Hadron Structure Theory I - Wright Laboratory

Hadron Structure Theory IAlexei Prokudin

The plan:lLecture I:Structure of the nucleonlLecture IITransverse Momentum Dependent distributions (TMDs)Semi Inclusive Deep Inelastic Scattering (SIDIS)lTutorialCalculations of SIDIS structure functions using Mathematica Lecture IIIAdvanced topics. Evolution of TMDs

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DOE funded Topical Collaboration for theory5 years of funding of 2,160,00018 institutionsTheory, phenomenology, lattice QCDSeveral postdoc positions.2 tenure track positions: Temple, NMSUSupport of undergraduates. 5 years of funding 18 institutions Theory, phenomenology, latticeQCD Several postdoc and tenure trackpositions to be created “To address the challenges ofextracting novel quantitativeinformation about the nucleon’sinternal landscape” “To provide compelling research,training, and career opportunitiesfor young nuclear theorists”5

Why is it so important for theory? We are a data-driven science!6

Standard model

InteractionsElectromagnetism (photon)Atomic and Molecular BindingGravitation (graviton)Stars and GalaxiesWeak Nuclear Interaction (W,Z bosons)Nuclear Beta DecayStrong Nuclear Interaction (gluon)Nuclear Binding

Standard modelThis talk

Quark modelProtonuuTwo “up”one “down”dNeutronddTwo “down”one “up”u10

Quark modelProtonuudCharge2/3 2/3 -1/3 1Quark chargesare fractionalof positron’s chargeNeutron2/3 - 1/3 -1/3 0dduQuarks arebound (confined)by strong interaction(gluons)11

Quark modelProtonuudChargeNo evidence of free quarksobserved directly in experiment2/3 2/3 -1/3 1Quark chargesare fractionalof positron’s chargeShort distance - quarksbehave as if they were freeNeutron2/3 - 1/3 -1/3 0dduLong distance - quarksare confined in hadronsQuarks arebound (confined)by strong interaction(gluons)12Asymptotic freedom later in this talk!

Quantum Electro Dynamics and Quantum Chromo DynamicsQEDGauge theory U(1)Force carrier:u photonu(electrically neutral)electrondpositronInteractionddu13

Quantum Electro Dynamics and Quantum Chromo DynamicsQEDGauge theory U(1)Force carrier:u photonu(electrically neutral)electrondpositronInteractionddRichard Feynman,NobelPrize1965u“for . fundamental work inquantum electrodynamics"14

Quantum Electro Dynamics and Quantum Chromo DynamicsQEDQCDGauge theory U(1)Gauge theory SU(3)Force carrier:u photonu(electrically neutral)Force ondgluons (carry color)InteractionstrongdRichard Feynman,NobelPrize1965uGluons interact with each other- non abelian theory“for . fundamental work inquantum electrodynamics"15

Asymptotic freedomThe coupling dependson the scale – consequence ofrenormalizability of the theoryAt short distancesquarks behave as if they werealmost free particles!“long” DISTANCE “short”“for the discovery of asymptotic freedomin the theory of the strong interaction"Gross, Politzer, Wilczek, Nobel Prize 2004

Scattering as the method of study“for his investigations into the disintegration ofthe elements, and the chemistry of radioactivesubstances"Ernest Rutherthord, Nobel Prize 19081911

Electron ScatteringDetector of electronsVirtuality of the photonelectronderettacsnortceelphotonDetector ofhadrons

Electron ScatteringDetector of electronsVirtuality of the photonelectronThe photon probesdistance of 1/Qinside of the proton.Asymptotic freedom photon scatters off a quarkderettacsnortceelphotonDetector ofhadrons

Electron Scattering: interpretationElectromagnetic probe resolves a quarkor anti-quark with momentum p xPinside of the proton of momentum P.Bjorken variableGives the fraction of longitudinalmomentum of the proton carriedby the parton

Electron Scattering: interpretationExperimental dataBehavior is almost flat– quarks are pointlike

Electron Scattering: interpretationUnlike the proton itself:Proton size 1 fm

Exploring the nucleon: a fundamental questKnow what weare made of !Understand thestrong force:“QCD”Use protons as toolfor discovery(e.g. LHC )23

Why Spin?Xiangdong Ji at DIS08Spin is a fundamental quantum degree of freedomSpin plays a critical role indetermining the basic structureof fundamental interactionsTest of a theory is not completewithout a full test of spin-dependentdecays and scatteringSpin provides a unique opportunity to probethe inner structure of a composite system(such as the proton)24

Spin and QCD“Experiments with spin have killed more theories than any other singlephysical parameter”Elliot Leader, Spin in Particle Physics, Cambridge U. Press (2001)“Polarization data has often been the graveyard of fashionable theories.If theorists had their way they might well ban such measurementsaltogether out of self-protection.”J. D. Bjorken, Proc. Adv. Research Workshop on QCD HadronicProcesses, St. Croix, Virgin Islands (1987).See lectures by Thomas Ullrich and Anselm Vossen

Nucleon landscapeNucleon is a many body dynamical system ofquarks and gluonsChanging x we probe different aspects of nucleonwave functionHow partons move and how they aredistributed in space is one of the directions ofdevelopment of nuclear physicsTechnically such information is encoded intoGeneralised Parton Distributions (GPDs) andTransverse Momentum Dependent distributions(TMDs)These distributions are also referred to as 3D(three-dimensional) distributions26

Unified View of Nucleon Structure5DWigner nctionsFormFactors1DAlexei Prokudin

"To address the challenges of extracting novel quantitative information about the nucleon's . Exploring the nucleon: a fundamental quest. 24 Spin is a fundamental quantum degree of freedom Test of a theory is not complete without a full test of spin-dependent decays and scattering