A Recursive Method to Calculate UV-divergent Parts at One-Loop Level in Dimensional Regularization

TL;DR

This paper presents a recursive method for calculating UV-divergent parts at one-loop level in dimensional regularization, simplifying the process by reducing integrals to scaleless forms that depend only on loop momentum.

Contribution

The paper introduces a novel recursive approach that simplifies the calculation of UV divergences at one-loop level, compatible with symbolic computation tools.

Findings

Method reduces integrals to scaleless forms

Implementation available in Mathematica

Eases calculation of UV divergences

Abstract

A method is introduced to calculate the UV-divergent parts at one-loop level in dimensional regularization. The method is based on the recursion, and the basic integrals are just the scaleless integrals after the recursive reduction, which involve no other momentum scales except the loop momentum itself. The method can be easily implemented in any symbolic computer language, and an implementation in Mathematica is ready to use.