Probing Anomalous Couplings of the Higgs Boson to Weak Bosons and Fermions with Precision Calculations

In this thesis I present a phenomenological study of the Higgs boson anomalous couplings to weak bosons and fermions. I focus on Higgs bosons produced in association with a weak boson (V → VH (V = W±, Z)) at hadron and lepton colliders, and direct production via proton-proton scattering followed by weak boson decay (pp → H → VV). The V → VH interactions as well as the interaction between the Higgs boson and fermions (Hff) are investigated along with the construction of event generators for the e−e+ → ZH and q ̄ q → VH processes. Within the framework of JHUGEN, I discuss numerical simulation code that calculates the amplitude for the q ̄q → VH process, including the anomalous HVV and Hf f couplings, to next-to-leading order precision in Quantum Chromodynamics (QCD). The gg → ZH process is also included due to its sizable contribution. The construction of event generators at leading and next-to-leading order are presented in detail. The pp → H → VV processes are calculated using modified event generators of MADGRAPH and MCFM with up to next-to-next-to-leading order QCD and NLO Quantum Electrodynamics effects taken into account. I also develop a method for constraining the anomalous Higgs boson (Yukawa) coupling to quarks in the first two generations, and I study the method using early data from the Large Hadron Collider.