On the Value of R=Gamma_hGamma_l at LEP

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1、OnthevalueofR=Γh/ΓlatLEPMaurizioConsoli1)andFernandoFerroni2)AbstractWeshowthatthepresentexperimentalLEPaverageR=Γh/Γl=20.795±0.040isnotunambiguousduetothepresenceofsubstantialsystematiceffectswhichcannotbeinterpretedwithingaussianstatistics.WefindbyMontecarlosimulationthattheC.L.oftheoriginalLEPs

2、ampleisonly3.8·10−4.WesuggestthatareliableextimateofthetrueR-valueis20.60

3、rminationofthestrongcouplingconstantattheZ-massscaleαs(Mz)isofpri-maryimportanceforaconsistencycheckofperturbativeQCD.Inthiscontext,thequantityR,definedastheratiobetweenthehadronicandtheleptonicpartialwidthsoftheZboson,playsafundamentalrole.Indeed,thisparticularobservable,operativelydefinedthrought

4、heratioofthepeakcross-sectionsinthecorrespondinghadronicandleptonicchannels,candetermineαs(Mz)toaveryhighdegreeofaccuracythusallowingadirectcomparisonwiththeperturbativeevo-lutionofαsfrompreciselow-energydataforDeepInelasticScattering(DIS).Thetheoreticalpredictionatone-loopintheelectroweaktheorya

5、ndincludingO(α3)sperturbativeQCDcorrections,canbeconvenientlyexpressedbyusingtheresultoftherecentanalysisbyHebbeker,Martinez,PassarinoandQuast[1]asTh(o)R=R(1+δQCD)(1)whereR(o)isthepurelyelectroweakvalueinthequark-partonmodelandδisconvenientlyQCDexpressedas[1]αsαs2αs3δQCD=1.06+0.9()−15()(2)πππByus

6、ingtheexperimentalLEPaveragepresentedattheGlasgowConference[2]LEPR=20.795±0.040(3)onededucesthevalue[2]αs(Mz)=0.126±0.006(4)or,byincludingalllineshapedata,[3]LEPαs(Mz)=0.127±0.005(5)Eqs.(4,5)shouldbecomparedwiththeprediction[4]fromDIS(includingafairextimateofthetheoreticalerror)DISαs(Mz)=0.113±0.

7、005(6)AspointedoutbyShifman[5],thediscrepancybetweenEqs.(4,5)andEq.(6)isdisturb-ing,implyingaratherlargedifferenceinthevaluesoftheQCDscaleparameter(intheMSschemeandwithfiveflavours),namelyΛQCD∼500MeVratherthanthevalueΛQC