Strong decays of $${P}_{\psi }^{N}{\left({444}0\right)}^{+}$$ and $${P}_{\psi }^{N}{\left({4457}\right)}^{+}$$ 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 $${P}_{\psi }^{N}{\left({444}0\right)}^{+}$$ and $${P}_{\psi }^{N}{\left({4457}\right)}^{+}$$ reported by LHCb in 2019. Taking into account both the mass ordering and the decay widths, our results favor the interpretation of $${P}_{\psi }^{N}{\left({444}0\right)}^{+}$$ and $${P}_{\psi }^{N}{\left({4457}\right)}^{+}$$ as the isospin- $$\frac{1}{2}$$ $$\left[{\overline{D} }^{*}{\Sigma}_{c}\right]$$ molecular states with J P configuration $${\left(\frac{3}{2}\right)}^{-}$$ and $${\left(\frac{1}{2}\right)}^{-}$$ , respectively. We first calculate the one-boson-exchange interaction kernel of $$\left[{\overline{D} }^{*}{\Sigma}_{c}\right]$$ in the isospin- $$\frac{1}{2}$$ configuration. Then we present the Bethe-Salpeter equation (BSE) and wave functions for the bound states of a vector meson and a $$\frac{1}{2}$$ baryon with $${J}^{P}=\frac{1}{2}^{-}$$ and $$\frac{3}{2}^{-}$$ . The obtained mass results for the $${\left(\frac{3}{2}\right)}^{-}$$ and $${\left(\frac{1}{2}\right)}^{-}$$ are 4.442 and 4.457 GeV, respectively. Combining the effective Lagrangians and the BS wave functions, we further calculate the strong decay channels $${\overline{D} }^{(*)0}{\Lambda}_{c}^{+}$$ , J / ψ ( η c ) p , and $$\overline{D}{\Sigma }_{c}^{(*)}$$ for the two $${P}_{\psi }^{N}$$ states. In the favored $$\frac{3}{2}^{-}$$ and $$\frac{1}{2}^{-}$$ 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 $${\overline{D} }^{0}{\Lambda}_{c}^{+}$$ and $${\overline{D} }^{(*)0}{\Lambda}_{c}^{+}$$ are the dominant decay channels to detect $${P}_{\psi }^{N}{\left({444}0\right)}^{+}$$ and $${P}_{\psi }^{N}{\left({4457}\right)}^{+}$$ , respectively.