Vector mesons in nuclear medium with small three momentum, a QCD sum rule approach

Abstract

Using the QCD Operator Product Expansion, we derive the real part of the transverse and longitudinal vector vector correlation function with the $\rho ,\omega$ quantum numbers to leading order in density and in ${\mathbf{q}}^2$ at $-{\omega }^2\to \infty$. To dimension 6, only twist-2 and 4 operators contribute. These OPE, through the energy dispersion relation, provide model independent constraints for the $\mathbf{q}$ dependence of the vector meson spectral density in nuclear medium. We further make a QCD sum rule type of analysis to extract the momentum dependence of the vector meson dispersion relation in medium. The contributions from twist-2 operators are added up to infinite order to check the validity of the OPE at the relevant Borel window.

Comments: 6 pages, talk presented at the workshop "QCD at finite baryon density" Zif, Bielefeld, April 27-30, 1998. Submitted to Nucl. Phys. A