Thermal production of the ρ meson in the π⁺π⁻ channel

Recent measurements of the π⁺π⁻ invariant-mass distribution at RHIC show a shifted peak for the ρ meson in 100A GeV in peripheral Au+Au and even in p+p collisions. A recent theoretical study based on a picture of in-medium production rates of pions showed that a large shift could result from a combination of the Boltzmann factor and the collisional broadening of the ρ. Here we argue that the two-pion density of states is the appropriate quantity if one assumes a sudden breakup of the system. Methods for calculating the density of states which include Bose effects are derived. The resulting invariant-mass distributions are significantly enhanced at lower masses and the ρ peak is shifted downward by ∼35 MeV.