The vector-scalar mixing in nuclear medium and the two quark component of scalar meson from QCD sum rules

Abstract

We derive the QCD sum rules for the vector and scalar meson mixing in nuclear medium, using a two quark interpolating field for both mesons. Modeling the mixing via a nucleon hole contribution with known coupling constant, the sum rule can be used to determine the overlap of the interpolating field and the scalar meson. In the I=0 channel, we find a stable Borel curve and an overlap that is about 10% of the corresponding value in the pseudo scalar or vector channel. The sum rule in the I=1 channel is less reliable but also consistent with a small value for the overlap. These results suggest that both the $\sigma$ and $a_0$ have a small two quark and thus probably a large tetraquark components. We discuss the possibility of observing these scalar mesons from vector mesons emanating from the nuclear medium.