High-precision analyses of supersymmetry parameters aim at reconstructing the fundamental supersymmetric theory and its breaking mechanism. A well defined theoretical framework is needed when higher-order corrections are included. We propose such a scheme, Supersymmetry Parameter Analysis SPA, based on a consistent set of conventions and input parameters. A repository for computer programs is provided which connect parameters in different schemes and relate the Lagrangian parameters to physical observables at LHC and high energy e + e − linear collider experiments, i.e., masses, mixings, decay widths and production cross sections for supersymmetric particles. In addition, programs for calculating high-precision low energy observables, the density of cold dark matter (CDM) in the universe as well as the cross sections for CDM search experiments are included. The SPA scheme still requires extended efforts on both the theoretical and experimental side before data can be evaluated in the future at the level of the desired precision. We take here an initial step of testing the SPA scheme by applying the techniques involved to a specific supersymmetry reference point.

We advocate a new approach to study models of fermion masses and mixings, namely anarchy proposed in Ref. [1]. In this approach, we scan the O(1) coefficients randomly. We argue that this is the correct approach when the fundamental theory is sufficiently complicated. Assuming there is no physical distinction among three generations of neutrinos, the probability distributions in MNS mixing angles can be predicted independent of the choice of the measure. This is because the mixing angles are distributed according to the Haar measure of the Lie groups whose elements diagonalize the mass matrices. The near-maximal mixings, as observed in the atmospheric neutrino data and as required in the LMA solution to the solar neutrino problem, are highly probable. A small hierarchy between the ∆m 2 for the atmospheric and the solar neutrinos is obtained very easily; the complex seesaw case gives a hierarchy of a factor of 20 as the most probable one, even though this conclusion is more measuredependent. U e3 has to be just below the current limit from the CHOOZ experiment. The CP-violating parameter sin δ is preferred to be maximal. We present a simple SU (5)-like extension of anarchy to the charged-lepton and quark sectors which works well phenomenologically.

We study the dynamical symmetry breaking in the gauge-Higgs unification of the five-dimensional theory compactified on an orbifold, S 1 /Z 2 . This theory identifies Wilson line degrees of freedom as ''Higgs doublets.'' We consider SU(3) c ϫSU(3) W and SU(6) models with the compactification scale of order of a few TeV. The gauge symmetries are reduced to SU(3) c ϫSU(2) L ϫU(1) Y and SU(3) c ϫSU(2) L ϫU(1) Y ϫU(1), respectively, through the orbifolding boundary conditions. We estimate the one loop effective potential of ''Higgs doublets,'' and find that the electroweak breaking is realized through the radiative corrections when there are suitable numbers of bulk fields possessing the suitable representations. The masses of ''Higgs doublets'' are O͑100͒ GeV in this scenario.

A new method to compute the symplectic structure of a quantum field theory with non trivial boundary conditions is proposed. Following the suggestion in [1, 2], we regard that the boundary conditions are second class constraints in the sense of the Dirac's method. However, we show that this proposal is more useful if we consider an inverse of the Holographic map between a theory defined in the boundary to another with constraints but without boundary.

A new framework for handling flavor symmetry breaking in the neutrino sector is discussed where the source of symmetry breaking is traced to the global property of right-handed neutrinos in extra-dimensional space. Light neutrino phenomenology has rich and robust predictions such as the tri/bi-maximal form of generation mixing, controlled mass spectrum, and no need of flavor mixing couplings in the theory.

The dynamical determination of the boundary conditions in SU(N ) gauge theory on the orbifold S 1 /Z 2 is investigated. We classify the equivalence classes of the boundary conditions, and then the vacuum energy density of the theory in each equivalence class is evaluated at one loop order. Unambiguous comparison of the vacuum energy densities in the two theories in different equivalence classes becomes possible in supersymmetric theories. It is found that in the supersymmetric SU(5) models with the Scherk-Schwarz supersymmetry breaking, the theory with the boundary conditions yielding the standard model symmetry is in the equivalence class with the lowest energy density, though the low energy theory is not identically the minimal supersymmetric standard model. We also study how particular boundary conditions are chosen in the cosmological evolution of the universe. at UNIVERSITY OF ARIZONA on May 30, 2015 http://ptp.oxfordjournals.org/ Downloaded from * ) See Refs. 26) and 27) for SUSY breaking and Ref. 18) for gauge symmetry breaking on S 1 /Z 2 by the Hosotani mechanism.

Recent neutrino experiments suggest the strong evidences of tiny neutrino masses and the lepton-flavor mixing. Neutrino-oscillation solutions for the atmospheric neutrino anomaly and the solar neutrino deficit can determine the texture of neutrino mass matrix according to the neutrino mass hierarchies as Type A: m 3 ≫ m 2 ∼ m 1 , Type B: m 3 ≪ m 2 ∼ m 1 , and Type C: m 3 ∼ m 2 ∼ m 1 . In this paper we study the stability of the lepton-flavor mixing matrix against quantum corrections for all types of mass hierarchy in the minimal supersymmetric Standard Model with the effective dimension-five operator which gives Majorana masses of neutrinos. The relative sign assignments of neutrino masses in each type play the crucial roles for the stability against quantum corrections. We find the lepton-flavor mixing matrix of Type A is stable against quantum corrections, and that of Type B with the same (opposite) signs of m 1 and m 2 are unstable (stable). For Type C, the lepton-flavormixing matrix approaches to the definite unitary matrix according to the relative sign assignments of neutrino mass eigenvalues, as the effects of quantum corrections become large enough to neglect squared mass differences of neutrinos.

We derive the low energy effective theory of Gauge-Higgs unification (GHU) models in the usual four dimensional framework. We find that the theories are described by only the zero-modes with a particular renormalization condition in which essential informations about GHU models are included. We call this condition "Gauge-Higgs condition" in this letter. In other wards, we can describe the low energy theory as the SM with this condition if GHU is a model as the UV completion of the Standard Model. This approach will be a powerful tool to construct realistic models for GHU and to investigate their low energy phenomena.