Using the effective weak mixing angle as an input parameter in SMEFT

Abstract: We implement electroweak renormalisation schemes involving the effective weak mixing angle to NLO in Standard Model Effective Field Theory (SMEFT). After developing the necessary theoretical machinery, we analyse a select set of electroweak precision observables in such input schemes. An attractive feature is that large corrections from top-quark loops appearing in other schemes are absorbed into the definition of the effective weak mixing angle. On the other hand, the renormalisation condition which achieves this involves a large number of flavour-specific SMEFT couplings between the $Z$ boson and charged leptons, motivating simple flavour assumptions such as minimal flavour violation for practical applications. The results of this paper provide a valuable new component for estimating systematic uncertainties in SMEFT fits by performing analyses in multiple input schemes.