Implications of finite family symmetry groups on the leptonic and scalar sector
2012417 pages
Supervisor:
Thesis: PhD - Walter Grimus()
- Wien U.,
- Vienna U.
- Published: 2012
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Abstract: (Wien U.)
One approach for an at least partial solution to the problem of lepton masses and mixing is the introduction of so-called finite family symmetry groups in the leptonic and scalar sector. This thesis concentrates on three questions arising from this approach. The first question is which groups are eligible as finite family symmetry groups. Since there are three generations of fermions, the group must possess at least one non-trivial three-dimensional representation. Concentrating on those groups which possess a faithful three-dimensional representation, we end up with the finite subgroups of U(3). Using the so-called SmallGroups library, we could create a list of all finite subgroups of U(3) of order smaller than 512 which possess a faithful three-dimensional irreducible representation and are not isomorphic to a direct product involving a cyclic group. By means of a theorem proven in this thesis we were also able to explicitly construct several infinite series of finite subgroups of U(3).
Since many finite subgroups of SU(3) are frequently used as finite family symmetry groups, we put special emphasis on the study of these groups. With the help of a theorem on the general structure of Abelian finite subgroups of SU(3) we were able to unveil the structure of the two classes (C) and (D) of finite subgroups of SU(3).
The second question that was discussed in this thesis, is the question how symmetries restrict the mass and mixing matrices. Elaborating on the simplest case, which is the case of Abelian family symmetries, we encounter the intensively studied possibility of texture zeros in the lepton mass matrices. In this respect we concentrated on the seven experimentally allowed types of two texture zeros in the neutrino mass matrix in the framework of a diagonal charged-lepton mass matrix. We could show that two of these seven types of texture zeros lead to nearly maximal atmospheric neutrino mixing in the limit of a quasi-degenerate neutrino mass spectrum, irrespective of the values of the other two mixing angles.
We furthermore studied the predictions of the seven types of two texture zeros in the light of the recent measurements of the reactor mixing angle.
Finally, the third question treated in this thesis, was whether one could infer symmetries in the lepton sector from the presently available data on the observables of neutrino physics. By means of a numerical analysis we could create correlation plots of the absolute values of the elements of the neutrino mass matrix. These plots beautifully show the experimentally allowed cases of two texture zeros in the neutrino mass matrix and reveal strong correlations for some pairs of matrix elements.- neutrino physics
- finite family symmetry groups
- finite subgroups of U(3) and SU(3)
- Neutrinophysik
- endliche Familiensymmetrien
- endliche Untergruppen von U(3) und SU(3)
- Elementarteilchenphysik
- Mathematische Methoden der Physik
- Gruppentheorie
- thesis
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