Strong decays of the hidden-charm molecular pentaquarks

TL;DR

This paper studies the strong decay behaviors of recently observed hidden-charm pentaquarks within a molecular framework, using effective Lagrangians to analyze their decay widths, branching ratios, and spin assignments.

Contribution

It introduces a detailed effective Lagrangian approach to analyze pentaquark decays and provides insights into their spin assignments and molecular nature based on decay width calculations.

Findings

Decay widths are sensitive to cutoff parameters.

Branching fractions are weakly dependent on cutoffs.

Favored spin assignments for P_{ψ}^N states.

Abstract

We investigate the strong decays of the recently observed hidden-charm pentaquarks \(P_{\psi}^N(4312)\), \(P_{\psi}^N(4440)\), and \(P_{\psi}^N(4457)\), as well as \(P_{\psi s}^\Lambda(4338)\) and \(P_{\psi s}^\Lambda(4459)\), within the molecular framework using the effective Lagrangian approach. We construct the effective Lagrangians describing the S-wave couplings between these pentaquarks and their constituent hadrons, namely \(\Sigma_c\bar{D}^{(*)}\) and \(\Xi_c\bar{D}^{(*)}\), and determine the coupling constants via the residues of the scattering \(T\)-matrix at the bound-state poles. Our results show that the decay widths are sensitive to the cutoff parameters in the form factors, whereas the branching fractions exhibit only weak dependence. Using \(P_{\psi}^N(4312)\) to calibrate the cutoff range, we further explore the spin assignments of \(P_{\psi}^N(4440)\) and \(P_{\psi}^N(4457)\). Our calculations favor the assignment where the lower-mass state \(P_{\psi}^N(4440)\) carries higher spin \(J = 3/2\) and the higher-mass state \(P_{\psi}^N(4457)\) carries lower spin \(J = 1/2\). In addition, the experimental widths of \(P_{\psi s}^\Lambda(4338)\) and \(P_{\psi s}^\Lambda(4459)\) can both be well reproduced under the molecular interpretation. We look forward to future experimental analyses with more accumulated data to clarify whether the lineshape of \(P_{\psi s}^\Lambda(4459)\) contains contributions from both spin-\(1/2\) and spin-\(3/2\) states.