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

TL;DR

This paper uses the Bethe-Salpeter equation to systematically study two-pseudoscalar meson systems, identifying several potential bound states and highlighting the importance of heavy meson exchange contributions.

Contribution

It provides a comprehensive numerical analysis of S-wave bound states of two pseudoscalar mesons, including heavy meson exchange effects, which was not thoroughly explored before.

Findings

Multiple bound states identified, including $Kar{K}$, $DK$, and others.

Heavy meson exchange significantly affects bound state formation.

Bound states with isospin zero can exist in various meson systems.

Abstract

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.