Experimental Studies of Power Corrections

S.KLUTH

Max-Planck-Institutf¨urPhysik,F¨ohringerRing6,D-80805M¨unchen,Germany,

skluth@mppmu.mpg.de

WepresentrecentresultsfromexperimentalstudiesofpowercorrectionsinthemodelofDokshitzer,MarchesiniandWebberusingdatafromtheprocesse+e−centre-of-massenergies.FittedO(α2s)+NLLAQCDpredictionscombined→withhadronspoweratseveralcorrec-tionstomodelhadronisationeffectssuccessfullydescribedifferentialdistributionsandmeanvaluesofeventshapeobservables.Thefitresultsforthestrongcouplingconstantandthefreeparameterofthepowercorrectioncalculationsfromthevariousobservablesareconsis-tentwitheachotherwithintheuncertainties.ThesamefitsarefurtheremployedtostudythegaugestructureofQCDbyadditionallyvaryingtheQCDcolourfactorsinthefits.TheresultsareconsistentwithQCDbasedontheSU(3)symmetrygroup.AnewmeasurementofthetransversecrosssectionisshownusingreanalyseddataoftheformerJADEexperimentatDESYanditsimplicationsforpowercorrectionarediscussed.

1TestsofPowerCorrections

Intheprocessofhadronproductionine+e−annihilationconfinementeffects,alsoreferredtoashadronisation,playanimportantrˆole.Theseeffectsstemmingfromthetransitionbetweenthepartonsproducedinthee+e−annihilationandthehadronsobservedinthedetectorarenotdirectlyaccessiblebyperturbativeQCDcalculations.SeveralQCDbasedhadronisationmodelsimplementedinMonteCarlosimulationprogramsexistandgenerallydescribethedatawell1,2,3.

Recentlynewanalyticmodelsofhadronisationhavebeendeveloped.Inthesethestructureofnon-perturbativecontributionssurpressedbypowersofthehardscale(powercorrections)isdeducedfromambiguitiesintheperturbativeresult4,5.InthemodelofDokshitzer,March-esiniandWebber(DMW)theeffectsofgluonradiationwithtransversemomentaO(Λ

breaksdowna.

Thisleadstotheintroductionofafreeparameterα0=1/µI󰀁µI

0αS(k)dkwhichmustbedeterminedfromthedata.

ThemainpredictionoftheDMWmodelisthatdistributionsoftheeventshapeobservables

1−T,MHorMH2,BT,BWandCaredescribedbytheperturbativeQCDpredictionRPTshiftedbyanamountproportionaltoα0/QwhereQ=

√

s=14to189GeV8.Thesolid

linesrepresentthefitresultwhilethedottedlinesindicateanextrapolationofthefit.ThefiguresontherightshowresultsforαS(MZ0)andα0(2GeV)offitstodistributions(top)andmeanvalues(bottom)asonestandard

deviationerrorellipses8.

2ColourFactors

Thesamefitsasdescribedinsection1aregeneralisedtostudythegaugestructureofQCDbyvaryingtheQCDcolourfactorsCA=3,CF=4/3orTF=1/2(orequivalentlythenumberofactivequarkflavoursnf=5)withtheSU(3)symmetrygroup9.ThesefitsavoidapotentialbiasoftraditionalanalysesoftheQCDgaugestructureusingangularcorrelationsin4-jetfinalstateswherehadronisationeffectsarecorrectedwithMonteCarlomodelsbasedonstandardQCD.Figure2(left)showstheresultsoffitswithαS(MZ0),α0(2GeV)andoneofthecolourfactorsasfreeparameters.GoodagreementwiththeexpectationsfromstandardQCDisobserved.Alternativefitswhereα0(2GeV)isfixedatavaluedeterminedfrompreviousmeasurementsyieldconsistentresults.Figure2(right)presentsthecombinedresultsforCAandCFfromsimultaneousfitsofαS(MZ0),CAandCFto1−TandC.TheresultsofthesimultaneousfitsarealsoconsistentwithstandardQCDwhilesomeotherpossibilitiesforthegaugesymmetrygroupofQCDareexcluded.AssumingSU(3)tobethecorrectgaugesymmetryofQCDtheseresultscanbeinterpretedasasuccessfulconsistencycheckoftheDMWmodel.

1-T2.5SU(5)CQCD fitBT2SU(3) QCD prediction0.10.1250.40.60510SU(4)αS(MZ)

α0nf1-T1.5CCF

BT10.10.1250.40.6234αS(MZ)

α0CASU(2)1-T0.5U(1)368% C.L.CBT95% C.L.BW

SU(1)0.050.100.512400123456αS(MZ)α0CFCA

Figure2:ThefigureontheleftshowsfitresultsforαS(MZ0),α0(2GeV)andoneofthecolourfactorsnf,CAorCF9.TheverticaldottedlinesindicatetheexpectationfromstandardQCDforthecolourfactor.ThefigureontherightpresentscombinedresultsforCAandCFfromfitsofαS(MZ0),CAandCF9.Thesquareandtriangle

symbolsindicateexpecationsforCAandCFfordifferentsymmetrygroups.

3TransverseCrossSection

AnewmeasurementoflongitudinalcrosssectionσLat

√

αS(MZ0)andα0(2GeV)withlargeerrors.Thepresentlyavailablemeasurementsdonotallowquantitativestudiesofthepowercorrection.

1/σtotdσ/ d(q·cosθ)σL/σtot 0.400.350.300.250.200.150.100.050-13/4 (σL /σtot) sinθch2 JADE - Data 36.6 GeV0.140.120.10.08

JADEOPALDELPHIJETSET hadronsJETSET partons2QCD O(αS)ch3/8 (σT /σtot)(1+cosθ )<>ch20.060.040.02

-0.8-0.6-0.4-0.200.20.40.60.8q·cosθ

10

203040506080100200Ecm /GeV

Figure3:Thefigureontheleftshowsthedistributionofanglesq·cosΘbetweenchargedhadronsandthe

chch

incominge−10.Superimposedarethefitresult(solidline)anditstwocomponentsproportionaltoσTandσL(dashedlines).ThefigureontherightshowstheresultforσLcomparedwithothermeasurementsandpredictions

fromtheJETSETMonteCarlosimulationandfromperturbativeQCD10.

4Summary

WehaveshownexperimentaltestsofpowercorrectionsinthemodelofDokshitzer,MarchesiniandWebberusingdatafrome+e−annihilationexperiments.TheDMWmodeltogetherwithperturbativeQCDdescribeswelldistributionsandmeanvaluesofselectedeventshapeobserv-ables.Theresultsforα0fromtheindividualobservablesaregenerallyconsistentwithinthetotaluncertainties.AmeasurementoftheQCDcolourfactorsusingthesameQCDpredictionscombinedwithpowercorrectionsgaveresultsconsistentwithQCDbasedonSU(3).AnewmeasurementofthelongitudinalcrosssectionσL(36.6GeV)waspresentedandcomparedwithaQCDpredictionincludingpowercorrections.1.2.3.4.5.6.7.8.9.10.11.12.

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