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

TL;DR

This paper uses the Bethe-Salpeter formalism to confirm a bound state in the $D_sar{D}_s$ system and analyzes its decay channels, highlighting the dominant decay into $Dar{D}$.

Contribution

First to confirm the $D_sar{D}_s$ bound state using Bethe-Salpeter equation with meson exchange kernels.

Findings

Confirmed existence of $D_sar{D}_s$ bound state.

Decay width into $Dar{D}$ is dominant.

Decay widths are sensitive to model parameter $eta$.

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 $\phi$ 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 $D\bar{D}$.