Loop integrals in three outstanding gauges: Feynman, Light-cone and Coulomb

TL;DR

This paper demonstrates the effectiveness of the negative dimensional integration method (NDIM) for calculating complex loop integrals across Feynman, light-cone, and Coulomb gauges, including multi-loop and prescriptionless cases.

Contribution

It introduces NDIM as a versatile technique for loop integrals in various gauges, successfully handling multi-loop and prescriptionless calculations beyond one-loop order.

Findings

NDIM effectively computes two-loop integrals in Feynman gauge.

NDIM handles prescriptionless calculations in light-cone gauge.

NDIM successfully evaluates Coulomb gauge integrals in split dimensional regularization.

Abstract

We apply negative dimensional integration method (NDIM) to three outstanding gauges: Feynman, light-cone and Coulomb gauges. Our aim is to show that NDIM is a very suitable technique to deal with loop integrals, being them originated from any gauge choice. In Feynman gauge we perform scalar two-loop four-point massless integrals; in the light-cone gauge we calculate scalar two-loop integrals contributing for two-point functions without any kind of prescriptions, since NDIM can abandon such devices -- this calculation is the first test of our prescriptionless method beyond one-loop order; finally, for the Coulomb gauge we consider a four propagator massless loop integral, in the split dimensional regularization context.