A Subtraction Scheme for Feynman Integrals

TL;DR

This paper introduces a systematic subtraction scheme for UV divergent scalar Feynman integrals using u-variables, enabling their expression as sums of convergent integrals with explicit epsilon-dependence.

Contribution

It develops a novel subtraction method employing u-variables, generalizing dihedral coordinates, to regularize Feynman integrals in dimensional regularization.

Findings

Provides an algorithmic prescription for divergence subtraction.

Expresses Feynman integrals as sums of convergent integrals with epsilon powers.

Offers a canonical approach applicable to multi-scale integrals.

Abstract

We present a subtraction scheme for ultraviolet (UV) divergent, infrared (IR) safe scalar Feynman integrals in dimensional regularization with any number of scales. This is done by the introduction of $u$-variables, which are a suitable generalization of dihedral coordinates on the open string moduli space to Feynman integrals. The subtraction scheme furnishes subtraction terms which are products of lower loop Feynman integrals deformed by order $\epsilon$ powers of $u$-variables and deformations of the degree of divergence. The result is a canonical and algorithmic prescription to express the Feynman integral as a sum of convergent integrals dressed with inverse powers of $\epsilon$.