We perform a model-independent analysis of the possible residual Klein and generalized CP symmetries associated with arbitrary lepton mixing angles in the case that there are three light Majorana neutrino species. This approach emphasizes the unique role of the Majorana phases and provides a useful framework in which to discuss the origin of the Dirac CP phase in scenarios with spontaneously broken flavor and generalized CP symmetries. The method is shown to reproduce known examples in the literature based on tribimaximal and bitrimaximal mixing patterns, and is used to investigate these issues for the case of a particular (GR1) golden ratio mixing pattern.

We investigate the question of electroweak naturalness within the deflected mirage mediation (DMM) framework for supersymmetry breaking in the minimal supersymmetric standard model (MSSM). The class of DMM models considered are nine-parameter theories that fall within the general classification of the 19-parameter phenomenological MSSM (pMSSM). Our results show that these DMM models have regions of parameter space with very low electroweak fine-tuning, at levels comparable to the pMSSM. These parameter regions should be probed extensively in the current LHC run.

We analyze a minimal flavored gauge mediation model in which the electroweak Higgs and messenger doublets are embedded in multiplets of a discrete non-Abelian symmetry. In this scenario, the minimal Higgs-messenger sector that is consistent with the 125 GeV Higgs mass has two vectorlike pairs of messenger fields. This scenario is obtained in a specific limit of the superpotential interactions of the Higgs-messenger fields and the matter fields. Due to the structure of the messenger-matter Yukawa couplings in this limit, sizable stop mixing and flavor-diagonal soft supersymmetry breaking parameters are achieved. In most of the parameter space, the masses of the colored superpartners are at most in the 5 − 6 TeV range. I. INTRODUCTIONThe 2012 discovery of the 125 GeV Higgs particle [1,2] and subsequent detailed measurements of its properties at the Large Hadron Collider (LHC) has provided significant limits on the allowed possibilities for extensions of the Standard Model (SM). In the context of theories with softly broken supersymmetry at the TeV scale (for reviews, see e.g. [3,4]), the Higgs mass is known to be within the theoretically allowed range for perturbative theories, but its relatively high value either requires large radiative corrections in the minimal supersymmetric standard model (MSSM), or an enlarged Higgs sector to boost the tree-level contributions. As such, it has long been known in the MSSM that large stop mixing or very heavy stops are needed (see e.g. [5]). This can place stringent constraints on specific models of the soft supersymmetry breaking terms, and also has important implications for the potential observability of superpartners at the LHC.The model-building constraints imposed by the Higgs measurements are particularly striking in the context of gauge mediation. In its minimal implementation, gauge-mediated supersymmetry breaking [6-9] predicts highly suppressed scalar trilinear couplings (A terms) at the messenger *

We explore the model building and phenomenology of flavored gauge-mediation models of supersymmetry breaking in which the electroweak Higgs doublets and the SUð2Þ messenger doublets are connected by a discrete non-Abelian symmetry. The embedding of the Higgs and messenger fields into representations of this non-Abelian Higgs-messenger symmetry results in specific relations between the Standard Model Yukawa couplings and the messenger-matter Yukawa interactions. Taking the concrete example of an S 3 Higgs-messenger symmetry, we demonstrate that, while the minimal implementation of this scenario suffers from a severe μ=B μ problem that is well known from ordinary gauge mediation, expanding the Higgs-messenger field content allows for the possibility that μ and B μ can be separately tuned, allowing for the possibility of phenomenologically viable models of the soft supersymmetrybreaking terms. We construct toy examples of this type that are consistent with the observed 125 GeV Higgs boson mass.

We use old quantization to predict features of the energy spectrum for bound states in spherically symmetric potentials. We review the application of this method to simple quantum mechanical systems with known analytic results and show that old quantization, while not generally capable of predicting the exact quantum-mechanical spectrum, does consistently give useful information. We then apply the method to a logarithmic potential and compare the results with a numerically calculated spectrum. Finally, we use these techniques to predict the number of bound states in the Yukawa potential and again compare the results with those obtained numerically. In all cases old quantization provides good predictive power for the main features of the true quantum-mechanical problem, and thus can serve as a “back-of-the-envelope” technique for providing rough, qualitative information about the system.