Mixed EW-QCD leading fermionic three-loop corrections at $\mathcal{O}(\alpha_s\alpha^2)$ to electroweak precision observables

TL;DR

This paper calculates specific three-loop mixed electroweak-QCD corrections involving fermions, crucial for precise Standard Model predictions of electroweak observables at future colliders.

Contribution

It provides the first detailed computation of mixed EW-QCD three-loop corrections with gluon exchange and fermion loops, enhancing theoretical precision for electroweak measurements.

Findings

Corrections significantly affect W-boson mass predictions.

Impact on effective weak mixing angle calculations.

Refined predictions for Z boson widths.

Abstract

Measurements of electroweak precision observables at future electron-positron colliders, such as the CEPC, FCC-ee, and ILC, will be sensitive to physics at multi-TeV scales. To achieve this sensitivity, precise predictions for the Standard Model expectations of these observables are needed, including corrections at the three- and four-loop level. In this article, results are presented for the calculation of a subset of three-loop mixed electroweak-QCD corrections, stemming from diagrams with a gluon exchange and two closed fermion loops. The numerical impact of these corrections is illustrated for a number of applications: the prediction of the W-boson mass from the Fermi constant, the effective weak mixing angle, and the partial and total widths of the Z boson. Two alternative renormalization schemes for the top-quark mass are considered, on-shell and $\overline{\mbox{MS}}$.