Strong decays of PψN(4440)⁺ and PψN(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 PψN(4440)⁺ and PψN(4457)⁺ reported by LHCb in 2019. Taking into account both the mass ordering and the decay widths, our results favor the interpretation of PψN(4440)⁺ and PψN(4457)⁺ as the isospin- 1/2 [D̄ *Σc] molecular states with J P configuration (3/2)⁻ and (1/2)⁻ , respectively. We first calculate the one-boson-exchange interaction kernel of [D̄ *Σc] in the isospin- 1/2 configuration. Then we present the Bethe-Salpeter equation (BSE) and wave functions for the bound states of a vector meson and a 1/2 baryon with JP=1/2⁻ and 3/2⁻ . 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 D̄ (*)0Λc⁺ , J / ψ ( η c ) p , and D̄Σ c(*) for the two PψN states. In the favored 3/2⁻ and 1/2⁻ 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 D̄ ⁰Λc⁺ and D̄ (*)0Λc⁺ are the dominant decay channels to detect PψN(4440)⁺ and PψN(4457)⁺ , respectively.