Coupled Channel Effects of the $Sigma_c^{(*)}bar{D}^{(*)}$-$Lambda_c(2595)bar{D}$ System and Molecular Nature of the $P_c$ Pentaquark States from One-Boson Exchange Model

The effects of the $Sigma_cbar{D}^*$-$Lambda_{c}(2595)bar{D}$ 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 $Sigma_cbar{D}^*$-$Lambda_{c}(2595)bar{D}$ 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) kept fail 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 $3/2^-$ $Sigma_cbar{D}^*$ 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.