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 overline{mathrm{MS}} .
Highlights
JHEP03(2021)215 are numerically enhanced by powers of the top-quark mass and the total flavor number of fermion flavors
We report on the computation of the leading fermionic correction at the order O(α2αs), which involves diagrams with two closed fermion loops and one gluon exchange
This article reports on the calculation of mixed electroweak-QCD O(α2αs) corrections with two closed fermion loops to several important electroweak precision observables: the W-boson mass predicted from the Fermi constant, the partial and total decay widths of the Z-boson, and the effective weak mixing angle
Summary
The on-shell (OS) renormalization scheme is adopted for electroweak radiative corrections. The values of the top-quark mass in these two schemes are related by a non-divergent function, which has been computed up to four-loop level [38,39,40,41,42,43]. The OS top mass is defined by imposing the condition Dt(p)|p2=Mt2−iMtΓt = 0 and expanding up to one-loop order (in which case the top width can be neglected), leading to δMt(αs) = Mt[Re ΣV (αs)(Mt2) + Re ΣS(αs)(Mt2)]. Σtγoγp denotes the derivative of the massive-top loop contribution to the photon selfenergy. Given that ∆α is inherently non-perturbative, it is not strictly associated with any loop order in (2.11)–(2.13), but one can maintain the correct book-keeping by including it in the one-loop counterterm
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