Feynman rules for the rational part of the Electroweak 1-loop amplitudes in the R_xi gauge and in the Unitary gauge

TL;DR

This paper provides comprehensive Feynman rules for calculating the rational parts of 1-loop electroweak amplitudes in different gauges, ensuring gauge independence and consistency across calculations.

Contribution

It introduces complete Feynman rules for the R_2 rational terms in the Electroweak Standard Model in R_xi and Unitary gauges, extending previous results in Feynman gauge.

Findings

Verified gauge independence of rational parts in specific processes

Confirmed equivalence of Unitary gauge limits with different loop integration orders

Provided explicit formulas for rational terms in multiple gauges

Abstract

We present the complete set of Feynman rules producing the rational terms of kind R_2 needed to perform any 1-loop calculation in the Electroweak Standard Model. Our formulae are given both in the R_xi gauge and in the Unitary gauge, therefore completing the results in the 't Hooft-Feynman gauge already presented in a previous publication. As a consistency check, we verified, in the case of the process H -> gamma gamma and in a few other physical cases, the independence of the total Rational Part R_1+R_2 on the chosen gauge. In addition, we explicitly checked the equivalence of the limits xi -> infinity after or before the loop momentum integration in the definition of the Unitary gauge at 1-loop.