Linear Realization Research Articles

Higgs form factors in associated production

We further develop a form factor formalism characterizing anomalous interactions of the Higgs-like boson (h) to massive electroweak vector bosons (V) and generic bilinear fermion states (F). Employing this approach, we examine the sensitivity of pp -> F ->Vh associated production to physics beyond the Standard Model, and compare it to the corresponding sensitivity of h -> V F decays. We discuss how determining the Vh invariant-mass distribution in associated production at LHC is a key ingredient for model-independent determinations of h V F interactions. We also provide a general discussion about the power counting of the form factor's momentum dependence in a generic effective field theory approach, analyzing in particular how effective theories based on a linear and non-linear realization of the SU(2)_L x U(1)_Y gauge symmetry map into the form factor formalism. We point out how measurements of the differential spectra characterizing h -> V F decays and pp -> F -> Vh associated production could be the leading indication of the presence of a nonlinear realization of the SU(2)_L x U(1)_Y gauge symmetry.

Higgs phenomenology in the Minimal Dilaton Model after Run I of the LHC

The Minimal Dilaton Model (MDM) extends the Standard Model (SM) by a singlet scalar, which can be viewed as a linear realization of general dilaton field. This new scalar field mixes with the SM Higgs field to form two mass eigenstates with one of them corresponding to the 125 GeV SM-like Higgs boson reported by the LHC experiments. In this work, under various theoretical and experimental constrains, we perform fits to the latest Higgs data and then investigate the phenomenology of Higgs boson in both the heavy dilaton scenario and the light dilaton scenario of the MDM. We find that: (i) If one considers the ATLAS and CMS data separately, the MDM can explain each of them well, but refer to different parameter space due to the apparent difference in the two sets of data. If one considers the combined data of the LHC and Tevatron, however, the explanation given by the MDM is not much better than the SM, and the dilaton component in the 125-GeV Higgs is less than about 20% at 2 sigma level. (ii) The current Higgs data have stronger constrains on the light dilaton scenario than on the heavy dilaton scenario. (iii) The heavy dilaton scenario can produce a Higgs triple self coupling much larger than the SM value, and thus a significantly enhanced Higgs pair cross section at hadron colliders. With a luminosity of 100 fb^{-1} (10 fb^{-1}) at the 14-TeV LHC, a heavy dilaton of 400 GeV (500 GeV) can be examined. (iv) In the light dilaton scenario, the Higgs exotic branching ratio can reach 43% (60%) at 2 sigma (3 sigma) level when considering only the CMS data, which may be detected at the 14-TeV LHC with a luminosity of 300 fb^{-1} and the Higgs Factory.

In-mediumη′mass andη′Ninteraction based on chiral effective theory

The in-medium ${\ensuremath{\eta}}^{\ensuremath{'}}$ mass and the ${\ensuremath{\eta}}^{\ensuremath{'}}N$ interaction are investigated in an effective theory based on the linear realization of the SU(3) chiral symmetry. We find that a large part of the ${\ensuremath{\eta}}^{\ensuremath{'}}$ mass is generated by the spontaneous breaking of chiral symmetry through the U${}_{A}$(1) anomaly. As a consequence of this observation, the ${\ensuremath{\eta}}^{\ensuremath{'}}$ mass is reduced in nuclear matter where chiral symmetry is partially restored. In our model, the mass reduction is found to be 80 MeV at the saturation density. Estimating the ${\ensuremath{\eta}}^{\ensuremath{'}}N$ interaction based on the same effective theory, we find that the ${\ensuremath{\eta}}^{\ensuremath{'}}N$ interaction in the scalar channel is attractive sufficiently to form a bound state in the ${\ensuremath{\eta}}^{\ensuremath{'}}N$ system with a several MeV binding energy. We discuss the origin of attraction by emphasizing the special role of the $\ensuremath{\sigma}$ meson in the linear sigma model for the mass generation of ${\ensuremath{\eta}}^{\ensuremath{'}}$ and $N$.

Effective field theory analysis of new physics in e + e −→W + W − at a linear collider

We analyze new physics contributions to $e^+e^-\to W^+W^-$ at the TeV energy scale, employing an effective field theory framework. A complete basis of next-to-leading order operators in the standard model effective Lagrangian is used, both for the nonlinear and the linear realization of the electroweak sector. The elimination of redundant operators via equations-of-motion constraints is discussed in detail. Polarized cross sections for $e^+e^-\to W^+W^-$ (on-shell) are computed and the corrections to the standard model results are given in an expansion for large $s/M^2_W$. The dominant relative corrections grow with $s$ and can be fully expressed in terms of modified gauge-fermion couplings. These corrections are interpreted in the context of the Goldstone boson equivalence theorem. Explicit new physics models are considered to illustrate the generation and the potential size of the coefficients in the effective Lagrangian. Brief comments are made on the production of $W^+W^-$ pairs at the LHC.

Production representation of partial wave scattering amplitudes and the f 0(600) particle

The establishment of production representation of partial wave scattering amplitudes is reviewed in the context of quantum field theory. Its relation to the production representation, or Ning Hu representation in quantum mechanical scattering theory is pointed out. One of the most important application of the production representation is the physics of the f0(600) and K(700) scalar hadron resonances, on which we also give a brief review. It is emphasized that all evidences accumulated so far are consistent with the picture that the f0(600) meson is the chiral partner of the Nambu-Goldstone bosons in a linear realization of chiral symmetry.

Line ordering of reversible circuits for linear nearest neighbor realization

Real quantum computing technologies have different restrictions and constraints which need to be considered during circuit synthesis. In certain technologies, only physically adjacent qubits can interact, which restricts their realizations to only linear nearest neighbor (LNN) architecture. In this work, we formulate the line ordering problem in LNN architecture as task assignment problem to find a mapping (permutation) between task graph and processor graph with minimum cost. We propose two different approaches, a greedy heuristic and a meta-heuristic algorithm based on Harmony Search to solve the task assignment problem. Experimental results show that our algorithms were able to reduce the quantum cost of benchmark circuits by approximately 30 % on average. Moreover, the proposed algorithms were compared to one recently proposed ordering algorithm and were found to further improve the cost by approximately 16 %.

The effective chiral Lagrangian for a light dynamical “Higgs particle”

We generalize the basis of CP-even chiral effective operators describing a dynamical Higgs sector, to the case in which the Higgs-like particle is light. Gauge and gauge-Higgs operators are considered up to mass dimension five. This analysis completes the tool needed to explore at leading order the connection between linear realizations of the electroweak symmetry breaking mechanism — whose extreme case is the Standard Model — and non-linear realizations with a light Higgs-like particle present. It may also provide a model-independent guideline to explore which exotic gauge-Higgs couplings may be expected, and their relative strength to Higgsless observable amplitudes. With respect to fermions, the analysis is reduced by nature to the consideration of those flavor-conserving operators that can be written in terms of pure-gauge or gauge-Higgs ones via the equations of motion, but for the standard Yukawa-type couplings.

Goldstino superfields in AdS 4

Spontaneous breaking of global supersymmetries results in Goldstino fields which provide a nonlinear realisation of the supersymmetry algebra. A finite supersymmetry transformation of a Goldstino field can be used to generate a superfield whose components provide a linear realisation of the supersymmetry algebra. This construction also automatically determines the action of the algebra of supercovariant derivatives on Goldstino superfields, essential to the efficient computation of manifestly supersymmetric component actions for the Goldstinos, including coupling to matter fields. In this paper, we extend known constructions of Goldstino superfields resulting from spontaneous breaking of supersymmetry in flat four-dimensional N =1 superspace to spontaneous breaking of N =1 and N =2 supersymmetry in AdS_4.

Codes on Graphs: Observability, Controllability, and Local Reducibility

This paper investigates properties of realizations of linear or group codes on general graphs that lead to local reducibility. Trimness and properness are dual properties of constraint codes. A linear or group realization with a constraint code that is not both trim and proper is locally reducible. A linear or group realization on a finite cycle-free graph is minimal if and only if every local constraint code is trim and proper. A realization is called observable if there is a one-to-one correspondence between codewords and configurations, and controllable if it has independent constraints. A linear or group realization is observable if and only if its dual is controllable. A simple counting test for controllability is given. An unobservable or uncontrollable realization is locally reducible. Parity-check realizations are controllable if and only if they have independent parity checks. In an uncontrollable tail-biting trellis realization, the behavior partitions into disconnected sub-behaviors, but this property does not hold for nontrellis realizations. On a general graph, the support of an unobservable configuration is a generalized cycle.

Low-lying scalars in an extended linearσmodel

We formulate an extended linear $\sigma$ model of a quarkonia nonet and a tetraquark nonet as well as a complex iso-singlet (glueball) by virtue of chiral symmetry $SU_L(3) \times SU_R(3)$ and $U_A(1)$ symmetry. In the linear realization formalism, we study the mass spectra and components of the low-lying scalars and pseudo scalars in this model. The mass matrices for physical staes are obtained and the glueball candidates are examined. We find that the model can accommodate the mass spectra of low-lying states quite well. Our fits indicate that the most glueball like scalar should be 2 GeV or higher while the glueball pseudoscalar is $\eta(1756)$. We also examine the parameter region where the lightest iso-scalar $f_0(600)$ can be the glueball and quarkonia dominant but find such a parameter region may be confronted with the problem of the unbounded vacuum from below.

Quadratic L2-gain performance linear parameter-varying realisation of parametric transfer functions and state-feedback gain scheduling control

The study deals with the quadratic L2-gain performance linear parameter-varying realisation of parametric transfer functions and state-feedback gain scheduling control. It is shown that any parametric transfer function, which has L2-gain performance with a bound for all constant parameters values, admits a state space realisation guaranteeing quadratic L2-gain performance with the bound under arbitrary parameter variations. A reasonably general procedure is provided to find such a realisation with linear matrix inequality optimal technique. Furthermore, according to the realisation, the state-feedback gain scheduling control design is also dealt with. Finally, a simple numerical example is given to illustrate the efficiency of the proposed method.

Identities in nonlinear realizations of supersymmetry

In this paper, we emphasize that a UV SUSY-breaking theory can be realized either linearly or nonlinearly. Both realizations form the dual descriptions of the UV SUSY-breaking theory. Guided by this observation, we find subtle identities involving the Goldstino field and matter fields in the standard nonlinear realization from trivial ones in the linear realization. Rather complicated integrands in the standard nonlinear realization are identified as total-divergences. Especially, identities only involving the Goldstino field reveal the self-consistency of the Grassmann algebra. As an application of these identities, we prove that the nonlinear Kahler potential without or with gauge interactions is unique, if the corresponding linear one is fixed. Our identities pick out the total-divergence terms and guarantee this uniqueness.

On the Number of Linear Feedback Shift Registers With a Special Structure

Given a primitive polynomial <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$p(x)$</tex> </formula> , of degree <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$n$</tex> </formula> , we deal with the problem of finding the number of possible linear feedback shift register realizations, with m-input m-output delay elements, such that the corresponding characteristic polynomial is <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$p(x)$</tex> </formula> . We show the equivalence between these realizations and a set of specially structured matrices. Furthermore, the number of realizations is computed for some special cases.

Experimental Realization of an Approximate Partial Transpose for Photonic Two-Qubit Systems

We report the first experimental realization of an approximate partial transpose for photonic two-qubit systems. The proposed scheme is based on the local operation on single copies of quantum states and classical communication, and therefore can be easily applied for other quantum information tasks within current technologies. Direct detection of entanglement, i.e., without performing quantum state tomography, using the partial transpose operation, is also demonstrated.

Optimal tuning of linear controllers for power electronics/power systems applications

This paper presents a new method for tuning various linear controllers such as Proportional–Integral (PI), Proportional–Integral–Derivative (PID) and Proportional–Resonant (PR) structures which are frequently used in power electronics and power system applications. The linear controllers maintain a general structure defined by the Internal Model Principle (IMP) of control theory. The proposed method in this paper is twofold. The first perspective uses the well-known concept of the Linear Quadratic Regulator (LQR) to address the problem as a regulation problem. The Q matrix of the LQR design is then finely adjusted in order to assure the desired transient response for the system. The second perspective redefines the LQR in order to add capability to address the optimal tracking problem and is then generalized to systems with more than two states. These methods are then applied to two specific examples, one in an uninterruptible power supply (UPS) inverter system and the other one in a distributed generation (DG) system. In these examples, the tuning of PR and PI controllers is studied in great detail. These proposed design methods provide an easy and algorithmic procedure without jeopardizing stability or robustness. These tuning methods can also be utilized for linear state-space realization of any power converters. Both examples are supported via simulation and the results, which confirm analytical derivations, are presented and discussed.

A memristor-based third-order oscillator: beyond oscillation

This paper demonstrates the first third-order autonomous linear time variant circuit realization that enhances parametric oscillation through the usage of memristor in conventional oscillators. Although the output has sustained oscillation, the linear features of the conventional oscillators become time dependent. The poles oscillate in nonlinear behavior due to the oscillation of memristor resistance. The mathematical formulas as well as SPICE simulations are introduced for the memristor-based phase shift oscillator showing a great matching.

A New Perspective on Relativistic Quantum Mechanics

Based on a linear realization formulation of a quantum relativity, — proposed relativity for 'quantum space-time', we introduce the new Poincaré-Snyder relativity and Snyder relativity as relativities in between the latter and the well known Galilean and Einstein cases. While there is supposed to be not separate notion of classical and quantum mechanics at the level of the very unconventional quantum relativity, the Poincaré-Snyder relativity is more like a mathematically extended form of Einstein relativity on which we can write down a formal canonical classical and quantum mechanics. We discuss how the Poincaré-Snyder relativity may provide a stronger framework for the description of the usual (Einstein) relativistic quantum mechanics and present a first look of the interesting picture from the new perspective.

Invariant correlation filter with linear phase coefficient holographic realization in 4-F correlator

Realization of distortion invariant correlation filters in optical image correlators open possibilities for object identification with remarkably high computational capabilities. Application of the linear phase coefficient composite filter (LPCCF) is attractive for recognition of binary edged images. We use methods of digital holographic synthesis to realize LPCCF in a coherent 4-F correlator as a computer-generated amplitude holographic filter. A high resolution spatial light modulator (SLM) has to be implemented for such a filter representation. Transparency limitations of high frame rate and high resolution SLM's and its effect on recognition performance of holographic filter in the 4-F correlator are discussed in the given paper.

Constructing multiple prolongation structures from homotopic maps

In this paper, we show how multiple prolongation structures developed out of homotopy theory, can be constructed from a differential ideal corresponding to an exterior differential system. We use this method to construct multiple prolongation structures for the Robinson–Trautman equations of Petrov type III. It is found that the introduction of two arbitrary pseudo-potentials in the carrier space of the vector fields of this equation imposes nontrivial constraints on the prolongation structures which prevents the algebra from growing rapidly. Specific choices of the newly introduced pseudo-potentials result a coupled Kac–Moody A 1 ⊕ A 1 and Virasoro algebra as prolongation structure. Other choices of the potentials reproduce previously established results, namely the contragradient algebra K 2 of infinite groiwth. The Lax pair and Riccati equations for pseudo-potentials can be formulated respectively from linear and nonlinear realizations of the prolongation structure.

Minimal Realizations of Linear Systems: The “Shortest Basis” Approach

Given a discrete-time linear system C, a shortest basis for C is a set of linearly independent generators for C with the least possible lengths. A basis B is a shortest basis if and only if it has the predictable span property (i.e., has the predictable delay and degree properties, and is non-catastrophic), or alternatively if and only if it has the subsystem basis property (for any interval J, the generators in B whose span is in J is a basis for the subsystem CJ). The dimensions of the minimal state spaces and minimal transition spaces of C are simply the numbers of generators in a shortest basis B that are active at any given state or symbol time, respectively. A minimal linear realization for C in controller canonical form follows directly from a shortest basis for C, and a minimal linear realization for C in observer canonical form follows directly from a shortest basis for the orthogonal system C⊥. This approach seems conceptually simpler than that of classical minimal realization theory.