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Published on October 15, 2007

Author: Jancis

Source: authorstream.com

Slide1:  EIC2006 & Hot QCD 19th July 2006 Towards Three-Dimensional Imaging of the Proton Dieter Müller Arizona State University Slide2:  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 Slide3:  Hadron mass spectra Magnetic moments, e.g., etc. 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”: Slide4:  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 Slide5:  How to resolve the proton? Experiments with highly energetic electromagnetic probe acting as a micro-scope Virtual photon resolves the proton on the distance: Slide6:  How to study the proton content? elastic, exclusive deeply inelastic, inclusive High energetic scattering experiments on a proton target or beam with 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 Factorization:  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: Slide8:  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 Slide9:  The electric and magnetic charge distributions inside the proton are measured in elastic electron-proton scattering epTe’p’: quark Form factor in QCD Proton is not point-like! R.Hofstadter, 1955 (1961 Nobel Prize) Slide10:  Interpretation of form factors momentum frame of a fast moving proton Form factors might be interpreted as transverse distribution of quarks irrespective of their longitudinal motion. Slide11:  “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) Slide12:  Parton densities (PDs) in QCD Deeply inelastic electron-proton scattering epTe’X : Proton has point-like constituents! D.Taylor, H.Kendall, J.Friedman, 1969 (1990 Nobel Prize) R.P.Feynman, 1972 Slide13:  “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) Slide14:  The spin of a composite particle is build from Building up the nucleon spin spin of its constituents orbital motion of constituents The sum rule for the proton spin The angular momentum is given by the energy momentum density X. Ji, 1996 Probing the proton with two photons:  Probing the proton with two photons 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 Slide16:  z Generalized parton distributions (GPDs) 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 X. Ji, 1996 Slide17:  GPDs as a unifying concept GPDs are reducible to form factors and parton densities! orbital angular momentum femto holography (3D picture of the proton) calculable in lattice QCD duality, etc.  mass and gravitomagnetic charges (matrix element of energy-momentum tensor) Slide18:  “Holography” with photo leptoproduction Slide19:  Geometric picture of DVCS Slide20:  Extracting interference Model A Model B A. Belitsky, D. Müller, A. Kirchner, 2001 Lepton-beam charge asymmetry Proton spin asymmetry Lepton-beam spin asymmetry Lepton-beam spin asymmetry CLAS HERMES Slide21:  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 The probability to find a quark in transversal direction from the proton center with momentum fraction x is Slide22:  The proton image at large W Photon leptoproduction measured at H1 & ZEUS (DESY) allows to extract the deeply virtual Compton cross section D. Müller 2006 FF GPD + FF + + interference 2 2 subtracted DVCS Bethe-Heitler Slide23:  A 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 function Moments are labeled by complex angular momentum n These moments contain spin & orbital momentum coupling Slide24:  Near 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: Q0~ 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 Slide25:  Small x-behavior of H arises from pomeron poles: x-independent pure gluonic input: DVCS data are described within three parameters: NG, BG , and Q0 Pomeron dominance yields double log approx., i.e., Slide26:  fit yield NG=1.97, BG=3.68 GeV-2 and Q0 =0.7 GeV in particular, parton distribution in impact parameter space mean squared value in transversal direction gluon distribution NOTE: J/Y production yield a ~25% smaller value Strikman &Weiss (05) quark and gluon GPDs at low x Slide27:  How one can measure GPDs? Deeply virtual Compton scattering (clean probe) Hard exclusive meson production (flavor filter) etc. A. Belitsky, D. Müller 2003 Slide28:  Current and future facilities 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? Slide29:  Conclusions Experimentally accessible: (see parallel session Exclusive Physics) hard exclusive electroproduction of photon or lepton pair hard meson electroproduction, etc. 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 The internal structure of the proton (hadrons) can be explored with generalized parton distributions from a new perspective: 3D partonic content of the proton decomposition of the proton spin Generalized parton distributions allow also to explore nuclei in terms of partonic degrees of freedom

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