Constraints on vector mesons with finite momentum in nuclear matter

Using the QCD operator product expansion, we derive the real part of the transverse and longitudinal vector-vector correlation function with the quantum numbers of the ρ and ω mesons to leading order in density and three-momentum (q²) for ω² → -∞. The operator product expansion provides, through the Borel transformed energy dispersion relation, a model independent constraint for the momentum dependence of the vector-meson spectral density in nuclear matter. Existing model calculations for the dispersion effect of the ρ, where the vector-meson nucleon scattering amplitude is obtained by resonance saturation in the s-channel, in general violate this constraint. We trace this to an inconsistent choice for the form factor of the ΔNρ vertex. With a consistent choice, where both the form factor and the coupling constant are obtained from the Bonn potential, the contribution of the Δ is substantially reduced and we find good agreement with the constraint equation. We briefly comment on the implications of our result for attempts to interpret the enhancement of low-mass dileptons in heavy-ion collisions.