Chiral symmetry breaking in the presence of a confining interaction

We study chiral symmetry breaking, making use of a generalized Nambu endash Jona-Lasinio (NJL) model that includes a description of confinement. The Schwinger-Dyson and Bethe-Salpeter equations are solved for our model of the self-energy of a quark. We show that our analysis is consistent with the Goldstone theorem. That is, the pion has zero mass, if the current quark masses are zero. We use a confining interaction with a (Dirac) matrix structure that leads to simple equations for the self-energy and for a vertex function that serves to sum a ladder of confining interactions. We consider spacelike values of q2, and carry out our analysis in a Euclidean momentum space. For timelike q2, we use calculational procedures that we have developed in our earlier work in order to exhibit properties of the confining vertex. For the spacelike values of q2 considered here, we see that the effects due to the introduction of our model of confinement are small. (However, such effects are very important for timelike q2. Their consideration is essential, if we wish to study mesons, such as the rho and omega, in our model.) copyright 1997 The American Physical Society