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

• Published in: The journal of high energy physics 2023-06, Vol.2023 (6), Article 189
• Main Authors: Li, Qiang, Chang, Chao-Hsi, Wang, Tianhong, Wang, Guo-Li
• Format: Article
• Language: English
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP06(2023)189

Based on the effective Lagrangian in the heavy quark limit, we calculate the one-boson-exchange interaction kernel of $$ {P}_{\psi}^N{(4312)}^{+} $$ P ψ N 4312 + as the $$ \overline{D}{\Sigma}_c $$ D ¯ Σ c molecular state in isospin- $$ \frac{1}{2} $$ 1 2 . We present the Bethe-Salpeter equation and wave function for the constituent particles to be a (pseudo)scalar meson and a $$ \frac{1}{2} $$ 1 2 baryon. By solving the Bethe-Salpeter equation, we obtain $$ {P}_{\psi}^N{(4312)}^{+} $$ P ψ N 4312 + as the $$ \overline{D}{\Sigma}_c $$ D ¯ Σ c molecular state with J P = $$ {\left(\frac{1}{2}\right)}^{-} $$ 1 2 − . Combining the effective Lagrangian and the obtained BS wave function, the partial decay widths of $$ {P}_{\psi}^N{(4312)}^{+} $$ P ψ N 4312 + to J / ψp , η c p , $$ {\overline{D}}^{\ast 0}{\Lambda}_c^{+} $$ D ¯ ∗ 0 Λ c + and $$ {\overline{D}}^0{\Lambda}_c^{+} $$ D ¯ 0 Λ c + are calculated to be 0 . 17, 0 . 085, 8 . 8, and 0 . 026 MeV, respectively, which are roughly consistent with the LHCb experimental measurements and some other theoretical researches. The obtain results indicate the fraction of $$ {\overline{D}}^{\ast 0}{\Lambda}_c^{+} $$ D ¯ ∗ 0 Λ c + channel amounts to ~ 90% of $$ {P}_{\psi}^N{(4312)}^{+} $$ P ψ N 4312 + , and is a highly promising channel to be discovered in the near future experiments. Our results favor the interpretation of $$ {P}_{\psi}^N{(4312)}^{+} $$ P ψ N 4312 + as the $$ \overline{D}{\Sigma}_c $$ D ¯ Σ c molecular state with J P = $$ {\left(\frac{1}{2}\right)}^{-} $$ 1 2 − and isospin I = $$ \frac{1}{2} $$ 1 2 .