A quasi-finite basis for multi-loop Feynman integrals

TL;DR

This paper introduces a novel method to decompose multi-loop Feynman integrals into quasi-finite forms, simplifying divergence analysis and enabling straightforward analytical or numerical evaluation.

Contribution

It develops a new approach that employs integration by parts reduction to produce quasi-finite integrals, improving practicality over previous methods.

Findings

Allows explicit divergence separation in integrals

Facilitates direct analytical integration

Enables numerical evaluation of convergent integrals

Abstract

We present a new method for the decomposition of multi-loop Euclidean Feynman integrals into quasi-finite Feynman integrals. These are defined in shifted dimensions with higher powers of the propagators, make explicit both infrared and ultraviolet divergences, and allow for an immediate and trivial expansion in the parameter of dimensional regularization. Our approach avoids the introduction of spurious structures and thereby leaves integrals particularly accessible to direct analytical integration techniques. Alternatively, the resulting convergent Feynman parameter integrals may be evaluated numerically. Our approach is guided by previous work by the second author but overcomes practical limitations of the original procedure by employing integration by parts reduction.