The quark gap equation in light-cone gauge

TL;DR

This paper investigates the quark self-energy in light-cone gauge using Dyson-Schwinger equations, revealing gauge-dependent features of quark propagators and simplifying the calculation of distribution amplitudes.

Contribution

It introduces a leading-truncation Dyson-Schwinger approach with a Ward identity-derived dressed vertex in light-cone gauge, highlighting gauge dependence of quark propagator functions.

Findings

Quark mass and wave functions depend on the quark momentum orientation.

A third complex amplitude arises with geometric gauge dependence.

Simplification of distribution amplitude calculations 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.