Quark gap equation in light-cone gauge

Abstract

An exploratory nonperturbative calculation of the quark propagator in light-cone gauge is motivated by distribution amplitudes whose definition implies a Wilson line. The latter serves to preserve the gauge invariance of the hadronic amplitudes and becomes trivial in light-cone gauge. To that end, we explore the corresponding Dyson-Schwinger equation in its leading truncation and with a dressed vertex derived from a Ward identity in light-cone gauge. The quark’s mass and wave renormalization functions are found to depend on the orientation of the quark momentum relative to the lightlike four-vector below 1 GeV, which expresses the light-cone gauge dependence of the propagator, while a third, complex-valued amplitude exhibits little dependence on that orientation and vanishes in the quark’s rest frame.