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

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 $a_0(980)$ .

Comments: 23 pages, LaTeX2e. Discussions on the legitimacy of the ladder approximation and the instantaneous approximation are added. Recognized typos have been corrected. Several references added