Scalar and vector one-loop massive tadpole light-front gauge Feynman integrals

TL;DR

This paper applies negative dimensional integration to compute finite parts of one-loop massive tadpole integrals in light-front gauge, providing new results in a challenging gauge setting.

Contribution

It introduces a novel application of NDIM to obtain finite parts of massive Feynman integrals in light-front gauge, expanding the limited existing results.

Findings

Derived new finite part results for one-loop massive tadpole integrals

Demonstrated the effectiveness of NDIM in light-front gauge calculations

Extended the set of known Feynman integrals in this gauge

Abstract

Light-front gauge is the most popular one to work with fundamental interactions, due to its characteristic maximum kinematical Poincare operators that it allows. However, it is also known to be one of the trickiest gauges one can work with for gauge theories, due to its singular nature. So, in terms of perturbative calculations in the light-front, there are only a few published and tabulated results for the pertinent Feynman integrals, mostly involving massless integrals. And the majority of the results given are only for the divergent parts of them and the complete closed form (or with the finite parts) of these are not known. In this manuscript, we use the technique of negative dimensional integration (NDIM) for the simplest of the one-loop massive integrals as a working bench for massive Feynman integrals in the light-front and show that novel results for the finite parts not known before are obtained.