Transient dynamics for sequence processing neural networks

An exact solution of the transient dynamics for a sequential associative memory model is discussed through both the path-integral method and the statistical neurodynamics. Although the path-integral method has the ability to give an exact solution of the transient dynamics, only stationary properties have been discussed for the sequential associative memory. We have succeeded in deriving an exact macroscopic description of the transient dynamics by analyzing the correlation of crosstalk noise. Surprisingly, the order parameter equations of this exact solution are completely equivalent to those of the statistical neurodynamics, which is an approximation theory that assumes crosstalk noise to obey the Gaussian distribution. In order to examine our theoretical findings, we numerically obtain cumulants of the crosstalk noise. We verify that the third- and fourth-order cumulants are equal to zero, and that the crosstalk noise is normally distributed even in the non-retrieval case. We show that the results obtained by our theory agree with those obtained by computer simulations. We have also found that the macroscopic unstable state completely coincides with the separatrix.Comment: 21 pages, 4 figure

Scenery from the Top: Study of the Third Generation Squarks at CERN LHC

In the minimal supersymmetric standard model (MSSM) properties of the third generation sfermions are important from the viewpoint of discriminating the SUSY breaking models and in the determination of the Higgs boson mass. If gluinos are copiously produced at CERN LHC, gluino decays into tb through stop and sbottom can be studied using hadronic decays of the top quark. The kinematical endpoint of the gluino decays can be evaluated using a W sideband method to estimate combinatorial backgrounds. This implies that fundamental parameters related to the third generation squarks can be reliably measured. The top-quark polarization dependence in the decay process may also be extracted by looking at the b jet distribution near the kinematical endpoint.Comment: 4 pages in PRL format, 4 Postscript figures, uses revtex

P and T Odd Asymmetries in Lepton Flavor Violating Tau Decays

We calculated the differential cross sections of the processes in which one of the pair created tau particles at an e^+ e^- collider decays into lepton flavor violating final states e.g. tau -> mu gamma, tau -> 3 mu, tau -> mu ee. Using the correlations between angular distributions of both sides of tau decays, we can obtain information on parity and CP violations of lepton flavor non-conserving interactions. The formulae derived here are useful in distinguishing different models, since each model of physics beyond the standard model predicts different angular correlations. We also calculate angular distributions of the major background process to tau -> l gamma search, namely tau -> l nu \bar{\nu} gamma, and discuss usefulness of the angular correlation for background suppression.Comment: 31 pages, 5 figure

Stochastic transitions of attractors in associative memory models with correlated noise

We investigate dynamics of recurrent neural networks with correlated noise to analyze the noise's effect. The mechanism of correlated firing has been analyzed in various models, but its functional roles have not been discussed in sufficient detail. Aoyagi and Aoki have shown that the state transition of a network is invoked by synchronous spikes. We introduce two types of noise to each neuron: thermal independent noise and correlated noise. Due to the effects of correlated noise, the correlation between neural inputs cannot be ignored, so the behavior of the network has sample dependence. We discuss two types of associative memory models: one with auto- and weak cross-correlation connections and one with hierarchically correlated patterns. The former is similar in structure to Aoyagi and Aoki's model. We show that stochastic transition can be presented by correlated rather than thermal noise. In the latter, we show stochastic transition from a memory state to a mixture state using correlated noise. To analyze the stochastic transitions, we derive a macroscopic dynamic description as a recurrence relation form of a probability density function when the correlated noise exists. Computer simulations agree with theoretical results.Comment: 21 page

Lepton Flavor Violating Processes and Muon g-2 in Minimal Supersymmetric SO(10) Model

In the recently proposed minimal supersymmetric SO(10) model, the neutrino Dirac Yukawa coupling matrix, together with all the other fermion mass matrices, is completely determined once free parameters in the model are appropriately fixed so as to accommodate the recent neutrino oscillation data. Using this unambiguous neutrino Dirac Yukawa couplings, we calculate the lepton flavor violating (LFV) processes and the muon g-2 assuming the minimal supergravity scenario. The resultant rates of the LFV processes are found to be large enough to well exceed the proposed future experimental bound, while the magnitude of the muon g-2 can be within the recent result by Brookhaven E821 experiment. Furthermore, we find that there exists a parameter region which can simultaneously realize the neutralino cold dark matter abundance consistent with the recent WMAP data.Comment: 18 pages, 10 figures. The version to be published in Phys. Rev.

Electroweak Symmetry Breaking via UV Insensitive Anomaly Mediation

Anomaly mediation solves the supersymmetric flavor and CP problems. This is because the superconformal anomaly dictates that supersymmetry breaking is transmitted through nearly flavor-blind infrared physics that is highly predictive and UV insensitive. Slepton mass squareds, however, are predicted to be negative. This can be solved by adding D-terms for U(1)_Y and U(1)_{B-L} while retaining the UV insensitivity. In this paper we consider electroweak symmetry breaking via UV insensitive anomaly mediation in several models. For the MSSM we find a stable vacuum when tanbeta < 1, but in this region the top Yukawa coupling blows up only slightly above the supersymmetry breaking scale. For the NMSSM, we find a stable electroweak breaking vacuum but with a chargino that is too light. Replacing the cubic singlet term in the NMSSM superpotential with a term linear in the singlet we find a stable vacuum and viable spectrum. Most of the parameter region with correct vacua requires a large superpotential coupling, precisely what is expected in the ``Fat Higgs'' model in which the superpotential is generated dynamically. We have therefore found the first viable UV complete, UV insensitive supersymmetry breaking model that solves the flavor and CP problems automatically: the Fat Higgs model with UV insensitive anomaly mediation. Moreover, the cosmological gravitino problem is naturally solved, opening up the possibility of realistic thermal leptogenesis.Comment: 27 pages, 3 figures, 1 tabl

Dynamical Doublet-Triplet Higgs Mass Splitting

We propose a new mechanism towards the solution to the doublet-triplet Higgs mass splitting problem in the supersymmetric grand unified theory. Our model is based on the gauge group $SU(5)_H \times SU(5)_{GUT}$, where $SU(5)_H$ and $SU(5)_{GUT}$ are a new strong gauge interaction and the ordinary grand unified gauge group, respectively. The doublet-triplet Higgs mass splitting is realized through the quantum deformation of moduli space caused by the strong $SU(5)_H$ gauge dynamics. The low energy description of our model is given by the minimal supersymmetric standard model.Comment: 9 pages, LaTeX, the version to be published in Phys. Rev. D. (some typographical errors have been corrected

Hitting sbottom in natural SUSY

We compare the experimental prospects of direct stop and sbottom pair production searches at the LHC. Such searches for stops are of great interest as they directly probe for states that are motivated by the SUSY solution to the hierarchy problem of the Higgs mass parameter - leading to a "Natural" SUSY spectrum. Noting that sbottom searches are less experimentally challenging and scale up in reach directly with the improvement on b-tagging algorithms, we discuss the interplay of small TeV scale custodial symmetry violation with sbottom direct pair production searches as a path to obtaining strong sub-TeV constraints on stops in a natural SUSY scenario. We argue that if a weak scale natural SUSY spectrum does not exist within the reach of LHC, then hopes for such a spectrum for large regions of parameter space should sbottom out. Conversely, the same arguments make clear that a discovery of such a spectrum is likely to proceed in a sbottom up manner.Comment: 18 pages, 8 figures,v2 refs added, JHEP versio

Muon anomalous magnetic moment, lepton flavor violation, and flavor changing neutral current processes in SUSY GUT with right-handed neutrino

Motivated by the large mixing angle solutions for the atmospheric and solar neutrino anomalies, flavor changing neutral current processes and lepton flavor violating processes as well as the muon anomalous magnetic moment are analyzed in the framework of SU(5) SUSY GUT with right-handed neutrino. In order to explain realistic mass relations for quarks and leptons, we take into account effects of higher dimensional operators above the GUT scale. It is shown that the supersymmetric (SUSY) contributions to the CP violation parameter in $K^0-\bar{K}^0$ mixing, $\epsilon_K$, the $\mu \to e \gamma$ branching ratio, and the muon anomalous magnetic moment become large in a wide range of parameter space. We also investigate correlations among these quantities. Within the current experimental bound of $\text{B}(\mu \to e \gamma)$, large SUSY contributions are possible either in the muon anomalous magnetic moment or in $\epsilon_K$. In the former case, the favorable value of the recent muon anomalous magnetic moment measurement at the BNL E821 experiment can be accommodated. In the latter case, the allowed region of the Kobayashi-Maskawa phase can be different from the prediction within the Standard Model (SM) and therefore the measurements of the CP asymmetry of $B\to J/\psi K_S$ mode and $\Delta m_{B_s}$ could discriminate this case from the SM. We also show that the $\tau \to \mu \gamma$ branching ratio can be close to the current experimental upperbound and the mixing induced CP asymmetry of the radiative B decay can be enhanced in the case where the neutrino parameters correspond to the Mikheyev-Smirnov-Wolfenstein small mixing angle solution.Comment: 70 pages, 14 figure

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