Strong decays of $P_ψ^N(4312)^+\to J/ψ(η_c) p$ within the Bethe-Salpeter framework

Abstract

Based on the effective Lagrangian in the heavy quark limit, we calculate the one-boson-exchange interaction kernel of DΣ c in the isospin-1 2 state. We present the Bethe-Salpeter equation and wave function for the constituent particles to be a (pseudo)scalar meson and a 1 2 baryon. By using the Bethe-Salpeter equation, we can obtain P N ψ (4312) + as the DΣ c molecular state with J P = ( 1 2 ) − . Combining the effective Lagrangian and the obtained BS wave function, the partial decay widths of P N ψ (4312) + to J/ψp and η c p are calculated to be 0.11 −0.04 +0.06 MeV and 5.6 −1.9 +2.6 × 10 −2 MeV, respectively, which are consistent with the LHCb experimental measurements. Our results indicate the fraction of J/ψp channel amounts to ∼ 1% of P N ψ (4312) + , and can reach to ∼ 30% when the interaction kernel is reduced by half. Our results favor the interpretation of P N ψ (4312) + as the DΣ c molecular state with J P = ( 1 2 ) − and isospin I = 1 2 .