In the scenario with degenerate neutrino masses at tree-level, we show how threshold corrections with either non-trivial or trivial mixing at tree-level have the power to generate the observed deviations from a degenerate spectrum. Moreover, it is possible to also generate the mixing fully radiatively when there is trivial mixing at tree-level.

We give a brief overview over the topic and discuss the outcome of threshold corrections for degenerate neutrino masses in a supersymmetric model. A detailed description can be found in TTP14-034.

We review a model of quark flavoured dark matter with new flavour violating interactions. This simplified model describes Dirac fermionic dark matter that is charged under a new U(3) flavour symmetry and couples to right-handed down quarks via a scalar mediator. The corresponding coupling matrix is assumed to be the only new source of flavour violation, which we refer to as the Dark Minimal Flavour Violation (DMFV) hypothesis. This ansatz ensures the stability of dark matter. We discuss the phenomenology of the simplest DMFV model in flavour violating observables, LHC searches, and direct dark matter detection experiments. Especially interesting is the non-trivial interplay between the constraints from the different sectors.

Degenerate neutrino masses are excluded by experiment. The experimentally measured mass squared differences together with the yet undetermined absolute neutrino mass scale allow for a quasi-degenerate mass spectrum. For the lightest neutrino mass larger than roughly 0.1 eV, we analyse the influence of threshold corrections at the electroweak scale. We show that typical one-loop corrections can generate the observed neutrino mixing as well as the mass differences starting from exactly degenerate masses at the tree-level. Those threshold corrections have to be explicitly flavour violating. Flavour diagonal, non-universal corrections are not sufficient to simultaneously generate the correct mixing and the mass differences. We apply the new insights to an extension of the Minimal Supersymmetric Standard Model with non-minimal flavour violation in the soft breaking terms and discuss the low-energy threshold corrections to the light neutrino mass matrix in that model.

The charged fermion masses of the three generations exhibit the two strong hierarchies m3≫m2≫m1m3≫m2≫m1. We assume that also neutrino masses satisfy mν3>mν2>mν1mν3>mν2>mν1 and derive the consequences of the hierarchical spectra on the fermionic mixing patterns. The quark and lepton mixing matrices are built in a general framework with their matrix elements expressed in terms of the four fermion mass ratios, mu/mcmu/mc, mc/mtmc/mt, md/msmd/ms and ms/mbms/mb, and me/mμme/mμ, mμ/mτmμ/mτ, mν1/mν2mν1/mν2 and mν2/mν3mν2/mν3, for the quark and lepton sector, respectively. In this framework, we show that the resulting mixing matrices are consistent with data for both quarks and leptons, despite the large leptonic mixing angles. The minimal assumption we take is the one of hierarchical masses and minimal flavor symmetry breaking that strongly follows from phenomenology. No special structure of the mass matrices has to be assumed that cannot be motivated by this minimal assumption. This analysis allows us to predict the neutrino mass spectrum and set the mass of the lightest neutrino well below 0.01 eV. The method also gives the 1σ allowed ranges for the leptonic mixing matrix elements. Contrary to the common expectation, leptonic mixing angles are found to be determined solely by the four leptonic mass ratios without any relation to symmetry considerations as commonly used in flavor model building. Still, our formulae can be used to build up a flavor model that predicts the observed hierarchies in the masses — the mixing follows then from the procedure which is developed in this work.

We consider power corrections due to a finite top quark mass M_t to the production of a Higgs boson pair within the Standard Model at next-to-leading order (NLO) in QCD. Previous calculations for this process and at this precision were done in the limit of an inifinitely heavy top quark. Our results for the inclusive production cross section at NLO include terms up to O(1/M_t^12). We present the Mathematica package TopoID which for arbitrary processes aims to perform the necessary steps from Feynman diagrams to unrenormalized results expressed in terms of master integrals. We employ it for advancing in this process towards next-to-next-to-leading order (NNLO) where further automatization is needed.

The parameters of the Higgs potential of the Minimal Supersymmetric Standard Model (MSSM) receive large radiative corrections which lift the mass of the lightest Higgs boson to the measured value of 126 GeV. Depending on the MSSM parameters, these radiative corrections may also lead to the situation that the local minimum corresponding to the electroweak vacuum state is not the global minimum of the Higgs potential. We analyze the stability of the vacuum for the case of heavy squark masses as favored by current LHC data. To this end we first consider an effective Lagrangian obtained by integrating out the heavy squarks and then study the MSSM one-loop effective potential V_eff, which comprises all higher-dimensional Higgs couplings of the effective Lagrangian. We find that only the second method gives correct results and argue that the criterion of vacuum stability should be included in phenomenological analyses of the allowed MSSM parameter space. Discussing the cases of squark masses of 1 and 2 TeV we show that the criterion of vacuum stability excludes a portion of the MSSM parameter space in which (mu tanbeta) and A_t are large.

We discuss how the double missing partner mechanism solution to the doublet-triplet 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 Clebsch-Gordan 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 present the results of the first complete analytic calculation of the quark mass and field anomalous dimensions to ${\cal O}(\alpha_s^5)$ in QCD.