R2SM: a package for the analytic computation of the R2 Rational terms in the Standard Model of the Electroweak interactions

TL;DR

This paper introduces R2SM, a FORM-based package that analytically computes the R2 rational terms in the electroweak sector of the Standard Model, aiding in NLO amplitude calculations.

Contribution

It provides the first automated, modular tool for deriving R2 rational terms in the Standard Model, adaptable to various gauges and regularization schemes.

Findings

Verified gauge independence of R1 + R2 in H -> gamma gamma decay

Automated derivation of Feynman rules for R2 terms in the Standard Model

Flexible framework applicable to different gauges and regularization schemes

Abstract

The analytical package written in FORM presented in this paper allows the computation of the complete set of Feynman Rules producing the Rational terms of kind R2 contributing to the virtual part of NLO amplitudes in the Standard Model of the Electroweak interactions. Building block topologies filled by means of generic scalars, vectors and fermions, allowing to build these Feynman Rules in terms of specific elementary particles, are explicitly given in the Rxi gauge class, together with the automatic dressing procedure to obtain the Feynman Rules from them. The results in more specific gauges, like the 't Hooft Feynman one, follow as particular cases, in both the HV and the FDH dimensional regularization schemes. As a check on our formulas, the gauge independence of the total Rational contribution (R1 + R2) to renormalized S-matrix elements is verified by considering the specific example of the H --> gamma-gamma decay process at 1-loop. This package can be of interest for people aiming at a better understanding of the nature of the Rational terms. It is organized in a modular way, allowing a further use of some its files even in different contexts. Furthermore, it can be considered as a first seed in the effort towards a complete automation of the process of the analytical calculation of the R2 effective vertices, given the Lagrangian of a generic gauge theory of particle interactions.