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

By Xu-Hao Yuan, Liang Tang, Mao-Zhi Yang and Xue-Qian Li


We calculate the correlation functions of $0^{++}$ $q\bar q$, $s\bar s$ and glueball in the QCD sum rules and obtain the mass matrix where non-diagonal terms 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, our calculations determine the fractions of $q\bar q$, $s\bar s$ and glueball in the physical states $f_0(1370)$, $f_0(1500)$ and $f_0(1710)$, the results are consistent with that gained by the phenomenological research.Comment: 15 pages, 6 figures, discussion slightly modified and more references adde

Topics: High Energy Physics - Phenomenology
Year: 2011
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