Investigating $S$-wave bound states composed of two pseudoscalar mesons

In this work, we systematically investigate the two-pseudoscalar meson systems with the Bethe-Salpeter equation in the ladder and instantaneous approximations. By solving the Bethe-Salpeter equation numerically with the kernel containing the one-particle exchange diagrams, we find that the $K\bar{K}$, $DK$, $B\bar{K}$, $D\bar{D}$, $B\bar{B}$, $BD$, $D\bar{K}$, $BK$, and $B\bar{D}$ systems with $I=0$ can exist as bound states. We also study the contributions from heavy meson ($J/\psi$ and $\Upsilon$) exchanges, and we find that the contribution from heavy meson exchange can not be ignored.