Color-Kinematic Numerators for Fermion Compton Amplitudes

TL;DR

This paper presents a new recursive method using Hopf algebra concepts to compute fermion Compton amplitudes, producing gauge-invariant numerators with physical poles and a graphical approach to streamline calculations.

Contribution

Introduces a recursive Hopf algebra-inspired approach and a graphical method for deriving color-kinematic numerators in fermion Compton amplitudes, reducing redundancies.

Findings

Derived minimal gauge-invariant numerators with massive poles

Developed a graphical method for numerator generation

Validated the approach through factorization properties

Abstract

We introduce a novel approach to compute Compton amplitudes involving a fermion pair inspired by Hopf algebra amplitude constructions. This approach features a recursive relation employing quasi-shuffle sets, directly verifiable by massive factorization properties. We derive results for minimal gauge invariant color-kinematic numerators with physical massive poles using this method. We have also deduced a graphical method for deriving numerators that simplifies the numerator generation and eliminates redundancies, thus providing several computational advantages.