Quarkonium production: velocity-scaling rules and long-distance matrix elements

The hierarchy of long-distance matrix elements (MEs) for quarkonium production depends on their scaling with the velocity $v$ of the heavy quark in the bound state. Ranges for the velocities in various bound states and uncertainties of colour-singlet MEs are estimated in a quark-potential model. Different possibilities for the scaling with $v$ of the MEs are discussed; they depend on the actual values of $v$ and the QCD scale. As an application, J/psi polarization in e^+e^- annihilation is discussed. The first non-perturbative estimates of colour-octet MEs are presented and compared with phenomenological determinations. Finally, various predictions of prompt quarkonium production at LEP are compared.Comment: 17 pages, Latex, uses 12pt.sty and epsfig.sty, 2 figure

Improving the equivalent-photon approximation in electron--positron collisions

The validity of the equivalent-photon approximation for two-photon processes in electron--positron collisions is critically examined. Commonly used forms to describe hadronic two-photon production are shown to lead to sizeable errors. An improved two-photon luminosity function is presented, which includes beyond-leading-logarithmic effects and scalar-photon contributions. Comparisons of various approximate expressions with the exact calculation in the case of the total hadronic cross section are given. Furthermore, effects of the poorly known low-Q2 behaviour of the virtual hadronic cross sections are discussed.Comment: 10 pages, Latex, uses 12pt.sty, no figur

On the non-perturbative part of the photon structure function

We discuss a dispersion relation in the photon mass and show how (in principle) model-independent constraints on the parton distribution functions of the photon, notably a momentum sumrule, can be obtained. We present two sets of parametrizations, SaS~1 and~2, corresponding to two rather extreme realizations of the non-perturbative part. Inclusive electron scattering off a real photon is found to be insufficient to constrain the non-perturbative components. The additional sensitivity provided by the photon virtuality is outlined. Previous approaches to model the non-perturbative input distributions are commented upon.Comment: Latex, 7 page

Three Mechanisms for Bar Thickening

We present simulations of bar-unstable stellar discs in which the bars thicken into box/peanut shapes. Detailed analysis of the evolution of each model revealed three different mechanisms for thickening the bars. The first mechanism is the well-known buckling instability, the second is the vertical excitation of bar orbits by passage through the 2:1 vertical resonance, and the third is a gradually increasing fraction of bar orbits trapped into this resonance. Since bars in many galaxies may have formed and thickened long ago, we have examined the models for fossil evidence in the velocity distribution of stars in the bar, finding a diagnostic to discriminate between a bar that had buckled from the other two mechanisms.Comment: 18 pages, 17 figures, accepted to appear in MNRAS, comments welcom

A scenario for high-energy gamma-gamma interactions

A real photon has a complicated nature, whereby it may remain unresolved or fluctuate into a vector meson or a perturbative q-qbar pair. In gamma-gamma events, this gives three by three combinations of the nature of the two incoming photons, and thus six distinct event classes. The properties of these classes are partly constrained by the choices already made in our related gamma-p model. It is therefore possible to predict the energy-dependence of the cross section for each of the six components separately. The total cross section gives support to the idea that a simple factorized ansatz with a pomeron and a reggeon term can be a good approximation. Event properties undergo a stepwise evolution from p-p to gamma-p to gamma-gamma events, with larger charged multiplicity, more transverse energy flow and a higher jet rate in the latter process.Comment: 1+27 pages, LaTeX2e, 20 ps/eps figures included in file using filecontents environment

On association in regression: the coefficient of determination revisited

Universal coefficients of determination are investigated which quantify the strength of the relation between a vector of dependent variables Y and a vector of independent covariates X. They are defined as measures of dependence between Y and X through theta(x), with theta(x) parameterizing the conditional distribution of Y given X=x. If theta(x) involves unknown coefficients gamma the definition is conditional on gamma, and in practice gamma, respectively the coefficient of determination has to be estimated. The estimates of quantities we propose generalize R^2 in classical linear regression and are also related to other definitions previously suggested. Our definitions apply to generalized regression models with arbitrary link functions as well as multivariate and nonparametric regression. The definition and use of the proposed coefficients of determination is illustrated for several regression problems with simulated and real data sets

Comparison of two model frameworks for fiber dispersion in the elasticity of soft biological tissues

This study compares two models that are used to describe the elastic properties of fiber-reinforced materials with dispersed fibers, in particular some soft biological tissues such as arterial walls and cartilages. The two model approaches involve different constitutive frameworks, one being based on a generalized structure tensor (GST) and the other on the method of angular integration (AI). By using two representative examples, with the same number of parameters for each model, it is shown that the predictions of the two models are virtually identical for a significant range of large deformations, which contradicts conclusions contained in several papers that are based on faulty analysis. Additionally, each of the models is fitted to sets of uniaxial data from the circumferential and axial directions of the adventitia of a human aorta, both models providing excellent agreement with the data. While the predictions of the two models are comparable and exclusion of compressed fibers can be accommodated by either model, it is well known that the AI model requires more computational time than the GST model when used within a finite element environment, in particular if compressed fibers are excluded

Vector-Meson Electroproduction from Generalized Vector Dominance

Including destructively interfering off-diagonal transitions of diffraction-dissociation type, we arrive at a formulation of GVD for exclusive vector-meson production in terms of a continuous spectral representation of dipole form. The transverse cross-section sigma_T for gamma* p -> V p behaves asymptotically as 1/Q^4, while R_V = sigma_L/sigma_T becomes asymptotically constant. Contributions violating s-channel helicity conservation stay at the 10-15% level established in low-energy photoproduction and diffractive hadron--hadron interactions. The data for phi- and rho-meson production for 0 \lsim Q^2 \lsim 20 GeV^2 from HERA are found to be in agreement with these predictions.Comment: 16 pages, latex, 3 figure