Determining Triple Gauge Couplings at Future e+e− Higgs Factories using Optimal Observables

After the discovery of the Higgs boson in 2012 at the LHC, and no further fundamental particles since, the focus of the next generation of experiments will be to measure the properties of the Higgs and the rest of the Standard Model (SM) to the utmost precision. The ideal experimental environment for this endeavour is offered by e+e− colliders, which offer a clean collision with a determined initial state. Instead of performing direct searches, it will be possible to systematically characterise the full SM using an effective field theory approach (SMEFT), providing an extended foundation of constraints for the next generation of models. One part of these SMEFT studies is the determination of the anomalous triple gauge couplings (aTGC), e.g. of modifications to the WWγ and WWZ vertices. These aTGCs can be studied in the copious amounts of WW events that are produced as "by-catch" at e+e− Higgs factories running at the ZH-production peak of ~250 GeV. The aTGC determination depends on angular measurements in the multi-dimensional phase space, complicating the usage of histogram-based fits. To make full use of the angular information, this thesis will use the method of optimal observables (OO) to determine the aTGC in the eνeqq final state of WW and single-W production using a full Geant4 simulation of the ILD detector concept. The OO method is matrix-element (ME) based and thus suffers from detector resolution effects, making it inapplicable to detector-level data in its original formulation. To mitigate this, the method is converted to a maximum likelihood fit of templated observables integrated over the full run of the experiment. Asimov fits are performed for multiple reconstruction effects and beam-polarisation settings, to compare the achievable statistical uncertainties. In addition, a procedure to build OOs for nuisance parameters is formulated and prototyped by the in-situ determination of the longitudinal beam-polarisations and the W boson mass mW. The OOs computation is automatised using the O'Mega ME-generator, allowing for the first time to use the full eνeqq ME in the OO definition, adding the additional information contained in the single-W events. The method yields competitive results for the aTGC, and mW uncertainties compared to earlier studies and its applicability to detector-level data is validated for e+e− Higgs factories. A combination of the eνeqq channel with a μνμqq proxy for the reference ILC250 scenario, with P(e−,e+) = (±80%,±30%) collecting 2 ab-1 with 45% in each opposite-sign and 5% in each same-sign polarisation configuration, using the LEP aTGC parametrisation, results in the uncertainties ΔgZ1 = 4.34×10-4, Δκγ = 6.74×10-4, λγ = 4.80×10-4, ΔmW = 2.79 MeV.