1. EIC2006 & Hot QCD 19 th July 2006 Towards Three-Dimensional Imaging of the Proton Dieter Müller Arizona State University

2. Outline Introductory remarks:Introductory remarks: A short look back in historyA short look back in history How to resolve the proton?How to resolve the proton? Factorization: How to work with Quantum Chromodynamics?Factorization: How to work with Quantum Chromodynamics? Exploring the proton contentExploring the proton content Form factorsForm factors Parton densitiesParton densities An unifying concept: generalized parton distributionsAn unifying concept: generalized parton distributions Present and future experiments Present and future experiments Summary Summary

3. Hadron mass spectra Hadron mass spectra Magnetic moments, e.g., Magnetic moments, e.g., etc. etc. Proton spin solely built from the quark spins! Proton spin solely built from the quark spins! Tremendously successful model in description of What is the proton made of? The variety of hadrons is explained by an underlying symmetry “eightfold way”: M. Gell-Mann, G. Zweig, 1964 Proton mass:Proton mass: Proton spin:Proton spin: u u d The proton is build from three quarks of masses andspin : masses ~ 300 MeV and spin s = 1/2:

4. Quantum mechanical duality of particle and waves Electron microscope E ~ 100 KeV resolution of allows for a deeper look into matter: Particle accelerator: SLAC 20 GeV electron beam (1966) exploring the femto universe, i.e., a resolution of

5. How to resolve the proton? Experiments with highly energetic electromagnetic probe acting as a micro-scope Experiments with highly energetic electromagnetic probe acting as a micro-scope Virtual photon resolves the proton on the distance Virtual photon resolves the proton on the distance: The change with the resolution scale is a QCD prediction,The change with the resolution scale is a QCD prediction, calculable within perturbation theory. calculable within perturbation theory. virtual photon mass (=virtuality) electron  Q  

6. How to study the proton content? elastic, exclusive deeply inelastic, inclusive High energetic scattering experiments on a proton target or beam with hadronizatio n hadron beam, e.g., Tevatron@Fermilab (1TeV proton + antiproton beams), LHC etc. lepton (electron, muon, or neutrino ) beam e.g., JLab@6GeV, DESY (27 GeV electron + 820 GeV proton beam) inelastic, exclusive M,gM,g

7. Factorization Precise measurements at the few percent level of (inclusive) observables The scattering process of high energy particles appear at short distances. However, in the asymptotic (initial and final) states hadrons are observed. The basic concept for the application of QCD is factorization:

8. Form factor in quantum mechanics Elastic scattering of fast electrons on atoms. Atomic form factor: is the Fourier transform of the charge density. The cross section: E.g., the hydrogen atom in the ground state: charge density with Bohr radius

9. The electric and The electric and magnetic charge distributions inside the proton elastic electron-proton scattering are measured in elastic electron-proton scattering ep T e’p’: quark Form factor in QCD electron virtual photon mass (= virtuality) electric form factor magnetic form factor Proton is not point-like! R.Hofstadter, 1955 (1961 Nobel Prize)

10. Interpretation of form factors Lorentz trans. proton at rest z y x momentum frame of a fast moving proton no spatial extent Form factors might be interpreted as transverse distribution of quarks irrespective of their longitudinal motion.

11. “Magnetic charge distribution” The QCD calculation of form factors remains challenging. Form factors might be represented by wave functions: Sensitivity to orbital momentum of quarks! Confronting model calculations with data leads to new insights into the proton (orbital momentum, wave function shape) (orbital momentum, wave function shape)

12. Parton densities (PDs) in QCD y x z Deeply inelastic electron-proton scattering : Deeply inelastic electron-proton scattering ep T e’X : Proton has point-like constituents! D.Taylor, H.Kendall, J.Friedman, 1969 (1990 Nobel Prize) R.P.Feynman, 1972 is the parton density, depending on is the parton density, depending on longitudinal momentum fraction longitudinal momentum fraction x=k||/p and transversal resolution scale No information on their transverse position! Qr1~   2 PD

13. “Spin crisis” A polarized lepton scatters differently off quarks polarized along or opposite to the nucleon’s spin providing The quark polarization inside the proton is measured within polarized scattering European Muon Collaboration (EMC) at CERN (1987): The fraction of the proton spin carried by quarks is: … the result implies that a rather small fraction of the spin of the proton is carried by the spin of the quarks. EMC Coll., 1987 “SPIN CRISIS”: Where is the rest? How to define it? How to measure it? (quark model prediction) p

14. The spin of a composite particle is build from Building up the nucleon spin spin of its constituentsspin of its constituents orbital motion of constituentsorbital motion of constituents The sum rule for the proton spin The angular momentum is given by the energy momentum density X. Ji, 1996

15. Probing the proton with two photons Bjorken limit Bjorken limit: time space n “Handbag” GPD Non-invasive exploration of the proton! quantum mechanical incoherence of physical processes at short and large distances scales ensures factorization D. Müller (PhD), 1992 et al. 1994 DVCS

16. z Generalized parton distributions (GPDs) y x GPDs simultaneously carry information on both longitudinal and transverse distribution of partons in a proton D. Müller (PhD) 1992 et al. 1994 X. Ji; A. Radyushkin, 1996 GPDs contain also information on quark (orbital) angular momentum GPD X. Ji, 1996

17. GPDs as a unifying concept GPDs are reducible to form factors and parton densities! orbital angular momentum orbital angular momentum GPD FF PD femto holography ( femto holography (3D picture of the proton) calculable in lattice QCD duality, etc. duality, etc.  mass and gravitomagnetic charges (matrix element of energy-momentum tensor)

18. “Holography” with photo leptoproduction GPD FF Bethe-Heitler DVCS reference source beam diffracted off a parton lepton beam detector ‘‘splitter’’ ‘‘mirror’’ NOTE: objects displayed in yellow are not present in real experiment!

19. Geometric picture of DVCS x y Initial state z x y z Final state azimuthal asymmetry Cross section:

20. Extracting interference Model A Model B A. Belitsky, D. Müller, A. Kirchner, 2001 Lepton-beam charge asymmetry Proton spin asymmetry Lepton-beam spin asymmetry CLASHERMES

21. The quark distribution in the proton Theoretical constraints together with plausible assumptions give already a rough idea about the average squared distance in dependence of x and no spatial extent The probability to find a quark in transversal direction from the proton center with momentum fraction x is

22. The proton image at large W The proton image at large W Photon leptoproduction measured at H1 & ZEUS (DESY)Photon leptoproduction measured at H1 & ZEUS (DESY) allows to extract the deeply virtual Compton cross section allows to extract the deeply virtual Compton cross section D. Müller 2006 FF GPD + FF + + interference 2 2 subtracted DVCS Bethe-Heitler

23. A new representation for GPDs allows to make contact with Regge phenomenologyA new representation for GPDs allows to make contact with Regge phenomenology [D. Müller, A. Schäfer (05)] (see also talk M. Kirch) Generalization of Mellin representation for DIS structure functionGeneralization of Mellin representation for DIS structure function Moments are labeled by complex angular momentum nMoments are labeled by complex angular momentum n These moments contain spin & orbital momentum couplingThese moments contain spin & orbital momentum coupling SnSn GPD H

24. Near the `pomeron’ pole evolution is driven by gluonsNear the `pomeron’ pole evolution is driven by gluons Assuming gluonic `pomeron’ dominance at low input scale, we arrive to the Aligned Jet Model/dipole-quark picture for DVCS:Assuming gluonic `pomeron’ dominance at low input scale, we arrive to the Aligned Jet Model/dipole-quark picture for DVCS: GPD H Q 0 ~ 0.5 GeV Q 2 GeV evolution Although, analyze can be performed in next-to-next-to-leading order [K. Kumerički, D.M., K. Passek- Kumerički, A. Schäfer (2006)] we will rely in the following on the leading order approximation

25. Small x -behavior of H arises from pomeron poles: x -independent pure gluonic input: `pomeron’ poles non-leading singularities -2 1 2 n DVCS data are described within three parameters: N G, B G, and Q 0 Pomeron dominance yields double log approx., i.e.,

26. fit yield N G =1.97, B G =3.68 GeV -2 and Q 0 =0.7 GeV in particular, parton distribution in impact parameter space mean squared valuein transversal direction h ~ b 2 i 100 GeV 2 10 GeV 2 2 GeV 2 gluons quarks gluon distribution NOTE: J/ Y production yield a ~25% smaller value Strikman &Weiss (05) quark and gluon GPDs at low x

27. How one can measure GPDs? Deeply virtual Compton scattering (clean probe)Deeply virtual Compton scattering (clean probe) Hard exclusive meson production (flavor filter)Hard exclusive meson production (flavor filter) etc.etc. scanned area of the surface as a functions of lepton energy A. Belitsky, D. Müller 2003

28. Current and future facilities Jefferson Lab @ 6 GeV:Jefferson Lab @ 6 GeV: Hall A: recoil detector*Hall A: recoil detector* * For full exclusivity of the scattering event! Hall B: near beam calorimeterHall B: near beam calorimeter Jefferson Lab @ 12 GeVJefferson Lab @ 12 GeV DESYDESY HERMES: recoil detector*HERMES: recoil detector* H1 and ZEUS: polarized protonH1 and ZEUS: polarized proton COMPASS @ CERN: recoil detector*COMPASS @ CERN: recoil detector* EIC @ BNL?EIC @ BNL? ELFE?ELFE?

29. Conclusions Experimentally accessible: (see parallel session Exclusive Physics)Experimentally accessible: (see parallel session Exclusive Physics) hard exclusive electroproduction of photon or lepton pairhard exclusive electroproduction of photon or lepton pair hard meson electroproduction, etc.hard meson electroproduction, etc. Generalized parton distributions are a new theoretical concept:Generalized parton distributions are a new theoretical concept: unified description of form factors and parton densitiesunified description of form factors and parton densities containing mass and gravitational form factors, etc.containing mass and gravitational form factors, etc. messuarable in QCD lattice simulationsmessuarable in QCD lattice simulations The internal structure of the proton (hadrons) can be explored with generalized parton distributions from a new perspective:The internal structure of the proton (hadrons) can be explored with generalized parton distributions from a new perspective: 3Dpartonic content of the proton3D partonic content of the proton decomposition of the proton spindecomposition of the proton spin Generalized parton distributions allow also to explore nuclei Generalized parton distributions allow also to explore nuclei in terms of partonic degrees of freedom in terms of partonic degrees of freedom