Study of molecular ND bound states in the Bethe-Salpeter equation approach

Abstract

We study the ${\mathrm{\ensuremath{\Lambda}}}_{c}(2595{)}^{+}$ and ${\mathrm{\ensuremath{\Sigma}}}_{c}(2800{)}^{0}$ states as the $ND$ bound systems in the Bethe-Salpeter formalism in the ladder and instantaneous approximations. With the kernel induced by $\ensuremath{\rho}$, $\ensuremath{\omega}$ and $\ensuremath{\sigma}$ exchanges, we solve the Bethe-Salpeter equations for the $ND$ bound systems numerically and find that the bound states may exist. We assume that the observed states ${\mathrm{\ensuremath{\Lambda}}}_{c}(2595{)}^{+}$ and ${\mathrm{\ensuremath{\Sigma}}}_{c}(2800{)}^{0}$ are $S$-wave $ND$ molecular bound states and calculate the decay widths of ${\mathrm{\ensuremath{\Lambda}}}_{c}(2595{)}^{+}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Sigma}}}_{c}^{0}{\ensuremath{\pi}}^{+}$ and ${\mathrm{\ensuremath{\Sigma}}}_{c}(2800{)}^{0}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}_{c}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$.