Scalar Form Research Articles

Constraint on the light quark mass mq from QCD sum rules in the I=0 scalar channel

In this paper, we reanalyze the $I=0$ scalar channel with the improved Monte-Carlo based QCD sum rules, which combines the rigorous H\"older-inequality-determined sum rule window and a two Breit-Wigner type resonances parametrization for the phenomenological spectral density that satisfies the the low-energy theorem for the scalar form factor. Considering the uncertainties of the QCD parameters and the experimental masses and widths of the scalar resonances $\sigma$ and $f_0(980)$, we obtain a prediction for light quark mass $m_q(2\,\textrm{GeV})$ = $\frac{1}{2}(m_u(2\,\textrm{GeV})$ + $m_d(2\,\textrm{GeV}))$ = $4.7^{+0.8}_{-0.7}\,\textrm{MeV}$, which is consistent with the PDG (Particle Data Group) value and QCD sum rule determinations in the pseudoscalar channel. This agreement provides a consistent framework connecting QCD sum rules and low-energy hadronic physics. We also obtain the decay constants of $\sigma$ and $f_0(980)$ at 2 GeV, which are approximately $0.64-0.83$ GeV and $0.40-0.48$ GeV respectively.

Stable Nonlinear Control of an Agonist-Antagonist Muscle-Driven System

We introduce an asymptotically stable nonlinear controller for a two-muscle system with an agonist-antagonist arrangement. A Hill model with series and parallel elasticity is used for each muscle. The controller is based on a combination of backstepping and algebraic virtual control matching to determine final activation control signals. Two definitions for the synthetic input used in the first backstepping stage are considered: a scalar form and a vector form. A novel feature of the vector approach is the ability to incorporate a minimum-effort optimality criterion as a way of resolve actuation redundancy. Minimum effort criteria reflect well-established biomechanical principles of human movement. The proposed approach is scalable and can serve as a “working controller” to facilitate studies in the field of human-machine interactions, including machine control systems and biomechanical state estimation.

Analysis method ofrecruitment needs for the regional economy: Occupational section

The paper deals with comparative analysis of occupations in the regional labor market. Occupation is treated as a multi-dimensional space of characte- ristics, whereas a scalar form of a characteristic makes it possible to carry out a comparative analysis of occupations. Using cluster analysis of a pilot region indicators five meaningfully interpretable clusters of occupations were identified, reflecting their regional specificity.

Coverage-dependent amplifiers of vegetation change on global water cycle dynamics

The terrestrial water cycle describes the circulation of water worldwide from one store to another via repeated evapotranspiration (E) from land and precipitation (P) back to the surface. The cycle presents significant spatial variability, which is strongly affected by natural climate and anthropogenic influences. As one of the major anthropogenic influences, vegetation change unavoidably alters surface property and subsequent the terrestrial water cycle, while its contribution is yet difficult to isolate from the mixed influences. Here, we use satellite and in-situ datasets to identify the terrestrial water cycle dynamics in spatial detail and to evaluate the impact of vegetation change. Methodologically, the water cycle is identified by the indicator of difference between evapotranspiration and precipitation (E-P). Then the scalar form of the indicator’s trend (ΔE+ΔP) is used for evaluating the dynamics of water cycle, with the positive value means acceleration and negative means deceleration. Then, the contributions of climate and vegetation change are isolated by the trajectory-based method. Our results indicate that 4 accelerating and 4 decelerating water cycles can be identified, affecting 42.11% of global land. The major water cycle type is characterized by non-changing precipitation and increasing evapotranspiration (PNO-EIN), which covers 20.88% of globally land. Vegetation change amplifies both accelerating and decelerating water cycles. It tends to intensify the trend of the decelerating water cycles, while climate change weakens the trend. In the accelerating water cycles, both vegetation and climate change present positive effect to intensify the trend. The effect of plant cover change varies with the coverage. In particular, vegetation change intensifies the water cycle in moderately vegetated regions (0.1<NDVI<0.6), but weakens the cycle in sparsely or highly vegetated regions (NDVI<0.1 or 0.6<NDVI<0.8). In extremely vegetated regions (NDVI>0.85), the water cycle is accelerated because of the significant increase of precipitation. We conclude that vegetation change acts as an amplifier for both accelerating and decelerating terrestrial water cycles, depending on the degree of vegetation coverage.

On the structure of modules of vector-valued modular forms

If \(\rho \) denotes a finite-dimensional complex representation of \(\mathbf {SL}_{2}(\mathbf {Z})\), then it is known that the module \(M(\rho )\) of vector-valued modular forms for \(\rho \) is free and of finite rank over the ring M of scalar modular forms of level one. This paper initiates a general study of the structure of \(M(\rho )\). Among our results are absolute upper and lower bounds, depending only on the dimension of \(\rho \), on the weights of generators for \(M(\rho )\), as well as upper bounds on the multiplicities of weights of generators of \(M(\rho )\). We provide evidence, both computational and theoretical, that a stronger three-term multiplicity bound might hold. An important step in establishing the multiplicity bounds is to show that there exists a free basis for \(M(\rho )\) in which the matrix of the modular derivative operator does not contain any copies of the Eisenstein series \(E_6\) of weight six.

The three-body decays B(s) → ρf0(X)→ρπ−π+ in pQCD factorization approach

In this paper, we study three-body decays B(s)→ρf0(X)→ρπ−π+ in the perturbative QCD (pQCD) factorization approach. By using two-pion distribution amplitudes (DAs), these decays can proceed mainly via quasi-two-body channels. The Flatté model for the f0(980) resonance and the Breit–Wigner formula for the f0(500), f0(1500), and f0(1790) resonances are adopted to parameterize the time-like scalar form factors. We also use Bugg's model for the wide f0(500) as a comparison. We evaluate S-wave resonance contributions, and show the contributions to the B(s)→ρπ+π− decay spectrums with respect to the two-pion invariant mass M(π+π−). The pQCD prediction of B→ρf0(500) is B(B0→ρ0f0(500))=4.43×10−8, B(B+→ρ+f0(500))=3.84×10−8 for Breit–Wigner model, and B(B0→ρ0f0(500))=4.91×10−8, B(B+→ρ+f0(500))=4.07×10−8 for Bugg's model. We also predict other resonance contributions B(Bs→ρ0f0(980))=8.91×10−8, B(Bs→ρ0f0(1500))=1.43×10−8 and B(Bs→ρ0f0(1790))=2.78×10−9. This study in pQCD approach can provide a ready reference to the running and forthcoming experiments. Further improvements in theories and experiments are expected so that we can understand the inner structure of the scalar mesons f0.

The S-wave resonance contributions in the B^{0}_{s} decays into psi (2S,3S) plus pion pair

The three-body decays B^0_s rightarrow psi (2S,3S) pi ^+ pi ^- are studied based on the perturbative QCD approach. With the help of the nonperturbative two-pion distribution amplitudes, the analysis is simplified into the quasi-two-body processes. Besides the traditional factorizable and nonfactorizable diagrams at the leading order, the next-to-leading order vertex corrections are also included to cancel the scale dependence. The f_0(980), f_0(1500) resonance contributions as well as the nonresonant contributions are taken into account using the presently known pi pi time-like scalar form factor for the sbar{s} component. It is found that the predicted B^0_s rightarrow psi (2S) pi ^+ pi ^- decay spectra in the pion pair invariant mass shows a similar behavior as the experiment. The calculated S-wave contributions to the branching ratio of B^0_s rightarrow psi (2S) pi ^+ pi ^- is 6.0times 10^{-5}, which is in agreement with the LHCb data mathcal {B}(B^0_s rightarrow psi (2S) pi ^+ pi ^-)=(7.2pm 1.2)times 10^{-5} within errors. The estimate of mathcal {B}(B^0_s rightarrow psi (3S) pi ^+ pi ^-) can reach the order of 10^{-5}, pending the corresponding measurements.

DEĞİŞKEN KESİTLİ TIMOSHENKO KİRİŞİNİN SERBEST TİTREŞİM ANALİZİ

The free vibration of beams with variable cross-section was investigated. The governing equations for beams with variable cross-section were obtained using Timoshenko beam theory. The effect of axial and shear deformations, rotary inertia and non-uniformity cross-section were considered in the formulations. Ordinary differential equations in scalar form obtained in the Laplace domain were solved numerically using the complementary functions method. The free vibration of beams with variable cross-section was analysed. The effects of non-uniformity parameter, boundary conditions on free vibration were investigated. The results obtained in this study were found to be in good agreement with those obtained from ANSYS. Keywords: Free vibration, non-uniform beams, complementary function method

Remarks on the Standard Model predictions for R(D) and R(D*)

Semileptonic $b \to c$ transitions, and in particular the ratios $R(D^{(*)}) = \frac{\Gamma(B \rightarrow D^{(*)} \tau \nu )}{\Gamma(B \rightarrow D^{(*)} \ell \nu )}$, can be used to test the universality of the weak interactions. In light of the recent discrepancies between the experimental measurements of these observables by BaBar, Belle and LHCb and the Standard Model predicted values, we study the robustness of the latter. Our analysis reveals that $R(D)$ might be enhanced by lepton mass effects associated to the mostly unknown scalar form factor. In constrast, the Standard Model prediction for $R(D^*)$ is found to be more robust, since possible pollutions from $B^*$ contributions turn out to be negligibly small, which indicates that $R(D^*)$ is a promising observable for searches of new physics.

Rational Differential Forms on the Line and Singular Vectors in Verma Modules over \widehat{sl}2

We construct a monomorphism of the De Rham complex of scalar multivalued meromorphic forms on the projective line, holomorphic on the complement to a finite set of points, to the chain complex of the Lie algebra of $sl_2$-valued algebraic functions on the same complement with coefficients in a tensor product of contragradient Verma modules over the affine Lie algebra $\hat{sl}_2$. We show that the existence of singular vectors in the Verma modules (the Malikov-Feigin-Fuchs singular vectors) is reflected in the new relations between the cohomology classes of logarithmic differential forms.

TMsim: An Algorithmic Tool for the Parametric and Worst-Case Simulation of Systems with Uncertainties

This paper presents a general purpose, algebraic tool—named TMsim—for the combined parametric and worst-case analysis of systems with bounded uncertain parameters. The tool is based on the theory of Taylor models and represents uncertain variables on a bounded domain in terms of a Taylor polynomial plus an interval remainder accounting for truncation and round-off errors. This representation is propagated from inputs to outputs by means of a suitable redefinition of the involved calculations, in both scalar and matrix form. The polynomial provides a parametric approximation of the variable, while the remainder gives a conservative bound of the associated error. The combination between the bound of the polynomial and the interval remainder provides an estimation of the overall (worst-case) bound of the variable. After a preliminary theoretical background, the tool (freely available online) is introduced step by step along with the necessary theoretical notions. As a validation, it is applied to illustrative examples as well as to real-life problems of relevance in electrical engineering applications, specifically a quarter-car model and a continuous-time linear equalizer.

Partial linear integrals of the Poincaré–Zhukovskii equations (the general case)

Abstract The existence conditions for a linear invariant relation of the Poincare–Zhukovskii equations in the general case when the matrix of the cross terms of the Hamiltonian can be asymmetric are obtained. A new scalar form of the equations is indicated, and they are reduced to the Riccati equation in the case of motion with a linear invariant relation. A particular solution of the Riccati equation, which defines a three-parameter family of periodic solutions of the Poincare–Zhukovskii equations, is presented. A four-parameter family of solutions of the Poincare–Zhukovskii equations, each of which exponentially rapidly approaches a corresponding periodic solution with time, is constructed. The conditions for precessional motion with a linear invariant relation are found.

Network realization of triplet-type quantum stochastic systems

This paper focuses on a problem of network synthesis for a class of quantum stochastic systems. The systems under consideration are of triplet-type form and stem from linear quantum optics and linear quantum circuits. A new quantum network realization approach is proposed by generalizing the scattering operator from the scalar form to a unitary matrix in network components. It shows that the triplet-type quantum stochastic system can be approximated by a quantum network which consists of some one-degree-of-freedom generalized open-quantum harmonic oscillators (1DGQHOs) via series, concatenation and feedback connections.

The S-wave resonance contributions to the three-body decays $$B^0_{(s)}\rightarrow \eta _c f_0(X)\rightarrow \eta _c\pi ^+\pi ^-$$ B ( s ) 0 → η c f 0 ( X ) → η c π + π - in perturbative QCD approach

In this paper, we study the three-body decays $B^0/B^0_s \to \eta_c f_0(X)\to \eta_c \pi^+\pi^-$ by employing the perturbative QCD (PQCD) factorization approach. We evaluate the $S$-wave resonance contributions by using the two-pion distribution amplitude $\Phi_{\pi\pi}^{\rm S}$. The Breit-Wigner formula for the $f_0(500)$, $f_0(1500)$, and $f_0(1790)$ resonances and the Flatt\'e model for the $f_0(980)$ resonance are adopted to parameterize the time-like scalar form factors $F_{s}(\omega^2)$. We also use the D.~V.~Bugg model to parameterize the $f_0(500)$ and compare the relevant theoretical predictions from different models. We found the following results: (a) the PQCD predictions for the branching ratios are ${\cal B}(B^0\to \eta_c f_0(500)[\pi^+\pi^-])= \left ( 1.53 ^{+0.76}_{-0.35} \right ) \times 10^{-6}$ for Breit-Wigner model and ${\cal B}(B^0\to \eta_c f_0(500)[\pi^+\pi^-])= \left ( 2.31 ^{+0.96}_{-0.48} \right ) \times 10^{-6}$ for D.~V.~Bugg model; (b) $ {\cal B}(B_s\to \eta_c f_0(X)[\pi^+\pi^-] ) =\left ( 5.02^{+1.49}_{-1.08} \right )\times 10^{-5}$ when the contributions from $f_0(X)=(f_0(980),f_0(1500),f_0(1790))$ are all taken into account; and (c) The considered decays could be measured at the ongoing LHCb experiment, consequently, the formalism of two-hadron distribution amplitudes could also be tested by such experiments.

Study of the Criteria for the Degrees of Observability, Controllability and Identifiability of the Linear Dynamical Systems

The article is devoted to approaches to determination of the degree of observability, controllability and identifiability of the parameters in the linear dynamical systems. Well-known criteria for determination of the observability, controllability and identifiability of the dynamical objects were presented. Those criteria only allow us to determine, which component of the state vector is observable or controllable better. They can only give a relative assessment of the quality of the observability and controllability ofa specific component ofthe state vector ofthe system, whereas, it is impossible to compare the quantitative characteristics of the state variables and parameters in various systems. Numerical criteria for calculation of the degree of observability and controllability of the state variables, as well as the degree of identifiability of the model parameters of the dynamical objects were researched using the scalar methods. The proposed numerical criteria have a clear physical meaning, and are characterized by simplicity and versatility. They allow us to determine the quality of the observability, controllability and identifiability in a scalar form, which can be very convenient for practical applications.

Bounds on universal extra dimension from LHC run I and II data

We discuss the collider bounds on minimal Universal Extra Dimension (mUED) model from LHC Run-I and II data. The phenomenology of mUED is determined by only two parameters namely, the compactification scale ($R^{-1}$) of the extra dimension and cutoff scale ($\Lambda$) of the theory. The characteristic feature of mUED is the occurrence of nearly degenerate mass spectrum for the Kaluza-Klein (KK) particles and hence, soft leptons, soft jets at the collider experiments. The degree of degeneracy of KK-mass spectrum crucially depends on $\Lambda$. The strongest direct bound on $R^{-1}$ ($\sim $950 GeV for large $\Lambda$) arises from a search for a pair of soft dimuons at the Large Hadron Collider (LHC) experiment with 8 TeV center-of-mass energy and $20~{\rm fb}^{-1}$ integrated luminosity. However, for small $\Lambda$ and hence, small splitting within the first KK-level, the bounds from the dimuon channel is rather weak. On the other hand, the discovery of 126 GeV Higgs boson demands small $\Lambda$ to prevent the scalar potential form being unbounded from below. We discuss LHC monojet searches as a probe of low $\Lambda$ region of mUED parameter space. We also compute bounds on the mUED parameter space from 13 TeV multijets results.

Pion scalar form factor with correct mass and width of scalar mesonsf0(500)andf0(980)

Construction of the pion scalar isoscalar form factor ${\mathrm{\ensuremath{\Gamma}}}_{\ensuremath{\pi}}(t)$ in the elastic region, with an emphasis on the values of the S-wave isoscalar $\ensuremath{\pi}\ensuremath{\pi}$ scattering length ${a}_{0}^{0}$ and the quadratic pion scalar radius $⟨{r}^{2}{⟩}_{s}^{\ensuremath{\pi}}$ to be in conformity with predictions of the chiral perturbation theory, is presented. It is based on a precise S-wave isoscalar $\ensuremath{\pi}\ensuremath{\pi}$ scattering phase shift generated by dispersive analysis of experimental data with and imposed crossing symmetry condition. The final result for values of the ${f}_{0}(500)$ scalar meson mass and width is ${m}_{\ensuremath{\sigma}}=(487\ifmmode\pm\else\textpm\fi{}31)\text{ }\text{ }\mathrm{MeV}$; ${\mathrm{\ensuremath{\Gamma}}}_{\ensuremath{\sigma}}=(542\ifmmode\pm\else\textpm\fi{}60)\text{ }\text{ }\mathrm{MeV}$ and for values of the ${f}_{0}(980)$ scalar meson mass and width is ${m}_{f(980)}=(988\ifmmode\pm\else\textpm\fi{}78)\text{ }\text{ }\mathrm{MeV}$; ${\mathrm{\ensuremath{\Gamma}}}_{f(980)}=(97\ifmmode\pm\else\textpm\fi{}29)\text{ }\text{ }\mathrm{MeV}$. The ${f}_{0}(500)$ scalar meson parameters are compatible with the results from dispersive analyses of the BERN and MADRID/CRACOW groups to be considered now as the most reliable values of the ${f}_{0}(500)$ scalar meson parameters, though in presented analysis another, unusual way has been applied. The ${f}_{0}(980)$ meson parameters agree well with values given by the Particle Data Group.

Predictions on the second-class current decaysτ−→π−η(′)ντ

We analyze the second-class current decays $\tau^{-}\to\pi^{-}\eta^{(\prime)}\nu_{\tau}$ in the framework of Chiral Perturbation Theory with resonances. Taking into account $\pi^{0}$-$\eta$-$\eta^{\prime}$ mixing, the $\pi^{-}\eta^{(\prime)}$ vector form factor is extracted, in a model-independent way, using existing data on the $\pi^{-}\pi^{0}$ one. For the participant scalar form factor, we have considered different parameterizations ordered according to their increasing fulfillment of analyticity and unitarity constraints. We start with a Breit-Wigner parameterization dominated by the $a_{0}(980)$ scalar resonance and after we include its excited state, the $a_{0}(1450)$. We follow by an elastic dispersion relation representation through the Omn\`{e}s integral. Then, we illustrate a method to derive a closed-form expression for the $\pi^{-}\eta$, $\pi^{-}\eta^{\prime}$ (and $K^{-}K^{0}$) scalar form factors in a coupled-channels treatment. Finally, predictions for the branching ratios and spectra are discussed emphasizing the error analysis. An interesting result of this study is that both $\tau^{-}\to\pi^{-}\eta^{(\prime)}\nu_{\tau}$ decay channels are promising for the soon discovery of second-class currents at Belle-II. We also predict the relevant observables for the partner $\eta^{(\prime)}_{\ell 3}$ decays, which are extremely suppressed in the Standard Model.

DAİRE EKSENLİ KİRİŞLERİN TAŞIMA VE RİJİTLİK MATRİSİ YÖNTEMİ İLE STATİK ANALİZİ

In this study static analysis of circular beams is investigated theoretically. The governing equations, for naturally twisted and curved spatial rods, obtained using Timoshenko beam theory and rewritten for circular beams rods. Effects of the axial and shear deformations are considered in the formulations. The Timoshenko beam theory is adopted in the derivation of the governing equation. The material of the rod is assumed to be homogeneous, linear elastic and isotropic. Ordinary differential equations in scalar form are solved by using transfer matrix and stiffness matrix method. Circular beams are analyzed through various examples for static analysis. Results are compared with ANSYS results based on finite element method and available in the literature.

Comparing scalar and vector forms of the finite element method by example of an elliptic cylinder

An algorithm for constructing the stiffness matrix of a quadrangular curvilinear finite element in the form of a fragment of the middle surface of an elliptic cylinder with 18 degrees of freedom in the node is given. Implementation of the finite-difference procedure includes two variants of approximation of the sought variables, i.e., a scalar one and a vector one. Numerical examples are given and prove that the vector approximation has principal advantages over the scalar approximation for arbitrary shells with significant gradients of curvature of the lines of the middle surface or allowing for displacement as a rigid body.