QCD Tests at e+e−e^+e^- Colliders

A short review of the history and a 'slide-show' of QCD tests in $e^+e^-$ annihilation is given. The world summary of measurements of $\alpha_s$ is updated.Comment: Revised version: some references added and corrected; world summary of $\alpha_s$ extended by result from polarized structure functions. 9 pages, 15 EPS figures; contribution to the CQD Euroconference 97 (Montpellier 1997

Experimental Tests of Asymptotic Freedom

Quantum Chromodynamics (QCD), the gauge field theory of the Strong Interaction, has specific features, asymptotic freedom and confinement, which determine the behaviour of quarks and gluons in particle reactions at high and at low energy scales. QCD predicts that the strong coupling strength \as decreases with increasing energy or momentum transfer, and vanishes at asymptotically high energies. In this review, the history and the status of experimental tests of asymptotic freedom are summarised. The world summary of measurements of \as is updated, leading to an unambiguous verification of the running of \as and of asymptotic freedom, in excellent agreement with the predictions of QCD. Averaging a set of measurements balanced between different particle processes and the available energy range, results in a new and improved world average of \amz = 0.1189 \pm 0.0010 .Comment: 38 pages, 18 figure

αs\alpha_s at Zinnowitz 2004

A review of measurements of $\alpha_s$ is given, representing the status of April 2004. The results prove the energy dependence of $\alpha_s$ and are in excellent agreement with the expectations of Quantum Chromodynamics, QCD. Evolving all results to the rest energy of the $Z^0$ boson, the world average of $\alpha_s(M_Z)$ is determined from measurements which are based on QCD calculations in complete NNLO perturbation theory, giving $\alpha_s(M_Z) = 0.1182 \pm 0.0027 .$Comment: 8 pages, 4 figures, talk presented at the workshop Loops and Legs in Quantum Field Theory, April 2004, Zinnowitz (Germany

Eleven Years of QCD at LEP

Studies of hadronic final states of $e^+e^-$ annihilations, observed at the Large Electron Positron Collider LEP at CERN, are reviewed. The topics included cover measurements of $\alpha_s$, hadronic event shapes and hadronisation studies, tests of asymptotic freedom and of the non-Abelian gauge structure of QCD, differences between quark and gluon jets, tests of power corrections and selected results of two-photon scattering processes. The improvements obtained at LEP are demonstrated by comparing to results from the pre-LEP era. This article consists of a reproduction of slides presented at the LEPFest in October 2000, supplemented by a short descriptive text and a list of relevant references.Comment: 10 pages of text plus reproduction of 27 transparencies presented at the LEPFest at CERN, October 2000. To be published in Eur. Phys. Jour (direct) C; a higher resolution version of the viewgraphs can be obtained from: http://www.mppmu.mpg.de/~bethke/LEPQCDtalk-higres.pd

Augmented GARCH sequences: Dependence structure and asymptotics

The augmented GARCH model is a unification of numerous extensions of the popular and widely used ARCH process. It was introduced by Duan and besides ordinary (linear) GARCH processes, it contains exponential GARCH, power GARCH, threshold GARCH, asymmetric GARCH, etc. In this paper, we study the probabilistic structure of augmented $\mathrm {GARCH}(1,1)$ sequences and the asymptotic distribution of various functionals of the process occurring in problems of statistical inference. Instead of using the Markov structure of the model and implied mixing properties, we utilize independence properties of perturbed GARCH sequences to directly reduce their asymptotic behavior to the case of independent random variables. This method applies for a very large class of functionals and eliminates the fairly restrictive moment and smoothness conditions assumed in the earlier theory. In particular, we derive functional CLTs for powers of the augmented GARCH variables, derive the error rate in the CLT and obtain asymptotic results for their empirical processes under nearly optimal conditions.Comment: Published in at http://dx.doi.org/10.3150/07-BEJ120 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Bivariant KKKK-Theory and the Baum-Connes conjecure

This is a survey on Kasparov's bivariant $KK$-theory in connection with the Baum-Connes conjecture on the $K$-theory of crossed products $A\rtimes_rG$ by actions of a locally compact group $G$ on a C*-algebra $A$. In particular we shall discuss Kasparov's Dirac dual-Dirac method as well as the permanence properties of the conjecture and the "Going-Down principle" for the left hand side of the conjecture, which often allows to reduce $K$-theory computations for $A\rtimes_rG$ to computations for crossed products by compact subgroups of $G$. We give several applications for this principle including a discussion of a method developed by Cuntz, Li and the author for explicit computations of the $K$-theory groups of crossed products for certain group actions on totally disconnected spaces. This provides an important tool for the computation of $K$-theory groups of semi-group C*-algebras.Comment: Some minor correction