Mass shift, width broadening and spectral density of $rho;-mesons produced in heavy ion collisions

Abstract

Modifications of ρ-mesons formed at the last stage of evolution of hadronic matter produced in heavy ion collisions are studied. It is found that while the mass shift is on the order of a few tens of MeV, the width and spectral density become so broad that ρ may lose its identity as a well defined resonance.The problem of how the properties of hadrons change in hadronic or nuclear matter in comparison to their free space values has attracted a lot of attention. It is clear on physical grounds that the in-medium mass shift and width broadening of a particle are only due to its interaction with the constituents of the medium, for not too dense media anyway. Thus one can use phenomenological information on this interaction to calculate the mass shift and width broadening [1,2].For meson a scattering on hadron b in the medium the contribution to the self-energy is:where E and p are the energy and momentum of the meson, ω 2 = m 2 b + k 2 , n b is the occupation number, and f ab is the forward scattering amplitude. The normalization of the amplitude corresponds to the standard form of the optical theorem σ = (4π/q cm )Imf (cm) (s). The applicability of eq. (1) is limited to those cases where interference between sequential scatterings is negligible. In the limit that the target particles b move nonrelativistically, Π ab = −4πf (b rest frame) ab ρ b , where ρ b is the spatial density. This corresponds to the mass shift and width broadening[2]These relations hold also in the general case provided the amplitudes are averaged over momentum distributions of the constituents. We assumed[3] that ρ-mesons are formed during the last stage of the evolution of hadronic matter created in a heavy ion collision, * On leave of absense from: ITEP,