Kinematic Effects in Radiative Quarkonia Decays

Non-relativistic QCD (NRQCD) predicts colour octet contributions to be significant not only in many production processes of heavy quarkonia but also in their radiative decays. We investigate the photon energy distributions in these processes in the endpoint region. There the velocity expansion of NRQCD breaks down which requires a resummation of an infinite class of colour octet operators to so-called shape functions. We model these non-perturbative functions by the emission of a soft gluon cluster in the initial state. We found that the spectrum in the endpoint region is poorly understood if the values for the colour octet matrix elements are taken as large as indicated from NRQCD scaling rules. Therefore the endpoint region should not be taken into account for a fit of the strong coupling constant at the scale of the heavy quark mass.Comment: LaTeX, 17 pages, 5 figures. The complete paper is also available via the www at http://www-ttp.physik.uni-karlsruhe.de/Preprints

Basic Module Theory over Non-Commutative Rings with Computational Aspects of Operator Algebras

The present text surveys some relevant situations and results where basic Module Theory interacts with computational aspects of operator algebras. We tried to keep a balance between constructive and algebraic aspects.Comment: To appear in the Proceedings of the AADIOS 2012 conference, to be published in Lecture Notes in Computer Scienc

A Phenomenological Analysis of Gluon Mass Effects in Inclusive Radiative Decays of the J/ψ\rm{J/\psi} and $\Upsilon

The shapes of the inclusive photon spectra in the processes \Jp \to \gamma X and \Up \to \gamma X have been analysed using all available experimental data. Relativistic, higher order QCD and gluon mass corrections were taken into account in the fitted functions. Only on including the gluon mass corrections, were consistent and acceptable fits obtained. Values of $0.721^{+0.016}_{-0.068}$ GeV and $1.18^{+0.09}_{-0.29}$ GeV were found for the effective gluon masses (corresponding to Born level diagrams) for the \Jp and \Up respectively. The width ratios \Gamma(V \to {\rm hadrons})/\Gamma(V \to \gamma+ {\rm hadrons}) V=\Jp, \Up were used to determine $\alpha_s(1.5 {\rm GeV})$ and $\alpha_s(4.9 {\rm GeV})$. Values consistent with the current world average $\alpha_s$ were obtained only when gluon mass correction factors, calculated using the fitted values of the effective gluon mass, were applied. A gluon mass $\simeq 1$ GeV, as suggested with these results, is consistent with previous analytical theoretical calculations and independent phenomenological estimates, as well as with a recent, more accurate, lattice calculation of the gluon propagator in the infra-red region.Comment: 50 pages, 11 figures, 15 table

Caledonian foreland basin sedimentation : A new depositional model for the Upper Silurian-Lower Devonian Lower Old Red Sandstone of the Midland Valley Basin, Scotland

Open Access via Wiley publishing agreement. We thank Stuart Archer, Brian Hampton and the anonymous reviewer for their thoughtful and constructive reviews of this manuscript, which has benefited greatly from their attention. We also thank the Associate Editors at Basin Research for their time, advice and suggestions during the submission process. DATA AVAILABILITY STATEMENT The data that support the findings of this study are available from the corresponding author upon reasonable request.Peer reviewedPublisher PD

Amenability of groups and GG-sets

This text surveys classical and recent results in the field of amenability of groups, from a combinatorial standpoint. It has served as the support of courses at the University of G\"ottingen and the \'Ecole Normale Sup\'erieure. The goals of the text are (1) to be as self-contained as possible, so as to serve as a good introduction for newcomers to the field; (2) to stress the use of combinatorial tools, in collaboration with functional analysis, probability etc., with discrete groups in focus; (3) to consider from the beginning the more general notion of amenable actions; (4) to describe recent classes of examples, and in particular groups acting on Cantor sets and topological full groups

Computation of the winding number diffusion rate due to the cosmological sphaleron

A detailed quantitative analysis of the transition process mediated by a sphaleron type non-Abelian gauge field configuration in a static Einstein universe is carried out. By examining spectra of the fluctuation operators and applying the zeta function regularization scheme, a closed analytical expression for the transition rate at the one-loop level is derived. This is a unique example of an exact solution for a sphaleron model in $3+1$ spacetime dimensions.Comment: Some style corrections suggested by the referee are introduced (mainly in Sec.II), one reference added. To appear in Phys.Rev.D 29 pages, LaTeX, 3 Postscript figures, uses epsf.st

Reciprocity as a foundation of financial economics

This paper argues that the subsistence of the fundamental theorem of contemporary financial mathematics is the ethical concept ‘reciprocity’. The argument is based on identifying an equivalence between the contemporary, and ostensibly ‘value neutral’, Fundamental Theory of Asset Pricing with theories of mathematical probability that emerged in the seventeenth century in the context of the ethical assessment of commercial contracts in a framework of Aristotelian ethics. This observation, the main claim of the paper, is justified on the basis of results from the Ultimatum Game and is analysed within a framework of Pragmatic philosophy. The analysis leads to the explanatory hypothesis that markets are centres of communicative action with reciprocity as a rule of discourse. The purpose of the paper is to reorientate financial economics to emphasise the objectives of cooperation and social cohesion and to this end, we offer specific policy advice