Proceedings of the 8th International Conference on Quarks and Nuclear Physics (QNP2018)
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Proc. 8th Int. Conf. Quarks and Nuclear Physics (QNP2018)
JPS Conf. Proc. 26, 022014 (2019)https://doi.org/10.7566/JPSCP.26.022014

Non-strange Dibaryon Resonances Observed in Coherent
Double Neutral-Pion Photoproduction on the Deuteron
Takatsugu Ishikawa1 , Hisako Fujimura1,7 , Hiroshi Fukasawa1 , Ryo Hashimoto2,8 ,Qinghua He1 , Yuki Honda1 , Takahiro Iwata2 , Shun Kaida1 , Hiroki Kanda4,13 ,Jirohta Kasagi1 , Atsushi Kawano3 , Shuzo Kuwasaki1 , Kazushige Maeda4 ,Shin’ichi Masumoto5 , Manabu Miyabe1 , Fusashi Miyahara1,9 , Kei’ichi Mochizuki1 ,Norihito Muramatsu1 , Akihiko Nakamura1 , Ken’ichi Nawa1 , Shoei Ogushi1 ,Yasuyuki Okada1 , Yoshihito Onodera1 , Kyoichiro Ozawa6 , Yasunobu Sakamoto3 ,Mamoru Sato1 , Hajime Shimizu1 , Hiroyuki Sugai1,10 , Koutaku Suzuki1,11 ,Yasuhisa Tajima2 , Shin’ichiro Takahashi1 , Yusuke Taniguchi1 , Yusuke Tsuchikawa1 ,Hirohito Yamazaki1,12 , Ryuji Yamazaki1 , and Hiroshi Y. Yoshida1 (the FOREST
collaboration)
1

Research Center for Electron Photon Science (ELPH), Tohoku University, Sendai 982-0826, Japan
Department of Physics, Yamagata University, Yamagata 990-8560, Japan3
Department of Information Science, Tohoku Gakuin University, Sendai 981-3193, Japan
4
Department of Physics, Tohoku University, Sendai 980-8578, Japan
5
Department of Physics, University of Tokyo, Tokyo 113-0033, Japan
6
Institute of Particle and Nuclear Studies (IPNS), High Energy Accelerator Research Organization(KEK), Tsukuba 305-0801, Japan
7
Department of Physics, Wakayama Medical University, Wakayama 641-8509, Japan
8
Institute of Materials Structure Science (IMSS), High Energy Accelerator Research Organization(KEK), Tsukuba 305-0801, Japan
9
Accelerator Laboratory, High Energy Accelerator Research Organization (KEK), Tsukuba
305-0801, Japan10
Department of Quantum Science and Energy Engineering, Tohoku University, Sendai 980-8579,
Japan
11
The Wakasa Wan Energy Research Center, Tsuruga 914-0192, Japan
12
Radiation Science Center, High Energy Accelerator Research Organization (KEK), Tsukuba
305-0801, Japan
13
Research Center for Nuclear Physics, Osaka University, Ibaraki 567-0047, Japan2

E-mail: ishikawa@lns.tohoku.ac.jp(Received January 17, 2019)
A B = 2 system (dibaryon) is an interesting object to investigate a phase change of the basic configuration from a molecule-like state (such as the deuteron) to a spatially-compact hexaquark hadronstate. To study dibaryon resonances, we have investigated coherent double neutral-pion photoproduction on the deuteron in which non-resonant processes are suppressed. The total cross section as
a function of the γd center-of-mass energy shows resonance-like behavior peaked at around 2.47
and 2.63 GeV. The measured angular distribution of deuteron emission is rather flat, which cannot be reproduced by kinematics for quasi-free π0 π0 production with deuteron coalescence. In π0 dinvariant-mass distributions, a clear peak is observed at 2.14 ± 0.01 GeV with a width of 0.09 ± 0.01
GeV. The present work gives strong evidence not only for the 2.14-GeV isovector dibaryon, which
is a key state to establish the theoretically predicted dibaryon sextet, but also for 2.47- and 2.63-GeV
isoscalar dibaryons.
KEYWORDS: Coherent double meson photoproduction, dibaryon resonances

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must maintain attribution to the author(s) and the title of the article, journal citation, and DOI.

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1. Introduction
The study of B = 2 systems (dibaryons) has a long history [1]. A dibaryon is an interesting object to study its basic configuration from a molecule-like state consisting of two baryons (such as thedeuteron) to a hexaquark hadron state, which is expected to appear as a spatially-compact exotic particle. An early work by Dyson and Xuong [2] predicts the sextet of non-strange dibaryons DI J withisospin I and spin J (D01 , D10 , D12 , D21 , D03 , and D30 ) based on the first known dibaryon, deuteron(D01 ), the 1S 0 -NN virtual states (D10 ), and a resonance-like structure (a candidate for D12 ) at M=2.16
GeV/c2 for the 1D2 -pp amplitude of the partial wave analysis for the π+ d → pp reaction [3]. The
recent observations of the d∗ (2380) (D03 ) by the CELSIUS/WASA and WASA-at-COSY collaborations [4, 5] have made us pay attention to this classification. It is important to establish the excitation
spectrum of dibaryons in order to understand their internal structures and basic building blocks ofhadrons. Many experimental investigations of the sextet members have been made, and candidates
for almost all the members seem to be found [6–10]. However, the dibaryonic interpretations of theexperimental data for some members are still questionable.
The candidate for the D12 state is given as the 3P2 multipole strength at M=2.18 GeV/c2 in π± delastic scattering by a partial-wave analysis [6]. The corresponding 1D2 -pp amplitude also shows
the same structure in the π+ d→pp reaction [7]. The SAID group provides a pole for D12 [8] froma combined analysis of these reactions. Although the πd system has a resonance-like structure at
approximately 2.15 GeV/c2 , the structure can be also understood as a quasi-free (QF) ∆ excitationfrom a nucleon in the deuteron. It is important to confirm whether the 2.15-GeV/c2 resonance can beinterpreted as a dibaryon or not. The D12 is a key state to understand the sextet of dibaryons.
In photoinduced reactions, the γd→π0 d reaction is a convenient approach to study D12 . Even if it
is observed, it can be also understood as a quasi-free (QF) ∆ excitation from a nucleon in the deuteronsimilarly to the π+ d → pp and π± d → π± d reactions. The γd→π0 π0 d reaction is more advantageous
to study D12 in the π0 d subsystem because the QF ∆ excitation is kinematically separable as discussed
later. Thus, we study the γd→π0 π0 d reaction, aiming to observe isovector D12 in the π0 d systemthrough π0 decay from a possible higher-mass isoscalar dibaryon in the π0 π0 d system.

2.

Kinematics

An important concept is discussed first to separate the mechanisms for QF π0 production anddibaryon production before moving on to the experiments. Possible mechanisms for the γd→π0 π0 dreaction can be classified in the following three:(a) QF π0 π0 production on a nucleon followed by deuteron coalescence (QFC),(b) the first π0 is emitted from the QF nucleon, subsequently the NN (∆N) reaction occurs withthe spectator nucleon to generate an isovector resonance RIV , followed by the second π0 anddeuteron emission, and(c) both one π0 is emitted from a photo-produced isoscalar dibaryon RIS , leaving an isovector
dibaryon RIV , successively another π0 is emitted from RIV .
In (a), the second π0 should be emitted to compensate for the momentum given to the QF participantnucleon by the first emitted π0 to coalesce into a deuteron. In this case, the angular distribution of
deuteron emission in the center-of-mass (CM) frame shows strongly backward peaking. As for (b),the condition to coalescence of RIV make the distribution sideway peaking at the incident photon
energy around 1.2 GeV. A rather flat distribution is obtained in (c). Since the three mechanisms givecompletely diﬀerent angular distributions, we can separate (or distinguish) the three mechanisms.
Fig. 1 shows the diagrams for the three possible mechanisms for the γd → π0 π0 d reaction. The
calculations performed by Fix and Ahrenhövel (FA) [11] are based on a QFC mechanism, and theangular distribution of deuteron emission actually shows strongly backward peaking as shown later in2■■■

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Fig. 3. The behavior of an angular distribution in each mechanism can also be given by a Monte-Carlosimulation easily.

(a)

γ

(b)

π
π

π
π

Np

Np

d

d

γ

d

Ns

Ns

RIV

d

(c)
γ
d

π

π
d

RIS

RIV

Fig. 1. Possible mechanisms for the γd → π0 π0 d reaction. (a) Two neutral pions are photoproduced on the
QF participant nucleon N p , followed by coalescence of N p and spectator nucleon N s into a deuteron. (b) One
pion is photoproduced on N p , successively coalescence of N p (or ∆ produced from N p ) and N s into an isovector
resonance RIV , decaying into a pion and deuteron. (c) An isoscalar resonance RIS is photoproduced from thedeuteron. The RIS decays into RIV by emitting a pion, and successively RIV decays into the deuteron by emitting
another pion.

3.

Experiments

The total and diﬀerential cross sections were measured for the γd→π0 π0 d reaction at the Research Center for Electron Photon Science (ELPH), Tohoku University [12]. A bremsstrahlung photon beam was provided by inserting a carbon fiber into the 1.2-GeV circulating electrons [13–16] ina synchrotron at ELPH. The energy of each photon was determined by measuring the trajectory of
the corresponding post-bremsstrahlung electron. The tagging energy of the photon beam ranged from0.75 to 1.15 GeV, and the typical tagging rate was 20 MHz. The target used in the experiments was
liquid deuterium with a thickness of 45.9 mm. All the final-state particles in the γd→π0 π0 d reaction
were measured with the FOREST detector [17]. FOREST consists of three diﬀerent electromagnetic
calorimeters (EMCs), and a plastic-scintillator hodoscope (PSH) is placed in front of each EMC to
identify charged particles.

4.

Results

The analysis of the γd → π0 π0 d reaction was made in the same way as in Ref. [19]. We selected
the events containing four neutral particles and a charged particle, and applied a kinematic fit withsix constraints: energy and three-momentum conservation, and every γγ invariant-mass being the π0mass. Events for which the χ2 probability is higher than 0.4 are selected to reduce those from otherbackground processes. A rather higher lower limit for the probability was introduced to suppress theevents from deuteron misidentification in the most competitive QF γp′ →π0 π0 p reaction.
The total cross section as a function of γd center-of-mass system Wγd shown in Fig. 1 is not
monotonically increasing but shows resonance-like behavior peaked at around 2.47 and 2.63 GeV. A
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naive interpretation of this behavior may be a QF excitation of the nucleon in the deuteron. Looking
into diﬀerential cross sections, the kinematic condition for the obtained data is found to completely
diﬀer from the QFC process.

120

PLB772, 398
this work
Fix and Ahrenhovel
Egorov and Fix
3 BW+phase space:

110

Total cross section σ (nb)

100
90
80
70
60
50
40
30

RIS (2.47 GeV )RIS (2.63 GeV )20
10

RIS (2.37 GeV )02350 2400 2450 2500 2550 2600 2650 2700 2750 2800 2850
CM energy Wγ d (MeV)
Fig. 2. Total cross section σ as a function of Wγd . The blue squares show σ obtained in this work, while
the cyan circles show that presented in Ref. [19]. The horizontal error of each data point corresponds to thecoverage of the incident photon energy, and the vertical error shows the statistical error of σ. The solid andgreen dotted curves show theoretical calculations given in Ref. [11] and [18], respectively. The dashed red
curve) shows the fitted function: a sum of three BW peaks and phase-space contributions. Each contribution to
it is shown in a dash-dotted magenta curve. The lower hatched blue and cyan histograms show the systematic
errors of σ in this work and in Ref. [19], respectively.

The diﬀerential cross sections, dσ/dMππ , dσ/dMπd , and dσ/dΩd , are obtained for each group ofphoton-tagging channels divided into four groups. Fig. 3 shows dσ/dMππ , dσ/dMπd and dσ/dΩd forthe photon tagging group corresponding to Wγd = 2.7–2.8 GeV. The angular distribution of deuteronemission (dσ/dΩd ) is rather flat, and the kinematic condition for the obtained data completely diﬀers
from the QFC (dashed green curve: strongly backward peaking) and semi-QF (dotted magenta curve:
sideway peaking) processes. Thus, we consider the possibility that the resonance-like structure in
Fig. 2 might be due to a manifestation of isoscalar dibaryons. In the observed reaction, both thetwo nucleons obviously participate before emitting π0 s. The diﬀerential cross section dσ/dMπd as
a function of πd invariant-mass Mπd shows two peaks. The centroid of the low-mass peak is ∼2.14
GeV/c2 independently of the incident energy. However, that of the high-mass peak decreases with adecrease of the incident energy, and finally the two peaks are merged into a bump. The high-mass peakreflects the appearance of the 2.14-GeV/c2 peak in dσ/dMπd between the other pion and deuteron(reflection). The dσ/dMππ shows no prominent feature, increasing monotonically with increase of4■■■

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300

200

RIV (2.14 GeV )

200

100

0

100

0.4

0.6
0.8
Mππ (GeV)

0

2

2.2
2.4
2.6
Mπd (GeV)dσ/dΩ d (nb/sr)

dσ/dMπd (nb/GeV)

dσ/dMππ (nb/GeV)

Mππ from the minimum to the maximum of the available energy. In contrast, the momenta of the two
π0 s are correlated in the QFC mechanism. This is partly because the quasi-free γn → π0 π0 n reaction
shows an enhancement in the central part of the Mππ spectrum [21, 22]. Additionally, to coalesce into
a deuteron, the two π0 s should be emitted so as to compensate for the momentum given to the QF
participant nucleon. Therefore, every FA calculation yields an enhancement in the central region of
the spectrum.

10

5

0

-1

-0.5

0
0.5
cosθ d1

Fig. 3. Diﬀerential cross sections dσ/dMππ (left), dσ/dMπd (central), and dσ/dΩd (right) for Wγd = 2.7–2.8
GeV. The lower hatched cyan histograms show the corresponding systematic errors. The dashed green curves
show the FA calculations based on the QFC mechanism. The solid red and dotted magenta curves correspondto the pure phase-space and semi-QF processes, respectively, where their yields are normalized so that the total
cross section should be the same.

The resonance-like structure RIV in Fig. 3 gives a mass of 2.14±0.01 GeV/c2 with a width of
0.09±0.01 GeV/c2 . The mass is slightly lower than the sum of the N and ∆ masses (∼2.170 GeV/c2 ),and the width is narrower than that of ∆ (∼0.117 GeV/c2 ) [23]. This may suggest that the peak isinterpreted as an N∆ quasi-bound state. The angular distributions for the two π0 s limit J π of the state
to 1+ , 2+ , or 3− . The 2+ assignment is consistent with the theoretically predicted D12 state, and withthe resonance structure of the 3P2 -πd amplitude. The details of the analysis for the 2.14-GeV peak in
dσ/dMπd are discussed in Ref. [20].

5.

Discussion

A preliminary result for the excitation function of the total cross section obtained by the A2 collaboration at the Mainz MAMI accelerator also apparently showed a similar enhancement above an
incident energy of 0.41 GeV (Wγd = 2.22 GeV) [24]. A set of diﬀerential cross sections is awaited toconfirm the dibaryonic interpretation of the observed peaks in the excitation function. Recently, preliminary results for D12 candidates observed in the γd→π+ π− d reaction are reported [25,26], showing
a peak with M = 2.1–2.2 GeV and Γ ≃ 0.1 GeV both in the π± d invariant-mass distributions. The
peak position is close to the sum of the N and ∆ masses. The observed peak seems to be interpreted
as D12 , and the final results are strongly desired to study a production mechanism of D12 .

6.

Summary

The total and diﬀerential cross sections have been measured for the γd→π0 π0 d reaction at ELPH
with incident energies from 0.75 to 1.15 GeV. The total cross section as a function of Wγd shows
resonance-like behavior peaked at around 2.47 and 2.63 GeV. The experimental angular distributionsof deuteron emission are rather flat, and they can never be understood in the QFC mechanism. A
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peak with M = 2.14 ± 0.01 GeV and Γ = 0.09 ± 0.01 GeV are observed in the π0 d invariantmass distribution. The present work shows evidence for the existence of the 2.14-GeV/c2 isovector
dibaryon in the π0 d channel, and of the 2.47- and 2.63-GeV isoscalar dibaryons in the π0 π0 d channel.
The details including figures can be found in Ref. [20].

Acknowledgments
The authors express their gratitude to the ELPH accelerator staﬀ for stable operation of the electron synchrotron and its injector linac during the FOREST experiments. They also acknowledge Mr.
Kazue Matsuda, Mr. Ken’ichi Nanbu, and Mr. Ikuro Nagasawa for their technical support. This work
was supported in part by the Ministry of Education, Culture, Sports, Science and Technology, Japanthrough Grants-in-Aid for Scientific Research (B) No. 17340063, for Specially Promoted ResearchNo. 19002003, for Scientific Research (A) No. 24244022, for Scientific Research (C) No. 26400287,
and for Scientific Research (A) No. 16H02188.
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