Strong decays of P ^N ({4440) }^+ and P ^N ({4457) }^+ within the Bethe-Salpeter framework

A bstract By combining the effective Lagrangian and Bethe-Salpeter framework, we studied the mass spectra, wave functions, and strong decay widths of the two pentaquark states P ^N ({4440) }^+ and P ^N ({4457) }^+ reported by LHCb in 2019. Taking into account both the mass ordering and the decay widths, our results favor the interpretation of P ^N ({4440) }^+ and P ^N ({4457) }^+ as the isospin- 12 D ^*₂ molecular states with J P configuration (3{2) }^- and (1{2) }^-, respectively. We first calculate the one-boson-exchange interaction kernel of D ^*₂ in the isospin- 12 configuration. Then we present the Bethe-Salpeter equation (BSE) and wave functions for the bound states of a vector meson and a 12 baryon with J^P=12^- and 32^-. The obtained mass results for the (3{2) }^- and (1{2) }^- are 4. 442 and 4. 457 GeV, respectively. Combining the effective Lagrangians and the BS wave functions, we further calculate the strong decay channels D ^ (*) 0₂^+, J / ψ (η c) p, and D ₂^ (*) for the two P ^N states. In the favored 32^- and 12^- configuration, the obtained total widths are 21. 8 MeV and 13. 0 MeV, respectively, which are substantially consistent with the LHCb data. Our results suggest that D ^0₂^+ and D ^ (*) 0₂^+ are the dominant decay channels to detect P ^N ({4440) }^+ and P ^N ({4457) }^+, respectively.