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(p4) 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 with the experimental values of the low-energy parameters.