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

Abstract

Abstract Measurements of electroweak precision observables at future electron-position 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 MS ¯ $$ \overline{\mathrm{MS}} $$ .

Keywords

• Quark Masses and SM Parameters
• Scattering Amplitudes