Multi-hadronic events produced in e+e- collisions provide an excellent
laboratory to study QCD, the theory of strong interactions, and in particular
to determine the strong coupling parameter alpha_s and demonstrate its
predicted behavior as a function of the energy scale. Determinations of alpha_s
at LEP will be reviewed with emphasis on event shape variables and jet rates in
3-jet and 4-jet events.Comment: Proceedings of DIS06, XIV International Workshop on Deep Inelastic
  Scattering, Tsukuba, Japan, 20-24 April 2006, 4 pages, 2 figure

Wengler, T.

English

arXiv

Multi-hadronic events produced in e+e- collisions provide an excellent laboratory to study QCD, the theory of strong interactions, and in particular to determine the strong coupling parameter alpha_s and demonstrate its predicted behavior as a function of the energy scale. Determinations of alpha_s at LEP will be reviewed with emphasis on event shape variables and jet rates in 3-jet and 4-jet events.Multi-hadronic events produced in e+e- collisions provide an excellent laboratory to study QCD, the theory of strong interactions, and in particular to determine the strong coupling parameter alpha_s and demonstrate its predicted behavior as a function of the energy scale. Determinations of alpha_s at LEP will be reviewed with emphasis on event shape variables and jet rates in 3-jet and 4-jet events.Multi-hadronic events produced in e+e- collisions provide an excellent laboratory to study QCD, the theory of strong interactions, and in particular to determine the strong coupling parameter alpha_s and demonstrate its predicted behavior as a function of the energy scale. Determinations of alpha_s at LEP will be reviewed with emphasis on event shape variables and jet rates in 3-jet and 4-jet events

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arXiv:hep-ex/0607030 v1   18 Jul 2006July 19, 2006 0:51 Proceedings Trim Size: 9in x 6in hfs-wenglerDETERMINATION OF THE STRONG COUPLINGCONSTANT AT LEP∗T. WENGLERUniversity of ManchesterSchool of Physics and AstronomyManchester, M13 9PL, U.K.E-mail: Thorsten.Wengler@manchester.ac.ukMAN/HEP/2006/22Multi-hadronic events produced in e+e− collisions provide an excellent laboratoryto study QCD, the theory of strong interactions, and in particular to determine thestrong coupling parameter αs and demonstrate its predicted behavior as a functionof the energy scale. Determinations of αs at LEP will be reviewed with emphasison event shape variables and jet rates in 3-jet and 4-jet events.1. αs from 3-jet observablesThe grouping of particles into a number of collimated jets is one of the moststriking features of hadronic final states produced in e+e− collisions, and iseasily reconcilable with the model of energetic and hence boosted partonsundergoing parton branchings and hadronisation processes as prescribedby QCD. To quantify this structure two types of observables are commonlyused: event shapes and jet rates.To calculate jet rates clustering algorithms are used to group the par-ticles of the hadronic final state into a number of jets, based on a resolu-tion criterion which determines when the clustering should stop. The rateof events with a given number of jets is directly related to the couplingstrengths involved. Event shapes on the other hand are constructed by cal-culating a single number for each event which classifies its topology. Theleft picture of Fig. 1 shows the Thrust, T , as an example for an event shapeobservable. The Thrust of an event is defined as the normalised sum ofabsolute momentum components of all observed particles projected alongthe axis that maximizes this sum. A well aligned, or ”pencil-like”, 2-jet∗published in proceedings of dis06, tsukuba, japan, 20-24 april 2006.1July 19, 2006 0:51 Proceedings Trim Size: 9in x 6in hfs-wengler210-11100.5 0.6 0.7 0.8 0.9 1JETSET PSHERWIGARIADNEJETSET MEL3 (188.6 GeV)T1 ds____s dT0.10.120.140.160.180.20 25 50 75 100 125 150 175 200Ö s [GeV]a SLEPJADEa S(MZ)=0.1210– 0.0022Figure 1. The left picture shows an example of an event shape distribution - the Thrust,T, as measured by L31. The picture2 on the right summarises the combined values ofαs based on the analysis of 3-jet observables by the LEP collaborations or using JADEdata.event with few branchings will result in a value of T close to unity, while amore spherical event with many branchings will tend to have smaller valuesof T .The experimental procedure to determine the value of αs starts withselecting multi-hadronic events, while rejecting events with initial state ra-diation and WW and ZZ events. The measured distributions are thencorrected for detector effects, background and efficiency, and theoreticalpredictions are fitted to determine αs. The best available theoretical pre-dictions involve calculations in next-to-leading order (NLO) perturbativeQCD matched to next-to-leading-log (NLLA) resummed calculations.The LEP experiments2 have chosen six event shapes for whichNLO+NLLA calculations are available in addition to jet rates to produce acombined value of αs: (1− T ), the heavy jet mass MH , the jet-broadeningobservables BT and BW , the C-parameter, and the value of the resolutionparameter of the Durham jet algorithm that marks the transition of a 2-jet event into a 3-jet event, y23. The value of αs determined at four LEPcentre-of-mass energies (CME) is shown in the right picture of Fig. 1.The yellow band in the right picture of Fig. 1 represents the value ofαs as determined from an NNLO analysis of inclusive observables, like theproperties of the Z line shape or the ratio of the longitudinal and totalcross section. There is an excellent agreement between these two methods,and also with values determined from JADE data at lower energies. TheJuly 19, 2006 0:51 Proceedings Trim Size: 9in x 6in hfs-wengler3a S(MZ)=0.1182±0.0027OPAL Durham 4-Jet Rate√s [ GeV ]aS0.080.090.10.110.120.1380 100 120 140 160 180 2000.10.150.20.250.30.350.410 10 2Ö s [GeV]a SNNLO incl.LEP 3-jet shapeJADE 3-jet shapeR4(D), R4(C)LEP fragm.a S(MZ)=0.1210– 0.0022Figure 2. The picture on the left shows the values of αs obtained by OPAL5 from fits tothe 4-jet rate in four intervals of the centre-of-mass energy (√s) at LEP2 . The picture2on the right is a summary of αs values determined at different values of√s. The yellowband represents the value of αs determined from inclusive variables at NNLO.overall combined value from event shapes and 3-jet rates at LEP quotedat the Z mass is αs(mZ) = 0.1201± 0.0053, where the systematic error isdominated by the theoretical uncertainty.2. αs from 4-jet observablesRecently measurements have emerged from three of the four LEP experi-ments using the 4-jet rate to determine αs. The 4-jet rate is a promisingobservable, as its sensitivity to the value of αs is double that of a 3-jetobservable. On the other hand this means an additional order of αs isneeded in theoretical calculations to reach NLO for this process, that isO(αs3). Such calculations are now available and have been matched withexisting NLLA calculations to produce the theoretical predictions neededto perform the fits to the data.ALEPH3 has fitted O(αs3)+NLLA calculations corrected for hadro-nisation and detector effects to data at the Z peak, yielding a value ofαs(mZ) = 0.1170 ± 0.0022. The uncertainty is dominated by theory.DELPHI4 has fitted an O(αs3) calculation corrected for hadronisation todata at the Z peak corrected for detector effects. Here no matching toan NLLA calculation is attempted, but the renormalisation scale, xµ, isoptimised experimentally to reduce the influence of the theoretical uncer-tainty. DELPHI determines αs(mZ) = 0.1175±0.003, with the uncertaintydominated by the hadronisation model, and not the variation of the renor-July 19, 2006 0:51 Proceedings Trim Size: 9in x 6in hfs-wengler4malisation scale, commonly used to assess the theoretical uncertainty. Itshould be mentioned that an increased variation of xµ here leads to a drasticincrease of the theoretical uncertainty. OPAL5 fits O(αs3)+NLLA calcu-lations corrected for hadronisation effects to data corrected for detectoreffects from 91 GeV to 209 GeV CME. Values of αs are presented at fourCME points in the left picture of Fig. 2. Also shown is the central value anduncertainty at the Z mass resulting from a combination of the four CMEpoints: αs(mZ) = 0.1182± 0.0026, where the uncertainty is dominated bytheory.A combination of all three results based on 4-jet rates as beenundertaken2 and yields a value of αs(mZ) = 0.1175± 0.0029.3. SummaryThe value of the strong coupling αs has been determined at LEP based ontheoretically and experimentally well behaved observables of event shapesand jet rates. αs determinations from 3-jet observables yield reliable andprecise results based on NLO+NLLA calculations. The uncertainty is usu-ally dominated by theory, and it is hoped that theoretical developmentswill allow a reduction of the uncertainty from now 5% to 2% in the near fu-ture. The first determinations of αs from 4-jet rates based on NLO+NLLAcalculations are available and reach a precision comparable to the mostprecise determinations today. Due to the small number of measurementsavailable so far the cross-checking of results is however not yet as rigorousas achieved for the 3-jet observables. A summary of αs determinations isshown in the right picture of Fig. 2.A very consistent picture has developed across the various methods ofdetermining αs in e+e− collisions. The wide spread of measurements inCME and the small uncertainties achieved for the individual values allowa clear demonstration of the asymptotic freedom of QCD.References1. L3 Collaboration, P. Achard et al., Phys. Rept. 399 71 (2004).2. S. Kluth, Rept. Prog. Phys. 69 1771 (2006), and references therein.3. ALEPH Collaboration, A. Heister et al., Eur. Phys. J. C27 1 (2003).4. DELPHI Collaboration, J. Abdallah et al., Eur. Phys. J. C38 413 (2005).5. OPAL Collaboration, G. Abbiendi et al., CERN-PH-EP-2005-057, Submittedto Eur. Phys. J. C.

Determination of the strong coupling constant at LEP

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