Dimensionful Coupling Research Articles

A new family of one dimensional martingale couplings

In this paper, we exhibit a new family of martingale couplings between two one-dimensional probability measures $\mu $ and $\nu $ in the convex order. This family is parametrised by two dimensional probability measures on the unit square with respective marginal densities proportional to the positive and negative parts of the difference between the quantile functions of $\mu $ and $\nu $. It contains the inverse transform martingale coupling which is explicit in terms of the quantile functions of these marginal densities. The integral of $|x-y|$ with respect to each of these couplings is smaller than twice the $\mathcal {W}_{1}$ distance between $\mu $ and $\nu $. When the comonotonous coupling between $\mu $ and $\nu $ is given by a map $T$, the elements of the family minimise $\int _{\mathbb {R}}\vert y-T(x)\vert \,M(dx,dy)$ among all martingale couplings between $\mu $ and $\nu $. When $\mu $ and $\nu $ are in the decreasing (resp. increasing) convex order, the construction is generalised to exhibit super (resp. sub) martingale couplings.

New physics scale from Higgs observables with effective dimension-6 operators

No matter what the scale of new physics is, deviations from the Standard Model (SM) for the Higgs observables will indicate the existence of such a scale. We consider effective six dimensional operators, and their effects on the Higgs productions and decays to estimate this new scale. We analyze and identify the parameter space consistent with known properties of the Higgs boson using recent Run II results from ATLAS and CMS experiments corresponding to ∼37 fb−1 of data. We then calculate the t¯th productions, as well as double Higgs production at the LHC using the effective couplings, and show that these can be much different than those predicted by the Standard Model, for a wide region of allowed parameter space. These predictions can be tested in the current or the future runs of the LHC. We find that the data are consistent with the existence of a new physics scale as low as 500 GeV for a significant region of parameter space of this six dimensional couplings with these new physics effects at the LHC. We also find that for some region of the parameter space, di-Higgs production can be much larger than that predicted by the Standard Model, giving rise to the prospect of its observation even in the current run II of the LHC.

Near-Optimal Active Learning of Halfspaces via Query Synthesis in the Noisy Setting

In this paper, we consider the problem of actively learning a linear classifier through query synthesis where the learner can construct artificial queries in order to estimate the true decision boundaries. This problem has recently gained a lot of interest in automated science and adversarial reverse engineering for which only heuristic algorithms are known. In such applications, queries can be constructed de novo to elicit information (e.g., automated science) or to evade detection with minimal cost (e.g., adversarial reverse engineering). We develop a general framework, called dimension coupling (DC), that 1) reduces a d-dimensional learning problem to d-1 low dimensional sub-problems, 2) solves each sub-problem efficiently, 3) appropriately aggregates the results and outputs a linear classifier, and 4) provides a theoretical guarantee for all possible schemes of aggregation. The proposed method is proved resilient to noise. We show that the DC framework avoids the curse of dimensionality: its computational complexity scales linearly with the dimension. Moreover, we show that the query complexity of DC is near optimal (within a constant factor of the optimum algorithm). To further support our theoretical analysis, we compare the performance of DC with the existing work. We observe that DC consistently outperforms the prior arts in terms of query complexity while often running orders of magnitude faster.

Lovelock Galileons and black holes

We study a scalar-tensor version of Lovelock theory with a non trivial higher order galileon term involving the coupling of the Lovelock two tensor with derivatives of the scalar galileon field. For a static and spherically symmetric spacetime we extend the Boulware-Deser solution to the presence of a Galileon field. The hairy solution has a regular scalar field on the black hole event horizon and presents certain self tuning properties for the bulk cosmological constant and the Gauss-Bonnet coupling. The combined time and radial dependence of the galileon field permits its horizon regularity. Furthermore in order to investigate the effects of linear time dependence we find spherically symmetric solutions in 4 and 5 spacetime dimensions. They are shown to have singular horizons. Afar from the Schwarzschild radius and for weak higher dimensional couplings the solutions are perturbratively close to GR representing GR like star solutions for scalar tensor theories.

New opportunities in h → 4ℓ

The Higgs decay h → 4l has played an important role in discovering the Higgs and measuring its mass thanks to low background and excellent resolution. Current cuts in this channel have been optimized for Higgs discovery via the dominant tree level ZZ contribution arising from electroweak symmetry breaking. Going forward, one of the primary objectives of this sensitive channel will be to probe other Higgs couplings and search for new physics on top of the tree level ZZ `back-ground'. Thanks to interference between these small couplings and the large tree level contribution to ZZ, the h → 4l decay is uniquely capable of probing the magnitude and CP phases of the Higgs couplings to and Z as well as, to a lesser extent, ZZ couplings arising from higher dimensional operators. With this in mind we examine how much relaxing current cuts can enhance the sensitivity while also accounting for the dominant non-Higgs continuum qq → 4l background. We find the largest enhancement in sensitivity for the hZy couplings (≳ 100%) followed by hyy (≳ 40%) and less so for the higher dimensional hZZ couplings (a few percent). With these enhancements, we show that couplings of order Standard Model values for hyy may optimistically be probed by end of Run-II at the LHC while for hZy perhaps towards the end of a high luminosity LHC. Thus an appropriately optimized h → 4l analysis can complement direct decays of the Higgs to on-shell and Z pairs giving a unique opportunity to directly access the CP properties of these couplings.

Some 2+1 Dimensional Super-Integrable Systems

Abstract In the article, we make use of the binormial-residue-representation (BRR) to generate super 2+1 dimensional integrable systems. Using these systems, we can deduce a super 2+1 dimensional AKNS hierarchy, which can be reduced to a super 2+1 dimensional nonlinear Schrödinger equation. In particular, two main results are obtained. One of them is a set of super 2+1 dimensional integrable couplings. The other one is a 2+1 dimensional diffusion equation. The Hamiltonian structure of the super 2+1 dimensional hierarchy is derived by using the super-trace identity.

Probing the Higgs couplings to photons in h→4ℓ at the LHC.

We explore the sensitivity of the Higgs decay to four leptons, the so-called golden channel, to higher dimensional loop-induced couplings of the Higgs boson to ZZ, Zγ, and γγ pairs, allowing for general CP mixtures. The larger standard model tree level coupling hZ(μ)Z(μ) is the dominant "background" for the loop-induced couplings. However, this large background interferes with the smaller loop-induced couplings, enhancing the sensitivity. We perform a maximum likelihood analysis based on analytic expressions of the fully differential decay width for h→4ℓ (4ℓ≡2e2μ,4e,4μ), including all interference effects. We find that the spectral shapes induced by Higgs couplings to photons are particularly different than the hZ(μ)Z(μ) background leading to enhanced sensitivity to these couplings. We show that even if the h→γγ and h→4ℓ rates agree with that predicted by the standard model, the golden channel has the potential to probe both the CP nature as well as the overall sign of the Higgs coupling to photons well before the end of a high-luminosity LHC.

Generation of Nonlinear Evolution Equations by Reductions of the Self-Dual Yang—Mills Equations

With the help of some reductions of the self-dual Yang Mills (briefly written as sdYM) equations, we introduce a Lax pair whose compatibility condition leads to a set of (2 + 1)-dimensional equations. Its first reduction gives rise to a generalized variable-coefficient Burgers equation with a forced term. Furthermore, the Burgers equation again reduces to a forced Burgers equation with constant coefficients, the standard Burgers equation, the heat equation, the Fisher equation, and the Huxley equation, respectively. The second reduction generates a few new (2 + 1)-dimensional nonlinear integrable systems, in particular, obtains a kind of (2 + 1)-dimensional integrable couplings of a new (2 + 1)-dimensional integrable nonlinear equation.

Quasiparticle Berry curvature and Chern numbers in spin-orbit-coupled bosonic Mott insulators

We study the ground-state topology and quasiparticle properties in bosonic Mott insulators with two- dimensional spin-orbit couplings in cold atomic optical lattices. We show that the many-body Chern and spin-Chern number can be expressed as an integral of the quasihole Berry curvatures over the Brillouin zone. Using a strong-coupling perturbation theory, for an experimentally feasible spin-orbit coupling, we compute the Berry curvature and the spin Chern number and find that these quantities can be generated purely by interactions. We also compute the quasiparticle dispersions, spectral weights, and the quasimomentum space distribution of particle and spin density, which can be accessed in cold-atom experiments and used to deduce the Berry curvature and Chern numbers.

An SO(10) grand unified theory of flavor

We present a supersymmetric SO(10) grand unified theory (GUT) of flavor based on an S 4 family symmetry. It makes use of our recent proposal to use SO(10) with type II seesaw mechanism for neutrino masses combined with a simple ansatz that the dominant Yukawa matrix (the 10-Higgs coupling to matter) has rank one. In this paper, we show how the rank one model can arise within some plausible assumptions as an effective field theory from vectorlike 16 dimensional matter fields with masses above the GUT scale. In order to obtain the desired fermion flavor texture we use S 4 flavon multiplets which acquire vevs in the ground state of the theory. By supplementing the S 4 theory with an additional discrete symmetry, we find that the flavon vacuum field alignments take a discrete set of values provided some of the higher dimensional couplings are small. Choosing a particular set of these vacuum alignments appears to lead to an unified understanding of observed quark-lepton flavor: (i) the lepton mixing matrix that is dominantly tri-bimaximal with small corrections related to quark mixings; (ii) quark lepton mass relations at GUT scale: m b ≃ m τ and m μ ≃ 3m s and (iii) the solar to atmospheric neutrino mass ratio m ⨀/m atm ≃ θ Cabibbo in agreement with observations. The model predicts the neutrino mixing parameter, $ {U_{e3}} \simeq {{{\theta_{\text{Cabibbo}}}} \mathord{\left/{\vphantom {{{\theta_{\text{Cabibbo}}}} {\left( {3\sqrt 2 } \right) \sim 0.05}}} \right.} {\left( {3\sqrt 2 } \right) \sim 0.05}} $ , which should be observable in planned long baseline experiments.

TWO (2+1)-DIMENSIONAL INTEGRABLE COUPLINGS OF THE KN HIERARCHY AND CORRESPONDING HAMILTONIAN STRUCTURES

A (2+1) zero curvature equation is generated from one of the reduced equations of the self-dual Yang–Mills equations. As its applications, two (2+1)-dimensional integrable couplings of the famous KN hierarchy are obtained with the help of a subalgebra of the Lie subalgebra R9, which can be reduced to the Burgers equation. Furthermore, their Hamiltonian structures are worked out by taking use of the quadratic-form identity and the variational identity, respectively.

A higher dimensional loop algebra and integrable couplings system of evolution equations hierarchy

An extension of the lie algebra A n−1 has been proposed [Phys. Lett. A, 2003, 310:19–24]. In this paper, the new lie algebra was used to construct a new higher dimensional loop algebra \(\tilde G\). Based on the loop algebra \(\tilde G\) , the integrable couplings system of the NLS-MKdV equations hierarchy was obtained. As its reduction case, generalized nonlinear NLS-MKdV equations were obtained. The method proposed in this letter can be applied to other hierarchies of evolution equations.

Phenomenological constraints on extra-dimensional scalars

We examine whether the ATLAS detector has sensitivity to extra-dimensional scalars (as opposed to components of higher-dimensional tensors which look like 4D scalars), in scenarios having the extra-dimensional Planck scale in the TeV range and n ⩾ 2 non-warped extra dimensions. Such scalars appear as partners of the graviton in virtually all higher dimensional supersymmetric theories. Using the scalar's lowest dimensional effective couplings to quarks and gluons, we compute the rate for the production of a hard jet together with missing energy. We find a non-trivial range of graviscalar couplings to which ATLAS could be sensitive, with experiments being more sensitive to couplings to gluons than to quarks. Graviscalar emission increases the missing-energy signal by adding to graviton production, and so complicates the inference of the extra-dimensional Planck scale from an observed rate. Because graviscalar differential cross-sections resemble those for gravitons, it is unlikely that these can be experimentally distinguished from one another should a missing-energy signal be observed.

6D Higgsless Standard Model

We present a six-dimensional Higgsless Standard Model with a realistic gauge sector. The model uses only the Standard Model gauge group SU(2)L×U(1)Y with the gauge bosons propagating in flat extra dimensions compactified on a rectangle. The electroweak symmetry is broken by boundary conditions, and the correct splitting between the W and Z gauge boson masses can be arranged by suitable choice of the compactification scales. The higher Kaluza–Klein excitations of the gauge bosons decouple from the effective low-energy theory due to dominant brane kinetic terms. The model has the following two key features compared to five-dimensional models. The dimensional couplings in the bulk Lagrangian, responsible for electroweak symmetry breaking using mixed boundary conditions, are of order the electroweak scale. Moreover, with respect to “oblique” corrections, the agreement with the precision electroweak parameters is improved compared to five-dimensional warped or flat space models. We also argue that the calculability of Higgsless models can be ameliorated in more than five dimensions.

Gauging Away the Strong CP Problem

We propose a new solution to the strong-CP problem. It involves the existence of an unbroken gauged $U(1)_X$ symmetry whose gauge boson gets a Stuckelberg mass term by combining with a pseudoscalar field $\eta (x)$. The latter has axion-like couplings to $F_{QCD}\wedge F_{QCD}$ so that the theta parameter may be gauged away by a $U(1)_X$ gauge transformation. This system leads to mixed gauge anomalies and we argue that they are cancelled by the addition of an appropriate Wess-Zumino term, so that no SM fermions need to be charged under $U(1)_X$. We discuss scenarios in which the above set of fields and couplings appear. The mechanism is quite generic, but a natural possibility is that the the $U(1)_X$ symmetry arises from bulk gauge bosons in theories with extra dimensions or string models. We show that in certain D-brane Type-II string models (with antisymmetric tensor field strength fluxes) higher dimensional Chern-Simons couplings give rise to the required D=4 Wess-Zumino terms upon compactification. In one of the possible string realizations of the mechanism the $U(1)_X$ gauge boson comes from the Kaluza-Klein reduction of the eleven-dimensional metric in M-theory.

CPviolation in weak interactions from orbifold reduction: Possible unification structures

We present a mechanism to generate complex phases from real 4+1 dimensional couplings in a model of weak interactions through dimensional reduction of a gauge theory. The orbifolding of a 4+1 dimensional Sp(4) \times U(1) group is the minimal setup which provides both CP violation and an SU(2) \times U(1) structure. We show that grand unification requires at least SO(11).

Nonlinearly realized local scale invariance: gravity and matter

That the scalar field theories with no dimensional couplings possess local scale invariance (LSI) via the curvature gauging is utilized to show that the Goldstone boson, released by the spontaneous LSI breakdown, is swallowed by the spacetime curvature in order to generate Newton's constant in the same spirit as the induction of vector boson masses via spontaneous gauge symmetry breaking. For Einstein gravity to be reproduced correctly, the Goldstone boson of spontaneous LSI breaking must be endowed with ghost dynamics. The matter sector, taken to be the standard model spectrum, gains full LSI property with the physical Higgs boson acting as the Goldstone boson released by LSI breakdown at the weak scale. The pattern of particle masses is identical to that of the standard model. There are unitary LSI gauges in which either the Goldstone ghost from gravity sector or the Higgs boson from matter sector is eliminated from the spectrum. The heavy right-handed neutrinos as well as softly broken supersymmetry naturally fit into the nonlinearly realized LSI framework.

Integrable couplings of soliton equations by perturbations I: A general theory and application to the KDV hierarchy

A theory for constructing integrable couplings of soliton equations is developed by using various perturbations around solutions of perturbed soliton equations being analytic with respect to a small perturbation parameter. Multi-scale perturbations can be taken and thus higher dimensional integrable couplings can be presented. The theory is applied to the KdV soliton hierarchy. Infinitely many integrable couplings are constructed for each soliton equation in the KdV hierarchy, which contain integrable couplings possessing quadruple Hamiltonian formulations and two classes of hereditary recursion operators, and integrable couplings possessing local 2+1 dimensional bi-Hamiltonian formulations and consequent 2+1 dimensional hereditary recursion operators.

Introduction to Supersymmetry: Cambridge Monographs on Mathematical Physics

Peter G 0 Freund 1986 Cambridge: Cambridge University Press x + 152 pp price £20 ISBN 0 521 26880X The success of gauge theories as a solution to the problem of interacting relativistic quantum fields, with the embarrassment of mass temporarily hidden in the Higgs mechanism, is obvious. The failure of such theories to deal with dimensional couplings such as gravity has been the spur to the development of supersymmetric theories in which the symmetry between the fermion and boson degrees of freedom leads to cancellations between some of the more embarrassing singularities.