → pf + η + 11 B and γ + 12 C → pf + (η + π 0 ) + 11 B background reactions. In
chapter 6 and 7, we evaluate the experimental upper limit of the production cross sectionof the η ′ -nucleus bound state with (η + ps ) emission. The excitation energy spectrum ofthe γ + 12 C → pf + η ′ + X was measured with very low background condition as shown in
Fig.4.3(b) and Fig.5.2. We also evaluate the cross section of the η ′ escape process dependingon the excitation energy.

71

Figure 5.10:
The two dimensional plot of each variable used for the kinematical selection and′Eex − E0η of the γ + 12 C → pf + (η + ps ) + X data. The black dots show events without thekinematical selections and blue circles show events after the kinematical selections except
for the kinematical selection with the variable used in the vertical axis. The red rectangles
indicate the regions to search for signals.

72

Chapter 6
Luminosity, acceptance and eﬃciency
for the cross section measurement
In this section, we describe the details of the cross section evaluation for the η ′ -bound stateswith an (η + ps ) emission. We also describe the cross section measurements of the η ′ escapeprocess.

6.1

The (η + ps) measurement

6.1.1

Formulation

The experimental cross section of the η ′ -bound states with (η + ps ) emission averaged inθp = 0.9 − 6.8◦ and Eγ = 1.28 − 2.4 GeV is expressed as
(

dσ
dΩpf

)(η+ps )=N(. 6.1)
Σ(Nγ × εDAQ × ΩRP C ) × ρN × Acc × εdetector × εf illing × Brη→2γHere, the meaning of the variables are as follows:• N : the observed number of events after the kinematical selection• Nγ : the number of beam photons in 1.28-2.4 GeV• εDAQ : the DAQ eﬃciency• ΩRP C : the solid angle covered with the RPC• ρN : the number density of target nucleons• Acc : the acceptance of the BGOegg, IPS and DC for the (η + ps ) pair and pf including
the events selection and kinematical selection• εdetector : the detector eﬃciency and over veto rate (Tagger, UpVeto, DC and RPC)73

• εf illing : the correction factor of the electron filling mode dependence• Brη→2γ : the branching fraction of the η → 2γ process
Because εDAQ depends on the photon beam rate and the storage ring electron filling pattern,
and the RPC has problematic chamber depending on run period, (Nγ × εDAQ × ΩRP C ) was
evaluated run by run and summed up over all runs. εdetector and εf illing are averaged value overall data taking periods. Other variables are independent from run periods. We summarize
the values in Table.6.1. We describe details of the variables in the following subsections.
Table 6.1: The summary of values used for the calculation of the cross sections.
value
Σ(Nγ × εDAQ × ΩRP C ) 1.59 × 1011
ρN
1.74 × 1023
Acc
13.2%
εdetector
81.9%
εf illing
91.1%
39.41%
Brη→2γ

6.1.2

error
0.02 × 1023
0.7%
2.9%
1.2%
0.20%

The number of photons weighted with the RPC acceptanceand the DAQ eﬃciency

The number of photons
We evaluated the number of photons hit the target from the following equation:
Nγ = Nscaler × fdead time × fnot shower × Ttrans .

(6.2)

Nscaler is the number of beam photon counted with a scaler. When there are hits in bothof pair tagger PLs, a logic signal is sent to the scaler. The width of the logic signal for the
scaler is 20 ns. Thereby, photons coming from the same electron bunch or coming in the
20 ns dead time are not counted with the scaler. We evaluated the dead time correction
factor fdead time using a Monte Carlo (MC) simulation. fdead time depends on the electron
bunch filling pattern and the laser-electron collision rate. It varies between around 1.0 and
1.5. We evaluated Nscaler × fdead time run by run.
There are some events that an recoiled electron hit the box wall of the tagger or thevacuum chamber and create an electron shower, and the shower electrons hit PLs. Such events
are not used in the analysis and should be excluded when we count the number of photons.
We evaluated the fraction of events not from such showers fnot shower , using a special datataken with a lead glass counter. We measured the photon beam energy using the lead glass
counter and evaluated the number of photons from the showers. The energy of photon beam
74

associated with a shower is smaller than 1.3 GeV, which is the lowest energy of in the tagger
acceptance for recoil electrons without shower. We obtained fnot shower = (95.75 ± 0.06)%.
Ttrans is the photon transmission rate from the collision point to the target. It is 77.2%
as described in section 2.1.4.
The total number of photon is Nγ = 5.87 × 1012 when we sum up over 1129 runs used forthe analysis.
The DAQ eﬃciency
The DAQ eﬃciency, εDAQ , depends on the laser-electron collision rate. We corrected εDAQ
run by run. A typical value of εDAQ was 83 − 97%.
The RPC solid angle
There are 32 RPC chambers. Some of them suﬀered from occasional oscillation of amplifiers
during data taking. In addition, the amplifier and the readout strip sometimes disconnected
because of weak soldering. We excluded those problematic chambers from the analysis. The
problematic chamber was defined run by run, thus the solid angle covered with the RPC
depends on run. Figure 6.1 shows the run dependence of the solid angle of the RPC.

Figure 6.1: The run dependence of the solid angle covered with the RPC.

Total
We evaluated (Nγ × εDAQ × ΩRP C ) run by run. After summing up over the all run periods,
we obtained Σ(Nγ × εDAQ × ΩRP C ) = 1.59 × 1011 .
75

6.1.3

Number density of the target

We evaluated the number density of target nucleons ρN as

ρN =dtarget × NA × x
.
A

(6.3)

Here, dtarget = 1.73 g/cm3 is the target density, NA = 6.02 × 1023 mol is the Avogadro
constant, x = 2.00 cm is the target thickness, and A = 12.01 is the standard atomic weightof C. We obtained ρN = (1.74 ± 0.02) × 1023 . The error mainly comes from the uncertaintyof the measurement of dtarget and x.

6.1.4

Acceptance

The acceptance for (η + ps ) pairs and pf was evaluated using a Monte Carlo (MC) simulation
based on Geant 4 [63]. All the detector system including support structures was implemented
in the simulation. The same event selection and kinematical selection criteria described inchapter 4 and 5 were applied to the MC. We evaluated the acceptance for an (η + ps ) pairand pf separately in diﬀerent simulations.
Acceptance for (η + ps )For evaluation of the acceptance for (η + ps ), we generated an hypothetical N ∗ → ηp reaction
with the MC simulation, in which we implemented Fermi motion of carbon nucleus to themomentum of the N ∗ [64]. Both the η and proton are assumed to have isotropic angler
distributions. We changed the mass of N ∗ in the range between 1850 and 1950 MeV. This
energy corresponds to the excitation energy region around −50 MeV < Eex − E0 < 50 MeV
for the case of the signal η ′ p → ηp reaction. We obtained the acceptance for the (η + p) pairps
ηin cos θlab
< 0.5 and cos θlab
< 0 to be Accη+ps = (13.9 ± 0.6)%. The systematic error mainly
comes from diﬀerences of the detector response between the MC and the real data. Detailsof the systematic error are described in Appendix F.
Acceptance for pf
As explained in section 6.1.2, we evaluated the acceptance for pf of the RPC run by run.
We examined the acceptance for pf of the DC by using a MC simulation. We generated an
pf< 7◦ , which roughly corresponds toγ +p → η ′ +pf reaction, in which the proton flights to θlab
the RPC acceptance. When pf interacts in the target, pf changes the direction and/or kicks
out another particle. Then there can be no track in the DC or an additional track/clusterin the DC/BGOegg. Those events are excluded at the event selection stage. We evaluatedthe probability to pass the event selection criteria, which the number of DC track is one andno additional particle hit in the BGOegg. We obtained the acceptance for pf of the DC,
AccDCpf = (94.7 ± 0.5)%. Details are described in Appendix F.

76

Total acceptance
In total, we obtained Acc = Accη+ps × AccDCfp = (13.2 ± 0.7)%. This value includes the
BGOegg, IPS reconstruction eﬃciencies and the over veto rate of the DC.

6.1.5

Detector eﬃciencies

In Table.6.2, we summarize the reconstruction, detection eﬃciencies of the tagger, DC and
RPC and the over veto rate of the UpVeto. We evaluated the tagger PL intrinsic eﬃciency
using events in which recoil electrons pass overlap regions of neighboring PLs. The tagger
track reconstruction eﬃciency and the UpVeto over veto rate are evaluated using the γ +12
C → 2π 0 + ps + X data sample. We estimated the reconstruction eﬃciencies of thesedetectors from the γ + p → ω + p, γ + p → η + p data samples with the liquid hydrogentarget after kinematical fitting. Details of the evaluation of the eﬃciencies are described inAppendix F. In total, we obtained εdetector = (81.9 ± 2.9)%.
Table 6.2: The detector eﬃciencies and the over veto rate.
Tagger PL intrinsic eﬃciency
Tagger track reconstruction eﬃciency
UpVeto over veto rate
DC reconstruction eﬃciency
RPC reconstruction eﬃciency
Total

6.1.6

value
98.8%
89.90%
97.84%
98.24%
95.89%
81.9%

error
1.2%
0.81%
0.27%
0.44%
2.32%
2.9%

Filling mode correction factor

Figure 6.2 shows the run dependence of the ratio of the number of measured events andNγ × εtag for the γ + 12 C → (π 0 + η) + pf + X and γ + 12 C → (ω + ps ) + X reactions.
Here, (π 0 + η) and (ω + ps ) were detected with BGOegg, and pf was detected with the
RPC. The electron filling modes of the storage ring are indicated with Alphabets. The
tagger reconstruction eﬃciency εtag depends on the electron filling mode and thus the tagger
eﬃciency depending on the cycle is taken into account. The electron bunch structure ofeach filling mode is summarized in Appendix A. We normalized the ratio so that the ratioof the first C-mode data (shown with thick letters) to be one. The red and blue points
shows the ratios of events with Eγ > 1.8 GeV and Eγ < 1.8 GeV, respectively. We observe
smaller ratio in the first A-mode (yellow letters) and D, E and H-mode (green letters). In
the first A-mode cycle, we observed smaller transmission rate of beam photons than otherperiods because of bad focus point of lasers. The low transmission rate was also observedin the liquid hydrogen target data taken in 2014 and there were Eγ dependence. On theother hand, the Eγ dependence of the transmission rate of the first A-mode of the carbon
77

data is small and negligible when we count the total number of photons. The details of
the drop of the transmission rate is described in Appendix F.3. The D, E and H-mode haveconcentrated train bunches as described in Appendix A. The smaller ratios of the D, E and Hmodes are considered to be from smaller event reconstruction eﬃciencies at the concentrated
bunch regions. We evaluated an correction factor of this filling mode dependence from theγ + 12 C → (ω +ps )+X data. We used all C-mode and 2nd A-mode cycle data (indicated withs(all cycle) /black colors) as a reference. The evaluated correction factor is εf illing = Nω+pγ ×εtagω+ps(reference cycle) = (91.10 ± 1.19)%.
Nγ ×εtag

Figure 6.2: The filling mode dependence of the ratio of the number of measured events andNγ × εtag of the γ + 12 C → (π 0 + η) + pf + X and γ + 12 C → (ω + ps ) + X reactions.

6.1.7

Pion contamination to the forward particle

Since we do not have the particle identification capability in the forward going particles, pions
can be contaminated to forward going protons. We investigated the contamination rate ofη ′ pfpions as follows. Figure 6.3 shows a scatter plot of TRP C − TRF and the missing energy Emissη ′ pfof the γ + 12 C → pf + η ′ + X data. The events in Emiss< −150 MeV are pions. The number
η ′ pfof events in −1000 MeV < Emiss < −200 MeV is 14 events in the η ′ tag data and 9 eventsin the η ′ invariant mass side band data. Thus, the pion contamination rate per 300 MeV ofη ′ pfEmiss(corresponds to the missing energy cut of −150 MeV < Emiss < 150 MeV, which we
selected with the event and kinematical selections) is 1.9 ± 1.8 events. This is (0.7 ± 0.7)%of the total 265 η ′ events. We set the upper limit of the pion contamination to 1.4%.

78

η′ p

f
Figure 6.3: A scatter plot of TRP C − TRF and the missing energy Emissof the γ + 12 C →′pf + η + X data.

6.1.8

Branching fraction of η → 2γ mode

According to the summary table by Particle Data Group (PDG) [1], the branching fractionof the 2γ decay mode of the η meson is Brη→2γ = (39.41 ± 0.20)%. We used this value forthe calculation of the cross section.

6.1.9

Systematic error

The systematic uncertainty of the cross section measurement was evaluated from a quadratic
sum of the systematic errors shown in Table.6.1 and the pion contamination fraction. The
obtained value is σsyst = 5.4%.

6.2

The η ′ escape measurement

6.2.1

Formulation′

η).
The acceptance for the η ′ meson depends on its kinetic energy (Tη′ ) and polar angle (θlab
Because there are final state interactions, it is diﬃcult to reproduce the experimental kinetic
energy and polar angle distributions with a Monte Carlo (MC) simulation. Therefore, weη′. Themade an acceptance correction event by event according to the measured Tη′ and θlabcross section of the η ′ escape process averaged in θp = 0.9 − 6.8◦ and Eγ = 1.28 − 2.4 GeV is79expressed as
(

dσ
dΩpf

)
1
1
×
(6.4)
.
′ →2γ
Acc[i]
Σ(N
×
ε
×
Ω
)
×
ρ
×
ε
×
ε
×
Br
γ
DAQ
RP
C
N
detectorfillingηi=0)η′ esc (∑N=

Here, i is the event number and N is the total number of events. Acc[i] is the acceptance forη ′ meson of the ith event. Other variables are described in section 6.1.1. They are common
to the (η + ps ) measurement, except for the branching fraction of the η ′ → 2γ process,Brη′ →2γ = (2.20 ± 0.08)% [1]. When we estimate cross sections with diﬀerent Eγ regions, Nγ
in each Eγ bin was estimated assuming the photon beam energy distribution of a backward
Compton scattering shown in Fig.2.5. To subtract the contribution of the combinatorial
background, the cross section of the side band of the invariant mass (4σ < |Mγγ | < 8σ) was
subtracted. The statistical error of the cross section is described as
v(
)
u N
u
∑
′
1
1
η esc
σstat
=t
×
.(6.5)
2
Acc[i]
Σ(Nγ × εDAQ × ΩRP C ) × ρN × εdetector × εf illing × Brη′ →2γ
i=0

6.2.2

The η ′ acceptance

We estimated the acceptance of BGOegg and the IPS for the η ′ meson as a function of Tη′η′and θlabby using a MC simulation. The procedure is common to the MC simulation forthe (η + ps ) measurement described in section 6.1.4. Instead of the N ∗ → ηp reaction, we
implemented a γ + p → η ′ + p reaction. In the MC simulation, the Fermi motion of a target
proton was taken into account but the final state iteration of η ′ and p was
not taken intoη′′account. In Table.6.3, we show the acceptance for η in each Tη′ and θlab region evaluatedwith the MC simulation. Several kinematical regions show very small acceptance.
Since the final state interaction was not taken into account in the MC simulation,
there canη′be discrepancy between the MC and the experimental data in the Tη′ and θlab distributions.
η′η′
Figure 6.4 shows the θlab
distribution in Tη′ < 100 MeV and Tη′ distribution in cos θlab
> 0.9,of the accepted events in the MC and the experimental data. The η ′ polar angle distributions
are consistent within the statistical error. On the other hand, the kinetic energy distributions
are inconsistent. Because the angle distributions are
consistent, we evaluated acceptance asη′only a function of Tη′ with the weight of the cos θlab
distribution of the MC. It is summarizedin Table.6.4. As the statistical error is described in Eq.(6.5), a small acceptance gives a largeη′helped to reduce the statistical error
statistical error. The averaged acceptance over cos θlabcoming from the small acceptance regions.

6.2.3

The η ′ angle region′ηand kinetic energy Tη′
Figure 6.5 shows the two-dimensional plot of the η ′ polar angle θlab′of the η tag events (red) and the invariant mass side band events (blue). They are plottedη′<0on the acceptance table same as Table.6.3. Although we have several events in cos θlab

80

Table 6.3: The acceptance of BGOegg
and the IPS for η ′ meson as a function of the η ′ kinetic′
ηenergy (Tη′ ) and polar angle (θlab) estimated with a MC simulation. “0” means no accepted
events and “–” means no generated events.
Tη′ [MeV]η′cos θlab
0.8 – 1.0
0.6 – 0.8
0.4 – 0.6
0.2 – 0.4
0.0 – 0.2
-0.2 – 0.0-0.4 – -0.2
-0.6 – -0.4
-0.8 – -0.6
-1.0 – -0.8

0–
100
0.687
0.667
0.656
0.629
0.609
0.652
0.444
0
0.167
–

100–
200
0.613
0.513
0.354
0.250
–
–
–
–
–
0

200– 300–
300
400
0.524 0.414
0.035 0.009
0
0
–
–
–
–
–
–
–
–
–
–
–
–
–
–

400–
500
0.286
0.007
–
–
–
–
–
–
–
–

500–
600
0.166
0
–
–
–
–
–
–
–
–

600–
700
0.089
0
–
–
–
–
–
–
–
–

700–
800
0.055
0
–
–
–
–
–
–
–
–

800–
900
0.027
–
–
–
–
–
–
–
–
–

900–
1000
0.013
–
–
–
–
–
–
–
–
–

Figure 6.4: The η ′ polar angle distributions and kinetic energy distributions of the experimental data (blue) and the MC (green).

in the experimental
data, there were almost no generated events in the MC. The numberη′of events in cos θlab < 0 is the same for the η ′ tag data and side band data. This meansη′that the combinatorial background events from multi pions are dominant in cos θlab
< 0. Weη′′evaluated the η coincidence cross section only in cos θlab > 0.

81

Table 6.4: The acceptance of BGOegg and the IPS for η ′ meson as a function of the η ′ kinetic
energy.
η ′ kinetic energy acceptance
0–100 MeV
68.1%
100–200 MeV
60.7%
200–300 MeV
51.5%
300–400 MeV
40.3%
400–500 MeV
27.7%
500–600 MeV
16.3%
600–1000 MeV
5.3%

Figure 6.5: The two-dimensional plot of the η ′ polar angle and kinetic energy of the η ′ tag
events (red) and side band events (blue) plotted on the acceptance table. “-0.1” means nogenerated events.

6.2.4

Systematic error

The systematic uncertainty of the η ′ cross section evaluation was estimated in the similar
way as (η + ps ) measurement. The obtained value is σsyst = 6.7%.

82

Chapter 7
Experimental results and discussion
7.1

Experimental results

7.1.1

Upper limit of the production cross section of the η ′ -nucleus
bound state with (η + ps ) emission

As shown in chapter 5, no (η + ps ) events from η ′ -nucleus bound states were observed in−50 MeV < Eex − E0 < 50 MeV after the kinematical cut. Assuming a Poisson distribution,
an upper limit of the number of events for a null result at the 90% confidence level is assigned
as [65]2
Nup = 2.30 × (1 + 2.30 × σsyst
/2),

(7.1)

where σsyst is the systematic error of the measurement. Then, the upper limit of the production cross section of the η ′ -nucleus bound state in coincidence with an (η + ps ) emission is
given as
(

dσ
dΩpf

)(η+ps )=up

Nup(. 7.2)
Σ(Nγ × εDAQ × ΩRP C ) × ρN × Acc × εdetector × εf illing × Brη→2γ

The meaning and value of the variables are described in section 6.1. We obtained that theupper limit of the production cross section of the η ′ -bound state in coincidence with an (η+ps )pf
ηpspair emission in cos θlab
< −0.9, −50 MeV < Eex − E0 < 50 MeV and θlab
= 0.9 − 6.8◦ ,under photon beam distribution of a backward Compton scattering in 1.28-2.4 GeV to be
2.2 nb/sr, at the 90% confidence level.

7.1.2

Cross section of the η ′ escape process

Figure 7.1 shows the excitation energy dependence of the cross section for the η ′ escapeprocess in five diﬀerent Eγ regions. We observed enhancement at 1.6 GeV < Eγ < 1.8 GeV.
This comes from the large transformation factor of the cross section from the center-ofmass frame to the laboratory frame near the production threshold (Eγ = 1.447 GeV for a83

dσ2/dΩdE [nb/(sr MeV)]√
protonat rest). At Eγ < 1.6 GeV, s can be smaller than the η ′ production threshold√( s = 1.896 GeV) even above Eγ = 1.447 GeV because of the Fermi motion of the target
proton, and thus the cross section decrease. The peak position of the excitation energy
spectrum moves to lower excitation energy with increasing Eγ . This is because of small
momentum transfer at lower Eγ . These behaviors are clearly understood by seeing Eγ vsexcitation energy distribution of a MC simulation. Figure 7.2(a) shows a two dimensional
plot of Eγ and excitation energy distribution of the experimental data. Figure 7.2(b) and(c) show the distributions of MC simulations of the γp → η ′ p reaction (b) with and (c)without Fermi motion. The distributions in (a) and (b) are quite similar. From Fig.7.2(c),we can see that the distributions moves to higher excitation energy with lower Eγ . The Eγ
dependence of the momentum transfer is shown in Fig.1.8. We can see that the shift of thepeak position of the excitation energy is correlated with the momentum transfer. The eventsin Eex − E0γγ < 200 MeV in Fig.7.2(c) corresponds to events in cos θηCM
< 0 and events in′γγCM
Eex − E0 > 200 MeV corresponds to events in cos θη′ > 0. Supplements of the η ′ escapecross section measurement is describe in Appendix H.
99(a) 1.3<Eγ <1.6 GeV
η’ coincidence
0.9°<θ <6.8°

8
7

8

9

(b) 1.6<Eγ <1.8 GeV

89(c) 1.8<Eγ <2.0 GeV89(d) 2.0<Eγ <2.2 GeV

8

7

7

7

7

6

6

6

6

5

5

5

5

4

4

4

4

3

3

3

3

3

2

2

2

2

2

1

1

1

1

1

0

0

0

0

0

6

p

cosθlab
η’ >0

5
4

−100

0

100

200 300 400 −100γγ
Eex-E0 [MeV]

0

100

200

300 400 −100γγ
Eex-E0 [MeV]

0

100

200

300 400 −100γγ
Eex-E0 [MeV]

0

100

200

(e) 2.2<Eγ <2.4 GeV

300 400 −100γγ
Eex-E0 [MeV]

0

100

200

300 400γγ
Eex-E0 [MeV]

Figure 7.1: The excitation energy spectra of the η ′ escape reaction in five diﬀerent Eγ region.

Figure 7.2: The Eγ vs excitation energy distributions. (a) experimental data, (b) MC simulation with Fermi motion, (c) MC simulation without Fermi motion.

84

As described in section 1.5, for the evaluation of the normalization factor F of the theoretical cross section, the η ′ escape cross section integrated over 0 MeV < Eex − E0γγ < 50 MeV,
and averaged in Eγ = 1.3 − 2.4 GeV is used. As can be seen in Fig.5.2, the observed numberof events in this region is 17.0 ± 4.4 events. (19 events in the η ′ tag data and 2 events in theη ′ side band data.) It is only 6% of all observed η ′ events. From Eq.(6.4), the cross sectionpfof η ′ escape events in θlab
= 0.9 − 6.8◦ , integrated in 0 MeV < Eex − E0γγ < 50 MeV, andaveraged over Eγ = 1.28 − 2.4 GeV was obtained as
(

7.2

dσ
dΩpf

)η′ esc= 60.2 ± 15.4(stat) ± 4.1(syst) nb/sr.

(7.3)

exp

Estimation of the η ′-nucleus potential V0

In this section, we estimate the real part of the η ′ -nucleus potential V0 . We estimate V0 fromthe experimental upper limit of the cross section and the theoretical expected cross section
calculated within a distorted wave impulse approximation (DWIA). We estimate V0 as afunction of the branching fraction of the η ′ N → ηN absorption process.

7.2.1

Overview

We calculated the expected excitation energy spectrum Eex − E0 of the η ′ -11 B nucleus boundstate in the framework of a distorted wave impulse approximation (DWIA) [23, 44]. The
calculation was carried out for the case of V0 = −100 and −20 MeV, and W0 = −12 MeV.
We chose W0 consistent with the measured value by the CBELSA/TAPS Collaboration,
W0 = −(13 ± 3(stat) ± 3(syst)) MeV [9]. The obtained spectrum is integrated in −50 MeV <Eex − E0 < 50 MeV and averaged over Eγ = 1.28 − 2.4 GeV to compare with the obtained
experimental upper limit of the cross section. The DWIA calculation is decomposed in
two processes; the η ′ escape and η ′ absorption. Although DWIA calculations nicely represent
spectral shapes of bound states, it hardly reproduces their absolute cross sections [25–30]. We
evaluated normalization factor F of the theoretical cross section from the η ′ escape process.
The branching fraction of the η ′ N → ηN absorption process in all the η ′ absorption process,Brη′ N →ηN , is unknown. In addition, the (η + N ) pair can be absorbed by nucleons due toηpsfinal state interaction even they were produced. We evaluated the probability Psrv
that anηps(η + ps ) pair is emitted in cos θlab < −0.9 using a quantum molecular dynamics (QMD)
transport model calculation. The experimental upper limit of the cross section of the η ′ bound states with (η + ps ) emission is compared with the theoretical cross section in diﬀerent
V0 cases as a function of Brη′ N →ηN . In section 7.2.2 and 7.2.3, we describe the formulationand procedure of the calculation. Details of the calculations are described in Appendix G. In
section 7.2.4, we describe the evaluation of the normalization factor F . We evaluate V0 fromthe comparison of the experimental upper limit of the cross section with theoretical crosssection in section 7.2.5 and 7.2.6.

85

7.2.2

Formulation

Within a DWIA, an excitation energy spectrum of the η ′ -11 B nucleus bound state can be
described as(()γ+p→p+η′)γ+12 C→p+η′ ⊗11 B
d2 σdσ
× R(Eex ).
(7.4)=(Eex )dΩpf dEex theory
dΩpf
lab
( dσ
)γ+p→p+η′Here, Eex is the excitation energy, dΩ(Eex ) lab
the Fermi-averaged cross section of theelementary γ + p → p + η ′ reaction [66], and R(E) the nuclear response function. An example( 2)γ+12 C→p+η′ ⊗11 Bd σ
for the case of Eγ = 2.05 GeV are shown in Fig.7.3
of results of dΩp dEexftheory(same figure as in Fig.1.9). The calculation results are decomposed into the η ′ escape andabsorption processes as()γ+12 C→p+η′ ⊗11 B ()η′ esc ()η′ abs
d2 σ
d2 σ
d2 σ
=
+
.
(7.5)
dΩpf dEex theorydΩpf dEex theory dΩpf dEex theory
The η ′ absorption process contributes below and above the production threshold Eex − E0 =0 MeV. On the other hand, the η ′ escape process contributes only above the production
threshold.

Figure 7.3: The excitation spectra calculated within the DWIA in the cases of V0 = −100and −20 MeV, W0 = −12 MeV, θp = 6◦ and Eγ = 2.05 GeV.

7.2.3

Calculation procedure

We integrated the theoretical cross sections over Eex , and averaged over Eγ to compare withthe experimental upper limit of the cross section. We calculated the theoretical cross sectionin the following procedure.
861. Calculate R(Eex ).
(2. Calculatedσ(Eex )
dΩpf)γ+p→p+η′.
lab

3. Integrate over Eex .
4. Average over Eγ .
Then, we evaluated the expected cross section of the (η + ps ) coincidence process as follows.
5. Evaluate the normalization factor F of the theoretical cross section from the η ′ escapeprocess.
ηpsηps
6. Evaluate the probability Psrv
in which an (η + ps ) pair is emitted in cos θlab
< −0.9′after the η N → ηN absorption process.

The nuclear response function R(E) is calculated by Nagahiro for the cases of V0 = −20,pf−100 MeV, W0 = −12 MeV, Eγ = 1.5, 2.05, 2.5 GeV, and θlab
= 6◦ [44]. For the calculation()γ+p→p+η′of dΩdσp (Eex ), we used the elementary cross section in the center-of-mass frame,f( dσ )γ+p→p+η′ lab√η′= 40 nb/sr in cos θc.m.
< −0.9 and s < 2.4 GeV, measured by the LEPSdΩ c.m.
[67] and CBELSA/TAPS [68] Collaborations. When we integrated over Eex , we took into
account the experimental detector resolutions. The integrated ranges of Eex were −50 MeV <Eex − E0 < 50 MeV and 0 MeV < Eex − E0 < 50 MeV for the η ′ absorption and η ′ escapeprocesses, respectively:)η′ abs)η′ abs(∫ +50 (
d2 σ
dσ=
dEex ,(7.6)
dΩpf theorydΩpf dEex theory−50)η′ esc)η′ esc(∫ +50 (dσ
d2 σ
dEex .
(7.7)=
dΩpf theorydΩpf dEex theory
0Then, they are averaged over Eγ , with the experimental Eγ distribution of a backward
Compton scattering (BCS), I(Eγ ), shown in Fig.2.4.
/∫()η′ abs)η′ abs∫ 2.4 (
2.4dσ
dσ=
I(Eγ )dEγ
I(Eγ )dEγ ,(7.8)
dΩpf theorydΩpf theory
1.28
1.28
/∫
)η′ esc)η′ esc(∫ 2.4 (
2.4dσ
dσ=
I(Eγ )dEγ
I(Eγ )dEγ(7.9)
dΩpf theorydΩpf theory
1.28
1.28
We evaluated the normalization factor F by comparing the experimental and theoreticalcross sections of the η ′ escape process:()η′ esc /()η′ escdσ
dσ
F =.
(7.10)dΩpf expdΩpf theory87

F is common for all Eex region as long as the DWIA calculation reproduces the experimental
spectrum shape, and is common to the η ′ escape and η ′ absorption process. The theoreticalproduction cross section of the η ′ bound states with (η + ps ) emission can be described as
(

dσ
dΩpf

(

)η+ps
=F×
theorydσdΩpf)η′ abs
ηps× Brη′ N →ηN × Psrv.

(7.11)

theoryHere, F is the normalization factor of the theoretical cross section. Brη′ N →ηN is the unknown
branching fraction of the η ′ N → ηN process in all the η ′ absorption process. The (η +N ) pairis originally emitted back-to-back. They interact with nucleons in nucleus and can change
their direction or be absorbed by (a) nucleon(s). We are interested in a case that an (η + ps )ηps
ηpspair, not an (η + n) pair, is emitted in cos θlab
< −0.9. We evaluated the probability Psrv
ηpsthat an (η + ps ) pair is emitted in cos θlab < −0.9 after interactions of an (η + N ) pair in theηpsresidual nucleus. We evaluated Psrv
using a quantum molecular dynamics (QMD) transportmodel calculation [57].
We describe the details of the procedure 1–4 in Appendix G. We describe the details of
the procedure of the calculation of the cross section with (η + ps ) emission (procedure 5 and6) in the following sections.

7.2.4

Normalization factor of the theoretical cross section

Comparison of the Eγ dependence
Because we use the average cross section over Eγ for evaluating F , we compared the Eγ
dependence of the experimental and theoretical cross sections of the η ′ escape process before evaluation of F . In Fig.7.4, black circles show the experimental cross section and red
points show the theoretical cross sections. Red lines are the fitting results of three points
by quadratic functions. The Eγ dependence of the experimental and theoretical cross sections agree, and thus we can compare the average cross section over Eγ . We note that, in
Ref.[44], the elementary cross section for a proton at rest is used in Eq.(7.4) instead of the
Fermi-averaged cross section. As shown by the blue line in Fig.7.4, the calculation without
Fermi motion is divergent near the production threshold because of a large CM-to-laboratorytransformation factor of the cross section. It is clearly unsuitable to use the calculation result
without Fermi motion for describing the observed Eγ dependence, and therefore we adopted
the Fermi averaged cross section in Eq.(7.4).
Evaluation of F
By averaging the red lines in Fig.7.4 over Eγ = 1.28 − 2.4 GeV, with weight of the BCS
photon beam energy distribution, we obtained the expected theoretical cross sections of the88[nb/sr]
η’ esc(dσ/dΩ)

450

γγ

p

0.9°<θ f <6.8°, 0<E -E0 <50 MeV
ex

lab

400

data
V0=-20 MeV (without Fermi ave.)
V0=-100 MeV (Fermi ave.)
V0=-20 MeV (Fermi ave.)
V0=-100 MeV (F=0.35)
V0=-20 MeV (F=0.38)

350
300
250
200
150
100
50
0
1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

Eγ [GeV](()η′ esc(black circles) and dΩdσp(red lines) infexp
theory)η′ esc(based on Ref.[44] without using
0 MeV < Eex − E0γγ < 50 MeV. The original dΩdσp
Figure 7.4: The Eγ dependence of

dσ
dΩpf

)η′ escftheorythe Fermi averaging method is shown by the blue line. The theoretical calculations after thenormalization are shown in green lines.

η ′ escape process:
(
(

dσ
dΩpf
dσ
dΩpf

)η′ esc= 173.8 nb/sr (V0 = −100 MeV),(7.12)= 159.1 nb/sr (V0 = −20 MeV).

(7.13)

theory)η′ esctheoryAs shown in the previous section, the experimental cross section in 0 < Eex − E0 < 50 MeV,
averaged over Eγ = 1.28 − 2.4 GeV is
(

dσ
dΩpf

)η′ esc= 60.2 ± 15.4(stat) ± 4.1(syst) nb/sr.

(7.14)

exp

By substituting the above values and the experimental cross section in Eq.(7.14) to Eq.(7.10),
we obtained
F = 0.35 ± 0.09(stat) ± 0.02(syst) (V0 = −100 MeV),
F = 0.38 ± 0.10(stat) ± 0.03(syst) (V0 = −20 MeV).
89(7.15)(7.16)

The theoretical cross sections after the normalization correction are shown with green lines
in Fig.7.4. The diﬀerence between two V0 cases is too small to distinguished each other.

7.2.5

Cross section of the (η + ps ) coincidence reaction

As described in section 7.2.3, the theoretical production cross section of the η ′ bound states
coincidence with (η + ps ) emission can be described as
(

dσ
dΩpf

(

)η+ps
=F×
theorydσdΩpf)η′ abs
ηps× Brη′ N →ηN × Psrv.

(7.17)

theoryF is obtained as in Eq.(7.15) and (7.16). We describe the details of other variables in thissection.
The cross section of the η ′ absorption process
The calculation results of the theoretical cross section of the η ′ absorption process integrated
over −50 MeV < Eex − E0 < 50 MeV and averaged over Eγ = 1.28 − 2.4 GeV indicated inEq.(7.8) are
(
(

dσ
dΩpf
dσ
dΩpf

)η′ asb= 292.2 nb/sr (V0 = −100 MeV),(7.18)= 79.7 nb/sr (V0 = −20 MeV).

(7.19)

theory)η′ abstheoryBranching fraction of the η ′ N → ηN process
The branching fraction of the η ′ N → ηN process in all the absorption process, Brη′ N →ηN , isunknown. An η ′ is mainly absorbed through either single-nucleon absorption (η ′ N → M B)
or two-nucleon absorption (η ′ N N → N N ) processes [69]. Here, M and B denote a mesonand a baryon, respectively. From the calculation within a chiral unitary approach in Ref.[69],the fraction of the single-nucleon absorptions process is expected to be between 40–97%.
Thereby, we expect that the fraction of the single-nucleon absorptions process is similaror larger compared with the fraction of the two-nucleon absorption process. From the samechiral unitary approach calculation in Ref.[43], the η ′ N → ηN process is considered to account
80% the single-nucleon absorption processes. For example, if the proportion of single-nucleon
absorptions is 50% of all absorption processes and the η ′ N → ηN process accounts for 80%of the single-nucleon absorption processes, Brη′ N →ηN is given by 50% × 80% = 40%. Because
the reliability of the evaluation of the branching fraction within the chiral unitary approachis unknown, we treated Brη′ N →ηN is an unknown value when we evaluate the η ′ -nucleus
potential. We assumed that Brη′ N →ηN is independent on Eex in −50 MeV < Eex − E0 <50 MeV.
90

Survival probability of (η + ps ) pairηps
ηps
We evaluated the survival probability of η and ps , Psrv
for cos θlab
< −0.9 by the quantum molecular dynamics (QMD) transport model calculation [57]. The details of th QMD
simulation is described in Appendix E. The primary reactions are η ′ p → ηp or η ′ n → ηn.
ηpsIn the case of the η ′ p → ηp reaction, Psrv
is 25.2%, which is consistent with the measured
transparency of carbon nuclei for η (∼ 44% [59]) and protons (∼ 60% [60–62]). In the case
ηpsof the η ′ n → ηn reaction, Psrv
is 1.2%. By taking a weighted average with the ratio of p/n
11
ηpsin a residual B nucleus, Psrv for the η ′ N → ηN reaction was deduced to be
ηpsPsrv= 12.1%.

(7.20)The uncertainties of the transparency of η and p are considered to be several %. Because
ηpsthey are multiplied and weighted with the p/n ratio, the uncertainty of Psrv
is considered tobe the level of 1%.

7.2.6

ResultIn Fig.7.5, we compare the experimental upper limit of the cross section of the η ′ bound states
(
)η+ps
(
)η+ps
and theoretical cross section dΩdσp, as a function
with (η + ps ) emission dΩdσpffexp
theory()η+psof Brη′ N →ηN . For dΩdσp, we substituted Eqs.(7.15), (7.16), (7.18), (7.19) and (7.20) toftheoryEq.(7.17). We exclude V0 = −100 MeV in Brη′ N →ηN > 24% at the 90% confidence level. The
upper limit of Brη′ N →ηN in the case of V0 = −20 MeV is 80% at the 90% confidence level.

7.3

Comparison with theoretical expectations and pastexperimental results

Comparison with the original DWIA calculation
As shown in section 7.2.4, we found that the DWIA calculation gave larger cross section witha factor of 2.0–4.3 compared with the experimental measurement. In the original DWIA
calculation in Ref.[44], a larger γp → η ′ p elementary cross section of 50 nb/sr in the centerof-mass system (1.25 times larger) was used. In addition, the Fermi averaged elementary crosssection in the laboratory system was not used in Ref.[44]. Thereby, the DWIA calculation
in Ref.[44] gave ∼1.7 times larger cross section than the value shown in this chapter. Thus,
the measured cross section was ∼1/3.4–1/7.3 of the original expectation in Ref.[44].
The expected number of (η + ps ) events in −50 MeV < Eex − E0 < 50 MeV using theoriginal DWIA results in Ref.[44] and Brη′ N →ηN = 40% is 24 and 6.5 events, for the case of
V0 = −100 MeV and V0 = −20 MeV, respectively. It is large enough to determine Brη′ N →ηN
in 0 MeV < Eex − E0 < 50 MeV, where η ′ absorption events are expected in any V0 cases(see Fig.7.3). We found the η ′ cross section is much small compared with the original DWIA
91

[nb/sr]
η+ps(dσ/dΩ)

16
14
12

η’

ηp

-50<Eex-E0 <50 MeV, cosθlabs<-0.9
ηps

DWIA, W0=-12 MeV, Psrv=12.1%
V0=-100 MeV (F=0.35±0.09)

V0=-20 MeV (F=0.38±0.10)

10
8
6
4

experimental upper limit

2
0
0

10

20

30

40

50

(
Figure 7.5: The experimental upper limit of
(
)η+ps
dσ
as a function of Brη′ N →ηN .
dΩp
f

60

dσ
dΩpf

70

80 90 100
Brη’N→ηN [%])η+psat the 90% confidence level, andexp

theorycalculation and we did not observe any events in −50 MeV < Eex − E0 < 50 MeV. Thus, we
treated Brη′ N →ηN as an unknown variable.
Comparison with theoretical expectations
As described in section 1.3, the NJL model and linear sigma model calculations expect
a deep η ′ -nucleus potential, V0 = −150 and –80 MeV, respectively, owing to the UA (1)anomaly term. When we assume the naive expectation of the η ′ N → ηN branching fraction, Brη′ N →ηN > 40%, our results reject such deep potentials. Both theoretical calculations
assume that the strength parameter of the UA (1) anomaly term is independent from the density. A modification of the strength parameter leads diﬀerent V0 . Thus, our result indicatessmaller Brη′ N →ηN than the naive expectation Brη′ N →ηN > 40% and/or a need of modificationof parameters used in the theoretical calculation.
Comparison with the result of the η-PRiME/Super-FRS Collaboration
The η-PRiME/Super-FRS Collaboration evaluated the upper limits of V0 and W0 by comparing their experimental upper limit of the cross section of the p +12 C → d + X reaction andthe theoretical calculation within the same DWIA calculation as ours as shown in Fig.7.6.
[21, 22, 24]. In the DWIA calculation, they used an estimated elementary cross section of92

the pn → η ′ d process because there is no experimental measurement. They estimated theuncertainty of the elementary cross section is a factor of ∼2. In addition, they were notable to evaluate the normalization factor F of the DWIA calculation itself because they did
not tag decay products. Our result indicates that there is uncertainty of F with a factorof 2.0–4.3 even if we use the measured elementary cross section. In total, the uncertaintyof the absolute value of their theoretical cross section is ∼4.0–8.6. Thereby, the total normalization factor can be smaller than 1/4, which is out of their evaluation range shown in
Fig.7.6. The uncertainty of our measurement is much smaller compared with the ones by
the η-PRiME/Super-FRS Collaboration because we obtained F from the elementary crosssection of the γp → η ′ p process.

Figure 7.6: The obtained upper limit of (V0 , W0 ) by the η-PRiME/Super-FRS Collaboration[21]. The numbers indicate the normalization factor of the theoretical cross section.

Comparison with the result of the CBELSA/TAPS Collaboration
The CBELSA/TAPS Collaboration deduced V0 = −(39 ± 7(stat) ± 15(syst)) MeV by comparing their experimental cross sections of the η ′ escape process with the theoretical crosssections calculated with a collision model. Our result is consistent with their result. Although
the DWIA calculations are widely used for describing bound states, such as hypernuclei andpionic atoms, the collision model is not. Thereby, the reliability and the uncertainty of thecollision model are unknown. The reproducibility of the known bound states is the advantageof the DWIA calculation used for our analysis.

93

Chapter 8
Summary and prospects
An η ′ meson is an interesting probe to investigate hadron masses in a finite density, where
the partial restoration of chiral symmetry is expected. Several model calculations expect
large mass reduction of 80 − 150 MeV of an η ′ meson in a nucleus, owing to the reduction of
the UA (1) anomaly. If there is large mass reduction, the system of an η ′ meson and a nucleus
may have a light mass as a bound state. The amount of mass shift can be described withthe real part of the η ′ -nucleus potential, V0 .
We searched for an η ′ -nucleus bound state by using a missing-mass spectroscopy of the
12C(γ, p) reaction. The missing-mass spectroscopy around η ′ -mass threshold suﬀers fromnumerous backgrounds arising from multiple light-meson productions. Therefore, we taggedan (η +p) pair which is the most promising decay mode in one-nucleon absorption of η ′ mesonin a nucleus, η ′ N → ηN [43]. This is the first measurement of the missing mass spectrum
around the η ′ production threshold in coincidence with decay products. We carried out theexperiment in 2015 at the SPring-8/LEPS2 beam line, using the BGOegg detector system.
We measured the γ + 12 C → pf + (η + ps ) + X reaction, where pf is the forward-going proton
pf
emitted in 0.9◦ < θlab
< 6.8◦ , used for the missing mass analysis, and ps is the side-goingps< 138.5◦ . 5.9 × 1012 photon beams in the energy range of
proton emitted in 28.5◦ < θlab
1.3 − 2.4 GeV hit a 2.0-cm thick carbon target.
Although we succeeded to suppress huge background from multi pion production by tagging an (η+ps ) pair, we found that there still remained large background events accompanying
an η meson and a side-going proton in the experimental data. Above the large background, noenhancement was observed around the η ′ production threshold. We found that the remaining
backgrounds are mainly from the γ + 12 C → pf + η + 11 B and γ + 12 C → pf + (η + π 0 ) + 11 B
reactions, in which an η is produced in the primary reaction, and another proton, ps is kickedout by either a primary η, π 0 or pf . We investigated the kinematics of the (η + ps ) pairfrom those background reactions and optimized kinematical selection criteria to suppress the
background events and to enhance the signal events from the η ′ -nucleus bound state. With
the kinematical selections, we reduced the background events associated with an (η + ps ) pair
to 0.4%, while 23% of signal events is preserved. After the kinematical selection, we observed
no signal events in the excitation energy region, −50 MeV < Eex − E0 < 50 MeV, the region
to search for the signal. The upper limit of the production cross section of the η ′ -nucleus
94

ηpsbound state with emission of an (η + ps ) pair in the opening angle of cos θlab
< −0.9 was
obtained to be 2.2 nb/sr at the 90% confidence level.
In addition to the measurement of the η ′ absorption process to search for the bound state,
the missing mass spectrum of the η ′ escape process, γ + 12 C → pf + η ′ + X, was also measured
for the fist time. By measuring the missing mass dependence of the cross section of the η ′escape process, we evaluated the production rate of η ′ meson around the bound state region.
The obtained experimental upper limit of the (η + ps ) coincidence cross section wascompared with the theoretical cross section calculated within a distorted wave impulse approximation (DWIA) in the case of V0 = −100 and −20 MeV, and W0 = −12 MeV. The
calculated cross section is decomposed to the η ′ absorption and escape processes. The DWIA
calculations nicely represent spectral shapes of bound states such as hypernuclei but hardly
reproduce their absolute cross sections. Thereby, we evaluated the normalization factor of
the theoretical cross section by comparing the experimental and theoretical cross sectionsof the η ′ escape process. The obtained normalization factor is in the range of 0.23–0.50,
within the statistical and systematic errors. We compared the theoretical and experimental
cross sections of the η ′ absorption process for diﬀerent V0 cases as a function of Brη′ N →ηN ,the branching fraction of the η ′ N → ηN process in all the η ′ absorption process . We exclude V0 = −100 MeV in Brη′ N →ηN > 24% at the 90% confidence level. The upper limitof Brη′ N →ηN in the case of V0 = −20 MeV is 80% at the 90% confidence level. Our result
indicates smaller Brη′ N →ηN than a naive expectation of Brη′ N →ηN = 40% and/or a shallow
V0 , while theories based on the UA (1) anomaly predict a deep V0 .

If the branching fraction of the one nucleon process is small, we can expect that the branching
fraction of the two nucleon absorption process, η ′ N N → N N is large. The measurement ofthe η ′ pp → pp process is planned in GSI by the η-PRiME/Super-FRS Collaboration [21]. It
is also possible to analyze the η ′ pp → pp mode with the existing BGOegg data although it ischallenging because the protons from the η ′ pp → pp process penetrate BGOegg, and particle
identification and energy measurement are diﬃcult. The measurement of the two nucleon
absorption process will help to diﬀerentiate the two possibilities; small η ′ N → ηN branching
fraction and shallow potential.
In the case of Σ hyper nuclei, one derives the Σ-nucleus potential by comparing thetheoretical and experimental cross sections in wide excitation energy range above threshold [25]. The DWIA calculation used in the present analysis is for the excitation energy in
Eex − E0 ≲ 50 MeV. In this region, there is only 6% of all the experimentally observed η ′meson. Because of small statistics of observed η ′ escape events, we were not able to distinguish diﬀerent V0 cases of the theoretical expected excitation energy spectra. By extending
the DWIA calculation to higher η ′ angular momentum and large excitation energy, we cancompare the experimental and theoretical excitation energy spectra with larger statistics.
Then, we will be able to evaluate the η ′ -nucleus potential from our η ′ escape data.

95

Acknowledgements
I would like to show my greatest appreciation to Prof. Masayuki Niiyama. He has trainedme since I was a master student. His instruction has been always careful and I learned a lot
from him.
I would like to express my gratitude to Prof. Norihito Muramatsu. He led the BGOegg
collaboration as a leader. He helped me a lot on the data analysis. He also carefully proofed
the submitted paper many times.
I would like to thank Prof. Tomofumi Nagae, the leader of the Experimental Nuclear andHadronic Physics Laboratory in Kyoto University. We could develop the RPC detector since
he let me go to the RPC2012 workshop when I was a master student. He also gave me a lotof suggestions to improve this thesis.
I am grateful to Prof. Masaru Yosoi. He taught and helped me many times when we
started the BGOegg experiment and when we took the experimental data.
I appreciate Prof. Hiroaki Ohnishi. We could build the RPC detector thanks to him. He
often encouraged me cheerfully.
I would like to express my gratitude to Prof. Takashi Nakano. The published paper wasmuch improved thank to the suggestion from him. He also supported my life as a scientist
from many aspects.
I greatly appreciate Prof. Hajime Shimizu. He has started the BGOegg experiment. He
gave me a lot of suggestion to improve the published paper. In addition, he often takes careof my life.
I would particularly like to thank Prof. Tomoyuki Maruyama. He helped me a lot for the
QMD simulation. We could carry out the simulation thanks to him.
I am deeply grateful to Prof. Hideko Nagahiro. We could derive the result thanks to her
calculation. She discussed a lot with us and taught us the details of the calculation.
I appreciate Prof. Toru Harada and Prof. Hiroyuki Noumi. They taught me how to carryout the calculation of the Fermi averaging method.
I thank Prof. Megumi Naruki. She gave me a lot of suggestions to improve this thesis.
She also has been taken care of my analysis as a PAC leader.
I particularly thank Prof. Yuki Nozawa. We have been classmates since we were undergraduate students. I could spend a good time in SPring-8 thanks to him.
I owe my gratitude to Dr. Tran Hai Nam, Mr. Toshikazu Hashimoto, Mr. Yuji Matsumura,
Mr. Hirotomo Hamano, Mr. Takuya Shibukawa and Dr. Keigo Miztani. They carried out
important calibrations of detectors needed for this experiment.

96

I would like to show my appreciation to the member of the BGOegg collaboration. We
could start and carry out the experiment thank to the collaborators. I especially thankProf. Takatsugu Ishikawa, Prof. Manabu Miyabe, Prof. Hirohito Yamazaki, Prof. Atsushi
Tokiyasu and Dr. Yusuke Tsuchikawa. They conducted the start-up of the BGOegg experiment. I also thank Prof. Strokovsky, Prof. Wen-Chen Chang, Prof. Jung Keun Ahn,
Prof. Yohei Morino and Prof. Kenneth Hicks. They gave me a lot of suggestions to improve
the published paper. I also appreciate Prof. Takeshi Ohta and Mr. Yuto Kasamatsu and shift
takers who helped to take the experimental data.
I want to thank Prof. Sunyoung Ryu and Prof. Kotaro Shirotori. They cheered me a lot
in my long analysis period at RCNP.
I thank the members of the Experimental Nuclear and Hadronic Physics Laboratory in
Kyoto University. I spent the best time there to carry out researches.
Last but not least, I express my appreciation to my family for their support.

97

Appendix A
Filling pattern of the SPring-8 storagering
In Table.A.1, we summarize the electron filling patterns of the SPring-8 storage ring in thepresent experimental period. In Table.A.1, “filling” means that bunches are in series of every
1.966 ns. We also show illustrations of each filling mode in Fig.A.1–A.5. The figures are from
SPring-8 web site [70].
Table A.1: The electron filling pattern of the SPring-8 storage ring.
mode
bunch
bunch period
A mode 203 bunches
23.6 ns
C mode 11 bunch train × 29
165.2 ns
D mode 1/7-filling × 5 bunches
684.3 ns
E mode 2/29-filling × 26 bunches
165.2 ns
H mode 11/29-filling × 1 bunch
1486 ns98

Figure A.1: A-mode.

Figure A.2: C-mode.

Figure A.3: D-mode.

Figure A.4: E-mode.

99

Figure A.5: H-mode.

100Appendix B
Detector module
In Table.B.1 and B.2, we summarize the supplied power, preamplifier, attenuator and discriminator of each detector. We adjusted the high voltage for the tagger-PL and the BGOegg
channel by channel. We adjusted the high voltage for the tagger-fiber PMT by PMT, thus it
was common for 16 channels. The power supply value of other detectors was common for all
channels or chambers. For the BGOegg and IPS, we used attenuators for charge measurement to reduce charge to meet with a range of analog-to-digital converter (ADC) modules.
The threshold level of discriminators was common for all channels of each detector except
for the tagger-PL.
Table B.1: The supplied voltage, preamplifier and attenuator used for each detector.
Detector
power supply
preamplifierattenuator
Tagger-PL
channel by channel ——Tagger-fiber PMT by PMT——
UpVeto+2200 V——
BGOeggchannel by channel —30 dB (1/31.2)
IPS
common (+67.9 V) LeCroy 612A channel by channelDCsense: +2200 V,
RPA-181—
potential: +100 V
RPC
common (13.5 kV) Ref.[51]—101Table B.2: The discriminator module and threshold of each detector.
Detector
discriminator threshold
Tagger-PL
OULNS
channel by channel
Tagger-fiber LeCroy 4413 common (-20 mV)
UpVetoPhillips 711-20 mV
BGOegg
LeCroy 4413 common (-20 mV)
IPS
LeCroy 4413 common (-60 mV)
DC
RPA-181
common (-600 mV)
RPC
Ref.[51]
common (-50 mV)

102

Appendix C
Photon beam energy calibration
The photon beam energy was evaluated from the track of recoil electrons from backward
Compton scattering. We evaluated the relation of the photon beam energy and tagger fiber
hit position as Eq.(3.1) and (3.3). We derived Eq.(3.1) and (3.3) by simultaneously fitting
expected photon energy of (a) the γ + p → 2π 0 + p reaction, (b) the γ + p → π 0 + pf
and γ + p → η + pf reactions, and (c) the maximum photon beam energy, using the liquidhydrogen target data. Here, π 0 , η, p are detected with BGOegg and pf with the RPC. In theanalysis of the γ + p → 2π 0 + p reaction, we used kinematical fitting and evaluated expected
photon beam energy. In the analysis of the γ + p → π 0 + pf and γ + p → η + pf reactions, weevaluated the missing mass of the p(γ, pf ) reaction and estimated the photon energy which
gives the mass of an η or π 0 meson. As described in section 2.1.3, the maximum photon beamenergy is 2.385 GeV. It is called Compton edge, and the maximum tagger fiber number which
had entries corresponds to the Compton edge. In Fig.C.1, we show the two-dimensional plotof the predicted photon beam energy from the analysis (a)-(c), and fiber hit position. We
fitted data points with quartic functions and obtained Eq.(3.1) and (3.3).
The photon energy resolution was evaluated using the γ + p → π 0 η + pf reaction withthe liquid hydrogen target. The photon beam energy was predicted with a kinematicalfitting using measured momentum of π 0 , η and pf . The sigma of the diﬀerence of themeasured photon beam energy and the predicted photon beam energy was 16.8 ± 0.9 MeV.
The contribution of the detector resolution was estimated to be 11.8±0.2 MeV using a Monte
Carlo simulation. By subtracting the detector resolution, the photon beam energy resolution
was estimated to be 12.0 ± 0.7 MeV.

103

Figure C.1: The two-dimensional plot of the predicted photon beam energy and fiber hit
position. Red open circles are from the analysis (a), blue full circles from (b), and blacksquare from (c). Lines are fitting results with quartic functions. The error bars are shown
although most of them are smaller than the size of circles.

104Appendix D
Timing selection criteria
In this Appendix, we describe the timing selection criteria of BGOegg and the IPS for particle
identifications of γ and ps .

D.1

Selection of gammas

the following timing cut conditions were required for neutral clusters to select events fromgammas.
Clusters in layer 2–20
For the neutral clusters whose core crystal is in layer 2–20, the following timing cut conditions
were required.
• -1.2 ns < Tcls − TRF ,• Tcls − TRF < 1.4 ns (clusters with energy greater than 800 MeV).
• Tcls − TRF < 0.8 ns (clusters with energy smaller than 800 MeV).
The cut conditions were optimized using a data set having two neutral cluster and one charged
cluster in BGOegg and a hit in the RPC. The selection criteria are shown in Fig.D.1 together
with the distribution of the neutral clusters of the (2 neutral + 1 charged + 1 RPC hit) data
sample. By applying those timing cuts, we removed clusters from neutrons which locatesaround Tcls − TRF = 1 ∼ 2 ns. This cut also removed events at around ±2 ns which indicatesmisselection of the RF signal. The cut conditions for events with cluster energy greater than
800 MeV was loosened because the time-walk correction does not work well at large energy
deposit region.
Clusters in layer 21
For the neutral clusters whose core crystal is in layer 21, the following timing cut conditions
were required.
105

Figure D.1: A scatter plot of the energy deposit and hit timing of neutral clusters in layer
2-20, in the (2 neutral + 1 charged + 1 RPC hit) data sample. The selection criteria areshown with black lines.

Figure D.2: A scatter plot of the energy deposit and hit timing of neutral clusters in layer 20,
21 and 22, in the (2 neutral + 1 charged + 1 RPC hit) data sample. The selection criteria
for layer 21 are shown with black lines.

• -1.2 ns < Tcls − TRF < 1.2 ns.
Figure D.2 shows a scatter plot of the energy deposit and hit timing of neutral clusters inlayer 20, 21, 22 of the (2 neutral + 1 charged + 1 RPC hit) data sample. Because of low
statistics, the time-walk corrections do not properly work for backward kayers, the layer 21
and 22. Thereby, we applied looser cut for layer 21 than ones for other layers. The cut
criteria are shown in Fig.D.2 (b). As described in section3.3, clusters in the most outer layer
22 were not used for the analysis.
106

D.2

Selection of protons

BGOegg timing selection
Figure D.3 shows a scatter plot of the hit timing and the energy deposit of the charged
cluster of the (η + 1 charged + 1 RPC hit) data sample after the energy deposit selection
described in chapter 4. There are some events around Tcls − TRF = 0 ns. They are considered
to be events in which a proton had kinetic energy greater than 450 MeV and penetrated
the BGOegg. We removed such events at −3σ shown with a red line in Fig.D.3. The cut
is applied when the cluster energgy is greater than 60 MeV. Below 60 MeV, the BGOegg
crystal response is slow and thus timing cuts were not applied. The cluster energy dependent
timing resolution σ is evaluated using the γ + 12 C → (ω + ps ) + X data sample.

Figure D.3: A scatter plot of the hit timing and the energy deposit of the charged cluster ofthe (η + 1 charged + 1 RPC hit) data sample. The −3σ selection criterion is shown with a
red line.

IPS timing selection
Figure D.4(a) shows a scatter plot of the hit timing and the energy deposit of the IPS of thecharged particle of the (η + 1 charged + 1 RPC hit) data sample after the energy deposit
selection and the BGOegg cluster timing selection. The time-walk correction of the IPS
was carried out period by period and channel by channel at a cluster energy in the rangeof 185–245 MeV. The correction obviously does not work properly at high energy deposit
region. Thereby, an additional time-walk correction were carried out which uses a common
107parameter for all periods and all channels. The distribution after the additional time-walkcorrection is shown in Fig.D.4(b). We select the region in ±1 ns.

Figure D.4: A scatter plot of the energy deposit and the hit timing of the IPS before (a) after(b) an additional time-walk correction. The selection criteria are shown with black lines.

108Appendix E
QMD model calculation
In this Appendix, we describe the details of the quantum molecular dynamics (QMD) modelηpcalculation used for evaluating the probability Psrv
that an (η + ps ) pair is emitted back-toback after interactions in a nucleus.

E.1

Basic description

The quantum molecular dynamics (QMD) model is originally developed to simulate behaviorof particles in heavy ion collisions. In the QMD model, the time evolution of particles
is calculated taking into account a Newtonian equation and two body interactions. The
QMD calculation is used together with the statistical decay model (SDM). The QMD model
is for dynamical process such as direct reactions in 10−22 s, and the SDM model is forstatistical process such as nuclear fissions and decays in 10−21 − 10−15 s. The details of the
QMD simulation is described in Ref.[57]. In the original QMD package in Ref.[57], only
the interaction of nucleons, pions and excited states of nucleons are implemented and theinteraction of η mesons is not implemented. Kinoshita et al. implemented the interactionof η mesons to the QMD simulation to describe photoproduction of η oﬀ nuclei targets [58].
We used the program developed by Kinoshita et al. and studied the interaction of η mesonand nucleons from the η ′ N → ηN process.

E.2

Signal simulation

We implemented the reaction in Eq.(1.29) as follows. A photon beam is injected to a 12 C
target, and then a forward going proton pf is emitted. The remaining momentum after theemission of pf is shared with the residual 11 B nucleus. The remaining energy is given toa nucleon and the nucleon become a N ∗ state. Then, the N ∗ decays to an η meson and anucleon back-to-back in the center of mass (CM) frame. Because the remaining momentum
is shared with the 11 B nucleus, the momentum of N ∗ is small. Thereby, the initial opening
angle of η − N is back-to-back even in the laboratory system. We simulated the interaction
ηpsthatof the η and N in the nucleus with the QMD model and evaluated the probability Psrv
109ηpan (η + p) pair is emitted in cos θlab
< −0.9 after the interaction. Most of such events arefrom N ∗ → ηp. N ∗ → ηn events are also included, in which the neutron kicked out a proton
when they interacted.
The input variables of the simulation are the photon beam energy and momentum of
pf . The kinematics of the (η + N ) depends only on the diﬀerence of the incident photon
momentum and the forward proton momentum. Thereby, we fixed the incident photon
energy to 2.4 GeV. We varied the pf kinetic energy in 1.10–1.72 GeV, which corresponds tothe excitation energy of −300 MeV < Eex − E0 < 300 MeV. We changed the pf initial polar
angle in −12.6 ∼ +12.6 degree. The angle can be changed after the interaction of the pf
with the nucleus. We selected the events in the RPC acceptance after the interaction with
nuclei.

E.3

Detector acceptance and resolution

The detector acceptance and resolution were implemented as follows. First, the events inwhich the pf angle is in the RPC acceptance is selected. The two gamma decay of η mesons
is simulated by using TGenPhaseSpace of ROOT [71]. The events in which two gammas andps are in the polar angle of 27.5–138.5 degree, corresponding to the BGOegg layer 2–21, wereselected. We implemented the gamma and ps energy resolution depending on the particle
energy, which is evaluated from the γ +p → η +p, γ +p → ω +p and γ +p → 2π 0 +p reactions
with the liquid hydrogen target. We implemented the photon beam energy resolution of
12.0 MeV. The RPC time resolution is 80 ps and the pf energy resolution depends on theenergy of pf . We evaluated the pf energy resolution with the weight of pf energy distribution
with the BCS photon beam energy distribution.

110Appendix F
Detector acceptance and eﬃciency
In this Appendix, we describe the details of the systematic uncertainty of the detector acceptance and how we evaluated the detector eﬃciencies.

F.1

Systematic uncertainty of the acceptance

F.1.1

Acceptance for (η + ps )We evaluated the acceptance including the reconstruction eﬃciency of (η + ps ) using a Monte
Carlo (MC) simulation. We carefully compared the MC and experimental data and foundthat there are diﬀerences in the fraction of the leak cluster, charge misidentification rate with
the IPS, and energy deposit calibration of the IPS. We took into account the diﬀerences when
we calculate the acceptance.
Leak cluster
As described in section 3.3.2, the number of BGOegg clusters can be more than 3 even when
only 3 particles (2γ’s and a proton) entered to BGOegg, because of the interactions in thedetector. In the present analysis, we assumed that clusters satisfying the following conditions
are leak cluster and excluded when we count the number of clusters:• Cluster energy is less than 60 MeV.
• Cluster hit timing Tcls − TRF > 3 ns.
• There is a gamma cluster in the distance less than 140 mm.
We examined the fraction of events having (a) leak cluster(s) and it is (8.9 ± 1.5)% in theexperimental data and 11.0% in the MC data. We note that we do not require Tcls − TRF >3 ns in the MC. There is a large diﬀerence of Tcls − TRF distribution between the MC andexperimental data. In the MC, all events are in Tcls − TRF < 3 ns, whereas most of events
are in Tcls − TRF > 3 ns in the experimental data. We took into account the diﬀerence of thefraction 11.0-(8.9-1.5)=4.0%, as a systematic uncertainty coming from the cluster counting.
111

Charge misidentification rate
When we identify that a particle in BGOegg is neutral, we required that the energy depositin the IPS is smaller than certain value. (See section 3.4). However, there are cases that a
γ is converted to an e+ e− pair in the target or the IPS and identified as a charged particle.
We examined the probability that a γ is identified as a charged particle using the γ + 12 C →pf + η ′ + X reaction in both the experimental and MC data. In the experimental data, weη ′ pfrequired −100 MeV < Emiss= Eγ + M12 C − M11 B − Eη′ − Epf < 0 MeV, where sample is cleaneven we remove the charge identification information of γ’s. The probability that one of γ
from an η ′ meson is identified as a charged particle is (89.12±2.65)% in the experimental data
and 92.11% for the MC data. Thereby, we derived the correction factor of the acceptance on
the charge misidentification rate to be (89.12 ± 2.65)/92.11 = (96.75 ± 1.57)%.
Energy deposit in the IPS
As described in section 4.4.3, we carried out the particle identification of side-going proton
by using the diﬀerence of the energy deposit in the IPS and expected energy deposit froma PSTAR calculation. The conversion factor of the unit of the PSTAR calculation (MeV)
to the unit used for the IPS of the MC was optimized to reproduce the distribution of theexperimental data. We tested two extreme cases of the conversion factor and the resulting
acceptance was 14.2% and 14.1%. We took into account this diﬀerence to the systematic
uncertainty.

F.1.2

Acceptance for pf

As describe in section 6.1.4, pf can interact in the target and can change its direction or
create an additional particle. We evaluated the acceptance for pf of the DC using a MC
simulation. We generated the γ + p → η ′ + p reaction requiring that the original forward
proton angle is less than 7◦ which is the region covered with the RPC. The fraction of events
that the number of DC tracks equals one was 94.7%. 2.2% of events had no track in the DC
and 3.3% of events have more then one track.
We compared the fraction of events with more than one track in the MC and experimental
data using a clean sample of the γ + p → η ′ + p reaction. We required that the number of
BGOegg cluster is two and the invariant mass of 2γ is more than 700 MeV/c2 . In the MC,
the fraction of events with more than one track is 1.5%. On the other hand, it is (2.0 ± 0.1)%
in the experimental data. We took in to account the diﬀerence (0.5%) to the systematic errorof the DC acceptance for pf .

112

F.2

Eﬃciency

F.2.1

TaggerTagger PL intrinsic eﬃciency
We evaluated the intrinsic eﬃciency of the tagger-PL using the liquid hydrogen target data.
Because a pair-PL hit is required at the trigger of the data acquisition, we used events with
two tracks. An example of events used for the eﬃciency measurement is shown in Fig.F.1.
When we measured the eﬃciency of the forward PL 3 (blue), we required two fiber clusters
consist of both fiber layers, another pair PL hit and a hit in the backward PL 3 (red). We
evaluated the eﬃciency PL by PL, and electron filling pattern by pattern. We found that the
PL dependence and the filling pattern dependence of the PL intrinsic eﬃciency is small. We
derived the PL intrinsic eﬃciency to be (98.8 ± 1.2)% by averaging the obtained eﬃciency
over all PL and all experimental period.

Figure F.1: A schematic drawing of the tagger with an example data for the intrinsic PL
eﬃciency measurement.

Tagger track reconstruction eﬃciency
We evaluated the tagger track reconstruction eﬃciency using the γ + 12 C → 2π 0 + p + X
reaction. Because the tagger reconstruction eﬃciency strongly depends on the tagger hit
rate and the filling pattern, we need to evaluate the tagger track reconstruction eﬃciency
using the carbon target data not the liquid hydrogen target data. For the evaluation of thetagger track reconstruction eﬃciency, we used two data samples; the loose cut sample andthe tight cut sample. Both samples detected 2π 0 + p with BGOegg. The loose cut sample
did not use the RF signal because we require a tagger track when we select the RF signal.
Because we need the RF signal for the particle identification, we did not carry out the particle
identification of charged particles in the loose cut sample and thus there were contaminationof pions to protons. In the tight sample, we selected the RF signal by using the BGOegg
hit timing. In addition, very tight kinematical cut and kinematical fitting were applied. The
tight cut sample is very clean but the statistics is 1/10 of the loose cut sample. Table.F.1
shows the tagger reconstruction eﬃciency measured using both samples. The measurements
113

of two data samples are consistent within the statistical error. In addition, there is no Eγ
dependence. We used the average eﬃciency obtained from the tight sample, (89.9 ± 0.8)%.
Table F.1: The tagger reconstruction eﬃciency.
modeloose sample tight sample
Eγ <1.6 GeV(90.0 ± 0.5)% (90.4 ± 1.5%)
1.6 GeV < Eγ < 1.8 GeV (90.8 ± 0.4)% (90.9 ± 1.8)%
1.8 GeV < Eγ < 2.0 GeV (90.1 ± 0.5)% (87.9 ± 2.8)%
2.0 GeV < Eγ < 2.2 GeV (91.6 ± 0.7)% (91.6 ± 2.0)%
2.2 GeV < Eγ < 2.4 GeV (91.6 ± 1.0)% (88.9 ± 1.6)%
all(90.6 ± 0.2)% (89.9 ± 0.8)%

F.2.2

UpVeto over veto rate

We measured the rate that the UpVeto over veto events with accidental hits. For the evaluation, we used the tight 2π 0 + p sample used for the tagger reconstruction eﬃciency measurement. The obtained over veto rate is (97.84 ± 0.27)%.

F.2.3

DC track reconstruction eﬃciency

We evaluated the DC track reconstruction eﬃciency using the γ + p → ω + p reaction withthe liquid hydrogen target. We used kinematical fitting and required that the proton angle
to be in the DC acceptance. We obtained the DC track reconstruction eﬃciency to be(98.24 ± 0.44)%.

F.2.4

RPC reconstruction eﬃciency

We evaluated the RPC reconstruction eﬃciency using the γ + p → η + p reaction with theliquid hydrogen target. We used kinematical fitting and required a track of proton in the DC
in the RPC acceptance. We obtained the RPC reconstruction eﬃciency to be (95.89±2.32)%.

F.3

Transmission rate

In Fig.F.2, we show the run dependence of the ratio of the number of π 0 tagged with BGOegg
and the number of photons counted with the tagger. We required that the number of tagger
tracks is one and the ratio is shown in ten diﬀerent colors for diﬀerent photon energies. The
electron filling pattern of the SPring-8 storage ring is shown with Alphabets. The ratio is
low in E and D modes because of low detector eﬃciencies. (See section 6.1.6.) In the firstA-mode, we observed drop of the ratio depending on the photon energy. This is considered
to come from the low transmission rate of photon beam coming from bad tuning of the 5th114mirror angle for laser injection (see section 2.1.2). When the mirror angle is bad and theelectron-laser collision point is downstream of the straight line, electrons and laser do notcollide at 180◦ because electrons are bent at the downstream of the straight line. Then, thescattered photon angle is also change and some of photons do not pass the collimator in the
beam line (see Fig.2.3). As in Eq.(2.1), the photon energy depends on the scattered angleof the photon beam. Therefore, there is Eγ dependence of the transmission rate in the firstA-mode. The overall drop of the transmission rate in A-mode is corrected with the fillingmode dependence correction factor described in section 6.1.6, which is independent with Eγ .
We ignored the Eγ dependence of the transmission of the first A-mode because its fraction(0.2%) is negligibly small compared with the statistical uncertainty of the Eγ dependence ofthe filling mode correction factor (5%).

Figure F.2: The run dependence of the ratio of the number of π 0 tagged with BGOegg andthe number of photons counted with the tagger.

115

Appendix G
Theoretical estimation of the crosssectionWe evaluated the expected production cross section of the η ′ -nucleus bound state in a frame
work of a distorted wave impulse approximation (DWIA). In this Appendix, we describe how
we calculated the expected cross section.

G.1

Overview

As described in section 7.2, we calculated the excitation energy spectra within DWIA as(d2 σdΩpf dEex)γ+12 C→p+η′ ⊗11 B(=

theory(Here, Eex is the excitation energy,)γ+p→p+η′dσ(Eex )
× R(Eex ).
dΩpf
lab

(G.1)

)γ+p→p+η′dσ(Eex )dΩpf

the Fermi-averaged cross section
labof the elementary γ + p → p + η ′ reaction [66], and R(E) the nuclear response function.
The excitation energy spectra are calculated for the cases of V0 = −20, −100 MeV andEγ = 1.5, 2.05, 2.5 GeV. We evaluated expected cross section averaged over Eγ in the following
procedure.
1. Calculate R(Eex ),(2. Calculatedσ(Eex )
dΩpf)γ+p→p+η′,lab

3. Integrate over Eex ,4. Average over Eγ .
We describe the details of each procedure in the following sections.

116

G.2

Nuclear response function R(Eex)

The nuclear response function R(Eex ) is calculated by Nagahiro with Green’s function method
as described in Ref.[44]. The Green’s function G(Eex ) of the γ + 12 C → p + η ′ ⊗ 11 B reaction
is defined as
G(Eex ; r, r ′ ) = ⟨p−1 |ϕη′ (r)1ϕ†η′ (r ′ )|p−1 ⟩ ,Eex − Hη′ + iϵ

(G.2)

where ϕ†η′ is an η ′ creation operator and |p−1 ⟩ is a proton hole state. The Hamiltonian Hη′contains the η ′ -nucleus potential U in Eq.(1.26). The response function R(E) is calculatedas∫
1 ∑R(Eex ) = − Im
drdr ′ Tf† (r)G(Eex ; r, r ′ )Tf (r ′ s),
(G.3)
π
f
where the summation is inclusively taken over all possible final states. The amplitude Tf
describes the transition of the incident photon to a proton hole and the outgoing proton;
Tf ((r)) = χ∗f (r)[Ylη∗′ (r̂) ⊗ ψjp (r)]JM χi (r),(G.4)

where ψjp is a proton hole wave function, χi and χf are distorted wave functions of initialand final particles, and Ylη′ (r̂) is an η ′ angular function. The calculation is carried out up
to lη′ = 6. The calculation results for Eγ = 2.5 GeV and several θp and V0 cases shown
in Ref.[44] is shown in Fig.G.1. Note that in Fig.G.1, the elementary cross section in the)γ+p→p+η′(= 519 nb/sr (1◦ ), 504 nb/srlaboratory frame without Fermi averaging, dΩdσp (Eex )flab(6◦ ) and 472 nb/sr (11◦ ) is multiplied in the Y axis. We can see R(Eex ) by multiplying)γ+p→p+η′(.
1/ dΩdσp (Eex )flab

R(Eex ) contains both η ′ escape and absorption processes. The decomposed calculation
was done only for V0 = 0, −100 MeV, Eγ = 2.5 GeV and the forward proton angle θpF orward= 1◦ case. If V0 is the same, the peak position of each η ′ and proton hole orbit is the samefor diﬀerent Eγ and diﬀerent proton angle. Only peak heights change depending on the Eγ
and proton angle. We assumed that the η ′ escape and absorption ratio is the same for thesame orbit of diﬀerent Eγ and diﬀerent proton angle. Then, we obtained η ′ escape spectraand η ′ absorption spectra separately for Eγ = 1.5, 2.05 GeV and θpF orward = 6◦ cases. We
used the escape/absorption ratio of V0 = 0 MeV case to obtain V0 = −20 MeV spectra.

G.3

Fermi averaging method

As described in section 7.2.4, we found that the Fermi averaging method is necessary toobtain Eγ dependence similar to the experimentally observed one. We calculate the Fermi
averaged cross section by weighting the elementary cross section in the laboratory frame with
the Fermi momentum distribution. The cross section in the laboratory frame is obtained by117

Figure G.1: The calculation result shown in [44].

transforming the cross section in the center-of-mass frame taking into account the target
proton Fermi momentum. We describe details of the calculation of the Fermi averaged crosssection.

G.3.1

Formalism

In Fig.G.2, we illustrate γ + p → η ′ + p reaction with Fermi motion. “pFermi” indicates thetarget proton which have Fermi motion and’ “pForward” indicates the scattered proton. The

118

Fermi averaged cross section is calculated as()γp→η′ pdσ(Eγ , ω, q)
dΩpf
lab
(
)γp→η′ p
∫ π
∫ ∞
dσ
2
sin θpF ermi dθpF ermi dppF ermi ppF ermi ρ(ppF ermi )(Eγ , ppF ermi , ω, q)dΩpf lab
0
0
∫ π
∫ ∞
=
sin θpF ermi dθpF ermi
dppF ermi p2pF ermi ρ(ppF ermi )
0

0

(G.5)
ppF ermi =p∗pF ermi

where
ω = Eγ − EpF orward ,q = pγ − ppF orward .

(G.6)
(G.7)

ρ(ppF ermi ) is the nucleon momentum distribution, and p∗pF ermi is a solution of the following
equation:√√(p∗pF ermi + q)2 + m2η′ − (p∗pF ermi + m2p )ω =≃ mη ′ − mp +
(

dσ
dΩpf

)γp→η′ plabp∗pF ermi · q mη′ − mp p∗2
q2
pF ermi
−
+
.
2mp
mη ′
mη ′
2mp

(G.8)

is the elementary cross section of the γ + p → η ′ + p reaction in the laboratory

system.

Figure G.2: The illustration of the γ + p → η ′ + p reaction with Fermi motion.

119G.3.2

Nucleon momentum distribution

For nucleon momentum distribution ρ(ppF ermi ), we used the harmonic oscillator model usedin [64]. For the case of carbon nuclei,
4b3
2 4b3
ρ(ppF ermi ) = 2 × √ exp(−b2 k 2 ) + 4 × × √ b2 k 2 exp(−b2 k 2 ),3ππ
b = 1.93,
ppF ermi = ℏk.

G.3.3

(G.9)
(G.10)(G.11)

Elementary cross section in the CM system

Interest kinematical region()γp→η′ p()γp→η′ pdσdσ
We calculated dΩpfrom the cross section in the center-of-mass system, dΩp
,
f

f

lab

CM

measured by the LEPS and the CBELSA/TAPS
collaboration. When we include the Fermi√
motion, the center-of-mass energy, s, and the center-of-mass angle, θηCM
, regions involved′in the reaction are wider than the case of a proton target√ at rest with the same beam energy
regions involved in ourand detector acceptance. Thereby, we examined the s and θηCM′
measurement
when Fermi motion is taken into account. Figure G.3 shows two dimensional√
vs Eex − E0 satisfying Eq.(G.8) for the case of highest beam energy
plots of s and θηCM′
Eγ = 2.4 GeV, and the proton angle at 6◦ . The distributions are weighted√ with the Fermi
momentum distribution in Eq.(G.9). We can see that the events in s < 2.5 GeV andθηCM> 160◦ (cos θηCM
< −0.94) are dominant when we weight with Fermi momentum.
′′√
Figure G.3: The s and θηCMvs missing mass distributions satisfying Eq.(G.8) with the′
Fermi weight for the case of Eγ = 2.4 GeV and the proton angle at 6◦ .

120

Elementary cross section
Figure G.4 shows the diﬀerential cross section of the γ + p → η ′ + p reaction in CM system< −0.9 reported by the LEPS and the CBELSA/TAPS collaborationsin −1.0 < cos θηCM′
[67, 68]. Those measurements cover the kinematicalregion discussed in the previous section.
√√
The LEPS data shows bump at around s = 2.35 GeV and decrease with increasing s
although the error is large. There√ is no bumb structure in the CBELSA/TAPS data. Thereis a strong correlation between s and the excitation√ energy as can be seen in Fig.G.3. The
bump structure of the cross section depending on s leads a bump structure in the excitationenergy spectrum. We have the value of R(E) only for discrete Eγ , 1.5, 2.05, 2.5 GeV, andobtain the expected yield√ from these three points. It is not appropriate to reflect a bump
structure in the small s region to estimate yield in wide Eγ region. Thus, we assumed thatthe diﬀerential cross section is constant at 40 nb/sr in the CM system when we calculate()γp→η′ pdσ(shown by the green line in Fig.G.4).
dΩp
f

lab

Figure G.4: The diﬀerential cross section of γ + p → η ′ + p in −1.0 < cos θηCM
< −0.9′measured by the LEPS and CBELSA group. The figure is from [67].

G.3.4

Elementary cross section in the laboratory system

Even the cross section in the CM system is constant in the kinematical region interestedin, the cross section in the laboratory system is not. The transformation factor of the crosssection from the CM system to the laboratory system depends on Eγ , ppF ermi and ppF orward .
121

The transformation is done using the generalized CM to laboratory transformation factor of
the cross section as()γp→η′ p)γp→η′ p(√dσ
ppF orward
s
dσ
= CM
dΩpf lab
ppF orward Eγ+EpF ermi −(Eγ cosθpF orward +ppF ermi cosθpF ermi )EpF orward dΩpf CM
ppF orward√√s = (Eγ + EpF ermi )2 − ((ppF ermi sin θpF ermi )2 + (Eγ + ppF ermi cos θpF ermi )2 ). (G.12)

G.3.5

Numerical result(

Figure G.5 shows the numerical results of the Fermi-averaged cross section,
as a function of the excitation energy.

dσ(Eγ , ω, q)dΩpf)γp→η′ p,lab

Figure G.5: The excitation energy dependence of the Fermi averaged cross section for diﬀerent
Eγ cases. The forward proton angle is 6◦ .

G.4

Inclusion of the detector resolution)η′ abs( 2
σandThe green lines of Fig.G.6 and Fig.G.7 shows the calculation results of dΩpd dEexf( 2)η′ esc()γp→η′ pd σ, respectively. We substituted R(Eex ) and dΩdσpin Eq.(G.12) to Eq.(G.1).
dΩp dEexfflab

To compare the theoretical expected cross section with the experimental cross section, we
included detector resolution to the theoretical excitation energy spectra. The details of the
inclusion of the detector resolution is described in the following sections.

G.4.1

The detector resolutions

The following detector resolutions were implemented to the theoretical excitation energy
spectra:122( 2)η′ absσFigure G.6: Calculation results of dΩpd dE.
exf
50 MeV < Eex − E0 < 70 MeV by linear functions.

The lines are the fitting results in• Eγ resolution = 12.0 MeV,
• TOF time resolution for EpF orward measurement = 80 ps,• the ambiguity of the energy deposit in the target = 1.8–3.6 MeV depending on theforward proton momentum.
The excitation energy resolution as a function of Eγ is shown in Fig.G.8.
′
For the η ′ escape measurement, we use Eex − E0η = M M (12 C(γ, p)) − M11 B − Mγγ insteadof M M (12 C(γ, p)) − M11 B − Mη′ . We used
• Mγγ resolution = 17.8 MeV,
which is the measured value.

G.4.2

The treatment above Eex − E0 = 50 MeV

After including the detector resolution, events in Eex − E0 > 50 MeV contaminate to Eex −E0 < 50 MeV. Thus, we need the expected cross section above Eex − E0 = 50 MeV. For the
123

( 2
)η′ escσ
Figure G.7: Calculation results of dΩpd dE. The lines are the fitting results in 0 MeV <exfEex − E0 < 50 MeV. by linear functions.

escape spectra, we fit 0 MeV < Eex − E0 < 50 MeV by linear functions and extend the value
up to Eex − E0 = 100 MeV. For the absorption spectra, we fit 50 MeV < Eex − E0 < 70 MeV
by linear functions and extend the value up to Eex − E0 = 100 MeV. The fitting results areshown by the red and blue lines in Fig.G.6 and G.7.

G.4.3

Excitation energy spectra

Figure G.9 and Fig.G.10 show the excitation spectra after including the detector resolutions
for the η ′ absorption mode and the η ′ escape mode, respectively. For the case of η ′ escapemode, we have more events below 0 MeV with larger Eγ because of the bad excitation resolution at large Eγ . We integrated the cross sections after inclusion of the detector resolution,over −50 MeV < Eex − E0 < 50 MeV and 0 MeV < Eex − E0 < 50 MeV, for the η ′ absorption
and escape process, respectively.

124

Figure G.8: The excitation energy resolution as a function of Eγ used for the η ′ absorption
mode.

(
Figure G.9:d2 σdΩpf dEex)η′ abs
including the detector resolutions.

125(Figure G.10:

d2 σdΩpf dEex)η′ escincluding the detector resolutions.

126

G.5

Eγ dependence

The Eγ dependence of the integrated cross section and the experimental cross section of theη ′ escape process are shown in section 7.2.4. They have consistent Eγ dependence. The Eγ
dependence of the integrated cross section of the η ′ absorption process is shown in Fig.G.11.
We fit the 3 points with a quadratic function. The fitted function is used for evaluating the
average cross section over Eγ .

Figure G.11: The Eγ dependence of the integrated cross section of the η ′ absorption processof the DWIA calculation.

G.6

Expected cross section

We evaluated the expected cross section by averaging the fitted function in Fig.7.4 and
Fig.G.11 over Eγ = 1.28 − 2.4 GeV, with the weight of the Eγ distribution of the backward
Compton scattering shown in Fig.2.5. The obtained cross section is summarized in Table.G.1.
Table G.1: The expected cross section with the DWIA calculation.
mode
η escape (0 MeV < Eex − E0 < 50 MeV)
η ′ absorption (−50 MeV < Eex − E0 < 50 MeV)′

127

V0 = −20 MeV
159.1 nb/sr
79.7 nb/sr

V0 = −100 MeV
173.8 nb/sr
292.2 nb/sr

G.7

pf polar angle dependence

Figure G.12 shows the excitation energy distributions of the η ′ escape events of the experimental data at θpF orward < 3◦ and θpF orward > 5◦ in Eγ >1.8 GeV. The number of events isincreasing together with excitation energy in 0 MeV < Eex − E0 < 100 MeV. Figure G.13
shows the excitation energy distributions of the η ′ escape events of the DWIA calculation at
θpF orward = 1◦ and 6◦ at Eγ = 2.5 GeV. In the case of θpF orward = 1◦ , the cross section starts

Figure G.12: The excitation energy distributions of the η ′ escape events of the experimental
data in θpF orward < 3◦ and θpF orward > 5◦ in Eγ > 1.8 GeV.

Figure G.13: The expected excitation energy distributions at θpF orward = 1◦ and 6◦ at Eγ =2.5 GeV based on the DWIA calculation.

128

to decrease at around Eex − E0 = 30 MeV. It is not consistent with the measurement. Thus,
we used only the calculation of θpF orward = 6◦ for the yield estimation.

129

Appendix H
The measurement of the η ′ escapeprocess
In this Appendix, we describe the details of the cross section measurement of the η ′ escapeprocess. We also show the comparison of the cross section measured by the CBELSA/TAPS
Collaboration.

H.1

Definition of the excitation energy

The definition of the excitation energy used for the (η + ps ) measurement is as follows:
Eex − E0η′

= M M (12 C(γ, pf )) − M11 B − Mη′ ,(H.1)

As described in chapter 5, instead of Eq.(H.1), we used the following definition of the excitation energy for the η ′ escape measurement:
Eex − E0γγ = M M (12 C(γ, pf )) − M11 B − Mγγ .

(H.2)

Here, we replaced the η ′ mass, Mη′ , with the invariant mass of two γs, Mγγ . We used thedefinition in Eq.(H.2) so that we can use the side band events of the invariant mass peakfor evaluating background events. It is clearly shown in Fig.H.1. In Fig.H.1(a) and (b), weshow two dimensional plots of the invariant mass of two γs and the excitation energy withthe definition in Eq.(H.1) and (H.2), respectively. When we use the definition in Eq.(H.1),
there is a correlation between the invariant mass and the excitation energy. Therefore, wecannot use the side band events of the invariant mass peak when we evaluate the background
events depending on the excitation energy. On the other hand, when we used the definition
in Eq.(H.2), we can use the invariant mass sideband events for evaluating background contamination. The energy resolution of the definition in Eq.(H.2) is worse than in Eq.(H.1)
with the invariant mass resolution, σMγγ = 17.8 MeV. This resolution is taken into accountfor the theoretical cross section described in Appendix G.

130Figure H.1: The two dimensional plots of the invariant mass of two γs and the excitationenergy with the definition in Eq.(H.1)(a) and (H.2)(b).

H.2

Eγ dependence of the cross section

The Eγ dependence of the cross section in diﬀerent excitation energy region is shown in
Figure H.2. The data points are common to Fig.7.1 and just the axis is diﬀerent.

H.3

Comparison with the measurementby CBELSA/TAPS

The CBELSA/TAPS Collaboration measured the cross section of the γ + 12 C → p + η ′ + X
reaction in 2◦ < θp < 11◦ [34]. They did not measure the proton momentum and thus theircross section is an integrated cross section over all the excitation energy region. Although theproton polar angle region is slightly diﬀerent from our measurement, we compared our crosssection with the one measured by the CBELSA/TAPS Collaboration. In Fig.H.3, we show
the Eγ dependence of the cross section for all excitation energy region of our measurement
in cosθηlab> 0, and the measurement by CBELSA/TAPS Collaboration [34]. In order to′compare with the measurement by CBELSA/TAPS, we used the same requirements as ones of
CBELSA/TAPS. We required the η ′ kinetic energy < 500 MeV, cos θηCM
< 0, and multiplied′a shadowing factor = 15%. The shadowing factor represents the absorption of the incoming
photon beam by nucleons. It is introduced just to compare their cross section with theoretical
calculations which are lines in Fig.H.3.
There are several questionable points in the CBELSA/TAPS results. Firstly, the definition of cos θηCM
is ambiguous. In Ref.[34], it is described that they calculated cos θηCM
from
′
′
′
CM
Eγ and the η energy, assuming that the target proton is at rest. In this case, cos θη′ can
not be defined below the production threshold at Eγ = 1.447 GeV. However, there is andata point below Eγ = 1.447 GeV in Fig.H.3. Secondary, the selection range of cos θηCM′
131

Figure H.2: The Eγ dependence of the η ′ coincidence cross section in diﬀerent excitationenergy region.

is ambiguous. Because of the Fermi motion, we have events in cos θηCM< −1 if we use′
the definition above. The cut condition of CBELSA/TAPS is explained as “backward” inthe text and “−1 < cos θηCM< 0” in figures [34]. It is not clear whether they included′CM
events in cos θη′ < −1 when they calculated the cross section. In out data points, events incos θηCM< −1 are included. Thirdly, there is no data point at η ′ kinetic energy > 500 MeV in′
the measurement by the CBELSA/TAPS collaboration. In the BGOegg data, we have several events with η ′ kinetic energy > 500 MeV. The diﬀerence might come from the diﬀerenceof the definition of cos θηCM
. As can be seen in Fig.H.3, the cross sections measured by the′
CBELSA/TAPS and our cross sections were consistent within the statistical error, except
for the lowest energy bin where the dentition of cos θηCM
is ambiguous. The systematic error′of the cross section of the CBELSA/TAPS measurement is 17%.

132

Figure H.3: The Eγ dependence of the cross section of our measurement (yellow) and themeasurement by CBELSA/TAPS collaboration (black), integrated over all the excitationenergy region. The figure is from [34].

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