Pi-Pi scattering lengths at finite temperature

Abstract

The $s$-wave $\pi -\pi$ 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 $m_{\pi }(T_M)=2m_q(T_M)$, while $a^0(T)$ is singular in addition at the lower temperature $T_d$, where $m_{\sigma }(T_d)=2m_{\pi }(T_d)$, $m_{\sigma }$ and $m_{\pi }$ being the masses of the $\sigma$ and $\pi$ mesons, respectively. Numerically we find $T_d=198$MeV and $T_M=215$MeV. We speculate on possible experimental consequences.

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