$P_c$ Resonances in the Compact Pentaquark Picture

TL;DR

This paper investigates $P_c$ resonances as compact pentaquark states using quark models and group theory, identifying possible configurations, decay channels, and suggesting specific $P_c$ states' spin assignments.

Contribution

It introduces a comprehensive classification of 17 possible compact pentaquark states with detailed decay analysis, providing insights into their structure and decay behaviors.

Findings

$pJ/$ is the dominant decay channel.

$P_c(4440)$ likely not a compact pentaquark.

$P_c(4312)$ and $P_c(4457)$ could be spin-1/2 and 3/2 states.

Abstract

$P_c$ resonances are studied in the approach of quark model and group theory. It is found that there are totally 17 possible pentaquark states with the quark contents $q^3Q \bar Q$ ($q$ are $u$ and $d$ quarks; $Q$ is $c$ quark) in the compact pentaquark picture, where the hidden heavy pentaquark states may take the color singlet-singlet ($[111]_{{qqq}}\otimes [111]_{{c \bar c}}$) and color octet-octet ($[21]_{{qqq}}\otimes [21]_{{c \bar c}}$) configurations. The partial decay widths of hidden heavy pentaquark states are calculated for all possible decay channels. The results show that the $pJ/\psi$ is the dominant decay channel for both the spin $3/2$ and $1/2$ pentaquark states, and indicate that the $P_c(4440)$ may not be a compact pentaquark state while $P_c(4312)$ and $P_c(4457)$ could be the spin-$\frac{1}{2}$ and spin-$\frac{3}{2}$ pentaquark states, respectively.