Automatic evaluation of UV and R2 terms for beyond the Standard Model Lagrangians: a proof-of-principle

TL;DR

This work tackles the challenge of performing reliable NLO calculations in beyond-the-Standard-Model (BSM) theories by automating the derivation of ultraviolet (UV) counterterms and R2 rational terms directly from a tree-level Lagrangian. It introduces a three-package workflow (FeynRules, NLOCT, FeynArts) that computes model-specific UV and R2 vertices and exports them in UFO format for use with tools like MG5_aMC@NLO and GoSam. The authors validate the approach against SM (QCD and EW) and MSSM benchmarks, and provide full QCD/R2 and EW counterterms for the 2HDM, enabling automated one-loop computations for this representative BSM scenario. The workflow significantly broadens the practical reach of automated NLO calculations to any renormalizable BSM model and sets the stage for extensions to effective field theories in the future.

Abstract

The computation of renormalized one-loop amplitudes in quantum field theory requires not only the knowledge of the Lagrangian density and the corresponding Feynman rules, but also that of the ultraviolet counterterms. More in general, and depending also on the methods used in the actual computation of the one-loop amplitudes, additional interactions might be needed. One example is that of the R2 rational terms in the OPP method. In this paper, we argue that the determination of all elements necessary for loop computations in arbitrary models can be automated starting only from information on the Lagrangian at the tree-level. In particular, we show how the R2 rational and ultraviolet counterterms for any renormalizable model can be computed with the help of a new package, which we name NLOCT and builds upon FeynRules and FeynArts. To show the potential of our approach, we calculate all additional rules that are needed to promote a Two Higgs Doublet Model Lagrangian to one-loop computations in QCD and electroweak couplings.