The gluon content of the η\eta and η′\eta^{\prime} mesons and the ηγ\eta\gamma, η′γ\eta^{\prime}\gamma electromagnetic transition form factors

We compute power-suppressed corrections to the \eta\gamma and \eta^{\prime}\gamma transition form factors Q^2F_{\eta(\eta^{\prime})\gamma}(Q^2) arising from the end point regions x \to 0,1 by employing the infrared-renormalon approach. The contribution to the form factors from the quark and gluon content of the \eta,\eta^{\prime} mesons is taken into account using for the \eta-\eta^{\prime} mixing the SU_f(3) singlet \eta_1 and octet \eta_8 basis. The theoretical predictions obtained this way are compared with the corresponding CLEO data and restrictions on the input parameters (Gegenbauer coefficients) B_2^q(\eta_1), B_2^g(\eta_1), and B_2^q(\eta_8) in the distribution amplitudes for the \eta_1,\eta_8 states with one nonasymptotic term are deduced. Comparison is made with the results from QCD perturbation theory.Comment: 25 pages, RevTeX4 used. 9 figures as EPS files. Text significantly changed to include variation of theoretical parameters. Figures modified. Corrected typo in equation (34) and trivial mistake in $\beta_1$-coefficient. References added. Conclusions unchange

Dynamics-based centrality for general directed networks

Determining the relative importance of nodes in directed networks is important in, for example, ranking websites, publications, and sports teams, and for understanding signal flows in systems biology. A prevailing centrality measure in this respect is the PageRank. In this work, we focus on another class of centrality derived from the Laplacian of the network. We extend the Laplacian-based centrality, which has mainly been applied to strongly connected networks, to the case of general directed networks such that we can quantitatively compare arbitrary nodes. Toward this end, we adopt the idea used in the PageRank to introduce global connectivity between all the pairs of nodes with a certain strength. Numerical simulations are carried out on some networks. We also offer interpretations of the Laplacian-based centrality for general directed networks in terms of various dynamical and structural properties of networks. Importantly, the Laplacian-based centrality defined as the stationary density of the continuous-time random walk with random jumps is shown to be equivalent to the absorption probability of the random walk with sinks at each node but without random jumps. Similarly, the proposed centrality represents the importance of nodes in dynamics on the original network supplied with sinks but not with random jumps.Comment: 7 figure

Collective fluctuations in networks of noisy components

Collective dynamics result from interactions among noisy dynamical components. Examples include heartbeats, circadian rhythms, and various pattern formations. Because of noise in each component, collective dynamics inevitably involve fluctuations, which may crucially affect functioning of the system. However, the relation between the fluctuations in isolated individual components and those in collective dynamics is unclear. Here we study a linear dynamical system of networked components subjected to independent Gaussian noise and analytically show that the connectivity of networks determines the intensity of fluctuations in the collective dynamics. Remarkably, in general directed networks including scale-free networks, the fluctuations decrease more slowly with the system size than the standard law stated by the central limit theorem. They even remain finite for a large system size when global directionality of the network exists. Moreover, such nontrivial behavior appears even in undirected networks when nonlinear dynamical systems are considered. We demonstrate it with a coupled oscillator system.Comment: 5 figure

The Projection Method for Reaching Consensus and the Regularized Power Limit of a Stochastic Matrix

In the coordination/consensus problem for multi-agent systems, a well-known condition of achieving consensus is the presence of a spanning arborescence in the communication digraph. The paper deals with the discrete consensus problem in the case where this condition is not satisfied. A characterization of the subspace $T_P$ of initial opinions (where $P$ is the influence matrix) that \emph{ensure} consensus in the DeGroot model is given. We propose a method of coordination that consists of: (1) the transformation of the vector of initial opinions into a vector belonging to $T_P$ by orthogonal projection and (2) subsequent iterations of the transformation $P.$ The properties of this method are studied. It is shown that for any non-periodic stochastic matrix $P,$ the resulting matrix of the orthogonal projection method can be treated as a regularized power limit of $P.$Comment: 19 pages, 2 figure

Coordination in multiagent systems and Laplacian spectra of digraphs

Constructing and studying distributed control systems requires the analysis of the Laplacian spectra and the forest structure of directed graphs. In this paper, we present some basic results of this analysis partially obtained by the present authors. We also discuss the application of these results to decentralized control and touch upon some problems of spectral graph theory.Comment: 15 pages, 2 figures, 40 references. To appear in Automation and Remote Control, Vol.70, No.3, 200

Topological Surface States and Dirac point tuning in ternary Bi2Te2Se class of topological insulators

Using angle-resolved photoemission spectroscopy, we report electronic structure for representative members of ternary topological insulators. We show that several members of this family, such as Bi2Se2Te, Bi2Te2Se, and GeBi2Te4, exhibit a singly degenerate Dirac-like surface state, while Bi2Se2S is a fully gapped insulator with no measurable surface state. One of these compounds, Bi2Se2Te, shows tunable surface state dispersion upon its electronic alloying with Sb (SbxBi2-xSe2Te series). Other members of the ternary family such as GeBi2Te4 and BiTe1.5S1.5 show an in-gap surface Dirac point, the former of which has been predicted to show nonzero weak topological invariants such as (1;111); thus belonging to a different topological class than BiTe1.5S1.5. The measured band structure presented here will be a valuable guide for interpreting transport, thermoelectric, and thermopower measurements on these compounds. The unique surface band topology observed in these compounds contributes towards identifying designer materials with desired flexibility needed for thermoelectric and spintronic device fabrication.Comment: 9 pages, 6 figures; Related results at http://online.kitp.ucsb.edu/online/topomat11/hasan

Energy States of Colored Particle in a Chromomagnetic Field

The unitary transformation, which diagonalizes squared Dirac equation in a constant chromomagnetic field is found. Applying this transformation, we find the eigenfunctions of diagonalized Hamiltonian, that describe the states with definite value of energy and call them energy states. It is pointed out that, the energy states are determined by the color interaction term of the particle with the background chromofield and this term is responsible for the splitting of the energy spectrum. We construct supercharge operators for the diagonal Hamiltonian, that ensure the superpartner property of the energy states.Comment: 25 pages, some calculation details have been removed, typos correcte

Chromomagnetic Catalysis of Color Superconductivity in a (2+1)-dimensional NJL Model

The influence of a constant uniform external chromomagnetic field $H$ on the formation of color superconductivity has been investigated. The consideration was performed in the framework of a (2+1)-dimensional Nambu--Jona-Lasinio model with two different four-fermionic structures responsible for $$and diquark$$ condensates. In particular, it was shown that there exists a critical value $H_c$ of the external chromomagnetic field such that at $H>H_c$ a nonvanishing diquark condensate is dynamically created (the so-called chromomagnetic catalysis effect of color superconductivity). Moreover, external chromomagnetic fields may in some cases enhance the diquark condensate of color superconductivity.Comment: 32 pages, 2 figures, revte

A measure of individual role in collective dynamics

Identifying key players in collective dynamics remains a challenge in several research fields, from the efficient dissemination of ideas to drug target discovery in biomedical problems. The difficulty lies at several levels: how to single out the role of individual elements in such intermingled systems, or which is the best way to quantify their importance. Centrality measures describe a node's importance by its position in a network. The key issue obviated is that the contribution of a node to the collective behavior is not uniquely determined by the structure of the system but it is a result of the interplay between dynamics and network structure. We show that dynamical influence measures explicitly how strongly a node's dynamical state affects collective behavior. For critical spreading, dynamical influence targets nodes according to their spreading capabilities. For diffusive processes it quantifies how efficiently real systems may be controlled by manipulating a single node.Comment: accepted for publication in Scientific Report

Determination of the η\eta and η′\eta' Mixing Angle from the Pseudoscalar Transition Form Factors

The possible range of $\eta-\eta'$ mixing angle is determined from the transition form factors $F_{\eta \gamma}(Q^2)$ and $F_{\eta' \gamma}(Q^2)$ with the help of the present experimental data. For such purpose, the quark-flavor mixing scheme is adopted and the pseudoscalar transition form factors are calculated under the light-cone pQCD framework, where the transverse momentum corrections and the contributions beyond the leading Fock state have been carefully taken into consideration. We construct a phenomenological expression to estimate the contributions to the form factors beyond the leading Fock state based on their asymptotic behavior at $Q^2\to 0$ and $Q^2\to\infty$. By taking the quark-flavor mixing scheme, our results lead to $\phi= 38.0^{\circ}\pm 1.0^{\circ}\pm 2.0^{\circ}$, where the first error coming from experimental uncertainty and the second error coming from the uncertainties of the wavefunction parameters. The possible intrinsic charm component in $\eta$ and $\eta'$ is discussed and our present analysis also disfavors a large portion of intrinsic charm component in $\eta$ and $\eta'$, e.g. $|f^c_{\eta'}|\le 50 {\rm MeV}$.Comment: 18 Pages, 3 figures. Several references added. To be published in EPJ