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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 instantaneousapproximations. By numerically solving the Bethe-Salpeter equation with akernel that includes the contributions from $\phi$ and $J/\psi$ exchanges, weconfirm the existence of a bound state in the $D_s\bar{D}_s$ system. We furtherinvestigate 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 widthsare sensitive to the parameter $\alpha$ in our model. Notably, we observe thatthe dominant decay channel for the $D_s\bar{D}_s$ bound state is that into$D\bar{D}$.

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