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

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 $a_0(980)$ .