- th / 9 71 20 51 v 1 1 5 D ec 1 99 7 ππ scattering in the ρ - meson channel at finite temperature

We study ππ scattering in the I = 1, JP = 1 channel at finite temperature in the framework of the extended Nambu-Jona-Lasinio model that explicitly includes vector and axial-vector degrees of freedom in addition to the usual scalar and pseudoscalar sector. The S-matrix in the coupled channels qq̄ and ππ is constructed via ρ-exchange in the s-channel. The self-energy of the ρ-meson contains both quark and pion loop contributions. The analytic structure of the S-matrix for T ≥ 0 is investigated and the motion of the ρ-pole as a function of coupling constant and temperature is followed in the complex √ s-plane. For numerical calculations, parameters are chosen in order that mπ, fπ and the experimental ππ phase shifts δ 1 1 at zero temperature are reproduced, and then the behavior of the ρ-pole as well as the ππ cross section is investigated as a function of the temperature. We find that the position of the ρ mass stays practically constant for 0 ≤ T ≤ 130 MeV, and then moves down in energy by about 200 MeV for 130 MeV≤ T ≤ 230 MeV. 25.75.-q, 12.39.Ba, 21.65.+f, 24.85.+p