Modifications of the rho-meson from the virtual pion cloud in hot and dense matter

The modification of the rho-meson self-energy due to the coupling to in-med ium pions is calculated consistently at finite baryon density and temperatu re, keeping the full 3-momentum dependence in a gauge invariant way. As a f unction of nucleon density, the rho-meson spectral function is strongly enh anced in the invariant mass region M less than or similar to 650 MeV, while the maximum, i.e., the pole mass, is slightly shifted upwards. As a functi on of temperature, for fixed nucleon density, the imaginary part of the sel f-energy increases further due to Bose-enhancement. At the same time the ma ss shift from the real part becomes very large. As a consequence of these m edium effects, the dilepton rate in the low-mass region M less than or simi lar to 650 MeV increases strongly, while the peak at M approximate to 770 M eV disappears. (C) 2000 Elsevier Science B.V. All rights reserved.