rho propagation and dilepton production at finite pion density and temperature

We study the propagation properties of the rho vector in a dense and hot pion medium. We introduce a finite value of the chemical potential associated to a conserved pion number and argue that such description is valid during the hadronic phase of a relativistic heavy-ion collision, between chemical and thermal freeze-out, where the strong interaction drives pion number to a fixed value. By invoking vector dominance and rho saturation, we also study the finite pion density effects into the low mass dilepton production rate. We find that the distribution moderately widens and the position of the peak shifts toward larger values of the pair invariant mass, at the same time that the height of the peak decreases when the value of the chemical potential grows. We conclude by arguing that for the description of the dilepton spectra at ultra-relativistic energies, such as those of RHIC and LHC, the proper treatment of the large pion density might be a more important effect to consider than the influence of a finite baryon density.