Regularization in the Gauged Nambu--Jona-Lasinio Model

Various prescriptions employed for regulating gauged Nambu--Jona-Lasinio type models such as the top-quark condensate model are discussed. The use of dimensional regularization maintains gauge invariance but destroys the quadratic divergence in the gap equation. If instead a simple ultraviolet momentum cutoff is used to regulate loop integrals, then gauge invariance is destroyed by a quadratically divergent term as well as by ambiguities associated with arbitrary routing of loop momenta. Finally it is shown that one can use dispersion relations to regulate the top-quark condensate model. This prescription maintains gauge invariance and does not depend on arbitrary shifts in loop momenta.