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

Abstract

The S-wave $\pi -\pi$ 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 ${\Lambda }_f$ and the meson momentum cut-off ${\Lambda }_b$, also the S-wave $\pi -\pi$ scattering lengths in NJL model can be uniquely determined.

12 pages, Revtex, 2 eps files, uses axodraw.sty

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