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

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 $I=\frac{1}{2}$ $\bar{D}{\Sigma }_c$ and ${\bar{D}}^{\ast }{\Sigma }_c$ bound states. Here we argue in favor of interpreting the $P_c(4457)$ pentaquark as a $I=\frac{3}{2}$ ${\bar{D}}^{\ast }{\Sigma }_c$ bound state (with spin $J=\frac{1}{2}$) 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 $I=\frac{1}{2}$ 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 $J=\frac{1}{2}$ and $\frac{3}{2}$ ($I=\frac{1}{2}$) ${\bar{D}}^{\ast }{\Sigma }_c^{\ast }$ molecular partners of the $P_c(4312)$ and $P_c(4440)$ have not been observed.

Comments: 7 pages, 2 tables, 1 figure, corresponds with the published version