Studying the scalar bound states of the $K\bar K$ system in the Bethe-Salpeter formalism

TL;DR

This paper investigates the existence of bound states in the $Kar K$ system using the Bethe-Salpeter formalism, revealing small decay widths and suggesting additional structures in certain mesons.

Contribution

It applies the Bethe-Salpeter formalism with ladder and instantaneous approximations to study $Kar K$ bound states, providing new insights into their properties.

Findings

Bound states of $Kar K$ exist with small decay widths.

The results imply other structures may contribute to observed mesons.

Supports the hypothesis of complex internal structures in $f_0(980)$ and $a_0(980)$.

Abstract

We study the possible bound states of the $K\bar K$ system in the Bethe-Salpeter formalism in the ladder and instantaneous approximations. We find that the bound states exist. However, these bound states have very small decay widths. Therefore, besides the possible $K\bar K$ component, there may be some other structures in the observed $f_0(980)$ and $a_0(980)$ .