The Strong CP Problem and Discrete Symmetries

We discuss a possible solution to the strong CP problem which is based on spontaneous CP violation and discrete symmetries. At the same time we predict in a simple way the almost right-angled quark unitarity triangle angle ($\alpha \simeq 90^\circ$) by making the entries of the quark mass matrices either real or imaginary. To prove the viability of our strategy we present a toy flavour model for the quark sector.Comment: 10 pages, 1 figure, contribution to the International Conference on Massive Neutrinos, Singapore, 9 - 13 February 201

GUT predictions for quark and lepton mass ratios

Group theoretical factors from GUT symmetry breaking can lead to predictions for the ratios of quark and lepton masses at the unification scale. Due to supersymmetric (SUSY) threshold corrections the viability of such predictions can depend strongly on the SUSY parameters. We derive possible new predictions for the GUT scale ratios m_\mu/m_s, y_\tau/y_b and y_t/y_b and compare them with the experimentally allowed ranges for three common SUSY breaking scenarios.Comment: Based on a talk given at SUSY 09; 5 pages, 1 figure, 2 table

Neutrino Mass Sum Rules and Symmetries of the Mass Matrix

Neutrino mass sum rules have recently gained again more attention as a powerful tool to discriminate and test various flavour models in the near future. A related question which was not yet discussed fully satisfactorily was the origin of these sum rules and if they are related to any residual or accidental symmetry. We will address this open issue here systematically and find previous statements confirmed. Namely, that the sum rules are not related to any enhanced symmetry of the Lagrangian after family symmetry breaking but that they are simply the result of a reduction of free parameters due to skillful model building.Comment: 10 pages, no figures, accepted for publication in European Physical Journal

Renormalisation Group Corrections to Neutrino Mass Sum Rules

Neutrino mass sum rules are an important class of predictions in flavour models relating the Majorana phases to the neutrino masses. This leads, for instance, to enormous restrictions on the effective mass as probed in experiments on neutrinoless double beta decay. While up to now these sum rules have in practically all cases been taken to hold exactly, we will go here beyond that. After a discussion of the types of corrections that could possibly appear and elucidating on the theory behind neutrino mass sum rules, we estimate and explicitly compute the impact of radiative corrections, as these appear in general and thus hold for whole groups of models. We discuss all neutrino mass sum rules currently present in the literature, which together have realisations in more than 50 explicit neutrino flavour models. We find that, while the effect of the renormalisation group running can be visible, the qualitative features do not change. This finding strongly backs up the solidity of the predictions derived in the literature, and it thus marks a very important step in deriving testable and reliable predictions from neutrino flavour models.Comment: 25 pages, 3 figures, 39 additional plots; version published in JHE

Confronting SUSY SO(10) with updated Lattice and Neutrino Data

We present an updated fit of supersymmetric SO(10) models to quark and lepton masses and mixing parameters. Including latest results from lattice QCD determinations of quark masses and neutrino oscillation data, we show that fits neglecting supersymmetric threshold corrections are strongly disfavoured in our setup. Only when we include these corrections we find good fit points. We present $\chi^2$-profiles for the threshold parameters, which show that in our setup the thresholds related to the third generation of fermions exhibit two rather narrow minima.Comment: 23 pages, 3 figures, and 5 tables; version published in JHE

New Aspects of Flavour Model Building in Supersymmetric Grand Unification

We derive predictions for Yukawa coupling ratios within GUTs generated from operators with mass dimension four and five. These relations are a characteristic property of unified flavour models and can reduce the large number of free parameters related to the flavour sector of the SM. The Yukawa couplings of the down-type quarks and charged leptons are affected within SUSY models by tan beta-enhanced threshold corrections. We analyse these corrections and give simple analytic expressions and numerical estimates for them. The threshold corrections sensitively depend on the soft SUSY breaking parameters. Especially, they determine if the affected Yukawa couplings are enhanced or suppressed. In a first approach, we make some plausible assumptions about the soft SUSY parameters. In a second, more sophisticated approach we use three common breaking schemes in which all the soft breaking parameters at the electroweak scale can be calculated from only a handful of parameters. Within this approach, we apply various phenomenological constraints on the supersymmetric parameters and find in this way new viable Yukawa coupling relations, for example y_mu/y_s = 9/2 or 6 or y_tau/y_b = 3/2 in SU(5). Furthermore, we study a special class of quark mass matrix textures for small tan beta where theta_13^u = theta_13^d = 0. We derive sum rules for the quark mixing parameters and find a simple relation between the two phases delta_12^u and delta_12^d and the right unitarity triangle angle alpha which suggests a simple phase structure for the quark mass matrices. To complement the aforementioned considerations, we give two explicit examples in an SU(5) context, one for large and one for small tan beta which implement the Yukawa coupling relations mentioned before. The models have interesting phenomenological consequences like, for example, quasi-degenerate neutrino masses in the case of small tan beta.Comment: PhD thesis, 205 pages, 25 figures (approx. 6 MB

GUT predictions for quark-lepton Yukawa coupling ratios with messenger masses from non-singlets

We propose new predictions from grand unified theories (GUTs) [applicable to both supersymmetric (SUSY) and non-SUSY models] for the ratios of quark and lepton Yukawa couplings. These new predictions arise from splitting the masses of the messenger fields for the GUT-scale Yukawa operators by Clebsch-Gordan factors from GUT symmetry breaking. This has the effect that these factors enter inversely in the predicted quark-lepton Yukawa coupling ratios, leading to new possible GUT predictions. We systematically construct the new predictions that can be realized in this way in SU(5) GUTs and Pati-Salam unified theories and discuss model building applications