PI-K SCATTERING LENGTHS AT FINITE-TEMPERATURE IN THE NAMBU-JONA-LASINIO MODEL

The transition amplitude for pi K scattering is evaluated within the S U(3) Nambu-Jona-Lasinio model. Ordering terms according to the expansi on in 1/N-c leads to a boxlike diagram, t channel diagrams that admit scalar isoscalar (sigma,sigma') exchanges, and a II channel exchange o f a scalar isodoublet sigma(K) that has quantum numbers corresponding to the K-0(1430). Both the Pauli-Villars and O(3) regularization proc edures are used to evaluate the T=0 values of the l=0 scattering lengt hs a(0)(3/2) and a(0)(1/2). The finite temperature dependence is studi ed. We find that the variation in the t channel in the calculation of a(0)(3/2) lends to a change in a(0)(3/2) of a factor of about two over the temperature range of T = 150 MeV.