On the Rational Terms of the one-loop amplitudes

TL;DR

This paper critically discusses the sources of Rational Terms in one-loop amplitudes and presents methods to compute them using Feynman rules and reduction strategies.

Contribution

It introduces explicit algorithms and strategies for calculating Rational Terms from different parts of the numerator in one-loop amplitudes.

Findings

Rational Terms from (n-4)-dimensional numerator parts can be derived via Feynman rules.

Two strategies are provided for Rational Terms from 4-dimensional numerator parts.

Algorithms for computing these Rational Terms are explicitly formulated.

Abstract

The various sources of Rational Terms contributing to the one-loop amplitudes are critically discussed. We show that the terms originating from the generic (n-4)-dimensional structure of the numerator of the one-loop amplitude can be derived by using appropriate Feynman rules within a tree-like computation. For the terms that originate from the reduction of the 4-dimensional part of the numerator, we present two different strategies and explicit algorithms to compute them.