PI-PI SCATTERING IN THE RHO-MESON CHANNEL AT FINITE-TEMPERATURE

We study pi pi 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 (q) over bar and pi pi is constructed via p-ex change in the s-channel. The self-energy of the p-meson contains both quark and pion loop contributions. The analytic structure of the S-mat rix for T greater than or equal to 0 is investigated and the motion of the p-pole as a function of coupling constant and temperature is foll owed in the complex root s-plane. For numerical calculations, paramete rs are chosen in order that m(pi) f(pi), and the experimental pi pi ph ase shifts delta 1/1 at zero temperature are reproduced, and then the behavior of the p-pole as well as the pi pi cross section is investiga ted as a function of the temperature. We find that the position of the p mass stays practically constant for 0 less than or equal to T less than or equal to 130 MeV, and then moves down in energy by about 200 M eV for 130 MeV less than or equal to T less than or equal to 230 MeV. (C) 1998 Elsevier Science B.V.