Vector mesons in the nuclear medium with a finite three-momentum

We formulate a QCD sum rule to find the three-momentum (q) dependence of the peak position of the vector meson spectral density in the nuclear medium. For both the longitudinal and transverse polarization direction of the vector meson with respect to q, we find less than a 2% (0.1%) shift of the peak position in nuclear matter density and at [Formula Presented] 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 the [Formula Presented] and [Formula Presented] reactions.