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

Using the QCD Operator Product Expansion, we derive the real part of the transverse and longitudinal vector vector correlation function with the ρ, ω quantum numbers to leading order in density and in q² at -ω² → ∞. To dimension 6, only twist-2 and 4 operators contribute. These OPE, through the energy dispersion relation, provide model independent constraints for the 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.