Strong decays of the hidden-charm molecular pentaquarks

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.