Showing papers on "Scalar potential published in 2008"

CERN LHC phenomenology of an extended standard model with a real scalar singlet

Abstract: Gauge singlet extensions of the standard model (SM) scalar sector may help remedy its theoretical and phenomenological shortcomings while solving outstanding problems in cosmology. Depending on the symmetries of the scalar potential, such extensions may provide a viable candidate for the observed relic density of cold dark matter or a strong first order electroweak phase transition needed for electroweak baryogenesis. Using the simplest extension of the SM scalar sector with one real singlet field, we analyze the generic implications of a singlet-extended scalar sector for Higgs boson phenomenology at the Large Hadron Collider (LHC). We consider two broad scenarios: one in which the neutral SM Higgs and singlet mix and the other in which no mixing occurs and the singlet can be a dark matter particle. For the first scenario, we analyze constraints from electroweak precision observables and their implications for LHC Higgs phenomenology. For models in which the singlet is stable, we determine the conditions under which it can yield the observed relic density, compute the cross sections for direct detection in recoil experiments, and discuss the corresponding signatures at the LHC.

Instability in cosmological topologically massive gravity at the chiral point

Abstract: This thesis explores three different aspects of quantum gravity. First we study D3-brane black holes in Calabi-Yau compactifications of type IIB string theory. Using the OSV conjecture and a relation between topological strings and matrix models we show that some black holes have a matrix model description. This is the case if the attractor mechanism fixes the internal geometry to a conifold at the black hole horizon. We also consider black holes in a flux compactification and compare the effects of the black holes and fluxes on the internal geometry. We find that the fluxes dominate. Second, we study the scalar potential of type IIB flux compactifications. We demonstrate that monodromies of the internal geometry imply as a general feature the existence of long series of continuously connected minima. This allows for the embedding of scenarios such as chain inflation and resonance tunneling into string theory. The concept of monodromies is also extended to include geometric transitions: passing to a different Calabi-Yau topology, performing its monodromies and then returning to the original space allows for novel transformations. All constructions are performed explicitly, using both analytical and numerical techniques, in the mirror quintic Calabi-Yau. Third, we study cosmological topologically massive gravity at the chiral point, a prime candidate for quantization of gravity in three dimensions. The prospects of this scenario depend crucially of the stability of the theory. We demonstrate the presence of a negative energy bulk mode that grows logarithmically toward the AdS boundary. The AdS isometry generators have non-unitary matrix representations like in logarithmic CFT, and we propose that the CFT dual for this theory is logarithmic. In a complementing canonical analysis we also demonstrate the existence of this bulk degree of freedom, and we present consistent boundary conditions encompassing the new mode.

General analysis of LARGE Volume Scenarios with string loop moduli stabilisation

Abstract: We study the topological conditions for general Calabi-Yaus to get a non-supersymmetric AdS exponentially large volume minimum of the scalar potential in flux compactifications of IIB string theory. We show that negative Euler number and the existence of at least one blow-up mode resolving point-like singularities are necessary and sufficient conditions for moduli stabilisation with exponentially large volumes. We also analyse the general effects of string loop corrections on this scenario. While the combination of α' and nonperturbative corrections are sufficient to stabilise blow-up modes and the overall volume, quantum corrections are needed to stabilise other directions transverse to the overall volume. This allows exponentially large volume minima to be realised for fibration Calabi-Yaus, with the various moduli of the fibration all being stabilised at exponentially large values. String loop corrections may also play a role in stabilising 4-cycles which support chiral matter and cannot enter directly into the non-perturbative superpotential. We illustrate these ideas by studying the scalar potential for various Calabi-Yau three-folds including K3 fibrations and briefly discuss the potential phenomenological and cosmological implications of our results.

Systematics of string loop corrections in type IIB Calabi-Yau flux compactifications

Abstract: We study the behaviour of the string loop corrections to the N = 1 4D supergravity Kahler potential that occur in flux compactifications of IIB string theory on general Calabi-Yau three-folds. We give a low energy interpretation for the conjecture of Berg, Haack and Pajer for the form of the loop corrections to the Kahler potential. We check the consistency of this interpretation in several examples. We show that for arbitrary Calabi-Yaus, the leading contribution of these corrections to the scalar potential is always vanishing, giving an ``extended no-scale structure''. This result holds as long as the corrections are homogeneous functions of degree -2 in the 2-cycle volumes. We use the Coleman-Weinberg potential to motivate this cancellation from the viewpoint of low-energy field theory. Finally we give a simple formula for the 1-loop correction to the scalar potential in terms of the tree-level Kahler metric and the conjectured correction to the Kahler potential. We illustrate our ideas with several examples. A companion paper will use these results in the study of Kahler moduli stabilisation.

Bulk viscosity of strongly coupled plasmas with holographic duals

Abstract: We explain a method for computing the bulk viscosity of strongly coupled thermal plasmas dual to supergravity backgrounds supported by one scalar field. Whereas earlier investigations required the computation of the leading dissipative term in the dispersion relation for sound waves, our method requires only the leading frequency dependence of an appropriate Green's function in the low-frequency limit. With a scalar potential chosen to mimic the equation of state of QCD, we observe a slight violation of the lower bound on the ratio of the bulk and shear viscosities conjectured in [1].

Bulk viscosity of strongly coupled plasmas with holographic duals

Abstract: We explain a method for computing the bulk viscosity of strongly coupled thermal plasmas dual to supergravity backgrounds supported by one scalar field. Whereas earlier investigations required the computation of the leading dissipative term in the dispersion relation for sound waves, our method requires only the leading frequency dependence of an appropriate Green's function in the low-frequency limit. With a scalar potential chosen to mimic the equation of state of QCD, we observe a slight violation of the lower bound on the ratio of the bulk and shear viscosities conjectured in arXiv:0708.3459.

Accidental inflation in string theory

Abstract: We show that inflation in type IIB string theory driven by the volume modulus can be realized in the context of the racetrack-based Kallosh–Linde model (KL) of moduli stabilization. Inflation here arises through the volume modulus slow-rolling down from a flat hilltop or inflection point of the scalar potential. This situation can be quite generic in the landscape, where by uplifting one of the two adjacent minima one can turn the barrier either into a flat saddle point or into an inflection point supporting eternal inflation. The resulting spectral index is tunable in the range of , and there is only negligible production of primordial gravitational waves r<10−6. The flatness of the potential in this scenario requires fine-tuning, which may be justified taking into account the exponential reward by volume factors preferring the regions of the universe with the maximal amount of slow-roll inflation. This consideration leads to a tentative prediction of the spectral index ns≈0.95 or 0.93, depending on whether the potential has a symmetry or not.

An augmented electric field integral equation for high-speed interconnect analysis

Abstract: The conventional electric field integral equation (EFIE) is augmented by including charge as the extra unknown, so that the contributions of the vector potential and the scalar potential are separated to avoid the imbalance at low frequencies. With the frequency scaling and the direct enforcement of the current continuity constraint, the new augmented EFIE is free of low-frequency breakdown for interconnect analysis. Mathematically, it can be categorized as a generalized saddle-point problem. The new equation is verified by numerical examples. © 2008 Wiley Periodicals, Inc. Microwave Opt Technol Lett 50: 2658–2662, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.23736

Supersymmetric Models with Higher Dimensional Operators

Abstract: Using a superfield language it is shown that a 4D N=1 supersymmetric theory with higher derivative operators in either the Kahler or the superpotential part of the Lagrangian and with an otherwise arbitrary superpotential, is equivalent to a 4D N=1 theory of second order (i.e. without higher derivatives) with additional superfields and renormalised interactions. If the theory has no other higher dimensional operators, under additional assumptions for the analytical continuation Minkowski-Euclidean space, the theory can be renormalisable. We provide examples where a free theory with trivial supersymmetry breaking provided by a linear superpotential becomes, in the presence of higher derivatives terms and in the second order version, a non-trivial interactive one with spontaneous supersymmetry breaking. The couplings of the equivalent theory acquire a threshold correction through their dependence on the scale of the higher dimensional operator(s). The scalar potential in the second order theory is not necessarily positive definite, and one can in principle have a vanishing potential with broken supersymmetry. We provide an application to MSSM and argue that at tree-level and for a mass scale associated to a higher derivative term in the TeV range, the Higgs mass can be lifted above the current experimental limits.

Superintegrability with third order integrals of motion, cubic algebras and supersymmetric quantum mechanics I:Rational function potentials

Abstract: We consider a superintegrable Hamiltonian system in a two-dimensional space with a scalar potential that allows one quadratic and one cubic integral of motion. We construct the most general cubic algebra and we present specific realizations. We use them to calculate the energy spectrum. All classical and quantum superintegrable potentials separable in Cartesian coordinates with a third order integral are known. The general formalism is applied to quantum reducible and irreducible rational potentials separable in Cartesian coordinates in E2. We also discuss these potentials from the point of view of supersymmetric and PT-symmetric quantum mechanics.

Flavor symmetry breaking and vacuum alignment on orbifolds

Abstract: Flavor symmetry has been widely studied for figuring out the masses and mixing angles of standard model fermions. In this paper we present a framework for handling flavor symmetry breaking where the symmetry breaking is triggered by boundary conditions of scalar fields in extra-dimensional space. The alignment of scalar expectation values is achieved without referring to any details of scalar potential and its minimization procedure. As applications to non-Abelian discrete flavor symmetries, illustrative lepton mass models are constructed where the ${S}_{3}$ and ${A}_{4}$ flavor symmetries are broken down to the directions leading to the tribimaximal form of lepton mixing and realistic mass patterns.

Fibre Inflation: Observable Gravity Waves from IIB String Compactifications

Abstract: We introduce a simple string model of inflation, in which the inflaton field can take trans-Planckian values while driving a period of slow-roll inflation. This leads naturally to a realisation of large field inflation, inasmuch as the inflationary epoch is well described by the single-field scalar potential $V = V_0 (3-4 e^{-\hat\varphi/\sqrt{3}})$. Remarkably, for a broad class of vacua all adjustable parameters enter only through the overall coefficient $V_0$, and in particular do not enter into the slow-roll parameters. Consequently these are determined purely by the number of \e-foldings, $N_e$, and so are not independent: $\varepsilon \simeq \frac32 \eta^2$. This implies similar relations among observables like the primordial scalar-to-tensor amplitude, $r$, and the scalar spectral tilt, $n_s$: $r \simeq 6(n_s - 1)^2$. $N_e$ is itself more model-dependent since it depends partly on the post-inflationary reheat history. In a simple reheating scenario a reheating temperature of $T_{rh}\simeq 10^{9}$ GeV gives $N_e\simeq 58$, corresponding to $n_s\simeq 0.970$ and $r\simeq 0.005$, within reach of future observations. The model is an example of a class that arises naturally in the context of type IIB string compactifications with large-volume moduli stabilisation, and takes advantage of the generic existence there of Kahler moduli whose dominant appearance in the scalar potential arises from string loop corrections to the Kahler potential. The inflaton field is a combination of Kahler moduli of a K3-fibered Calabi-Yau manifold. We believe there are likely to be a great number of models in this class -- `high-fibre models' -- in which the inflaton starts off far enough up the fibre to produce observably large primordial gravity waves.

Hilltop Non-Gaussianity

Abstract: We study non-Gaussianity induced by a pseudo Nambu-Goldstone boson with a cosine-type scalar potential. We focus on how the non-Gaussianity is affected when the pseudo Nambu-Goldstone boson rolls down from near the top of the scalar potential where the deviation from a quadratic potential is large. We find that the resultant non-Gaussianity is similar to that obtained in the quadratic potential, if the pseudo Nambu-Goldstone boson accounts for the curvature perturbation; the non-Gaussianity is enhanced, otherwise.

Autonomous vehicle control for ascending/descending along a potential field with two applications

Abstract: In this paper, we present a reactive control law that can navigate a single, sensor-enabled vehicle to ascend or descend a scalar potential field. The design builds on our previous work on developing an online following control. The model framework enables us to establish performance bounds for the developed ascending/descending control that are related to the geometrical parameters of the field. The efficacy of our approach is demonstrated through two possible applications - source-centric mapping of a potential field and tracking of a single target, emitting a distance-related potential field.

General Analysis of LARGE Volume Scenarios with String Loop Moduli Stabilisation

Abstract: We study the topological conditions for general Calabi-Yaus to get a non-supersymmetric AdS exponentially large volume minimum of the scalar potential in flux compactifications of IIB string theory. We show that negative Euler number and the existence of at least one blow-up mode resolving point-like singularities are necessary and sufficient conditions for moduli stabilisation with exponentially large volumes. We also analyse the general effects of string loop corrections on this scenario. While the combination of alpha' and nonperturbative corrections are sufficient to stabilise blow-up modes and the overall volume, quantum corrections are needed to stabilise other directions transverse to the overall volume. This allows exponentially large volume minima to be realised for fibration Calabi-Yaus, with the various moduli of the fibration all being stabilised at exponentially large values. String loop corrections may also play a role in stabilising 4-cycles which support chiral matter and cannot enter directly into the non-perturbative superpotential. We illustrate these ideas by studying the scalar potential for various Calabi-Yau three-folds including K3 fibrations and briefly discuss the potential phenomenological and cosmological implications of our results.

Skin effect in a small symmetrically driven capacitive discharge

Abstract: The so-called 'electrostatic' approximation postulates that the electric field can be represented by the gradient of a scalar potential, even under dynamical conditions. This assumption reduces the set of Maxwell's equations to the much simpler Poisson equation and is often employed for modeling and simulation of radio frequency driven capacitive low pressure discharges. While it is now widely acknowledged that the neglect of induction phenomena breaks down for large-area plasma sources driven at high frequencies (such as used for VLSI processing), smaller experimental devices excited at moderate frequencies (e.g. 13.56 MHz) are generally thought to be uncritical. This paper demonstrates the opposite: even small plasma reactors of the size of the Gaseous Electronics Conference reference cell exhibit a considerable skin effect in the low pressure, high density regime and render the electrostatic approximation invalid. The point is made, however, that this phenomenon is not 'fully electromagnetic' (in the sense that its analysis requires the full set of Maxwell's equations), but can be understood by means of a simplified model which assumes quasi-neutrality and may therefore be called 'magnetostatic'.

Reconstruction of scalar potentials in two-field cosmological models

Abstract: We study the procedure of the reconstruction of phantom-scalar field potentials in two-field cosmological models. It is shown that, while in the one-field case the chosen cosmological evolution defines uniquely the form of the scalar potential, in the two-field case one has an infinite number of possibilities. The classification of a large class of possible potentials is presented and the dependence of cosmological dynamics on the choice of initial conditions is investigated qualitatively and numerically for two particular models.

Reconstructing a model of quintessential inflation

Abstract: We present an explicit cosmological model where inflation and dark energy both could arise from the dynamics of the same scalar field. We present our discussion in the framework where the inflaton field attains a nearly constant velocity m−1P|d/dN| ≡ α + βexp(βN) (where N ≡ ln a is the e-folding time) during inflation. We show that the model with |α| < 0.25 and β < 0 can easily satisfy inflationary constraints, including the spectral index of scalar fluctuations (ns = 0.96 ± 0.013), tensor-to-scalar ratio (r < 0.28) and also the bound imposed on Ω during the nucleosynthesis epoch (Ω(1 ~ MeV) < 0.1). In our construction, the scalar field potential always scales proportionally to the square of the Hubble expansion rate. One may thereby account for the two vastly different energy scales associated with the Hubble parameters at early and late epochs. The inflaton energy could also produce an observationally significant effective dark energy at a late epoch without violating local gravity tests.

The exact solution of the s-wave Klein–Gordon equation for the generalized Hulthén potential by the asymptotic iteration method

Abstract: The bound state solution of the (1+1)-dimensional Klein?Gordon (KG) equation for the generalized Hulth?n potential has been studied in the framework of the asymptotic iteration method (AIM). The energy values and the corresponding eigenfunctions are obtained for mixed forms of the Hulth?n vector potential and scalar potential.

Relativistic solutions for double ring-shaped oscillator potential via asymptotic iteration method

Abstract: The three dimensional Klein–Gordon equation is solved with a double ring-shaped oscillator for the case of the equal vector and scalar potential, , by using the asymptotic iteration method which is very efficient, systematic and practical. The bound states energy eigenvalues and corresponding eigenfunctions are presented for a particle bound in a potential of a double ring-shaped oscillator.

Two-field Kähler moduli inflation in large volume moduli stabilization

Abstract: In this paper we present a two-field inflation model, which is distinctive in having a non-canonical kinetic Lagrangian and comes from the large volume approach to the moduli stabilization in flux compactification of type IIB superstring on a Calabi–Yau orientifold with h(1,2)>h(1,1)≥4. The Kahler moduli are classified as the volume modulus, heavy moduli and two light moduli. The axion–dilaton, complex structure moduli and all heavy Kahler moduli including the volume modulus are frozen by a non-perturbatively corrected flux superpotential and the α'-corrected Kahler potential in the large volume limit. The minimum of the scalar potential at which the heavy moduli are stabilized provides the dominant potential energy for the surviving light Kahler moduli. We consider a simplified case where the axionic components in the light Kahler moduli are further stabilized at the potential minimum and only the geometrical components are taken as scalar fields to drive an assisted-like inflation. For a certain range of moduli stabilization parameters and inflation initial conditions, we obtain a nearly flat power spectrum of the curvature perturbation, with ns≈0.96 at Hubble exit, and an inflationary energy scale of 3 × 1014 GeV. In our model, there is significant correlation between the curvature and isocurvature perturbations on super-Hubble scales, so at the end of inflation a great deal of the curvature power spectrum originates from this correlation.

Geometric potentials in quantum optics: A semi-classical interpretation

Abstract: We propose a semi-classical interpretation of the geometric scalar and vector potentials that arise due to Berry's phase when an atom moves slowly in a light field. Starting from the full quantum Hamiltonian, we turn to a classical description of the atomic centre-of-mass motion while still treating the internal degrees of freedom as quantum variables. We show that the scalar potential can be identified as the kinetic energy of an atomic micro-motion caused by quantum fluctuations of the radiative force, and that the Lorentz-type force appears as a result of the motion-induced perturbation of the internal atomic state. For a specific configuration involving two counter-propagating Gaussian laser beams, we relate the geometric forces to the radiation pressure and dipole forces known from quantum optics. The simple physical pictures provided by the present analysis may help for the design and the implementation of novel geometric forces.

Scalar Potential Formulation and Inverse Problem Applied to Thin Magnetic Sheets

Abstract: Our goal is to identify sheet steel magnetization with near field measurements. Indeed, direct calculation of the whole magnetization is impossible because the remanent part of the magnetization is nondeterminist. Consequently, our strategy is to obtain a magnetostatic formulation able to compute magnetic field as close as possible to the sheet and which is adapted to solve an inverse problem. In this paper, a scalar potential integral formulation is introduced and compared to a magnetization formulation. We are especially interested in the magnetic anomaly created by ferromagnetic ships.

On the electromagnetic origin of inertia and inertial mass

Abstract: We address the problem of inertial property of matter through analysis of the motion of an extended charged particle. Our approach is based on the continuity equation for momentum (Newton's second law) taking due account of the vector potential and its convective derivative. We obtain a development in terms of retarded potentials allowing an intuitive physical interpretation of its main terms. The inertial property of matter is then discussed in terms of a kind of induction law related to the extended charged particle's own vector potential. Moreover, it is obtained a force term that represents a drag force acting on the charged particle when in motion relatively to its own vector potential field lines. The time rate of variation of the particle's vector potential leads to the acceleration inertia reaction force, equivalent to the Schott term responsible for the source of the radiation field. We also show that the velocity dependent term of the particle's vector potential is connected with the relativistic increase of mass with velocity and generates a longitudinal stress force that is the source of electric field lines deformation. In the framework of classical electrodynamics, we have shown that the electron mass has possibly a complete electromagnetic origin and the obtained covariant equation solves the "4/3 mass paradox" for a spherical charge distribution.

Network Representation of Conducting Regions in 3-D Finite-Element Description of Electrical Machines

Abstract: The paper introduces a network description of conducting regions in electrical machines. Resistance models are considered, where loop equations are equivalent to an edge element formulation using the electric vector potential T, as well as conductance models, for which the nodal equations refer to a nodal element description by means of the scalar potential V. Network models for multiply connected regions are derived for both Omega-T-T0 and A-T-T0 formulations. A network representation of the edge value of potential T0 is suggested. Convergence of the iterations of the T-T0 method may be accelerated by supplementing equations for the edge values of T0.

Two-field K\"ahler moduli inflation on large volume moduli stabilization

Abstract: In this paper we present a two-field inflation model, which distinguishes itself with a non-canonical kinetic lagrangian and comes from the large volume approach to the moduli stabilization in flux compactification of type IIB superstring on a Calabi-Yau orientifold of $h^{(1,2)} > h^{(1,1)}\geq 4$. The Kahler moduli are classified as volume modulus, heavy moduli and two light moduli. The axion-dilaton, complex structure moduli and all heavy Kahler moduli including the volume modulus are frozen by nonperturbatively corrected flux superpotential and the $\alpha^\prime$-corrected Kahler potential in the large volume limit. The minimum of the scalar potential at which the heavy moduli are stabilized provides the dominant potential energy for the survived light Kahler moduli. We consider a simplified case where the axionic components in the light Kahler moduli are further stabilized at the potential minimum and only the geometrical components are taken as the scalar fields to drive an assisted-like inflation. For a certain range of moduli stabilization parameters and inflation initial conditions, we obtain a nearly flat power spectrum of the curvature perturbation, with $n_s\approx 0.96$ at Hubble-exit, and an inflationary energy scale of $3 \times 10^{14}$ GeV. In our model, significant correlation exists between the curvature and isocurvature perturbations on super-Hubble scales so that at the end of inflation a great deal of the curvature power spectrum originates from this correlation.

Minimal conductivity of rippled graphene with topological disorder

Abstract: We study the transport properties of a neutral graphene sheet with curved regions induced or stabilized by topological defects. The proposed model gives rise to Dirac fermions in a random magnetic field and in a random scalar potential acting like a space-dependent Fermi velocity induced by the curvature. The last term leads to a singular long-range correlated disorder with special characteristics. The Drude minimal conductivity at zero energy is found to be inversely proportional to the density of topological disorder, a signature of diffusive behavior.

Groups and Analysis: Sharp spectral inequalities for the Heisenberg Laplacian

Abstract: In this thesis, which comprises four research papers, two operators in mathe- matical physics are considered. The former two papers contain results for the Schrodinger operator with an Aharonov-Bohm magnetic field. In Paper I we explicitly compute the spectrum and eigenfunctions of this operator in R2 in a number of cases where a radial scalar potential and/or a constant magnetic field are superimposed. In some of the studied cases we calculate the sharp constants in the Lieb-Thirring inequality for γ = 0 and γ ≥ 1. In Paper II we prove semi-classical estimates on moments of the eigenvalues in bounded two-dimensional domains. We moreover present an example where the generalised diamagnetic inequality, conjectured by Erdős, Loss and Vougalter, fails. Numerical studies complement these results. The latter two papers contain several spectral estimates for the Heisenberg Laplacian. In Paper III we obtain sharp inequalities for the spectrum of the Dirichlet problem in (2n + 1)-dimensional domains of finite measure. Let λk and μk denote the eigenvalues of the Dirichlet and Neumann problems, respectively, in a domain of finite measure. N. D. Filonov has proved that the inequality μk+1 < λk holds for the Euclidean Laplacian. In Paper IV we extend his result to the Heisenberg Laplacian in three-dimensional domains which fulfil certain geometric conditions.