Rethinking the $P_c(4457)^+$ as the $P_{\psi}^{\Delta^+}(4457)$ isoquartet $\bar{D}^* \Sigma_c$ molecule

TL;DR

This paper proposes reinterpreting the $P_c(4457)$ pentaquark as an isospin 3/2 $ar{D}^* \Sigma_c$ molecule, leading to different decay widths and a revised spectrum of hidden-charm molecular pentaquarks.

Contribution

It introduces a novel isospin 3/2 interpretation of the $P_c(4457)$, contrasting with the traditional isospin 1/2 view, and explores implications for the pentaquark spectrum.

Findings

The $P_c(4457)$ can be an isospin 3/2 $ar{D}^* \Sigma_c$ bound state.

Decay widths are similar for $P_c(4457)$, $P_c(4312)$, and $P_c(4440)$ under this interpretation.

The spectrum of hidden-charm pentaquarks is reduced to 4-5 states, explaining the non-observation of certain partners.

Abstract

The nature of the $P_{c}(4312)$, $P_c(4440)$ and $P_c(4457)$ pentaquarks is a fascinating theoretical question. Within the molecular picture their more usual interpretation is that of $I=\tfrac{1}{2}$ $\bar{D} \Sigma_c$ and $\bar{D}^* \Sigma_c$ bound states. Here we argue in favor of interpreting the $P_c(4457)$ pentaquark as a $I=\tfrac{3}{2}$ $\bar{D}^* \Sigma_c$ bound state (with spin $J=\tfrac{1}{2}$) instead. Owing to isospin symmetry breaking effects, with this identification the partial decay width of the $P_c(4457)^+$ into $J/\psi p$ will be of the same order of magnitude as the $P_{c}(4312)^+$ and $P_c(4440)^+$, in contrast with the considerably larger partial decay width in the $I=\tfrac{1}{2}$ scenario. In turn, this leads to a different hidden-charm molecular pentaquark spectrum, in which there are only four or five $P_{\psi}^N$ bound states instead of the usual seven, which might explain why the predicted $J=\tfrac{1}{2}$ and $\tfrac{3}{2}$ ($I=\tfrac{1}{2}$) $\bar{D}^* \Sigma_c^*$ molecular partners of the $P_c(4312)$ and $P_c(4440)$ have not been observed.