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

TL;DR

This paper introduces an automated method and a new software package, NLOCT, for deriving ultraviolet and R2 rational counterterms in quantum field theories from the Lagrangian, simplifying one-loop amplitude calculations.

Contribution

The paper presents a novel automation approach and a software tool that derive all necessary counterterms for one-loop computations directly from the Lagrangian.

Findings

Successfully computed R2 and UV counterterms for a Two Higgs Doublet Model.

Demonstrated automation reduces manual effort in loop amplitude calculations.

Potential to extend to arbitrary renormalizable models.

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.