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Abstract

The renormalizable couplings of the Standard Model are invariant under two accidental global symmetries, which correspond to conserved baryon and lepton numbers. In this thesis, we discuss possible roles of these symmetries in extension of the Standard Model. Two approaches are considered: explicit violation of lepton number by two units in the renormalizable couplings of the Lagrangian, and promotion of the global symmetries to local gauge symmetries that are spontaneously broken. The former approach directly leads to Majorana neutrino masses and neutrinoless double beta decay. We discuss the interplay of the contributions to this decay in a one-loop neutrino mass model, the colored seesaw mechanism. We find that, depending on the parameters of the model, both the light Majorana neutrino exchange and the contribution of the new colored particles may be dominant. Additionally, an experimental test is presented, which allows for a discrimination of neutrinoless double beta decay from unknown nuclear background using only one isotope. In the latter approach, fascinating implications originate from the attempt to write down an anomaly-free and spontaneously broken gauge theory for baryon and lepton numbers, such as an automatically stable dark matter candidate. When gauging the symmetries in a left–right symmetric setup, the same fields that allow for an anomaly-free theory generate neutrino masses via the type III seesaw mechanism.