$P_c(4312)$ 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 ${\mathrm{\Sigma }}_c$ and $\overline{D}$ masses, it is naturally tempted to be considered as a molecular state composed of ${\mathrm{\Sigma }}_c$ and $\overline{D}$. Moreover, $P_c(4312)$ is observed in the channel with $J/\psi p$ final state, requiring that isospin conservation $P_c(4312)$ 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 $P_c(4312)$ is an excellent target because of the available data. We calculate the spectrum of $P_c(4312)$ 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.

• Received 5 November 2019

DOI:https://doi.org/10.1103/PhysRevD.101.014024

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society