<p>In this work, we consider the addition of a single neutral massive vector boson to the Standard Model (SM). This boson, which we refer to as N⁰, induces dipolar transitions between electrons and muons. We obtain bounds on the strength of its coupling and its mass: from the scattering process e+e- to mu+mu-; from its contribution to muonium-antimuonium oscillations; and from its possible contribution to the rare muon decay mu- to e+e-e-. In particular, we examine the two cases where the mediator is both heavy and light compared with the scattering energies for, and place constraints on the relevant parameters based on their contributions to the cross section and the forward-backward asymmetry. For muonium-antimuonium oscillations, we consider only the case where the mediator is heavy compared to all other scales, reducing its effect to an effective contact interaction. Finally, we consider an SU(2) invariant theory from which the N⁰ interaction emerges, and find that flavour diagonal interactions also emerge, giving a tree-level path for the decay mu- to e+e-e-. We find that the heavy N⁰ is not strongly constrained by this contribution, while the light N⁰ is very strongly constrained by it. Very generally, we find that the heavy N⁰ is much less constrained than other lepton flavour violating processes, while the constraints on the light N0 vary in strength between processes.</p> / Master of Science (MSc)

In dieser Arbeit wird die Berechnung der farbführenden Zweischleifen-QCD-Korrekturen für die Top-Quark-Paarproduktion mit einem zusätzlichen Jet an einem Lepton-Collider präsentiert. Das Matrixelement wird in Vektor- und Axial-Vektorströme zerlegt und die Ströme werden weiter in Dirac-Spinorstrukturen und Formfaktoren zerlegt. Die Formfaktoren werden mit Projektoren extrahiert. Die auftretenden Feynmanintegrale werden mittels IBP-Identitäten und Dimensionsverschiebungstransformationen durch eine Basis quasi-finiter Masterintegrale in 6−2ϵ Dimensionen ausgedrückt. Die Mehrheit der Feynmanintegrale gehört zu einer Doppelbox-Integralfamilie. Die Berechnung der Masterintegrale erfolgt durch numerisches Lösen von Differentialgleichungen in kinematischen Invarianten. Asymptotische Reihenentwicklungen der Masterintegrale in der Top-Quarkmasse werden verwendet, um die Anfangsbedingungen für die numerischen Lösungen der Differentialgleichungen zu bestimmen. Die führenden Terme dieser Entwicklung werden mit der Expansion-by-Regions-Methode berechnet. Höhere Reihenkoeffizienten werden durch die Anwendung einer Differentialgleichung auf einen Ansatz für die Reihenentwicklung bestimmt. Die renormierten Formfaktoren und die farbführende Zweischleifenamplitude werden an einem Referenzphasenraumpunkt zu hoher Präzision numerisch ausgewertet. Die Resultate werden mit elektroschwachen Ward-Identitäten und durch numerische Vergleiche der IR-Singularitäten mit der erwarteten Singularitätsstruktur überprüft. / In this work, the calculation of the leading-colour two-loop QCD corrections for top-quark pair production with an additional jet at a lepton collider is presented. The matrix element is decomposed into vector and axial-vector currents and the currents are further decomposed into Dirac spinor structures and form factors. The form factors are extracted with projectors. The Feynman integrals are reduced to a quasi-finite basis in 6 − 2ϵ dimensions using IBP identities and dimension-shift transformations. The majority of master integrals belong to a double-box integral family. The master integrals are computed by numerically solving systems of differential equations in the kinematic invariants. Asymptotic expansions of the master integrals in the top-quark mass variable are used to calculate initial conditions for the numerical differential equation solutions. The leading terms of the expansion are obtained with the expansion by regions and the higher orders are calculated by solving a system of equations obtained from applying the differential equation onto an ansatz of the expansion. The renormalized form factors and the leading-colour two-loop amplitude are evaluated numerically to high precision at a benchmark phase space point. The results are cross-checked with electroweak Ward identities and by numerically comparing the IR singularities with the expected singularity structure.