Scalar Vector Research Articles

Sivers and Boer–Mulders GTMDs in light-front holographic quark–diquark model

We calculate the time reversal odd (T-odd) generalized transverse momentum dependent parton distributions (GTMDs) $F^o_{1,2}$ and $H^o_{1,1}$ in a light-front quark-diquark model based on ADS/QCD. In the limit of zero momentum transfer, these reduce to the Sivers and Boer-Mulders TMDs respectively. We have incorporated both scalar and axial vector diquarks in the model and obtained an overlap representation of the GTMDs using the light-front wave functions (LFWFs). Contribution from the final state interaction is incorporated at the level of one gluon exchange as a phase factor in the LFWF. We show that the final state interaction term can be factored out in this model and this part is the same for both GTMDs. We also present the corresponding Wigner distributions.

Closed-Form Spectral-Domain Green's Functions for Infinitesimal Current Source in Multilayer Soil

This article deals with an infinitesimal current source (ICS) in a multilayer conducting medium that consists of air and multilayer soil. Closed-form kernel functions of the spectral-domain Green's function for scalar electric and vector magnetic potentials (Lorentz potentials) were obtained for every layer of the multilayered medium as analytic solutions of the systems of linear equations. Validation of the proposed closed-form expressions is performed by numerical solving of the system of linear equations and by numerical comparison with expressions derived from existing closed-form expressions developed for the source layer of the multilayer dielectric medium. For an arbitrary-oriented ICS, scalar electric potential of its horizontal component is chosen as a unique scalar electric potential. Accordingly, dyadic Green's function of vector magnetic potential is corrected.

Massive neutron stars with a color superconducting quark matter core

We construct the equation of state for high-density neutron star matter at zero temperature using the two-flavor Nambu--Jona-Lasinio (NJL) model as an effective theory of QCD. We build nuclear matter, quark matter, and the mixed phases from the same NJL Lagrangian, which has been used to model free and in-medium hadrons as well as nuclear systems. A focus here is to determine if the same coupling constants in the scalar diquark and vector meson channels, which give a good description of nucleon structure and nuclear matter, can also be used for the color superconducting high-density quark matter phase. We find that this is possible for the scalar diquark (pairing) interaction, but the vector meson interaction has to be reduced so that superconducting quark matter becomes the stable phase at high densities. We compare our equation of state with recent phenomenological parametrizations based on generic stability conditions for neutron stars. We find that the maximum mass of a hybrid star, with a color superconducting quark matter core, exceeds $2.01\ifmmode\pm\else\textpm\fi{}0.04\phantom{\rule{0.16em}{0ex}}{M}_{\ensuremath{\bigodot}}$, which is the value of the recently observed massive neutron star PSR $\text{J0348}+0432$. The mass-radius relation is also consistent with gravitational wave observations (GW170817).

Impact of dynamical chiral symmetry breaking and dynamical diquark correlations on proton generalized parton distributions

We calculate the leading-twist, helicity-independent generalized parton distributions (GPDs) of the proton, at finite skewness, in the Nambu--Jona-Lasinio (NJL) model of quantum chomodynamics (QCD). The NJL model reproduces low-energy characteristics of QCD, including dynamical chiral symmetry breaking (DCSB). The proton bound-state amplitude is solved for using the Faddeev equation in a quark-diquark approximation, including both dynamical scalar and axial vector diquarks. GPDs are calculated using a dressed non-local correlator, consistent with DCSB, which is obtained by solving a Bethe-Salpeter equation. The model and approximations used observe Lorentz covariance, and as a consequence the GPDs obey polynomiality sum rules. Extractions of electromagnetic and gravitational form factors are performed. We find a D-term of $-1.08$ when the non-local correlator is properly dressed, and $0.85$ when the bare correlator is used instead, suggesting that within this framework proton stability requires the constituent quarks to be dressed consistently with DCSB. We also find that the anomalous gravitomagnetic vanishes, as required by Poincar\'{e} symmetry.

A comparative study of the S_1 and U_1 leptoquark effects in the light quark regime

We study the phenomenology of two leptoquarks, the Standard Model SU(2) singlets S_1 and U_1, with regard to the latest experimental data from the low-energy flavor physics measurements, LHC, and the IceCube neutrino experiment. We consider a scenario when scalar (vector) leptoquark S_1 (U_1) couples exclusively to the down quark and the neutrinos (charged leptons) of all flavors, where the leptoquark in question couples to the SM lepton doublets. The couplings of S_1 (U_1) to the up-type quarks and the charged leptons (neutrinos) are in turn uniquely determined via SU(2) symmetry. We find that the most important constraints on the leptoquark parameter space originate from flavor physics measurements, followed by the LHC search limits that take over the flavor physics ones in the large LQ mass regime. We furthermore show that S_1 (U_1) marginally improves (spoils) the fit of the current IceCube data with respect to the SM case within the region of parameter space that is otherwise consistent with various low-energy flavor physics measurements and the latest LHC input. Our study offers an up-to-date analysis for these two leptoquarks in view of the latest experimental data.

Using Spaced Combined Receiving Modules to Study the Scalar–Vector Characteristics of an Acoustic Field

Field experiments to measure the scalar–vector structure of an acoustic field at a Moscow State University hydroacoustic test site with an ice cover are analyzed. The anisotropy of the noise field in the water is estimated. Noise cross-correlation functions are constructed using the directional characteristics of two spaced combined receiving modules.

Качественный анализ вин и виноматериалов методами поляризованно-люминесцентной голографии на основе использования их оптических поляризационных спектров

The article describes the qualitative analysis of wines and wine products using polarization-luminescent holography methods. Identification and classification of wines is carried out on the basis of combined processing of various types of polarization spectra of multiplex reflective luminescent holograms of Denisyuk, obtained from the analyzed samples of the wine products (specific brands of wine). The following types of optical spectra of dynamic holograms were selected for analysis: 1) spectral intensity distribution of polarized luminescence (parameter-I); 2) the spectral distribution of the degree of anisotropy of luminescence (parameter-r) and - the ellipticity coefficient (Ce parameter) of the luminescence of the reconstructed virtual image of an object (object beam). An experimental study has been performed of the polarization properties of a reflective hologram Denisyuk, obtained in a luminescent photoanisotropic-gyrotropic material using a linearly polarized coherent light source. The dependence of the polarization state of the reconstructed image on the polarization of the recovering beam (polarization-holographic memory) is observed.An experiment is described on the investigation of samples, conducted to verify the possibility of using polarization spectra for identification of wine. Not individual fragments of the spectra are processed, as when using scalar spectroscopy methods and vector spectra as a whole, which increases the information content and reliability of the analysis. The results presented in the article can serve as the basis for creating guidelines, using spectral-holographic “portrait” of specific brands of wine, according to the set of characteristic features. This will allow revealing the authenticity of wine products, including such properties as variety composition of the annual harvest.

Taylor expansion for matrix functions of vector variable using the Kronecker product

Taylor expansion is one of the many mathematical tools that is applied in Mechanics and Engineering. In this paper, using the partial derivative of a matrix with respect to a vector and the Kronecker product, the formulae of Taylor series of vector variable for scalar functions, vector functions and matrix functions are built and demonstrated. An example regarding the linearization of the differential equations of an elastic manipulator is presented using Taylor expansion.

Interference properties of two-component matter wave solitons

Wave properties of solitons in a two-component Bose–Einstein condensate are investigated in detail. We demonstrate that dark solitons in one of components admit interference and tunneling behavior, in sharp contrast to the scalar dark solitons and vector dark solitons. Analytic analyses of interference properties show that spatial interference patterns are determined by the relative velocity of solitons, while temporal interference patterns depend on the velocities and widths of two solitons, differing from the interference properties of scalar bright solitons. Especially, for an attractive interactions system, we show that interference effects between the two dark solitons can induce some short-time density humps (whose densities are higher than background density). Moreover, the maximum hump value is remarkably sensitive to the variation of the solitons’ parameters. For a repulsive interactions system, the temporal-spatial interference periods of dark–bright solitons have lower limits. Numerical simulation results suggest that interference patterns for the dark–bright solitons are more robust against noises than bright–dark solitons. These explicit interference properties can be used to measure the velocities and widths of solitons. It is expected that these interference behaviors can be observed experimentally and can be used to design matter wave soliton interferometer in vector systems.

Exact cosmological black hole solutions in scalar tensor vector gravity

We find an exact solution of scalar-tensor-vector gravity field equations that represents a black hole embedded in an expanding universe. This is the first solution of such a kind found in the theory. We analyze the properties of the apparent horizons as well as the essential singularities of the metric, and compare them with the McVittie spacetime of general relativity. Depending on the cosmological model adopted and the value of the free parameter of the theory, the solution describes a cosmological black hole, an inhomogeneity in an expanding universe, or a naked singularity. We use the results to set further constraints on the free parameters of the theory and we study geodesic motion in this spacetime.

Pressure - velocity projection method with mixed type approximation for Oseen discrete operator

We are considering the problem of divergence - free projection in rectangular domains for the Oseen (stationary Navier-Stokes) operator. It uses nodal Finite Element method to reconstruct pressure and Finite Difference method for scalar functions and vector functions for other parts of the equations. This allows us to use simple finite difference schemes for linear part and WENO-type schemes for the the nonlinear part in the space of discrete velocities. The boundary conditions are formulated in Finite Volume conservative approach for velocity and in Finite Element approach for pressure. We illustrate that the convergence rate depends on the smoothness of the projected function and that the projection method allows one to obtain divergence-free solutions with desired tolerance. We numerically analize the projection operator that acts in the space of divergence operator image. It is shown that all eigenvalues of the operator are less than unity for Oseledets-type wall boundary conditions for velocity and zero Neumann conditions for the Poisson equation. We show that for smooth functions we obtain forth order convergence in divergence. Finally we demonstrate the method by solving the stationary lid driven cavity problem for the 2D Oseen operator.

Canonical quantization of anisotropic Bianchi I cosmology from scalar vector tensor Brans Dicke gravity

We applied a generalized scalar-vector-tensor Brans Dicke gravity model to study canonical quantization of an anisotropic Bianchi I cosmological model. Regarding an anisotropic Harmonic Oscillator potential we show that the corresponding Wheeler de Witt wave functional of the system is described by Hermit polynomials. We obtained a quantization condition on the ADM mass of the cosmological system which raises versus the quantum numbers of the Hermit polynomials. Our calculations show that the inflationary expansion of the universe can be originate from the big bang with no naked singularity due to the uncertainty principle.

Finite Difference Generated Transient Potentials of Open-Layered Media by Parallel Computing Using OpenMP, MPI, OpenACC, and CUDA

The implementation of time-domain Green’s functions (TDGFs) in the graphics processing unit (GPU) and the central processing unit (CPU) using a finite-difference scheme is shown. The TDGFs represent the transient electric scalar and magnetic vector potentials due to a horizontal electric dipole (HED) in open-layered media. The layered media is bounded with a perfectly matched layer (PML), symmetry axis, and perfect electric conductor (PEC). We adopted four different parallel approaches as follows: 1) open multiprocessing (OpenMP) CPU implementation; 2) message passing interface (MPI) CPU implementation; 3) open accelerators (OpenACC) GPU implementation; and 4) compute unified device architecture (CUDA) GPU implementation. The accuracy and efficiency of the utilized programming models are validated by comparing and verifying the obtained results using a sequential CPU implementation. Compared to single threaded CPU implementation, speed-ups obtained by the OpenMP, MPI, OpenACC, and CUDA programming models are $4.8\times $ , $6.12\times $ , $45.97\times $ , and $96.53\times $ higher, respectively. The final result shows that GPU implementation leads to a considerable speed-up while the solution’s accuracy is fixed.

Spontaneous scalarization within Scalar-Tensor theory using new conformal function in quark stars

General relativity had been succeeding to describe gravitational phenomenon in weak-field gravity but some deviation had been observed in compact objects such as neutron stars and quark stars. This phenomenon of spontaneous scalarization which shown for the first time by Damour and Espasito-Farese appears in one of the modified gravity theories i.e., scalar tensor theory of gravity. We will study such novel phenomenon in quark stars. Furthermore, different to that of previous study, here we introduce new conformal function. A(φ) = 1 − Ln[1 − 0.5β(φ − φ0)2] We found that spontaneous scalarization using such conformal function appears for the first time when β ≈ −4.5. Furthermore, the scalarization effect depends on the equation of state (EoS) of the quark stars. The corresponding effect appears rather different when scalar Coulomb EoS or vector Coulomb EoS are used.

On an integrable multi-dimensionally consistent 2n + 2n-dimensional heavenly-type equation.

Based on the commutativity of scalar vector fields, an algebraic scheme is developed which leads to a privileged multi-dimensionally consistent 2n + 2n-dimensional integrable partial differential equation with the associated eigenfunction constituting an infinitesimal symmetry. The 'universal' character of this novel equation of vanishing Pfaffian type is demonstrated by retrieving and generalizing to higher dimensions a great variety of well-known integrable equations such as the dispersionless Kadomtsev-Petviashvili and Hirota equations and various avatars of the heavenly equation governing self-dual Einstein spaces.

Static State of a Black Hole Supported by Dark Matter

The possibility of an equilibrium state of a gravitating scalar field (describing ordinary matter) inside a black hole, compressed to the state of boson condensate, in balance with a longitudinal vector field (describing dark matter) from the outside, is considered. Analytical analysis, confirmed numerically, shows that there are regular static solutions to the Einstein equations with no limitation on the mass of a black hole. The metric tensor component grr(r) changes sign twice. The behavior of the gravitational field and material fields in the vicinity of these two Schwarzschild radii were studied in detail. The equality of the energy–momentum tensors of the scalar and longitudinal vector fields at the interface supports the phase equilibrium of a black hole and dark matter. Considering the gravitating scalar field as an example, a possible internal structure of a black hole and its influence on the dark matter at the periphery of a galaxy are clarified. In particular, the speed on the plateau of a galaxy rotation curve as a function of a black hole’s mass is determined.

Correlation functions of sourced gravitational waves in inflationary scalar vector models. A symmetry based approach

We use conformal symmetry to constrain the shape of inflationary correlators in the presence of long-lived vector field perturbations. Applying conformal Ward identities, we derive general expressions, up to amplitudes and normalization factors, for the two and three-point correlators in the presence of vector fields mediated by the interaction fleft(phi right)kern0.1em left({F}_{mu v}{F}^{mu v}+kern0.5em alpha {tilde{F}}_{mu v}{F}^{mu v}right) , where f(ϕ) is a suitable coupling function between the scalar and the vector field. This interaction allows for isotropy and parity symmetry breaking and is consistent with super horizon conformal symmetry. As an application of the conformal field theory techniques followed here, we evaluate the mixed tensor-scalar 〈γζ〉 and tensor-scalar-scalar 〈γζζ〉 correlators which are interesting to look for parity violating effects related with chiral gravitational waves. Finally, we derive consistency relations for the three-point correlators obtained.

Eigenspectra and statistical properties of the Klein–Gordon equation with Cornell potential: Unequal mixings of scalar and time-like vector potentials

The D-dimensional Klein–Gordon (KG) wave equation with unequal scalar and time-like vector Cornell interactions was solved by the Laplace transform method. We have obtained the bound state energy eigenvalues of the spinless relativistic heavy quarkonium systems under such a potential. Further, the stationary states are calculated due to the well behavior of wave functions at the origin and at infinity. The statistical properties of this model were also investigated. Our results have been found to be of great importance in particle physics.

Scalar and Vector Solitons in a Bidirectional Mode-Locked Fibre Laser

Recent discovery on scalar–vector features of ultrashort pulses sheds new light on the polarization dynamics of ultrafast fibre lasers. Here, we report on the generation of scalar and vector solitons in a bidirectional fibre laser based on nonlinear polarization rotation (NPR). Through introducing different polarization evolving mechanisms into the counter-propagation branches, the fibre laser respectively approaches the scalar-soliton regime and vector-soliton regime in the clockwise and counterclockwise directions. It is found that the strong local birefringence facilitates the energy to flow between two orthogonal polarization directions, consequently inducing the pulse evolution toward vector solitons even against obvious polarization discrimination effect introduced by the NPR mode-locking mechanism. Furthermore, the polarization resolved measurement is implemented to both analyze the scalar–vector feature of the emitted solitons and realize the manipulation of vector solitons. In addition, numerical simulations are carried out to clarify the manipulation process of the vector solitons. To our knowledge, this is the first observation of scalar–vector operation in a bidirectional fibre laser, which both enriches our understanding toward polarization dynamics of optical solitons and paves potential application scenarios of pulsed fibre lasers.

Correlation between {R}_{D^{left(ast right)}} and top quark FCNC decays in leptoquark models

Some interpretations of {R}_{D^{left(ast right)}} anomaly in B meson decay using leptoquark (LQ) models can also generate top quark decays through Flavor Changing Neutral Current (FCNC). In this work we focus on two LQs, i.e. scalar S1 and vector U1 which are both singlet under the SU(2)L gauge group in the Standard Model (SM). We investigate their implications on the 3-body top FCNC decays t → cℓiℓj at tree level and the 2-body t → cV at one-loop level, with ℓ being the SM leptons and V = γ, Z, g being the SM gauge bosons. We utilize the 2σ parameter fitting ranges of the LQ models and find that Br(t → cℓiℓj) at tree level can reach mathcal{O} (10−6) and Br(t → cV) at one-loop level can reach mathcal{O} (10−10). Some quick collider search prospects are also analyzed.