Pseudo-Evanescent Feynman Integrals from Local Subtraction

TL;DR

This paper presents a novel method for computing pseudo-evanescent Feynman integrals using local subtraction, simplifying two-loop calculations and enabling a new computation of the two-loop all-plus five-point amplitude.

Contribution

The paper introduces a new approach leveraging local subtraction techniques to evaluate pseudo-evanescent integrals, simplifying complex two-loop calculations.

Findings

Many pseudo-evanescent integrals reduce to products or one-fold integrals of one-loop integrals.

Recomputed the two-loop all-plus five-point amplitude using the new method.

Soft and collinear contributions cancel against infrared structures, leaving ultraviolet contributions as finite remainders.

Abstract

We introduce a new approach for the computation of the class of Feynman integrals whose integrands vanish in strictly four-dimensions, so-called ''pseudo-evanescent'' integrals. We argue that, up to $\mathcal{O}(\epsilon)$ corrections, local subtraction techniques can be used to express pseudo-evanescent integrals in terms of contributions from infrared and ultraviolet regions of loop-momentum space. We study two-loop examples and find that many pseudo-evanescent Feynman integrals are reduced to either products of one-loop integrals or one-fold integrals thereof. As a demonstration of the power of our approach, we use it to recompute the two-loop all-plus five-point amplitude. We find that, up to scheme-dependent logarithms, all contributions from soft and collinear regions cancel exactly against known infrared structure and that the finite remainder is entirely given by contributions from ultraviolet regions.