Effective chiral meson Lagrangian for the extended Nambu–Jona-Lasinio model

Abstract

We present a derivation of the low-energy effective meson Lagrangian of the extended Nambu--Jona-Lasinio (ENJL) model. The case with a linear realization of broken $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)$ chiral symmetry is considered. There are two crucial points why this revision is needed. First, it is the explicit chiral symmetry breaking effect. On the basis of symmetry arguments we show that relevant contributions related with the current quark mass terms are absent from the effective Lagrangians derived so far in the literature. Secondly we suggest a chiral covariant way to avoid the nondiagonal terms responsible for the pseudoscalar--axial-vector mixing from the effective meson Lagrangian. In the framework of the linear approach this diagonalization has not been done correctly. We discuss as well the $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)/SU(2)$ coset space parametrization for the revised Lagrangian (nonlinear ansatz). Our Lagrangian differs in an essential way from those that have been derived until now on the basis of both linear and nonlinear realizations of chiral symmetry.