Next-to-Leading Order QCD Corrections and Massive Quarks in e+e−→3e^+e^-\to 3 Jets

We present in detail a calculation of the next-to-leading order QCD corrections to the process $e^+e^-\to 3$ jets with massive quarks. To isolate the soft and collinear divergencies of the four parton matrix elements, we modify the phase space slicing method to account for masses. Our computation allows for the prediction of oriented three jet events involving heavy quarks, both on and off the Z resonance, and of any event shape variable which is dominated by three jet configurations. We show next-to-leading order results for the three jet fraction, the differential two jet rate, and for the thrust distribution at various c.m. energies.Comment: 51 pages, LaTeX, 16 postscript figure

Infrared structure of e+e−→3e^+e^- \to 3 jets at NNLO: QED-type contributions

The NNLO QCD corrections to the $e^+e^- \to 3$ jets can be decomposed according to their colour factors. Out of the seven colour factors, three are of QED-type: $1/N^2$, $N_F/N$ and $N_F^2$. We use the antenna subtraction method to compute these contributions, providing complete expressions for the subtraction terms in $N_F/N$ and $N_F^2$.Comment: Talk presented at Loops and Legs 2006, Eisenac

Pair Production of Neutral Higgs Particles in Gluon--Gluon Collisions

Pair production processes of neutral Higgs particles will allow us to study the trilinear Higgs couplings at future high--energy colliders. Several mechanisms give rise to multi--Higgs final states in hadron interactions. In the present paper we investigate Higgs pair production in gluon--gluon collisions. After recapitulating pair production in the Standard Model, the analysis of the cross sections is carried out in detail for the neutral Higgs particles in the minimal supersymmetric extension.Comment: 23 pages, latex, 9 figures appended as uuencoded fil

Measurement of the strong coupling alpha_S from the three-jet rate in e+e- - annihilation using JADE data

We present a measurement of the strong coupling alpha_S using the three-jet rate measured with the Durham algorithm in e+e- -annihilation using data of the JADE experiment at centre-of-mass energies between 14 and 44 GeV. Recent theoretical improvements provide predictions of the three-jet rate in e+e- -annihilation at next-to-next-to-leading order. In this paper a measurement of the three-jet rate is used to determine the strong coupling alpha_s from a comparison to next-to-next-to-leading order predictions matched with next-to-leading logarithmic approximations and yields a value for the strong coupling alpha_S(MZ) = 0.1199+- 0.0010 (stat.) +- 0.0021 (exp.) +- 0.0054 (had.) +- 0.0007 (theo.) consistent with the world average.Comment: 27 pages, 8 figure

Analytic Perturbation Theory for Practitioners and Upsilon Decay

Within the ghost-free Analytic Perturbation Theory (APT), devised in the last decade for low energy QCD, simple approximations are proposed for 3-loop analytic couplings and their effective powers, in both the space-like (Euclidean) and time-like (Minkowskian) regions, accurate enough in the large range (1--100 GeV) of current physical interest.\par Effectiveness of the new Model is illustrated by the example of $\Upsilon(1\mathrm{S})$ decay where the standard analysis gives $\alpha_s(M_{\Upsilon})=0.170\pm 0.004$ value that is inconsistent with the bulk of data for $\alpha_s$. Instead, we obtain $\alpha_s^{Mod}(M_{\Upsilon})=0.185\pm 0.005$ that corresponds to $\alpha_s^{Mod}(M_Z)=0.120\pm 0.002$ that is close to the world average.\par The issue of scale uncertainty for $\Upsilon$ decay is also discussed.Comment: 12 pages, 0 figures. Model slightly modified to increase its accuracy. Numerical results upgraded, references added. The issue of scale uncertainty is discusse

Determination of the Strong Coupling \boldmath{\as} from hadronic Event Shapes and NNLO QCD predictions using JADE Data

Event Shape Data from $e^+e^-$ annihilation into hadrons collected by the JADE experiment at centre-of-mass energies between 14 GeV and 44 GeV are used to determine the strong coupling $\alpha_S$. QCD predictions complete to next-to-next-to-leading order (NNLO), alternatively combined with resummed next-to-leading-log-approximation (NNLO+NLLA) calculations, are used. The combined value from six different event shape observables at the six JADE centre-of-mass energies using the NNLO calculations is $\alpha_S(M_Z)$= 0.1210 +/- 0.0007(stat.) +/- 0.0021(expt.) +/- 0.0044(had.) +/- 0.0036(theo.) and with the NNLO+NLLA calculations the combined value is $\alpha_S$= 0.1172 +/- 0.0006(stat.) +/- 0.0020(expt.) +/- 0.0035(had.) +/- 0.0030(theo.) . The stability of the NNLO and NNLO+NLLA results with respect to missing higher order contributions, studied by variations of the renormalisation scale, is improved compared to previous results obtained with NLO+NLLA or with NLO predictions only. The observed energy dependence of $\alpha_S$ agrees with the QCD prediction of asymptotic freedom and excludes absence of running with 99% confidence level.Comment: 9 pages, EPHJA style, 4 figures, corresponds to published version with JADE author lis

Resummation of heavy jet mass and comparison to LEP data

The heavy jet mass distribution in e+e- collisions is computed to next-to-next-to-next-to leading logarithmic (NNNLL) and next-to-next-to leading fixed order accuracy (NNLO). The singular terms predicted from the resummed distribution are confirmed by the fixed order distributions allowing a precise extraction of the unknown soft function coefficients. A number of quantitative and qualitative comparisons of heavy jet mass and the related thrust distribution are made. From fitting to ALEPH data, a value of alpha_s is extracted, alpha_s(m_Z)=0.1220 +/- 0.0031, which is larger than, but not in conflict with, the corresponding value for thrust. A weighted average of the two produces alpha_s(m_Z) = 0.1193 +/- 0.0027, consistent with the world average. A study of the non-perturbative corrections shows that the flat direction observed for thrust between alpha_s and a simple non-perturbative shape parameter is not lifted in combining with heavy jet mass. The Monte Carlo treatment of hadronization gives qualitatively different results for thrust and heavy jet mass, and we conclude that it cannot be trusted to add power corrections to the event shape distributions at this accuracy. Whether a more sophisticated effective field theory approach to power corrections can reconcile the thrust and heavy jet mass distributions remains an open question.Comment: 33 pages, 14 figures. v2 added effect of lower numerical cutoff with improved extraction of the soft function constants; power correction discussion clarified. v3 small typos correcte

Renormalization scale uncertainty in tne DIS 2+1 jet cross-section

The deep inelastic scattering 2+1 jet cross- section is a useful observable for precision tests of QCD, e.g. measuring the strong coupling constant alpha(s). A consistent analysis requires a good understanding of the theoretical uncertainties and one of the most fundamental ones in QCD is due to the renormalization scheme and scale ambiguity. Different methods, which have been proposed to resolve the scale ambiguity, are applied to the 2+1 jet cross-section and the uncertainty is estimated. It is shown that the uncertainty can be made smaller by choosing the jet definition in a suitable way.Comment: 24 pages, uuencoded compressed tar file, DESY 94-082, TSL-ISV-94-009

Standard Model Physics at LEP

Selected topics on precision tests of the Standard Model of the Electroweak and the Strong Interaction at the LEP $e^+e^-$ collider are presented, including an update of the world summary of measurements of $\alpha_s$, representing the state of knowledge of summer 1999. This write-up of lecture notes consists of a reproduction of slides, pictures and tables, supplemented by a short descriptive text and a list of relevant references.Comment: lecture given at Intern. Summer School at Nijmegen, August 1999, 44 pages, 36 (mostly coloured) figures, LaTeX, needs crckapb.st

A Precision Calculation of the Next-to-Leading Order Energy-Energy Correlation Function

The O(alpha_s^2) contribution to the Energy-Energy Correlation function (EEC) of e+e- -> hadrons is calculated to high precision and the results are shown to be larger than previously reported. The consistency with the leading logarithm approximation and the accurate cancellation of infrared singularities exhibited by the new calculation suggest that it is reliable. We offer evidence that the source of the disagreement with previous results lies in the regulation of double singularities.Comment: 6 pages, uuencoded LaTeX and one eps figure appended Complete paper as PostScript file (125 kB) available at: http://www.phys.washington.edu/~clay/eecpaper1/paper.htm