How to reveal the nature of three or more pentaquark states?

TL;DR

This study uses a chiral unitary approach with heavy quark spin symmetry to analyze coupled channel interactions near thresholds, supporting the molecular nature of observed pentaquark states and predicting their decay behaviors.

Contribution

It introduces pion exchange contributions via box diagrams to lift degeneracies and fits experimental data to support the molecular interpretation of pentaquark states.

Findings

LHCb pentaquarks are produced indirectly through final state interactions.

Certain pentaquarks have large decay widths into η_c N, observable in invariant mass distributions.

Future η_c N channel studies can clarify the nature of specific pentaquark states.

Abstract

Within the chiral unitary approach and with the constraints of heavy quark spin symmetry, we study the coupled channel interactions of ${\bar D}^{(*)}\Sigma_c^{(*)}$ channels, close to whose thresholds three pentaquark-like $P_c$ states have been reported by the LHCb Collaboration. In the present work, we take into account the contributions of pion exchanges via box diagrams to the interaction potentials, and therefore lift the degeneracy in the masses of ${\bar D}^*\Sigma_c^{(*)}$ spin multiplets. Fitting the $J/\psi p$ invariant mass distributions in the $\Lambda_b^0 \to J/\psi K^- p$ decay, we find that the LHCb pentaquark states can not be reproduced in the direct $J/\psi p$ production in the $\Lambda_b^0$ decay, and can only be indirectly produced in the final state interactions of the $\Lambda_b^0$ decay products, ${\bar D}^*\Sigma_c^{(*)}$, which further supports the nature of these states as $\bar{D}\Sigma_c$ molecules. Based on the fit results obtained, we study the partial decay widths/branching ratios to other decay channels, $\bar{D}^* \Lambda_c$, $\bar{D} \Lambda_c$, and $\eta_c N$, and the corresponding invariant mass distributions. The resonances with $J^P=\frac{1}{2}^-$, $P_c(4312)$, $P_c(4440)$ and the one of $\bar{D}^* \Sigma_c^*$ around 4500 MeV, have large partial decay width into $\eta_c N$, and thus, can be easily seen in the $\eta_c N$ invariant mass distributions. By contrast, the states with $J^P=\frac{3}{2}^-$, $P_c(4457)$, the (predicted) narrow $P_c(4380)$ and the bound state of $\bar{D}^* \Sigma_c^*$ with a mass of about 4520 MeV, do not decay into $\eta_c N$. Therefore, the $\eta_c N$ channel should be studied in future to provide further insights into the nature of these states, especially that of the $P_c(4440)$ and $P_c(4457)$.