π-π scattering lengths at finite temperature

The s-wave π-π scattering lengths a1(T) at finite temperature T and isospin I = 0,2 are calculated within the SU(2) Nambu-Jona-Lasinio model. a2(T) displays a singularity at the Mott temperature TM, defined as mπ(TM) = 2mq(TM), while a0(T) is singular in addition at the lower temperature Td, where mσ(Td) = 2mπ(Td), mρ and mπ being the masses of the σ and π mesons, respectively. Numerically we find Td = 198 MeV and TM = 215 MeV. We speculate on possible experimental consequences.