Constraints on the Fiite-Density Spectral Densities of Vector Channel

Sum rules for the variation of finite-density spectral density of vector channel with baryon density are derived based on dispersion relations and the operator product expansion. These sum rules may serve as constraints on the phenomenological models for the finite-density spectral densities used in the approaches motivated from QCD. Applying these sum rules to the rho meson in nuclear medium with a simple pole-plus-continuum ansatz for the spectral densities, we found that the qualitative features of the QCD sum-rule predictions for the spectral parameters are consistent with these sum rules; however, the quantitative QCD sum-rule results violate the sum rules to certain degree.