Phys. Rev. D 101, 014024 (2020)

Study on possible molecular states composed of ${\Lambda }_c\overline{D}$ (${\Lambda }_{b}B$) and ${\Sigma }_c\overline{D}$ (${\Sigma }_{b}B$) within the Bethe-Salpeter framework

Hong-Wei Ke^1,*, Mei Li¹, Xiao-Hai Liu^1,†, and Xue-Qian Li^2,‡

¹ School of Science, Tianjin University, Tianjin 300072, China

² School of Physics, Nankai University, Tianjin 300071, China

* khw020056@tju.edu.cn

† xiaohai.liu@tju.edu.cn

‡ lixq@nankai.edu.cn

ABSTRACT

$P_c\left(4312\right)$ observed by the LHCb collaboration is confirmed as a pentaquark and its structure, production, and decay behaviors attract great attention from theorists and experimentalists. Since its mass is very close to sum of ${\Sigma }_c$ and $\overline{D}$ masses, it is naturally tempted to be considered as a molecular state composed of ${\Sigma }_c$ and $\overline{D}$. Moreover, $P_c\left(4312\right)$ is observed in the channel with $J/\psi p$ final state, requiring that isospin conservation $P_c\left(4312\right)$ is an isospin-$1/2$ eigenstate. In the literature, several groups used various models to estimate its spectrum. We systematically study the pentaquarks within the framework of the Bethe-Salpeter equation; thus $P_c\left(4312\right)$ is an excellent target because of the available data. We calculate the spectrum of $P_c\left(4312\right)$ in terms of the Bethe-Salpter equations and further study its decay modes. Some predictions on other possible pentaquark states that can be tested in future experiments are made.