EIC2006 & Hot QCD 19 th July 2006

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

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

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

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

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

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

7. Factorization • 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: • Precise measurements at the few • percent level of (inclusive) observables

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

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

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

11. “Magnetic charge distribution” The QCDcalculation of form factorsremains 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)

12. Parton densities (PDs) in QCD y 2 PD z x is the parton density, depending on longitudinal momentum fractionx=k||/pand transversal resolution scale No information on their transverse position! d r ~ 1 Q ^ R.P.Feynman, 1972 Deeply inelastic electron-proton scattering epTe’X : Proton has point-like constituents! D.Taylor, H.Kendall, J.Friedman, 1969 (1990 Nobel Prize)

13. “Spin crisis” p The quark polarization inside the proton is measured within polarized scattering European Muon Collaboration (EMC) at CERN (1987): A polarized lepton scatters differently off quarks polarized along or opposite to the nucleon’s spin providing The fraction of the proton spin carried by quarks is: (quark model prediction) … 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?

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

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

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

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

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

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

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

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

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

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

24. Near the `pomeron’ pole evolution is driven by gluons GPD H GPD H • Assuming gluonic `pomeron’ dominance at low input scale, we arrive to the Aligned Jet Model/dipole-quark picture for DVCS: Q 2 GeV evolution Q0~ 0.5 GeV 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. n `pomeron’ poles non-leading singularities 1 -2 -1 2 • Small x-behavior of H arises from pomeron poles: • x-independent pure gluonic input: Pomeron dominance yields double log approx., i.e., DVCS data are described within three parameters:NG, BG , and Q0

26. 100 GeV2 10 GeV2 2 GeV2 ~ 2 h i b gluons quarks • fit yieldNG=1.97, BG=3.68GeV-2and Q0 =0.7GeV quark and gluon GPDs at low x in particular, parton distribution in impact parameterspace mean squared value in transversal direction NOTE: J/Y production yield a ~25% smaller value Strikman &Weiss (05) gluon distribution

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

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

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