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We calculate the correlation functions of $0^{++}$ $q\bar q$, $s\bar s$ andglueball in the QCD sum rules and obtain the mass matrix where non-diagonalterms are determined by the cross correlations among the three states.Diagonalizing the mass matrix and identifying the eigenstates as the physical$0^{++}$ scalar mesons, we can determine the mixing. Concretely, ourcalculations determine the fractions of $q\bar q$, $s\bar s$ and glueball inthe physical states $f_0(1370)$, $f_0(1500)$ and $f_0(1710)$, the results areconsistent with that gained by the phenomenological research.

Study on the mixing among the $0^{++}$ mesons around $1\sim 2$ $\mathrm{GeV}$ with the QCD sum rules