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The mass shift, width broadening, and spectral density for and mesons in a heat bath of nucleons and pions are calculated using a general formula which relates the self-energy to the real and imaginary parts of the forward scattering amplitude. We use experimental data to saturate the scattering amplitude at low energies with resonances and include a background Pomeron term, while at high energies a Regge parametrization is used. The real part obtained directly is compared with the result of a dispersion integral over the imaginary part. The peaks of the spectral densities are little shifted from their vacuum positions, but the widths are considerably increased due to collisional broadening. Where possible we compare with the UrQMD model and find quite good agreement. At normal nuclear matter density and a temperature of 150 MeV the spectral density of the meson has a width of 345 MeV, while that for the is in the range 90-150 MeV. 64 035202-1 FIG. 6. The vector meson widths as a function of momentum p. Results are shown for nucleon densities of 0, n 0 , and 2n 0 ͑where equilibrium nuclear matter density n 0 ϭ0.16 fm Ϫ3 ) and temperatures of 100 and 150 MeV. For the meson results are given for the multiresonance and the two-resonance models.PROPERTIES OF and MESONS AT FINITE . . . PHYSICAL REVIEW C 64 035202 035202-7

Mass shifts ∆m of particles in nuclear matter relative to their vacuum values are considered. A general formula relating ∆m(E) (E is the particle energy) to the real part of the forward particle-nucleon scattering amplitude Ref (E) is presented and its applicability domain is formulated. The ρ-meson mass shift in nuclear matter is calculated at 2 < ∼ E ρ < ∼ 7 GeV for transversally and longitudinally polarized ρ-mesons with the results: ∆m T ρ ∼ 50 MeV and ∆m L ρ ∼ 10 MeV at normal nuclear density.PACS numbers: 21.65.+f, 12.40.Vv The problem of how the properties of mesons and baryons change in nuclear matter in comparison to their free values has attracted a lot of attention recently. Among these properties the first of interest are mass shifts of particles in nuclear matter. This interest is related to the fact that it was possible to calculate by QCD sum rules and on the lattice almost all masses of low lying mesons and baryons, and a hope appears to extend these calculations to the case of particles is embedded in nuclear medium. On the other hand, the values of particle masses can be measured experimentally -at least some of them -and some data started to appear. In this aspect experiments on heavy ion collisions, in which the dependence of particle masses on nuclear density can be found, are very promising.In early theoretical investigations of this problem [1,2] one or another model of strong 1