Dressing the Quark with QCD Condensates

Abstract

A condensate of $\pvec = 0$ partons in the perturbative vacuum gives rise to a term $\propto\delta^4(p)$ in the free PQCD propagators. The leading condensate contribution to the quark propagator can be exactly summed since there is a factor $\delta^4(p)$ associated to each loop. We calculate the dressed quark propagator in the presence of either a gluon or a quark condensate, for a number of colors $N \to \infty$. The dressed quark propagator satisfies a Dyson-Schwinger type equation which can be exactly solved within our framework. In the case of a gluon condensate the dressed quark propagator has no pole, hence quarks cannot appear in asymptotic states, and moreover the DS equation has a solution which spontaneously breaks chiral symmetry. We also calculate the dressed quark-photon vertex and verify that the corresponding Ward-Takahashi identity is satisfied, and that the dressed self-energy correction to the photon propagator does not shift the physical photon pole.