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Although the Standard Model (SM) of particle physics describes observations well, there are several shortcomings of it. The most crucial of these are that the SM cannot explain the origin of neutrino masses and the existence of dark matter. Furthermore, there are several aspects of it that are seemingly ad hoc, such as the choice of gauge group and the cancellation of gauge anomalies. These shortcomings point to a theory beyond the SM. Although there are many proposed models for physics beyond the SM, in this thesis, we focus on grand unified theories based on the SO(10) gauge group. It predicts that the three gauge groups in the SM unify at a higher energy into one, which contains the SM as a subgroup. We focus on the Yukawa sector of these models and investigate the extent to which the observables such as fermion masses and mixing parameters can be accommodated into different models based on the SO(10) gauge group. Neutrino masses and leptonic mixing parameters are particularly interesting, since SO(10) models naturally embed the seesaw mechanism. The difference in energy scale between the electroweak scale and the scale of unification spans around 14 orders of magnitude. Therefore, one must relate the parameters of the SO(10) model to those of the SM through renormalization group equations. We investigate this for several different models by performing fits of SO(10) models to fermion masses and mixing parameters, taking into account thresholds at which heavy right-handed neutrinos are integrated out of the theory. Although the results are in general dependent on the particular model under consideration, there are some general results that appear to hold true. The observ- ables of the Yukawa sector can in general be accommodated into SO(10) models only if the neutrino masses are normally ordered and that inverted ordering is strongly disfavored. We find that the observable that provides the most tension in the fits is the leptonic mixing angle θ2l3, whose value is consistently favored to be lower in the fits than the actual value. Furthermore, we find that numerical fits to the data favor type-I seesaw over type-II seesaw for the generation of neutrino masses. / <p>Examinator: Professor Mark Pearce, Fysik, KTH</p>

The goal of this Master thesis is to demonstrate Witteńs mechanism in selected extensions of the Standard model based on the Pati-Salam gauge group. The purpose of this mechanism is to obtain an extremely large Majorana mass term for right-handed neutrinos at the two-loop level and consequently light physical masses of neutrinos using the type I see-saw mechanism. The existence of corresponding Feynman diagrams without any interactions of vector bosons is presented. While it is impossible to construct this type of corrections in minimal SO(10) or SU(5)xU(1) model in Pati-Salam model they may be even dominant. Subsequently, implications of possible partial gauge coupling unification or even embedding of the Pati-Salam group into a gauge group of "Great Unified Theory" are considered. At the end the possibility of unacceptably fast proton decay is inspected. The discussed models are concluded to be potentially realistic but only at the cost of predictivity, since completely unknown Yukawa couplings appear in numerous key relations. 1