Analysis of the $X(1835)$ as a baryonium state with Bethe-Salpeter equation

In this article, we take the X(1835) as a pseudoscalar baryonium state, and calculate the mass spectrum of the baryon-antibaryon bound states $p\bar{p}$, $\Sigma\bar{\Sigma}$, $\Xi\bar{\Xi}$, and $\Lambda\bar{\Lambda}$ in the framework of the Bethe-Salpeter equation with a phenomenological potential. The numerical results indicate the $p\bar{p}$, $\Sigma\bar{\Sigma}$ and $\Xi\bar{\Xi}$ bound states maybe exist, and the $X(1835)$ can be tentatively identified as the $p\bar{p}$ bound state.