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 JP 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(ηc)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.
