Landau-Khalatnikov-Fradkin transformations for the two loop massless quark propagator

TL;DR

This paper derives the Landau-Khalatnikov-Fradkin transformations for the two-loop massless quark propagator, providing a more efficient way to evaluate gauge dependence in quantum chromodynamics.

Contribution

We explicitly derive the LKFT for the quark propagator at two loops and demonstrate a faster evaluation method by simplifying the diagram calculations.

Findings

Faster evaluation of gauge-dependent terms

Explicit two-loop LKFT derivation for quark propagator

Comparison with previous literature confirms consistency

Abstract

Landau-Khalatnikov-Fradkin transformations (LKFTs) yield the gauge dependence of correlation functions within the class of linear covariant gauges. We derive the LKFT for the quark propagator and explicitly evaluate it up to the two loop level in the chiral limit. Although the number of diagrams to be evaluated is significantly larger than with the conventional computational scheme, the diagrams are simpler in nature, thereby leading to a considerably faster evaluation of the gauge dependent part than naively expected. Finally, we also resum the LKFT generated terms and compare our results with earlier work in the literature.