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

TL;DR

This paper uses QCD sum rules to analyze the mixing of scalar mesons around 1-2 GeV, identifying their quark and glueball components and comparing results with phenomenological studies.

Contribution

It introduces a method to determine the mixing fractions of quark-antiquark and glueball components in scalar mesons using the QCD sum rules framework.

Findings

Determined the mixing fractions of $q\bar q$, $s\bar s$, and glueball in $f_0(1370)$, $f_0(1500)$, and $f_0(1710)$.

Results are consistent with previous phenomenological research.

Provided a mass matrix approach to analyze scalar meson mixing.

Abstract

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.