Mixings of four-quark components in light nonsinglet scalar mesons in QCD sum rules

Mixings of four-quark components in the nonsinglet scalar mesons are studied in the QCD sum rules. We propose a formulation to evaluate the cross correlators of $q\overline{q}$ and $qq\overline{q}\overline{q}$ operators and to define the mixings of different Fock states in the sum rule. It is applied to the nonsinglet scalar mesons, $a_0$ and $K_0^{*}$. It is found that the four-quark operators predict lower masses than the $q\overline{q}$ operators and that the four-quark states occupy about 70%–90% of the lowest mass states.