Generalizing Minimal Supergravity

In Grand Unified Theories (GUTs), the Standard Model (SM) gauge couplings need not be unified at the GUT scale due to the high-dimensional operators. Considering gravity mediated supersymmetry breaking, we study for the first time the generic gauge coupling relations at the GUT scale, and the general gaugino mass relations which are valid from the GUT scale to the electroweak scale at one loop. We define the index k for these relations, which can be calculated in GUTs and can be determined at the Large Hadron Collider and the future International Linear Collider. Thus, we give a concrete definition of the GUT scale in these theories, and suggest a new way to test general GUTs at future experiments. We also discuss five special scenarios with interesting possibilities. With our generic formulae, we present all the GUT-scale gauge coupling relations and all the gaugino mass relations in the SU(5) and SO(10) models, and calculate the corresponding indices k. Especially, the index k is 5/3 in the traditional SU(5) and SO(10) models that have been studied extensively so far. Furthermore, we discuss the field theory realization of the U(1) flux effects on the SM gauge kinetic functions in F-theory GUTs, and calculate their indices k as well.Comment: RevTex4, 14 pages, 4 tables, references added, version in PL

Electroweak Supersymmetry around the Electroweak Scale

Inspired by the phenomenological constraints, LHC supersymmetry and Higgs searches, dark matter search as well as string model building, we propose the electroweak supersymmetry around the electroweak scale: the squarks and/or gluinos are around a few TeV while the sleptons, sneutrinos, bino and winos are within one TeV. The Higgsinos can be either heavy or light. We consider bino as the dominant component of dark matter candidate, and the observed dark matter relic density is achieved via the neutralino-stau coannihilations. Considering the Generalized Minimal Supergravity (GmSUGRA), we show explicitly that the electroweak supersymmetry can be realized, and the gauge coupling unification can be preserved. With two Scenarios, we study the viable parameter spaces that satisfy all the current phenomenological constraints, and we present the concrete benchmark points. Furthermore, we comment on the fine-tuning problem and LHC searches.Comment: RevTex4, 28 pages, 8 figures, 8 tables, version to appear in EPJ

WMAP Data and Recent Developments in Supersymmetric Dark Matter

A brief review is given of the recent developments in the analyses of supersymmetric dark matter. Chief among these is the very accurate determination of the amount of cold dark matter in the universe from analyses using WMAP data. The implications of this data for the mSUGRA parameter space are analyzed. It is shown that the data admits solutions on the hyperbolic branch (HB) of the radiative breaking of the electroweak symmetry. A part of the hyperbolic branch lies in the so called inversion region where the LSP neutralino $\chi_1^0$ becomes essentially a pure Higgsino and degenerate with the next to the lightest neutralino $\chi_2^0$ and the light chargino $\chi_1^{\pm}$. Thus some of the conventional signals for the observation of supersymmetry at colliders (e.g., the missing energy signals) do not operate in this region. On the other hand the inversion region contains a high degree of degeneracy of $\chi_1^0$, $\chi_2^0$, $\chi_1^{\pm}$ leading to coannihilations which allow for the satisfaction of the WMAP relic density constraints deep on the hyperbolic branch. Further, an analysis of the neutralino-proton cross sections in this region reveals that this region can still be accessible to dark matter experiments in the future. Constraints from $g_{\mu}-2$ and from $B^0_s\to \mu^+\mu^-$ are discussed. Future prospects are also discussed.Comment: 15 pages Latex. Invited talk at the IV International Conference on Non-accelerator New Physics (NANP'03), Dubna, Russia, June 23-28, 200

General Gauge and Anomaly Mediated Supersymmetry Breaking in Grand Unified Theories with Vector-Like Particles

In Grand Unified Theories (GUTs) from orbifold and various string constructions the generic vector-like particles do not need to form complete SU(5) or SO(10) representations. To realize them concretely, we present orbifold SU(5) models, orbifold SO(10) models where the gauge symmetry can be broken down to flipped SU(5) X U(1)_X or Pati-Salam SU(4)_C X SU(2)_L X SU(2)_R gauge symmetries, and F-theory SU(5) models. Interestingly, these vector-like particles can be at the TeV-scale so that the lightest CP-even Higgs boson mass can be lifted, or play the messenger fields in the Gauge Mediated Supersymmetry Breaking (GMSB). Considering GMSB, ultraviolet insensitive Anomaly Mediated Supersymmetry Breaking (AMSB), and the deflected AMSB, we study the general gaugino mass relations and their indices, which are valid from the GUT scale to the electroweak scale at one loop, in the SU(5) models, the flipped SU(5) X U(1)_X models, and the Pati-Salam SU(4)_C X SU(2)_L X SU(2)_R models. In the deflected AMSB, we also define the new indices for the gaugino mass relations, and calculate them as well. Using these gaugino mass relations and their indices, we may probe the messenger fields at intermediate scale in the GMSB and deflected AMSB, determine the supersymmetry breaking mediation mechanisms, and distinguish the four-dimensional GUTs, orbifold GUTs, and F-theory GUTs.Comment: RevTex4, 45 pages, 15 tables, version to appear in JHE

Realistic Standard Model Fermion Mass Relations in Generalized Minimal Supergravity (GmSUGRA)

Grand Unified Theories (GUTs) usually predict wrong Standard Model (SM) fermion mass relation m_e/m_{\mu} = m_d/m_s toward low energies. To solve this problem, we consider the Generalized Minimal Supergravity (GmSUGRA) models, which are GUTs with gravity mediated supersymmetry breaking and higher dimensional operators. Introducing non-renormalizable terms in the super- and K\"ahler potentials, we can obtain the correct SM fermion mass relations in the SU(5) model with GUT Higgs fields in the {\bf 24} and {\bf 75} representations, and in the SO(10) model. In the latter case the gauge symmetry is broken down to SU(3)_C X SU(2)_L X SU(2)_R X U(1)_{B-L}, to flipped SU(5)X U(1)_X, or to SU(3)_C X SU(2)_L X U(1)_1 X U(1)_2. Especially, for the first time we generate the realistic SM fermion mass relation in GUTs by considering the high-dimensional operators in the K\"ahler potential.Comment: JHEP style, 29 pages, no figure,references adde

Dynamic Interpretation of Hedgehog Signaling in the Drosophila Wing Disc

Morphogens are classically defined as molecules that control patterning by acting at a distance to regulate gene expression in a concentration-dependent manner. In the Drosophila wing imaginal disc, secreted Hedgehog (Hh) forms an extracellular gradient that organizes patterning along the anterior–posterior axis and specifies at least three different domains of gene expression. Although the prevailing view is that Hh functions in the Drosophila wing disc as a classical morphogen, a direct correspondence between the borders of these patterns and Hh concentration thresholds has not been demonstrated. Here, we provide evidence that the interpretation of Hh signaling depends on the history of exposure to Hh and propose that a single concentration threshold is sufficient to support multiple outputs. Using mathematical modeling, we predict that at steady state, only two domains can be defined in response to Hh, suggesting that the boundaries of two or more gene expression patterns cannot be specified by a static Hh gradient. Computer simulations suggest that a spatial “overshoot” of the Hh gradient occurs, i.e., a transient state in which the Hh profile is expanded compared to the Hh steady-state gradient. Through a temporal examination of Hh target gene expression, we observe that the patterns initially expand anteriorly and then refine, providing in vivo evidence for the overshoot. The Hh gene network architecture suggests this overshoot results from the Hh-dependent up-regulation of the receptor, Patched (Ptc). In fact, when the network structure was altered such that the ptc gene is no longer up-regulated in response to Hh-signaling activation, we found that the patterns of gene expression, which have distinct borders in wild-type discs, now overlap. Our results support a model in which Hh gradient dynamics, resulting from Ptc up-regulation, play an instructional role in the establishment of patterns of gene expression

Neutralino Dark Matter, b-tau Yukawa Unification and Non-Universal Sfermion Masses

We study the implications of minimal non-Universal Boundary Conditions in the sfermion Soft SUSY Breaking (SSB) masses of mSUGRA. We impose asymptotic b-tau Yukawa coupling Unification and we resort to a parameterization of the deviation from Universality in the SSB motivated by the multiplet structure of SU(5) GUT. A set of cosmo-phenomenological constraints, including the recent results from WMAP, determines the allowed parameter space of the models under consideration. We highlight a new coannihilation corridor where neutralino-sbottom and neutralino-tau sneutrino-stau coannihilations significantly contribute to the reduction of the neutralino relic density.Comment: 38 pages, 27 Figures, Latex; Version accepted for publication in PR

Constraining the string scale: from Planck to Weak and back again

String and field theory ideas have greatly influenced each other since the so called second string revolution. We review this interrelation paying particular attention to its phenomenological implications. Our guiding principle is the radical shift in the way that we think about the fundamental scale, in particular the way in which string models have been able to accommodate values from the Planck $M_\mathrm{Pl}\sim 10^{18}$ GeV down to the electroweak scale $M_{EW}\sim$ TeV.Comment: Invited review aimed at an experimental audienc

Helium and Deuterium Abundances as a Test for the Time Variation of the Fine Structure Constant and the Higgs Vacuum Expectation Value

We use the semi-analytic method of \citet{Esma91} to calculate the abundances of Helium and Deuterium produced during Big Bang nucleosynthesis assuming the fine structure constant and the Higgs vacuum expectation value may vary in time. We analyze the dependence on the fundamental constants of the nucleon mass, nuclear binding energies and cross sections involved in the calculation of the abundances. Unlike previous works, we do not assume the chiral limit of QCD. Rather, we take into account the quark masses and consider the one-pion exchange potential, within perturbation theory, for the proton-neutron scattering. However, we do not consider the time variation of the strong interactions scale but attribute the changes in the quark masses to the temporal variation of the Higgs vacuum expectation value. Using the observational data of the helium and deuterium, we put constraints on the variation of the fundamental constants between the time of nucleosynthesis and the present time.Comment: 27 pages, 1 figure, replaced to match published version, new references adde

The fundamental constants and their variation: observational status and theoretical motivations

This article describes the various experimental bounds on the variation of the fundamental constants of nature. After a discussion on the role of fundamental constants, of their definition and link with metrology, the various constraints on the variation of the fine structure constant, the gravitational, weak and strong interactions couplings and the electron to proton mass ratio are reviewed. This review aims (1) to provide the basics of each measurement, (2) to show as clearly as possible why it constrains a given constant and (3) to point out the underlying hypotheses. Such an investigation is of importance to compare the different results, particularly in view of understanding the recent claims of the detections of a variation of the fine structure constant and of the electron to proton mass ratio in quasar absorption spectra. The theoretical models leading to the prediction of such variation are also reviewed, including Kaluza-Klein theories, string theories and other alternative theories and cosmological implications of these results are discussed. The links with the tests of general relativity are emphasized.Comment: 56 pages, l7 figures, submitted to Rev. Mod. Phy