Vector meson dispersion in medium

In nuclear medium, in addition to possible change in the vector meson mass, there will be breaking of Lorentz invariance and to leading order in the three momentum, the vector meson dispersion relation would be modified to ω² - (1 + a)q² - m²_V = 0 with a ≠ 0. We formulate a QCD sum rule to find a to leading order in density, for ρ, ω and φ mesons. For both the longitudinal and transverse polarization direction of the vector meson with respect to q, we find less than 2 % (0.1 %) shift of the peak position at nuclear matter density and at q = 0.5 GeV/c for the ρ, ω (φ) mesons. This justifies neglecting the three momentum dependence and the polarization effect when implementing the universal scaling laws of the vector mesons in understanding the dilepton spectrum in A-A and p-A reaction.