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In this paper, we investigate the discovery prospect of simplified fermionic dark sectors models through Higgs precision measurements at e+e- colliders and direct searches at hadron colliders. These models extend the Standard Model with two Majorana or Dirac fermions that are singlets, doublets or triplets under the weak SU(2) group. For all models, we consider two scenarios where the lightest new fermion is either stable, or where it decays into other visible final states. For the Higgs precision observables we primarily focus on σ(e+e-→ZH), which can deviate from the Standard Model through one-loop corrections involving the new fermions. Deviations of 0.5% or more, which could be observable at future e+e- colliders, are found for TeV-scale dark sector masses. By combining the constraints from the oblique parameters, Br(H→γγ), and direct production of the new fermions at the LHC, a comprehensive understanding of the discovery potential of these models can be achieved. In both scenarios, there exist some parameter regions where the Higgs precision measurements can provide complementary information to direct LHC searches. 

This paper describes a modular framework for the description of electroweak scattering and decay processes, including but not limited to Z-resonance physics. The framework consistently combines a complex-pole expansion near an s-channel resonance with a regular fixed-order perturbative description away from the resonance in a manifestly gauge-invariant scheme. Leading vertex correction contributions are encapsulated in form factors that can be predicted or treated as numerical fit parameters. This framework has been implemented in the publicly available object-oriented C++ library GRIFFIN. Version 1.0 of this library provides Standard Model predictions for the IR-subtracted matrix elements for the process f\bar{f} \to f'\bar{f}' with full NNLO and leading higher-order contributions on the Z-resonance, and with NLO corrections off-resonance. The library can straightforwardly be extended to include higher-order corrections, should they become available, or predictions for new physics models. It can be interfaced with Monte-Carlo programs to account for QED and QCD initial-state and final-state radiation. 

A bstract Two-loop electroweak corrections to polarized Møller scattering are studied in two different schemes at low energies. We find the finite Q 2 corrections to be well under control. The hadronic and perturbative QCD corrections to the γZ two-point function are incorporated through the weak mixing angle at low energies, which introduce an error of 0 . 08 × 10 − 3 in the weak charge of the electron $$ {Q}_W^e $$ Q W e . Furthermore, by studying the scheme dependence, we obtain an estimate of the current perturbative electroweak uncertainty, $$ \delta {Q}_W^e $$ δ Q W e ≈ 0 . 23 × 10 − 3 , which is five times smaller than the precision estimated for the MOLLER experiment ( $$ \delta {Q}_W^e $$ δ Q W e = 1 . 1 × 10 − 3 ). Future work is possible to reduce the theory error further. 

In this proceeding, we highlight the computation of leading fermionic three-loop corrections to electroweak precision observables (EWPOs) accomplished recently. We summarize the numerical analysis and provide an outlook. 

A bstract Precision studies of the Higgs boson at future e + e − colliders can help to shed light on fundamental questions related to electroweak symmetry breaking, baryogenesis, the hierarchy problem, and dark matter. The main production process, e + e − → HZ , will need to be controlled with sub-percent precision, which requires the inclusion of next-to-next-to-leading order (NNLO) electroweak corrections. The most challenging class of diagrams are planar and non-planar double-box topologies with multiple massive propagators in the loops. This article proposes a technique for computing these diagrams numerically, by transforming one of the sub-loops through the use of Feynman parameters and a dispersion relation, while standard one-loop formulae can be used for the other sub-loop. This approach can be extended to deal with tensor integrals. The resulting numerical integrals can be evaluated in minutes on a single CPU core, to achieve about 0.1% relative precision.