Can discovery of hidden charm strange pentaquark states help determine the spins of $P_c(4440)$ and $P_c(4457)$?

TL;DR

This paper explores whether discovering hidden charm strange pentaquark states can help determine the spins of the $P_c(4440)$ and $P_c(4457)$ states using effective field theory and flavor symmetry considerations.

Contribution

It introduces a theoretical framework to relate hidden charm strange pentaquark states to the spins of specific pentaquarks, providing a new approach to determine their quantum numbers.

Findings

Existence of a complete hidden charm strange multiplet of molecules.

Discovery of certain molecules can help determine the spins of $P_c(4440)$ and $P_c(4457)$.

Abstract

The pentaquark states, $P_{c}(4312)$, $P_{c}(4440)$ and $P_{c}(4457)$, could be nicely arranged into a multiplet of seven molecules of $\bar{D}^{(\ast)}\Sigma_{c}^{(\ast)}$ dictated by heavy quark spin symmetry. However, the spins of $P_c(4440)$ and $P_c(4457)$ are not yet fully determined. In this work we employ the contact-range effective field theory to investigate the $SU(3)$-flavor counterparts of $\bar{D}^{(\ast)}\Sigma_{c}^{(\ast)}$, and study the possibility whether their discovery can help determine the spins of $P_c(4457)$ and $P_c(4440)$. We find the existence of a complete hidden charm strange multiplet of $\bar{D}^{(\ast)}\Xi_{c}^{(\prime\ast)}$ molecules irrespective of the spins of $P_c(4440)$ and $P_c(4457)$. On the other hand, we find that although molecules of $\bar{D}^{(\ast)}\Xi_{c}$ are also likely, depending on the realization of the underlying dynamics, their discovery can be more useful to determine the spins of $P_{c}(4440)$ and $P_{c}(4457)$ and to tell how the heavy quark and light quark interaction depends on the spin of the light quark pair.