Lattice simulations and analytical computations of five-dimensional gauge theories to study the Higgs boson as an extra-dimensional gauge field

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The Standard Model of elementary particles has so far been very successful in predicting the properties of particles as they are measured in accelerator experiments. The mechanism of mass generation relies on the existence of the Higgs scalar, which has not been discovered so far. The parameters of the Higgs sector are inputs in the Standard Model and it is an open question, whether they can be understood from a deeper principle. The goal of this project is to study extensions of the Standard Model, where the Higgs scalar is identified with five-dimensional components of a gauge field. The scalar potential is generated by quantum effects and is believed to be finite, what makes these models attractive. Since five-dimensional gauge theories are trivial, they require a cut-off. The formulation on a Euclidean lattice provides a gauge invariant cut-off. Contrary to previous results from 1-loop perturbative computations, lattice Monte Carlo simulations showed spontaneous symmetry breaking in non-Abelian gauge theories on a five-dimensional orbifold space. We want to predict the Higgs mass from these simulations and make a connection with perturbative computations done using an effective theory which accounts for the cut-off effects.