Bosonized Lagrangians in higher orders of the chiral expansion

The derivation of effective mesonLagrangians in higher orders of the chiral expansion from bosonization of the four-quark interaction of the extended Nambu–Jona-Lasinio (NJL) model, treated as a local approximation of low-energy QCD, is reviewed. The calculated heat-kernel coefficients for the quark determinant of the bosonized NJL model through seventh order are presented in a systematic way. The results are used to fix the structure coefficients of the effective chiral Lagrangians in orders p 4 and p 6 of the momentum expansion. Various aspects of the use of bosonized Lagrangians to describe low-energy meson processes are discussed: the reduction of vector, axial-vector, and scalar resonances, regularization of graphs with meson loops, and the dependence of the phenomenological structure coefficients on the renormalization scheme and regularization parameters. Questions related to the physical justification of the NJL model as a low-energy limit of QCD are also discussed. Nonlocal corrections to the structure coefficients of bosonized Lagrangians are studied in this context.