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BasicsofQCDandjetphysicsMatteoCacciariLPTHEParisLHCPhenoNetWinterSchoolJanuary2012,AsconaMatteoCacciari-LPTHELHCPhenoNetWinterSchool-January2012-AsconaBracketsmatter....2(BasicsofQCD)and(jetphysics)Basicsof(QCDandjetphysics)orMatteoCacciari-LPTHELHCPhenoNetWinterSchool-January2012-AsconaBibliography:QCD3•T.Muta,FoundationsofQuantumChromodynamics,WorldScientific(1987)•R.D.Field,ApplicationsofperturbativeQCD,AddisonWesley(1989)•R.K.Ellis,W.J.StirlingandB.R.Webber,QCDandColliderPhysics,CambridgeUniversityPress(1996)•G.Sterman,AnIntroductiontoQuantumFieldTheory,CambridgeUniversityPress(1993)•Dokshitzer,Khoze,Muller,Troyan,BasicsofperturbativeQCD,~yuri•Dissertori,Knowles,Schmelling,QuantumChromodynamics:HighEnergyExperimentsandTheory,OxfordSciencePublications•M.L.Mangano,IntroductiontoQCD,•S.Catani,IntroductiontoQCD,CERNSummerSchoolLectures1999•G.Salam,ElementsofQCDforhadroncolliders,:1011.5131•F.Maltoni,BasicsofQCDfortheLHC,ficexamplesofdetailedcalculationsPhenomenology-orientedAQFTbook,butapplicationstiltedtowardsQCDForthebraveonesThemostrecentQCDbookMatteoCacciari-LPTHELHCPhenoNetWinterSchool-January2012-AsconaOutlineof‘BasicsofQCD’4•stronginteractions•QCDlagrangian•colour•ghosts•runningcoupling•infrareddivergenciesandIRCsafety•calculationsofobservables•factorisationtheorem•powercorrections•theoreticaluncertaintiesestimates“...thebrevityoflifedoesnotallowsustheluxuryofspendingtimeonproblemswhichwillleadtononewresults’’LevLandauFundamentalProblemsPauliMemorialVolume,p.245Interscience1960“...noronrewritingfromscratch‘BasicsofQCD’slidesalreadywrittenntimesbymorelearnedcolleagues’’thishumblelecturerHence,quitealotof‘borrowing’intheselecturesMatteoCacciari-LPTHELHCPhenoNetWinterSchool-January2012-AsconaPoll6•Howmanytheorists?Howmanyexperimenters?•HowmanyQCD,EW/BSM,strings?•Howmanyhavedone(aredoing)treelevel/1loop/2loopcalculations?•Howmanyarerunning/writingMonteCarlos?•HowmanyhavealreadyhadQCDlectures?Jetlectures?2011SchoolofHigh-EnergyPhysicsFabioMaltoniStronginteractionsStronginteractionsarecharacterizedatmoderateenergiesbyasingle*dimensionfulscale,!S,offewhundredsofMeV:h!1/!s2!10mb#h!!sR!1/!s!1fmNohinttothepresenceofasmallparameter!Veryhardtounderstandandmanyattempts...*neglectingquarkmasses..!!!8“Thecorrecttheory[ofstronginteractions]willnotbefoundinthenexthundredyears”FreemanDyson“WearedriventotheconclusionthattheHamiltonianmethodforstronginteractionsisdeadandmustbeburied,althoughofcoursewithdeservedhonor”LevLandauMatteoCacciari-LPTHELHCPhenoNetWinterSchool-January2012-AsconaWhythepessimism9•Whicharethefundamentalfields?•pion-nucleoncouplingverylarge.Perturbativeexpansionnotpossible.•zero-chargeproblem:inallknownQFTs(likeQED)thephysicalchargewasfoundtovanishwhensendingtheUVcutofftoinfinity(triviality).NotaproblemfirQED(assumedtobe‘incomplete’,butanissueforstronginteractions).Whywasarelativisticquantumfieldtheoryformulationofstronginteractionsconsideredunlikely?2011SchoolofHigh-EnergyPhysicsFabioMaltoniStronginteractionsNowadayswehaveasatisfactorymodelofstronginteractionsbasedonanon-abeliangaugetheory,QCD.WhyisQCDagoodtheory?1.Hadronspectrum2.Scaling3.QCD:aconsistentQFT4.Lowenergysymmetries5.MUCHmore....92011SchoolofHigh-EnergyPhysicsFabioMaltoni3f⊗3f⊗3f=10S⊕8M⊕8M⊕1AWeneedanextraquantumnumber(color)tohavethe!++withsimilarpropertiestothe0.Allparticlesinthemultiplethavesymmetricspin,flavourandspatialwave-function.Checkthatnq-nqbar=nxNc,withninteger.HadronspectrumNotethatphysicalstatesareclassifiedinmultipletsoftheFLAVORSU(3)fgroup!122011SchoolofHigh-EnergyPhysicsFabioMaltoniHowmanycolors?Γ∼N2c!Q2u−Q2d2m3πf2πΓEXP=7.7±0.6eVΓTH=!Nc327.6eVR=σ(e+e−→hadrons)σ(e+e−→µ+µ−)∼Nc!qe2q=2(Nc/3)q=u,d,s=3.7(Nc/3)q=u,d,s,c,b132011SchoolofHigh-EnergyPhysicsFabioMaltoniScalingcmsenergy2momentumtransfer2scalingvariableenergylossrel.energylossrecoilmasss=(P+k)2Q2=−(k−k!)2x=Q2/2(P·q)ν=(P·q)/M=E−E!y=(P·q)/(P·k)=1−E!/EW2=(P+q)2=M2+1−xxQ2dσelasticdq2=!dσdq2point·F2elastic(q2)δ(1−x)dxdσinelasticdq2=!dσdq2point·F2inelastic(q2,x)dxWhatshouldweexpectforF(q2,x)?142011SchoolofHigh-EnergyPhysicsFabioMaltoniTwoplausibleandonecrazyscenariosforthe|q2|!(Bjorken)limit:1.Smoothelectricchargedistribution:(classicalpicture)F2elastic(q2)!F2inelastic(q2)1i.e.,externalprobepenetratestheprotonasknifethroughthebutter!2.Tightlyboundpointchargesinsidetheproton:(boundquarks)F2elastic(q2)!1andF2inelastic(q2)1i.e.,quarksgethitassingleparticles,butmomentumisimmediatelyredistributedastheyaretightlyboundtogether(confinement)andcannotflyaway.3.Andnowthecrazyone:(freequarks)F2elastic(q2)1andF2inelastic(q2)~1i.e.,therearepoints(quarks!)insidetheprotons,howeverthehitquarkbehavesasafreeparticlethatfliesawaywithoutfeelingorcaringaboutconfinement!!!Scaling152011SchoolofHigh-EnergyPhysicsFabioMaltoniRemarkable!!!Puredimensionalanalysis!Therighthandsidedoesnotdependon!S!T