PI-PI SCATTERING LENGTHS AT FINITE-TEMPERATURE

The s-wave pi-pi scattering lengths a(1)(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.