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Constraint on K Kbar compositeness of the a0(980) and f0(980) resonances from their mixing intensity

Structure of the $a_{0}(980)$ and $f_{0}(980)$ resonances is investigated with the $a_{0}(980)$-$f_{0}(980)$ mixing intensity from the viewpoint of compositeness, which corresponds to the amount of two-body states composing resonances as well as bound states. For this purpose we first formulate the $a_{0}(980)$-$f_{0}(980)$ mixing intensity as the ratio of two partial decay widths of a parent particle, in the same manner as the recent analysis in BES experiments. Calculating the $a_{0}(980)$-$f_{0}(980)$ mixing intensity with the existing Flatte parameters from experiments, we find that many combinations of the $a_{0}(980)$ and $f_{0}(980)$ Flatte parameters can reproduce the experimental value of the $a_{0}(980)$-$f_{0}(980)$ mixing intensity by BES. Next, from the same Flatte parameters we also calculate the $K \bar{K}$ compositeness for $a_{0}(980)$ and $f_{0}(980)$. Although the compositeness with the correct normalization becomes complex in general for resonance states, we find that the Flatte parameters for $f_{0}(980)$ imply large absolute value of the $K \bar{K}$ compositeness and the parameters for $a_{0}(980)$ lead to small but nonnegligible absolute value of the $K \bar{K}$ compositeness. Then, connecting the mixing intensity and the $K \bar{K}$ compositeness via the $a_{0}(980)$- and $f_{0}(980)$-$K \bar{K}$ coupling constants, we establish a relation between them. As a result, a small mixing intensity indicates a small value of the product of the $K \bar{K}$ compositeness for the $a_{0}(980)$ and $f_{0}(980)$ resonances. Moreover, the experimental value of the $a_{0}(980)$-$f_{0}(980)$ mixing intensity implies that the $a_{0}(980)$ and $f_{0}(980)$ resonances cannot be simultaneously $K \bar{K}$ molecular states.