Relations between strong decay widths of the $P_c$ pentaquarks in the SU(4) flavor-spin model

Abstract

In a previous work we have studied the isospin 1/2 lowest positive and negative parity states of the pentaquark $uudc\overline{c}$, in a constituent quark model with a linear confinement and an SU(4) flavor-spin hyperfine interaction and we compared the results with the $P^+_c(4312)$, $P^+_c(4440)$ and $P^+_c(4457)$ pentaquarks observed at LHCb in 2019. Here we extend the previous work by calculating ratios of decay rates of the $P_c$ pentaquarks to $J/\Psi$ and $\eta_c$ and similarly the ratio of decay rates to $\Lambda_c {\bar D}^*$ and $\Lambda_c \bar D$. Our predictions are based on the SU(4)$\times$SU(2) structure of compact pentaquarks.