Strong decays of $$ {P}_{\psi}^N{(4312)}^{+} $$ to J/ψ(ηc)p and $$ {\overline{D}}^{\left(\ast \right)}{\Lambda}_c $$ within the Bethe-Salpeter framework

• DOI: 10.1007/jhep06(2023)189
• Publication Date: 2023-06-29T20:25:23Z
• Authors: Qiang Li; Chao-Hsi Chang; Tianhong Wang; Guo-Li Wang
• Keywords: Bar (unit); Bethe–Salpeter equation; Pentaquark

Based on the effective Lagrangian in heavy quark limit, we calculate one-boson-exchange interaction kernel of $P_\psi^N(4312)^+$ as $\bar D\Sigma_c$ molecular state isospin-$\frac12$. We present Bethe-Salpeter equation and wave function for constituent particles to be a (pseudo)scalar meson $\frac12$ baryon. By solving equation, obtain with $J^P=(\frac{1}{2})^-$. Combining obtained BS function, partial decay widths $J/\psi p$, $\eta_c D^{*0}\Lambda_c^+$ D^0\Lambda_c^+$ are calculated $0.17$, $0.085$, $8.8$, $0.026$ MeV, respectively, which roughly consistent LHCb experimental measurements some other theoretical researches. The results indicate fraction channel amounts $\sim90\%$ $P_\psi^N(4312)^+$, is highly promising discovered near future experiments. Our favor interpretation $J^P=(\frac{1}{2})^-$ isospin $I=\frac12$.