Eur. Phys. J. C (2011) 71: 1605
https://doi.org/10.1140/epjc/s10052-011-1605-6

Special Article - Tools for Experiment and Theory

R2SM: a package for the analytic computation of the R ₂ Rational terms in the Standard Model of the Electroweak interactions

¹ INFN, Italia & Departamento de Física Teórica y del Cosmos y CAFPE, Universidad de Granada, 18071, Granada, Spain
² Department of Theoretical High Energy Physics, Institute for Mathematics, Astrophysics and Particle Physics, Radboud Universiteit Nijmegen, 6525 AJ, Nijmegen, The Netherlands

^* e-mail: garzelli@to.infn.it

Received: 23 January 2011
Published online: 24 March 2011

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 corrections 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 R _ξ 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→γγ 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.