Possible bound states of Heavy Baryonium and Heavy Dibaryon systems

In this work, we systematically study the heavy baryonium and heavy dibaryon systems using the Bethe-Salpeter equation in the ladder and instantaneous approximations for the kernel. Our results indicate that all the heavy baryonium systems, specifically ${\mathrm{\Lambda }}_Q{\bar{\mathrm{\Lambda }}}_Q$, ${\mathrm{\Xi }}_Q{\bar{\mathrm{\Xi }}}_Q$, ${\mathrm{\Sigma }}_Q{\bar{\mathrm{\Sigma }}}_Q$, ${\mathrm{\Xi }}_Q^{\mathrm{\prime }}{\bar{\mathrm{\Xi }}}_Q^{\mathrm{\prime }}$, and ${\mathrm{\Omega }}_Q{\bar{\mathrm{\Omega }}}_Q$ ($Q=c,b$), can form bound states. Among the heavy dibaryon systems, only the ${\mathrm{\Xi }}_Q{\mathrm{\Xi }}_Q$ system with $I=0$ and the ${\mathrm{\Sigma }}_Q{\mathrm{\Sigma }}_Q$ systems with $I=0$ and $I=1$ can exist as bound states. Additionally, the ${\mathrm{\Sigma }}_Q{\bar{\mathrm{\Sigma }}}_Q$ system with $I=2$ and the ${\mathrm{\Sigma }}_Q{\mathrm{\Sigma }}_Q$ system with $I=1$ are not deeply bound.