arXiv2021
The effects of the $Σ_c\bar{D}^*$-$Λ_{c}(2595)\bar{D}$ 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 $ρ$-meson exchanges are considered for the $Σ_c\bar{D}^*$-$Λ_{c}(2595)\bar{D}$ coupled-channel dynamics. It is found that the role of the $Λ_{c}(2595)\bar{D}$ 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 $δ(\vec{r})$ 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 $δ(\vec{r})$ term results in a too large mass splitting for the $J^P=1/2^-$ and $3/2^-$ $Σ_c\bar{D}^*$ bound states with total isospin $I=1/2$. The OBE model with only the OPE $δ(\vec{r})$ term dropped may fit the splitting much better but somewhat underestimates the splitting. Since the $δ(\vec r)$ 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 $δ(\vec r)$ potential and find that the masses of the $P_c(4312)$, $P_c(4440)$, and $P_c(4457)$ can be reproduced simultaneously with the $δ(\vec r)$ 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.