Valid QCD sum rules for vector mesons in nuclear matter

QCD sum rules for vector mesons (ρ, ω, φ) in nuclear matter are reexamined with an emphasis on the reliability of various sum rules. Monitoring the continuum contribution and the convergence of the operator product expansion plays a crucial role in determining the validity of a sum rule. The uncertainties arising from less than precise knowledge of the condensate values and other input parameters are analyzed via a Monte Carlo error analysis. Our analysis leaves no doubt that vector-meson masses decrease with increasing density. This resolves the current debate over the behavior of the vector-meson masses and the sum rules to be used in extracting vector meson properties in nuclear matter. We find a ratio of ρ-meson masses of ${\mathit{m}}_{\mathrm{\rho }}^{\mathrm{*}}$/${\mathit{m}}_{\mathrm{\rho }}$=0.78±0.08 at nuclear matter saturation density.