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

TL;DR

This study investigates the coupled-channel dynamics and molecular nature of the LHCb pentaquark states using an one-boson-exchange model, highlighting the importance of short-distance interactions and proposing specific spin-parity assignments.

Contribution

It demonstrates that reducing the short-range delta function contribution in the OBE model allows simultaneous reproduction of the pentaquark masses and suggests specific spin-parity assignments for $P_c(4440)$ and $P_c(4457)$.

Findings

The $ar{D}^*$-$ar{D}$ coupled-channel effects are not significant for the pentaquark states.

Naive OBE models with full delta function fail to reproduce the observed states.

Reducing the delta function strength by about 80% aligns the model with experimental masses.

Abstract

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