$\pi -\pi$ 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 $\pi -\pi$ scattering lengths $a_0^0$ and $a_0^2$ are calculated. The numerical results are in agreement with that analyzed from recent experiment $\pi N\to \pi \pi N$ data by using Chew-Low-Goebel technique, and the corresponding chiral condensate $<\bar{q}q>$ is around $-(250\mathrm{MeV}{)}^3$, which is close to the ones obtained from lattice and sum rules.

Comments: 1 RevTeX file, 9 pages with two tables