$π- π$ Scattering Lengths and Chiral Condensate in NJL Model

Abstract

Within the general framework of SU(2) Nambu-Jona-Lasinio model beyond mean-field approximation, the S-wave $π- π$ scattering lengths $a_0^0$ and $a_0^2$ are calculated. The numerical results are in agreement with that analyzed from recent experiment $πN \to ππN$ data by using Chew-Low-Goebel technique, and the corresponding chiral condensate $<{\bar q}q>$ is around $-(250 {\rm MeV})^3$, which is close to the ones obtained from lattice and sum rules.