The quark gap equation in light-cone gauge

Abstract

We calculate the quark self-energy correction in light-cone gauge 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. Therefore, the calculation of the distribution amplitudes simplifies significantly provided that wave functions and propagators are obtained in that gauge. In here, 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, as well as a third complex-valued amplitude, are found to depend on the relative orientation of the quark momentum and a light-like four-vector, which expresses a geometric gauge dependence of the propagator.

Accepted for publication in PRD. An improved numerical treatment of divergences that occur in the C functions and use of the Cornwall gluon propagator derived in pinch technique lead to revised numerical results. In particular, the C functions in Figs. 3 and 6 are very small or consistent with zero depending on the frame of the quark. The conclusions are barely modified