2.0 ρ K * φ N Λ Σ Ξ ∆ Σ ∗ Ξ ∗ Ω vector meson octet baryon decuplet baryon

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QCDTableofContents09.04.2013–18.07.2013 Lecturehomepageishttp://www.physik.uni-bielefeld.de/~yorks/qcd13 1.Introduction...2 1.1QCDAppetizer...2 1.2Realitychecks...5 1.3ColorchargeinQCD...7 1.4Elementsofgaugetheory...9 1.5Notationandconventions...11 2.Basics...12 2.1Reminder:QEDandgaugeinvariance...12 2.2Generalization:Yang-MillsLagrangian...15 2.3QCDanditssymmetries...18 2.4Quantization,pathintegral(remarksonly)...21 2.5QCDFeynmanrules...24 3.Fundamentals...29 3.1One-loopdivergencesinQCD...30 3.2More1-loopdivergencesinQCD...34 3.3One-loopcountertermsinQCD...37 3.4QCDβfct,runningcoupling...40 4.QCDine+e−-annihilation...43 4.1e+e−→hadronsatleadingorder...43 4.2TheZ-peakinR(s)...46 4.3QCDcorrectionstoR(s)...48 4.3.1Realcorrections:σe+e−→q¯qg...48 4.3.2Virtualcorrections:σe+e−→q¯qatO(αs)...52 4.3.3Results...55 4.3.4Higher-ordercorrectionstoR(s)...57 5.Deepinelasticscattering(DIS)...59 5.1Structurefunctions...59 5.2Partondistributionfunctions...62 5.3QCDcorrectionsinDIS...64 5.3.1DISatNLO:eq→eqg...65 5.3.2DISatNLO:1-loopeq→eq...67 5.3.3Factorization,evolution...68 5.3.4DISatNLO:eg→q¯q...71 6.“Anomalies”...72 6.1Vectorcurrentconservation...73 6.2Axialcurrentnon-conservation...75 7.Outlook...78

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0.0 0.5

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2.0 ρ K * φ N Λ Σ Ξ ∆ Σ ∗ Ξ ∗ Ω vector meson octet baryon decuplet baryon

mass [GeV]

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641.Plotsofcrosssectionsandrelatedquantities σandRine+e−Collisions 10

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√ s [G eV ]

Figure41.6:Worlddataonthetotalcrosssectionofe+e−→hadronsandtheratioR(s)=σ(e+e−→hadrons,s)/σ(e+e−→µ+µ−,s). σ(e+e−→hadrons,s)istheexperimentalcrosssectioncorrectedforinitialstateradiationandelectron-positronvertexloops,σ(e+e−→ µ+µ−,s)=4πα2(s)/3s.Dataerrorsaretotalbelow2GeVandstatisticalabove2GeV.Thecurvesareaneducativeguide:thebrokenone (green)isanaivequark-partonmodelprediction,andthesolidone(red)is3-looppQCDprediction(see“QuantumChromodynamics”sectionof thisReview,Eq.(9.7)or,formoredetails,K.G.Chetyrkinetal.,Nucl.Phys.B586,56(2000)(Erratumibid.B634,413(2002)).Breit-Wigner parameterizationsofJ/ψ,ψ(2S),andΥ(nS),n=1,2,3,4arealsoshown.Thefulllistofreferencestotheoriginaldataandthedetailsof theRratioextractionfromthemcanbefoundin[arXiv:hep-ph/0312114].Correspondingcomputer-readabledatafilesareavailableat http://pdg.lbl.gov/current/xsect/.(CourtesyoftheCOMPAS(Protvino)andHEPDATA(Durham)Groups,May2010.)Seefull-color versiononcolorpagesatendofbook.

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41.Plotsofcrosssectionsandrelatedquantities7 RinLight-Flavor,Charm,andBeautyThresholdRegions 10-1

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Sumofexclusive measurementsInclusive measurements 3looppQCD Naivequarkmodel

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Mark-I Mark-I+LGW Mark-II PLUTO DASP CrystalBall BES

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MD-1ARGUSCLEOCUSBDHHM CrystalBallCLEOIIDASPLENA Υ(1S) Υ(2S)Υ(3S) Υ(4S)

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Figure41.7:Rinthelight-flavor,charm,andbeautythresholdregions.Dataerrorsaretotalbelow2GeVandstatisticalabove2GeV. ThecurvesarethesameasinFig.41.6.Note:CLEOdataaboveΥ(4S)werenotfullycorrectedforradiativeeffects,andweretain themontheplotonlyforillustrativepurposeswithanormalizationfactorof0.8.Thefulllistofreferencestotheoriginaldataand thedetailsoftheRratioextractionfromthemcanbefoundin[arXiv:hep-ph/0312114].Thecomputer-readabledataareavailableat http://pdg.lbl.gov/current/xsect/.(CourtesyoftheCOMPAS(Protvino)andHEPDATA(Durham)Groups,May2010.)Seefull-color versiononcolorpagesatendofbook.

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Figure1:ThestructurefunctionF2asafunctionofxforvariousQ2values,exhibitingBjorken scaling,takenfrom[Ellis/Stirling/Webber] Figure2:PartondistributionfunctionsetAfromtheMartin-Roberts-Stirlinggroup,takenfrom [Ellis/Stirling/Webber].Notethatthisusesthecommonnotationofdefiningvalencequarkdistri- butions,fuv≡fu−f¯u,fdv≡fd−f¯d. 1

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Figure3:ResultsofarecentcompilationofαSvalues,see[arXiv:0803.0979[hep-ph],arXiv:hep- ex/0606035].Thescaledependenceshowsexcellentagreementwiththepredictionsofperturbative QCDoverawideenergyrange.WhentranslatedintomeasurementsofαS(Mz),theseparate measurementsclusterstronglyaroundtheaveragevalue,αS(Mz)=0.1204±0.0009 110 2 F

x=1.3E-05 (x 18) x=2E-05 (x 10) x=3.2E-05 (x 4) x=5E-05 (x 2) x=8E-05 (x 1)

H1SVX95 H194 H195NVX prel. H196NVX prel. E665 NMC BCDMS H1 QCDFit96 prel 110

x=0.00013 (x 10) x=0.0002 (x 5) x=0.00032 (x 3) x=0.0005 (x 1.8) x=0.0008 (x 0.8)

x=0.0013 (x 12) x=0.002 (x 8) x=0.0032 (x 4) x=0.005 (x 2.2) x=0.008 (x 1.3) 110 10-1110102103104

x=0.013 (x 18) x=0.02 (x 10) x=0.032 (x 6) x=0.05 (x 3.5) x=0.08 (x 2) 10-1110102103104 Q2 [GeV2 ]

x=0.13(x 32) x=0.2 (x 16) x=0.32 (x 8) x=0.5(x 6) Figure4:FittotheF2dataoverawiderangeofQ2values,exhibitingviolationofBjorkenscaling 2

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