Pi-Pi scattering lengths at finite temperature

E. Quack; P. Zhuang; Y. Kalinovsky; S. P. Klevansky; J. Hüfner

doi:10.1016/0370-2693(95)00128-8

paper

Pi-Pi scattering lengths at finite temperature

arXiv:hep-ph/9410243 · doi:10.1016/0370-2693(95)00128-8

Abstract

The $s$ -wave $π - π$ scattering lengths $a^{I} (T)$ at finite temperature $T$ and isospin $I = 0, 2$ are calculated within the SU(2) Nambu--Jona-Lasinio model. $a^{2} (T)$ displays a singularity at the Mott temperature $T_{M}$ , defined as $m_{π} (T_{M}) = 2 m_{q} (T_{M})$ , while $a^{0} (T)$ is singular in addition at the lower temperature $T_{d}$ , where $m_{σ} (T_{d}) = 2 m_{π} (T_{d})$ , $m_{σ}$ and $m_{π}$ being the masses of the $σ$ and $π$ mesons, respectively. Numerically we find $T_{d} = 198$ MeV and $T_{M} = 215$ MeV. We speculate on possible experimental consequences.

10 pages, 2 figures, GSI-94-65 and HD-TVP-94-19