Gauge invariance and confinement in a generalized Nambu-Jona-Lasinio model.

Abstract

We discuss the quark-antiquark loop diagrams of an extended version of the Nambu{endash}Jona-Lasinio (NJL) model that includes a description of confinement. We show how the constraints of gauge invariance affect the calculations of such diagrams, if the {ital q{bar q}} system has the quantum numbers of the rho or omega mesons. In the NJL model without confinement, gauge invariance may be maintained by using a regularization scheme that respects that symmetry. Alternatively, gauge-invariance constraints may be imposed by introducing a substraction procedure when evaluating the {ital q{bar q}} loop integrals (vacuum polarization diagrams). We discuss the merits of such subtraction procedures in the presence of a confining interaction. We also provide a calculation of the vacuum polarization diagrams of the NJL model that includes the effects of confinement and also satisfies the constraints imposed by gauge invariance. Our analysis provides some justification for the subtraction procedure used in several studies of the NJL model. We also show, in a rather clear fashion, how confinement serves to change the analytic properties of the polarization tensors, so that the tensor for the theory with confinement has only a physical cut structure in the region of interest. {copyright} {ital 1996 The American Physicalmore » Society.}« less