Determination Of Αs Research Articles

A TEST OF OPTIMIZED PERTURBATIVE QCD TO ${\mathcal O}(\alpha _s^2)$ AND ${\mathcal O}(\alpha_s^3)$ FROM Z0 AND τ DECAYS, AND A METHOD TO DEAL WITH THE RENORMALIZATION SCALE AMBIGUITY

A QCD analysis of the published LEP data on 11 observables measured in the Z0 and τ decays is performed in order to probe the renormalization scale optimization of perturbative QCD to [Formula: see text] and [Formula: see text]. The explicit dependence of the fundamental QCD parameter [Formula: see text] on the renormalization scale μ2 is extracted from the data. The theoretical predictions for the optimized scale are calculated using various QCD-inspired procedures, and are compared to the experimental results. An experimental procedure is presented to deal with the renormalization scale ambiguity in the determination of αs. Applying this procedure to 11 observables, we obtain αs(Mz0)=0.114±0.004 as our final result.

The determination of αs (MZ) from the Z0 lineshape and asymmetry data

The derivation of αs (MZ) from lineshape and asymmetry data around the Z0 peak or from the ratio Rl = Γh/Γl, as reported by the LEP Collaborations, is discussed with particular emphasis on the most recent developments in the field of radiative corrections and on a proper treatment of the experimental systematic errors in the error matrix approach. The correlation with the top quark mass is also analysed.

Determination of αS from the scaling violation in the fragmentation functions in e+e− annihilation

A determination of the hadronic fragmentation functions of the Z 0 boson is presented from a study of the inclusive hadron production with the DELPHI detector at LEP. These fragmentation functions were compared with the ones at lower energies, thus covering data in a large kinematic range: 196 ⩽ Q 2 ⩽ 8312 GeV 2 and x (= P h E beam ) > 0.08 . A large scaling violation was observed, which was used to extract the strong coupling constant in second order QCD: α s ( M Z ) = 0.118 ± 0.005. The corresponding QCD scale for five quark flavours is: Λ (5) MS = 230 ± 60 MeV .

Determination of αS for b quarks at the Z0 resonance

The strong coupling constant for b quarks has been determined, and its flavour independence, as predicted by QCD, investigated. The analysis involved events with lepton candidates selected from approximately 356 000 hadronic decays of the Z 0, collected by the DELPHI detector at LEP in 1990 and 1991. A method based on a direct comparison of the three-jet fraction in a b enriched sample, selected by requiring leptons with large momenta, to that of the entire hadronic sample, illustrated the significant effect of the b quark mass on the multi-jet cross section, and verified the flavour independence of the strong coupling constant to an accuracy of ±6%. A second procedure based on a fit to the momentum and transverse momentum spectra of the lepton candidates in both two-jet and three (or more)-jet event samples simultaneously determined the b content in each, and, using second order QCD calculations, gave an absolute measurement of α s for b quarks of 0.118±0.004 (stat.)±0.003 (syst.)±0.008 (scale). A comparison with α s for all quark flavours, as measured from the three-jet fraction in all hadronic events, further allowed the coupling strength for b quarks to be expressed in terms relative to that for udsc quarks, thereby cancelling certain common systematic uncertainties, and yielded α s b α s udsc = 1.00 ± 0.04 ( stat.) ± 0.03 ( syst.) .

Determination of αs from hadronic event shapes measured on the Z 0 resonance

We present a study of the global event shape variables thrust and heavy jet mass, of energy-energy correlations and of jet multiplicities based on 250 000 hadronic Z 0 decays. The data are compared to new QCD calculations including resummation of leading and next-to-leading logarithms to all orders. We determine the strong coupling constant α s (91.2 GeV) = 0.125±0.003 (exp) ± 0.008 (theor). The first error is the experimental uncertainty. The second error is due to hadronization uncertainties and approximations in the calculations of the higher order corrections.

Determination of αs from jet production rates and energy-energy correlations on the Z 0 resonance

This presentation uses data obtained from the DELPHI experiment at LEP. The strong coupling constant α s is determined in two different analyses of the Z° decay into multi-hadronic final states. The first uses the jet production rates and the second the asymmetry of energy-energy correlations. Both methods compare experimental data with second order of perturbative QCD predictions. The results are α s(M z)=0.114±0.003±0.004±0.012 using the jet rates method and α s(M z)=0.106±0.003±0.003+0.003 from the energy-energy correlations method.

Determination of αs from energy-energy correlations measured on the Z 0 resonance

We present a study of energy-energy correlations based on 83 000 hadronic Z 0 decays. From this data we determine the strong coupling constant α s to second order QCD: α s(91.2 GeV)=0.121±0.004(exp.)±0.002(hadr.) −0.006 +0.009(scale)±0.006(theor.) from the energy-energy correlation and α s(91.2 GeV)=0.115±0.004(exp.) −0.004 +0.007(hadr.) −0.000 +0.002(scale) −0.005 +0.003 (theor.) from its asymmetry using a renormalization scale μ 1=0.1 s. The first error (exp.) is the systematic experimental uncertainly, the statistical error is negligible. The other errors are due to hadronization (hadr.), renormalization scale (scale) uncertainties, and differences between the calculated second order corrections (theor.).

A measurement of energy correlations and a determination of αs( M2Z 0) e +e - annihilations at √ s=91 GeV

From an analysis of multi-hadron events from Z 0 decays, values of the strong coupling constant α s( M 2 Z 0)=0.131±0.006 (exp)±0.002(theor.) and α s( M z 0 2) = −0.009 +0.007(exp.) −0.002 +0.006(theor.) are derived from the energy-energy correlation distribution and its asymmetry, respectively, assuming the QCD renormalization scale μ= M Z 0 . The theoretical error accounts for differences between O( α 2 s) calculations. A two parameter fit Λ MS and the renormalization scale μ leads to Λ MS =216±85 MeV and μ 2 s =0.027±0.013 or to α s( M 2 Z 0 )=0.117 +0.006 −0.008(exp.) for the energy-energy correlation distribution. The energy-energy correlation asymmetry distribution is insensitive to a scale change: thus the α s value quoted above for this variable includes the theoretical uncertainty associated with the renormalization scale.

Better Determination of αs by Measuring Cross Section Differences in Hadronic Collisions

Three methods are proposed for the determination of αs by measuring some special cross section differences in hadronic collisions. In these methods the calculated ratios αs/α depend on neither gluon and sea quark distribution functions nor any other parton fragmentation functions. So using experimental data one can determine αs more precisely in comparison with other methods of hadronic collisions.

Jet model with exclusive parton hadron duality

We discuss a model for hadron jets in hard collisions, in which the observed hadrons originate at the end of a purely hadronic cascade. We assume that this hadronic cascade evolves according to the same laws approximately as a parton cascade in QCD. We obtain a simple relation between hadron and parton final states at an almost exclusive level, which allows in many cases to replace partons by hadrons. As application we discuss jet multiplicities at variable resolution, in particular scaling laws, αs determination and production of axial vector mesons (A1B, ...).

Determination of αs from a measurement of the direct photon spectrum in Γ(1S) decays

Using the ARGUS detector at the DORIS II e +e − storage ring we have measured direct photons from the decay ???(1 S)→ γgg. The ratio R γ = Γ(???(1S)→ γgg)/ Γ(???(1S)→ ggg)=(3.00±0.13±0.18)% has been determined, from which we deduce values of the strong coupling constant α s=0.225±0.011±0.019 and the QCD scale parameter Λ MS =115±17±28 MeV defined in the modified minimal-subtraction scheme. The shape of the measured spectrum clearly rules out the predictions of the lowest order QCD calculations.

Topological properties of the colour field in hard processes

Topological properties of the confining force field which is stretched between the outgoing quarks and gluons in hard processes are important for the distribution of final state hadrons. Different colour factors in the amplitudes obtained in perturbative QCD can be associated with different field configurations, and we discuss in detail some examples. It turns out that the amplitudes for different configurations are not always orthogonal. However it is possible that topological properties of QCD, not exhibited in perturbation theory, play a fundamental role and have to be included in order to completely specify a quantum mechanical state, in which case the interference terms would vanish. This question is important e.g. for the determination of αs and Λ from Υ decay.