Electroweak Input Schemes in the Standard Model Effective Field Theory

Abstract

We consider the use of different electroweak input schemes in the Standard Model Effective Field Theory (SMEFT). First, we provide a review of the implementation of three commonly used input schemes in the literature, detailing the definitions of counterterms and present analytic formulas. An analysis of these three schemes follows, where we discuss general features and provide benchmark numerical results for heavy boson decays in each of the schemes at next-to-leading order (NLO) in the dimension-six SMEFT. Exploring the sensitivity to Wilson coefficients and perturbative convergence of different schemes, we show that the pattern of convergence is more complicated than in the Standard Model, yet the large- limit provides a valid approximation to the largest corrections. Using a benchmark process of the boson decay to leptons, a set of universal corrections are defined on the leading order results. Remaining NLO corrections thus become of a similar size between schemes.

Secondly, we develop the necessary theoretical machinery to define two new input schemes for the SMEFT. These involve the effective weak mixing angle as an input parameter. Again, we provide definitions and formulas for the counterterms. We analyse a set of precision observables to find an attractive feature of the two schemes is that large correction from top loops appearing in other schemes are absorbed into the definition of the weak mixing angle. Conversely, this same renormalisation condition undesirably introduces numerous flavour specific couplings between the boson and charged leptons, motivating a need for flavour assumptions for any practical application. Once more, a large- analysis provides a good approximation, in most instances, to the full NLO results, allowing for the largest scheme dependent corrections to be understood. However, the non-trivial pattern of perturbative convergence across all the schemes is remarked on, and examples of prefactors multiplying different Wilson coefficients in multiple schemes are given, highlighting the influence and importance of the scheme choice in precision electroweak calculations.