Typability in partial groupoids

Adapting a claim of M. Kracht, we establish a characterization of the typable partial applicative algebras.Comment: 5 page

QCD in e+e- collisions at 2 TeV

We discuss some topics in QCD studies at 2 TeV. Particular emphasis is given to the separation of pure QCD events from the WW and the t-tbar backgroundsComment: 10 pages, Latex, epsfig, 7 figures To appear in the Proceedings of the 1995 "Workshop on Physics with e+e- Linear Colliders", Annecy-Gran Sasso-DES

Tests of Power Corrections to Event Shape Distributions from e+e- Annihilation

A study of differential event shape distributions using e+e- data at centre-of-mass energies of 35 to 183 GeV is presented. We investigated non-perturbative power corrections for the thrust, C-parameter, total and wide jet broadening observables. We observe a good description of the distributions by the combined resummed QCD calculations plus power corrections from the dispersive approach. The single non-perturbative parameter \alpha_0 is measured to be \alpha_0 (2 GeV) = 0.502 +- 0.013 (stat.) ^{+0.046)_{-0.032} (exp. syst.) ^{+0.074}_{-0.053} (theo. syst.) and is found to be universal for the observables studied within the given systematic uncertainties. Using revised calculations of the power corrections for the jet broadening variables, improved consistency of the individual fit results is obtained. Agreement is also found with results extracted from the mean values of event shape distributions.Comment: 19 pages, LaTeX2e, 8 .eps-files included, paper contributed to the EPS-HEP99 conference in Tampere, Finlan

Tests of Power Corrections for Event Shapes in e+e- Annihilation

A study of perturbative QCD calculations combined with power corrections to model hadronisation effects is presented. The QCD predictions are fitted to differential distributions and mean values of event shape observables measured in e+e- annihilation at centre-of-mass energies from 14 to 189 GeV. We investigate the event shape observables thrust, heavy jet mass, C-parameter, total and wide jet broadening and differential 2-jet rate and observe a good description of the data by the QCD predictions. The strong coupling constant alpha_S(M_Z) and the free parameter of the power correction calculations alpha_0(2 GeV) are measured to be alpha_S(M_Z) = 0.1171 +/- 0.0032/0.0020 and alpha_0(2 GeV) = 0.513 +/- 0.066/0.045. The predicted universality of alpha_0 is confirmed within the uncertainties of the measurements.Comment: 28 pages, LaTeX2e, 21 .eps-files included, accepted by Eur. Phys. J.

Convergence properties of simple genetic algorithms

The essential parameters determining the behaviour of genetic algorithms were investigated. Computer runs were made while systematically varying the parameter values. Results based on the progress curves obtained from these runs are presented along with results based on the variability of the population as the run progresses

C-Parameter and Jet Broadening at PETRA Energies

e^+e^- annihilation data recorded by the JADE detector at PETRA were used to measure the C-parameter for the first time at \sqrt{s}= 35 and 44 GeV. The distributions were compared to a resummed QCD calculation. In addition, we applied extended resummed calculations to the total and wide jet broadening variables, B_T and B_W. We combined the results on \alpha_s with those of our previous study of differential 2-jet rate, thrust, and heavy jet mass, obtaining \alpha_s(35 GeV) = 0.1448 +0.0117 -0.0070 and \alpha_s(44 GeV) = 0.1392 +0.0105 -0.0074. Moreover power corrections to the mean values of the observables mentioned above were investigated considering the Milan factor and the improved prediction for the jet broadening observables. Our study, which considered e^+e^- data of five event shape observables between \sqrt{s}= 14 and 183 GeV, yielded \alpha_s(M_{Z^0})=0.1177 +0.0035 -0.0034.Comment: 14 pages, LaTeX2e, 9 .eps-files included, abbreviated version of the paper contributed to the ICHEP'98 conference in Vancouver, submitted to Phys. Lett.

A Study of Event Shapes and Determinations of alpha_s using data of e^+e^- Annihilations at sqrt{s} = 22 to 44 GeV

Data recorded by the JADE experiment at the PETRA e^+e^- collider were used to measure the event shape observables thrust, heavy jet mass, wide and total jet broadening and the differential 2-jet rate in the Durham scheme. For the latter three observables, no experimental results have previously been presented at these energies. The distributions were compared with resummed QCD calulations (O(alpha_s^2)+NLLA), and the strong coupling constant alpha_s(Q) was determined at different energy scales Q=sqrt{s}. The results, \alpha_s(22 GeV) = 0.161 ^{+0.016}_{-0.011}, \alpha_s(35 GeV) = 0.143 ^{+0.011}_{-0.007}, \alpha_s(44 GeV) = 0.137 ^{+0.010}_{-0.007}, are in agreement with previous combined results of PETRA albeit with smaller uncertainties. Together with corresponding data from LEP, the energy dependence of alpha_s is significantly tested and is found to be in good agreement with the QCD expectation. Similarly, mean values of the observables were compared to analytic QCD predictions where hadronisation effects are absorbed in calculable power corrections.Comment: 36 pages, LaTeX2e, 34 .eps-files included, submitted to Z. Phys. C, revised version, with comments of referee included and some typos corrected, accepted for publicatio