Nambu Jona-Lasinio Like Models and the Low Energy Effective Action of QCD

We present a derivation of the low energy effective action of an extended Nambu Jona-Lasinio (ENJL) model to $O(p^4)$ in the chiral counting. Two alternative scenarios are considered on how the ENJL model could originate as a low energy approximation to QCD. The low energy effective Lagrangian we derive includes the usual pseudoscalar Goldstone modes, as well as the lower scalar, vector and axial-vector degrees of freedom. By taking appropriate limits, we recover most of the effective low-energy models discussed in the literature; in particular the gauged Yang-Mills vector Lagrangian, the Georgi-Manohar constituent quark-meson model, and the QCD effective action approach model. Another property of the ensuing effective Lagrangian is that it incorporates most of the short-distance relations which follow from QCD. (We derive these relations in the presence of all possible gluonic interactions to leading order in the $1/N_c$-expansion.) Finally the numerical predictions are compared to the experimental values of the low energy parametersComment: 50 pages, LaTeX, 4 LaTeX figures include

Chiral Lagrangians and Nambu-Jona-Lasinio like models

We discuss the low-energy analysis of models involving quarks and four-fermion couplings. The relation with QCD and with other models of mesons and meson plus quarks at low energies is discussed. A short description of how the heat-kernel expansion can be used to get regularization independent information, is given. The anomaly within this class of models and a physical prescription to obtain the correct flavour anomaly while keeping as much of the VMD aspects as possible is discussed. The major part is the discussion within this framework of the order $p^4$ action and of two and some three-point functions to all orders in momenta and quark masses. Some results on hadronic matrix elements are given.Comment: LaTex, 85 pages, 15 figures (included), uses epsf.sty, review articl