$ππ$ scattering in the $ρ$-meson channel at finite temperature

Abstract

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 $q\bar q$ 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 $T\geq 0$ is investigated and the motion of the $ρ$-pole as a function of coupling constant and temperature is followed in the complex $\sqrt{s}$-plane. For numerical calculations, parameters are chosen in order that $m_π$, $f_π$ 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 $0\leq T\leq 130$ MeV, and then moves down in energy by about 200 MeV for 130 MeV$\leq T\leq 230$ MeV.