Feynman integrals with tensorial structure in the negative dimensional integration scheme

TL;DR

This paper extends the negative dimensional integration method (NDIM) to efficiently compute Feynman integrals with tensorial structures, revealing new degeneracies and alternative calculation methods.

Contribution

It introduces a straightforward approach to handle tensorial Feynman integrals with NDIM and uncovers unexpected degeneracies in the results.

Findings

NDIM can be applied to tensorial Feynman integrals.

Two alternative calculation methods are proposed.

Degeneracies in the final results are identified.

Abstract

Negative dimensional integration method (NDIM) is revealing itself as a very useful technique for computing Feynman integrals, massless and/or massive, covariant and non-covariant alike. Up to now, however, the illustrative calculations done using such method are mostly covariant scalar integrals, without numerator factors. Here we show how those integrals with tensorial structures can also be handled with easiness and in a straightforward manner. However, contrary to the absence of significant features in the usual approach, here the NDIM also allows us to come across surprising unsuspected bonuses. In this line, we present two alternative ways of working out the integrals and illustrate them by taking the easiest Feynman integrals in this category that emerges in the computation of a standard one-loop self-energy diagram. One of the novel and as yet unsuspected bonus is that there are degeneracies in the way one can express the final result for the referred Feynman integral.