Molecular states from interaction

Jun He; Dian-Yong Chen

doi:10.1140/epjc/s10052-019-7419-7

EPJ

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2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2019) 79: 887
https://doi.org/10.1140/epjc/s10052-019-7419-7

Regular Article - Theoretical Physics

Molecular states from $\varSigma ^{()}_c{\bar{D}}^{()}-\varLambda _c{\bar{D}}^{(*)}$ interaction

Jun He¹^* and Dian-Yong Chen²

¹ Department of Physics and Institute of Theoretical Physics, Nanjing Normal University, Nanjing, 210097, China
² School of Physics, Southeast University, Nanjing, 210094, China

^* e-mail: junhe@njnu.edu.cn

Received: 15 September 2019
Accepted: 19 October 2019
Published online: 4 November 2019

Abstract

In this work, we systemically investigate the molecular states from the $\varSigma ^{(*)}_c{\bar{D}}^{(*)}-\varLambda _c{\bar{D}}^{(*)}$ interaction with the help of the Lagrangians with heavy quark and chiral symmetries in a quasipotential Bethe–Salpeter equation (qBSE) approach. The molecular states are produced from isodoublet (I=1/2) $\varSigma _c{\bar{D}}$ interaction with spin parity $$J^P=1/2^-$$ and $\varSigma _c{\bar{D}}^*$ interaction with $$1/2^-$$ and $$ 3/2^-$$ . Their masses and widths are consistent with the $$P_c(4312)$$ , $$P_c(4440)$$ and $$P_c(4457)$$ observed at LHCb. The states, $\varSigma _c^*{\bar{D}}^*(1/2^-)$ , $\varSigma _c^*{\bar{D}}^*(3/2^-)$ and $\varSigma ^*_c{\bar{D}}(3/2^-)$ , are also produced with the same parameters. The isodoublet $\varSigma _c^*{\bar{D}}^*$ interaction with $$5/2^-$$ , as well as the isoquartet (I=3/2) $\varSigma _c{\bar{D}}^*$ interactions with $$1/2^-$$ and $$3/2^-$$ , $\varSigma _c^*{\bar{D}}^*$ interaction with and , are also attractive while very large cutoff is required to produce a molecular state. We also investigate the origin of the widths of these molecular states in the same qBSE frame. The $\varLambda {\bar{D}}^*$ channel is dominant in the decays of the states, $\varSigma _c{\bar{D}}^*(1/2^-)$ , $\varSigma _c{\bar{D}}^*(3/2^-)$ , $\varSigma _c^*{\bar{D}}(3/2^-)$ , and $\varSigma _c{\bar{D}}(1/2^-)$ . The $\varSigma ^*_c{\bar{D}}^*(1/2^-)$ state has large coupling to $\varSigma _c{\bar{D}}$ channel while the $\varSigma _c{\bar{D}}^*$ , $\varSigma ^*_c{\bar{D}}$ and $\varLambda _c{\bar{D}}^*$ channels provide similar contributions to the width of the $\varSigma ^*_c{\bar{D}}^*(3/2^-)$ state. These results will be helpful to understand the current LHCb experimental results, and the three predicted states and the decay pattern of these hidden-charmed molecular pentaquarks can be checked in future experiments.