$P_c(4440)$ and $P_c(4457)$ decay into $\bar{D}\Sigma_c$ and $\bar{D}\Lambda_c$ and the spin of the $P_c$ states

TL;DR

This paper investigates the decay widths and spin assignments of the $P_c(4440)$ and $P_c(4457)$ pentaquark states, proposing methods to determine their spins through decay channel analysis.

Contribution

It introduces a combined approach using vector meson exchange and pion exchange triangle diagrams to analyze decay widths and spin assignments of the pentaquark states.

Findings

Widths depend strongly on the spin of the states.

Favored spin assignment is $1/2^-$, $3/2^-$.

Decay channel measurements can determine the spin unambiguously.

Abstract

We address the issue of the width and spin assignment of the $P_c(4440)$ and $P_c(4457)$ pentaquark states. We calculate the partial decays widths of the particles into $J/\psi N$, $\bar{D} \Sigma_c$ and $\bar{D} \Lambda_c$ with the first one obtained within a unitary approach with the coupled channels of $J/\psi N$ and $\bar{D}^* \Sigma_c$ with the interaction driven by vector meson exchange, and the last two by means of triangle diagrams involving pion exchange which break the spin degeneracy of the vector meson exchange. The widths obtained depend much on the spin of the particles and we study the possible scenarios for spin assignment, favoring the $1/2^-$ , $3/2^-$ order. We predict values for decays in different channels and show that their determination would allow to decide unambiguously the spin of the states.