Feynman Rules for the Rational Part of the QCD 1-loop amplitudes

TL;DR

This paper derives Feynman rules for the rational parts of QCD 1-loop amplitudes, simplifying calculations by showing only up to four-point vertices are needed, and provides results in different regularization schemes.

Contribution

It provides a complete set of Feynman rules for the rational terms in QCD 1-loop calculations, applicable to processes with many external legs.

Findings

Only up to four-point vertices are needed for R_2 contributions.

Results are expressed in both 't Hooft Veltman and Four Dimensional Helicity schemes.

Explicit color configurations and color connection language are used.

Abstract

We compute the complete set of Feynman Rules producing the Rational Terms of kind R_2 needed to perform any QCD 1-loop calculation. We also explicitly check that in order to account for the entire R_2 contribution, even in case of processes with more than four external legs, only up to four-point vertices are needed. Our results are expressed both in the 't Hooft Veltman regularization scheme and in the Four Dimensional Helicity scheme, using explicit color configurations as well as the color connection language.