Leptons and Higgs with discrete flavour and charge-parity symmetries

Abstract

This thesis concerns itself with two seemingly disjoint topics that are interesting on their own, but that come to their full bloom when combined. These two topics are the violation of CP and the so-called flavour problem. CP violation is simply necessary for all our existence, however currently no strong enough source of it is known to ensure successful baryogenesis. The flavour problem on the other hand is a loose collection of questions concerning fermions in the standard model, especially why several flavours exist at all, and why their properties appear to be so chaotic. The overlap between the two topics happens, as in the SM CP is violated in the flavour sector. After an introduction, so-called residual flavour and CP symmetries are explored as possible explanations of the parameter structure of the lepton Yukawa sector. Such residual symmetries are embedded into larger groups at high energy and from the breaking patterns constraints on observables are derived. There it was found that an important class of subgroups of U(3), namely (6n²) groups, can indeed explain the observed lepton mixing. Several variations of this approach, combining residual flavour and CP symmetries, are explored. This was the first time that such an infinite series of finite groups was analysed in this way. After this, motivated by the need for breaking of flavour and CP symmetries and the search for additional sources of CP violation, a large number of candidate scalar potentials are explored, especially for their CP properties. A necessary tool for this are CP-odd Higgs basis invariants, the theory of which was further developed to enable such analyses. Using this approach, many very complicated potentials were tested for their CP properties for the first time and new sources of CP violation were found in new and known potentials.

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