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Register a new userLeading fermionic three-loop corrections to electroweak precision observables
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Future electron-position colliders, such as CEPC and FCC-ee, have the capability to dramatically improve the experimental precision for W and Z-boson masses and couplings. This would enable indirect probes of physics beyond the Standard Model at multi-TeV scales. For this purpose, one must complement the experimental measurements with equally precise calculations for the theoretical predictions of these quantities within the Standard Model, including three-loop electroweak corrections. This article reports on the calculation of a subset of these corrections, stemming from diagrams with three closed fermion loops to the following quantities: the prediction of the W-boson mass from the Fermi constant, the effective weak mixing angle, and partial and total widths of the Z boson. The numerical size of these corrections is relatively modest, but non-negligible compared to the precision targets of future colliders. In passing, an error is identified in previous results for the two-loop corrections to the Z width, with a small yet non-zero numerical impact.
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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 $overline{mbox{MS}}$.
We present the first calculation of the two-loop electroweak fermionic correction to the flavour-dependent effective weak-mixing angle for bottom quarks, sin^2 theta_{eff}^{b anti-b}. For the evaluation of the missing two-loop vertex diagrams, two methods are employed, one based on a semi-numerical Bernstein-Tkachov algorithm and the second on asymptotic expansions in the large top-quark mass. A third method based on dispersion relations is used for checking the basic loop integrals. We find that for small Higgs-boson mass values, M_H ~ 100 GeV, the correction is sizable, of order O(10^{-4}).
Nonperturbative QCD corrections are important to many low-energy electroweak observables, for example the muon magnetic moment. However, hadronic corrections also play a significant role at much higher energies due to their impact on the running of standard model parameters, such as the electromagnetic coupling. Currently, these hadronic contributions are accounted for by a combination of experimental measurements, effective field theory techniques and phenomenological modeling but ideally should be calculated from first principles. Recent developments indicate that many of the most important hadronic corrections may be feasibly calculated using lattice QCD methods. To illustrate this, we will examine the lattice computation of the leading-order QCD corrections to the muon magnetic moment, paying particular attention to a recently developed method but also reviewing the results from other calculations. We will then continue with several examples that demonstrate the potential impact of the new approach: the leading-order corrections to the electron and tau magnetic moments, the running of the electromagnetic coupling, and a class of the next-to-leading-order corrections for the muon magnetic moment. Along the way, we will mention applications to the Adler function, which can be used to determine the strong coupling constant, and QCD corrections to muonic-hydrogen.
We evaluate the two-loop corrections to Bhabha scattering from fermion loops in the context of pure Quantum Electrodynamics. The differential cross section is expressed by a small number of Master Integrals with exact dependence on the fermion masses me, mf and the Mandelstam invariants s,t,u. We determine the limit of fixed scattering angle and high energy, assuming the hierarchy of scales me^2 << mf^2 << s,t,u. The numerical result is combined with the available non-fermionic contributions. As a by-product, we provide an independent check of the known electron-loop contributions.
Theoretical predictions for Bhabha scattering observables are presented including complete one-loop electroweak radiative corrections. A longitudinal polarization of the initial beams is taken into account. Numerical results for the asymmetry $A_{LR}$ and the relative correction $delta$ are given for the set of the energy $E_{cm}=250, 500, 1000$~GeV with various polarization degrees.
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