Hidden-charm and hidden-bottom molecular pentaquarks in chiral perturbation theory

Abstract

The newly observed $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$ at the LHCb experiment are very close to the ${\Sigma }_c\bar{D}$ and ${\Sigma }_c{\bar{D}}^{\ast }$ thresholds. In this work, we perform a systematic study and give a complete picture on the interactions between ${\Sigma }_c^{(\ast )}$ and ${\bar{D}}^{(\ast )}$ systems in the framework of heavy hadron chiral perturbation theory, where the short-range contact interaction, long-range one-pion-exchange contribution, and intermediate-range two-pion-exchange loop diagrams are all considered. We first investigate the three $P_c$ states without and with considering the ${\Lambda }_c$ contribution in the loop diagrams. It is difficult to simultaneously reproduce the three $P_c$s unless the effect of ${\Lambda }_c$ is included. The coupling between ${\Sigma }_c^{(\ast )}{\bar{D}}^{(\ast )}$ and ${\Lambda }_c{\bar{D}}^{(\ast )}$ channels is crucial for the formation of these $P_c$s. Our calculation supports the $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$ to be the $S$-wave hidden-charm $[{\Sigma }_c\bar{D}{]}_{J=1/2}^{I=1/2}$, $[{\Sigma }_c{\bar{D}}^{\ast }{]}_{J=1/2}^{I=1/2}$ and $[{\Sigma }_c{\bar{D}}^{\ast }{]}_{J=3/2}^{I=1/2}$ molecular pentaquarks, respectively. Our calculation disfavors the spin assignment $J^P={\frac{1}{2}}^{-}$ for $P_c(4457)$ and $J^P={\frac{3}{2}}^{-}$ for $P_c(4440)$, because the excessively enhanced spin-spin interaction is unreasonable in the present case. We obtain the complete mass spectra of the $[{\Sigma }_c^{(\ast )}{\bar{D}}^{(\ast )}{]}_J$ systems with the fixed low energy constants. Our result indicates the existence of $[{\Sigma }_c^{\ast }{\bar{D}}^{\ast }{]}_J(J=\frac{1}{2},\frac{3}{2},\frac{5}{2})$ hadronic molecules. The previously reported $P_c(4380)$ might be a deeper bound one. Additionally, we also study the hidden-bottom ${\Sigma }_b^{(\ast )}{B}^{(\ast )}$ systems, and predict seven bound molecular states, which could serve as a guidance for future experiments....

Comments: 42 pages, 15 figures, and 4 tables