Coupled-channel effects of the ${\Sigma }_c^{(\ast )}{\bar{D}}^{(\ast )}$-${\Lambda }_c(2595)\bar{D}$ system and molecular nature of the $P_c$ pentaquark states from one-boson exchange model

Abstract

The effects of the ${\Sigma }_c{\bar{D}}^{\ast }$-${\Lambda }_c(2595)\bar{D}$ coupled-channel dynamics and various one-boson-exchange (OBE) forces for the LHCb pentaquark states, $P_c(4440)$ and $P_c(4457)$, are reinvestigated. Both the pion and $\rho$-meson exchanges are considered for the ${\Sigma }_c{\bar{D}}^{\ast }$-${\Lambda }_c(2595)\bar{D}$ coupled-channel dynamics. It is found that the role of the ${\Lambda }_c(2595)\bar{D}$ channel in the descriptions of the $P_c(4440)$ and $P_c(4457)$ states is not significant with the OBE parameters constrained by other experimental sources. The naive OBE models with the short-distance $\delta (\vec{r})$ term of the one-pion exchange (OPE) keep failing to reproduce the $P_c(4440)$ and $P_c(4457)$ states simultaneously. The OPE potential with the full $\delta (\vec{r})$ term results in a too large mass splitting for the $J^P=1/2^{-}$ and $3/2^{-}$ ${\Sigma }_c{\bar{D}}^{\ast }$ bound states with total isospin $I=1/2$. The OBE model with only the OPE $\delta (\vec{r})$ term dropped may fit the splitting much better but somewhat underestimates the splitting. Since the $\delta (\vec{r})$ potential is from short-distance physics, which also contains contributions from the exchange of mesons heavier than those considered explicitly, we vary the strength of the $\delta (\vec{r})$ potential and find that the masses of the $P_c(4312)$, $P_c(4440)$, and $P_c(4457)$ can be reproduced simultaneously with the $\delta (\vec{r})$ term in the OBE model reduced by about 80\%. While two different spin assignments are possible to produce their masses, in the preferred description, the spin parities of the $P_c(4440)$ and $P_c(4457)$ are $3/2^{-}$ and $1/2^{-}$, respectively.

Comments: 34 pages, 6 figures, 8 tables