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.
Bibliographical noteFunding Information:
We would like to thank T. Hatsuda, E Klingl, M. Lutz, W. Weise for useful discussions. The work of S. H. Lee is supported by KOSEF through grant no. 971-0204-017-2 and 976-0200-002-2, by the Korean Ministry of Education through grant no. 98-015-D00061 and by a Humboldt fellowship. The work of H. Kim is supported by a Research Fellowships of the Japan Society for the Promotion of Science.
All Science Journal Classification (ASJC) codes
- Nuclear and High Energy Physics