ππ scattering in the ϱ-meson channel at finite temperature

We study ππ scattering in the I = 1, J^P = 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 q overlineq 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 m_π, ƒ _π and the experimental ππ phase shifts δ₁¹ 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.