We calculate the values and 1σ ranges of the running quark and lepton Yukawa couplings as well as of the quark mixing parameters at various energy scales, i.e. at M Z , 1 TeV, 3 TeV, 10 TeV and at the GUT scale, to provide useful input for model building. Above TeV energies, we assume the minimal supersymmetric extension of the Standard Model, and include the tan β-enhanced one-loop supersymmetric threshold corrections which arise when matching the SM to its SUSY extension. We calculate the GUT scale values of the running parameters as well as their 1σ ranges, with the supersymmetric threshold corrections included and with their effects parametrised in a simple way.

We analyze how a large value of the leptonic mixing angle θ MNS 13 can be generated via charged lepton corrections in unified flavor models, using novel combinations of Clebsch-Gordan factors for obtaining viable quark-lepton mass ratios for the first two families. We discuss how these Clebsch-Gordan factors affect the relations between down-type quark mixing and charged lepton mixing in SU(5) grand unified theories and Pati-Salam unified models and calculate the resulting possible predictions for θ MNS 13 for models with θ ν 13 , θ e 13 ≪ θ e 12 . While symmetric mass matrices with zero (1,1)-elements always lead to comparatively small θ MNS 13 ≈ 2.8 • , we find novel combinations of Clebsch-Gordan factors for nonsymmetric mass matrices which can yield θ MNS 13 ≈ 5.1 • , 6.1 • , 7.6 • or 10.1 • , as favored by the current experimental hints for large θ MNS 13 . We discuss applications to classes of models with underlying tribimaximal or bimaximal mixing in the neutrino sector.1

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We discuss how the double missing partner mechanism solution to the doublettriplet splitting problem in four-dimensional supersymmetric SU(5) Grand Unified Theories (GUTs) can be combined with predictive models for the quark-lepton Yukawa coupling ratios at the GUT scale. It is argued that towards this goal a second SU(5) breaking Higgs field in the adjoint representation is very useful and we discuss all possible renormalizable superpotentials with two adjoint Higgs fields and calculate the constraints on the GUT scale and effective triplet mass from a two-loop gauge coupling unification analysis. Two explicit flavour models with different predictions for the GUT scale Yukawa sector are presented, including shaping symmetries and a renormalizable messenger sector. Towards calculating the rates for proton decay induced by the exchange of colour triplets, the required ClebschGordan coefficients for their couplings are calculated for the possible dimension five and six operators. They are provided in detailed tables in the appendix, together with additional helpful material for GUT flavour model building.

We analyse the fine-tuning in the Constrained Minimal Supersymmetric Standard Model (CMSSM) in the light of the present and expected ATLAS and CMS SUSY searches. Even with 10 fb −1 of data and no discovery of SUSY valid regions might remain with finetuning less than 20. Moreover we investigate the fine-tuning price of GUT scale Yukawa coupling relations. Considering a 2σ constraint for (g − 2) µ and fine-tuning less than 30 yields an allowed range of y τ /y b = [1.31, 1.70], which points towards the alternative GUT prediction y τ /y b = 3/2. Relaxing the (g − 2) µ constraint to 5σ extends the possible region to [1.02,1.70], allowing for approximate b − τ Yukawa coupling unification.