Properties of ρ and ω mesons at finite temperature and density as inferred from experiment

Abstract

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

Dilepton radiation at the CERN super-proton synchrotron

“…The build-up of the chemical potentials (necessary to preserve the experimentally observed hadron ratios throughout the hadronic cooling) therefore facilitates the observation of in-medium effects in the dilepton spectra. A strong broadening of the ρ in hot and dense matter has also been reported in other calculations at finite T and ̺ B [47,48]. The in-medium ρ-spectral function has been rather extensively employed to calculate dilepton spectra in heavyion collisions.…”

Vector and axial-vector mesons at finite temperature

“…Since the pion gas is rather dilute even at a temperature ∼ 100 MeV, this formula should hold upto higher temperatures than the results of chiral perturbation expansion to first order only. But the problem here is to construct the scattering amplitude, which is reliable [24].…”

All orders Boltzmann collision term from the multiple scattering expansion of the self-energy

“…Equations Eq. (23) and (56) are often used in various calculations such as in-medium particle property calculations [43,44,45,46,47,48,49] and MonteCarlo simulations of many-body systems; but, as far as we know, a systematic derivation has been lacking. Within our quasi-particle approximation, our result is valid for all orders of perturbation theory and any number of participating particles.…”