S-wave $π- π$ Scattering Lengths in the SU(2) NJL Model Beyond Mean-field Approximation

Abstract

The S-wave $π- π$ scattering lengths $a_0$ and $a_2$ are calculated to the lowest order of $1/N_c$ expansion in the general framework of SU(2) NJL model beyond mean-field approximation. It is shown that using the universal curve of $a_0$ and $a_2$ the four NJL parameters, i.e., the current quark mass $m_0$, the four fermion coupling constant $G$, the quark momentum cut-off $Λ_f$ and the meson momentum cut-off $Λ_b$, also the S-wave $π- π$ scattering lengths in NJL model can be uniquely determined.