The properties of the $S$-wave $D_s{\bar{D}}_s$ bound state

Abstract

In this work, we investigate possible bound states of the $D_s{\bar{D}}_s$ system in the Bethe-Salpeter formalism in the ladder and instantaneous approximations. By numerically solving the Bethe-Salpeter equation with a kernel that includes the contributions from $\varphi$ and $J/\psi$ exchanges, we confirm the existence of a bound state in the $D_s{\bar{D}}_s$ system. We further investigate the partial decay widths of the $D_s{\bar{D}}_s$ bound state into $D\bar{D}$, ${\eta }_c\eta$, and $J/\psi \omega$, finding that these partial widths are sensitive to the parameter $\alpha$ in our model. Notably, we observe that the dominant decay channel for the $D_s{\bar{D}}_s$ bound state is that into $D\bar{D}$.