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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.
