Pc pentaquarks with chiral tensor and quark dynamics
Y. Yamaguchi1,2), H. Garcia-Tecocoatzi3), A. Giachino4), A. Hosaka5,1) , E. Santopinto4) ,S. Takeuchi6,2,5) and M. Takizawa7,2,8)
1) : Advanced Theoretical Physics Gr., JAEA 2): Nishina Center, RIKEN 3): Univ. of La Plata4): INFN Genova 5): RCNP, Osaka Univ. 6): Japan College of Social Work
7): Showa Pharmaceutical Univ. 8): J-PARC Branch, KEK Theory Center

In recent years, the research on hadrons with unusualstructures has been actively conducted. Hadrons are composed ofquarks that are a type of elementary particles. The ordinary
hadrons can be classified by a baryon consisting of three quarks(𝑞𝑞𝑞) and a meson of quarks-antiquarks (𝑞𝑞̅) as shown in Fig.
1(a). The baryon and meson pictures have explained the nature ofmany hadron states observed in the experiments, e.g. protons andneutrons being 𝑢𝑢𝑑 and 𝑢𝑑𝑑 baryons, respectively, consistingof up (𝑢) and down (𝑑) quarks.
In the recent accelerator experiments, "Exotic hadrons" thatcannot be explained by the ordinary hadron picture have beenreported. In 2015, the exotic hadron named 𝑃𝑐 was reported bythe Large Hadron Collider beauty (LHCb) experiment in protonproton collisions [1]. The 𝑃𝑐 state is not classified within theordinary hadrons, while it is considered to be a 𝑢𝑢𝑑𝑐𝑐̅ five-quark
state having a charm (𝑐) and an anti-charm (𝑐̅) quarks. Such astate consisting of five quarks is called pentaquark. So far, fourpentaquarks 𝑃𝑐 (4312) , 𝑃𝑐 (4380) , 𝑃𝑐 (4440) , and 𝑃𝑐 (4457)
have been reported [1,2].
The 𝑃𝑐 states are assumed to be pentaquarks, but how the fivequarks make them up is not understood. In the theoretical studies,
the compact five-quark state and hadronic molecule have been
discussed (Fig. 1(b)). The compact five-quark state is realized as
a compact bound state of the five quarks. The hadronic molecule
is a loosely bound state of a meson and baryon, where three ofthe five quarks in 𝑃𝑐 make up the baryon, and the remaining
quarks (quark and antiquark) do the meson. The hadronicmolecular picture was inspired because the 𝑃𝑐 states were found(∗)̅ (∗) meson (Σ𝑐(∗) =near the thresholds of the Σ𝑐 baryon and the 𝐷̅ (∗) = 𝐷
̅, 𝐷̅ ∗ ).
Σ𝑐 , Σ𝑐∗ and 𝐷
In the previous studies, the authors considered models
employing either the compact state or hadronic molecule picture.
However, the rearrangement of quarks allows the two states tomix. In this study, we introduce the mixture of the compact statein the hadronic molecule and predict masses and decay widths ofthe pentaquarks. By comparing our results with the LHCb data,
we investigate the 𝑃𝑐 structures.
The mixture of the compact state is introduced as a short-range(∗)̅ (∗) in the hadronic molecule channels.
force between Σ𝑐 and 𝐷
In Ref. [3], we found that this short-range force produces anattraction due to the level repulsion, because the masses of the(∗) ̅ (∗)
compact states are larger than those of the Σ𝑐 𝐷thresholds.
We also introduce the one pion exchange potential (OPEP). The
tensor term of the OPEP produces an attraction through thecoupled channel effects and has been known as the driving force
to bind atomic nuclei.
(∗) ̅ (∗)
By solving the Schrodinger equations for the Σ𝑐 𝐷system
coupled to the compact five-quark state, we obtain masses anddecay widths of the pentaquarks as shown in Fig. 2. Our model
predicts three states whose masses and widths are reasonablyagreement with those of 𝑃𝑐 (4312), 𝑃𝑐 (4440), and 𝑃𝑐 (4457) inthe LHCb experiment. The two bars connected by the arrows areFig. 1 Ordinary hadrons (baryon and meson) and exotic hadrons (compactstate and hadronic molecule). These exotic structures havebeen considered to be candidates of the structures of 𝑷𝒄
pentaquarks.

Fig. 2 Experimental data (LHCb) and our predictions of masses and widthsof the pentaquarks. A center of the bars are located at the central
values of the masses, while their lengths correspond to the decaywidths. The horizontal dashed lines show the baryon-meson
thresholds. The values are in unit of MeV, taken from [4].

the corresponding experimental data and predicted states. These
results indicate that the 𝑃𝑐 pentaquarks are described as the hybrid
states of the compact state and hadronic molecule.
We also obtain the state whose mass is close to the one of𝑃𝑐 (4380) . However, the widths are disagreement. Since
𝑃𝑐 (4380) has the broad width of about 200 MeV, further
theoretical and experimental studies would be necessary tounderstand that nature.
In addition, our model predicts new three states below the̅ ∗ threshold, that have not been reported in experiments yet.
Σ𝑐∗ 𝐷
It is interesting to search for such pentaquark states in the future.
Understanding the exotic structures would lead to theelucidation of the quark confinement that is the fundamental
problem how matter in the universe is created from quarks.
References[1] R. Aaij et al., Phys. Rev. Lett. 115, 072001 (2015).
[2] R. Aaij et al., Phys. Rev. Lett. 122, 222001 (2019).
[3] Y. Yamaguchi et al., Phys. Rev. D 96, 014018 (2017).
[4] Y. Yamaguchi et al., Phys. Rev. D 101, 091502(R) (2020).