  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 ${\bf q}^2$ 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 ${\bf q}$ 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.
