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Nucleon tomography through exclusive and semi-inclusive processes

International Workshop on Hadron Structure and Spectroscopy Lisbon, 16-18 April 2012. Nucleon tomography through exclusive and semi-inclusive processes. Cédric Lorcé. and. 17 Apr 2012, LIP, Lisbon, Portugal. Outline. Exclusive vs. Semi-inclusive DVCS vs. SIDIS GPDs vs. TMDs

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Nucleon tomography through exclusive and semi-inclusive processes

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  1. International Workshop on Hadron Structure and Spectroscopy Lisbon, 16-18 April 2012 Nucleon tomography through exclusive and semi-inclusive processes Cédric Lorcé and 17 Apr 2012, LIP, Lisbon, Portugal

  2. Outline • Exclusive vs. Semi-inclusive • DVCS vs. SIDIS • GPDs vs. TMDs • Partonic interpretation • 3D imaging • Twist-2 and Twist-3 • Hadron structure • Angular momentum decompositions • Quark spin and OAM • Interesting relations

  3. DVCS vs. SIDIS Incoherent scattering DVCS SIDIS FFs GPDs TMDs Factorization Compton form factor Cross section hard soft • process dependent • perturbative • « universal » • non-perturbative

  4. GPDs vs. TMDs GPDs TMDs Dirac matrix Correlator Correlator Off-forward! Forward! Wilson line ISI FSI e.g. DY e.g. SIDIS

  5. Partonic interpretation Twist-2 ~ LO in U L T GPDs TMDs 3D imaging 3D imaging IPDs Impact parameter Transverse center of momentum [Soper (1977)] [Burkardt (2000,2003)] [Diehl, Hägler (2005)] Interpretation in gauge

  6. Complete picture GTMDs and Wigner distributions GTMDs 5D imaging TMDs TMFFs GPDs Wigner distribution TMSDs PDFs FFs Charges [C.L., Pasquini, Vanderhaeghen (2011)] [C.L., Pasquini (2011)]

  7. Twist-2 structure Monopole Dipole GPDs TMDs Quadrupole Quark polarization Quark polarization Nucleon polarization Nucleon polarization -odd Naive T-odd

  8. Twist-3 structure Parametrization [Meißner, Metz, Schlegel (2009)] GPDs TMDs Quark polarization Quark polarization Nucleon polarization Nucleon polarization -odd Naive T-odd

  9. Angular momentum decompositions Ji Jaffe-Manohar [Ji (1997)] [Jaffe, Manohar (1990)] Kinematic Canonical Pros: Pros: • Gauge-invariant decomposition • Accessible in DIS and DVCS • Satisfies canonical relations • Complete decomposition Cons: Cons: • Does not satisfy canonical relations • Incomplete decomposition • Gauge-variant decomposition • Missing observables for the OAM Improvements: Improvements: • Complete decomposition • Gauge-invariant extension [Wakamatsu (2009,2010)] [Chen et al. (2008)] • OAM accessible via Wigner distributions [C.L., Pasquini (2011)] [C.L., Pasquini, Xiong, Yuan(2011)] [Hatta (2011)]

  10. Quark spin and OAM GPDs TMDs Quark spin Quark spin Pretzelosity Ji sum rule [Ji (1997)] Twist-3 [Burkardt (2007)] [Efremov, Schweitzer, Teryaev, Zavada (2008,2010)] [She, Zhu, Ma (2009)] [Avakian, Efremov, Schweitzer, Yuan (2010)] [C.L., Pasquini (2011)] PPSS sum rule • Model-dependent • Not intrinsic OAM Pure twist-3! [Penttinen, Polyakov, Shuvaev, Strikman (2000)] TMDs Genuine sum rule GTMDs

  11. Interesting relations *=SU(6) Model relations Linear relations Quadratic relation Flavor-dependent * * * * * Flavor-independent * * * * * * * Bag LFcQSM LFCQM S Diquark AV Diquark Cov. Parton Quark Target [Jaffe, Ji (1991), Signal (1997), Barone & al. (2002), Avakian & al. (2008-2010)] [C.L., Pasquini, Vanderhaeghen (2011)] [Pasquini & al. (2005-2008)] [Ma & al. (1996-2009), Jakob & al. (1997), Bacchetta & al. (2008)] [Ma & al. (1996-2009), Jakob & al. (1997)][Bacchetta & al. (2008)] [Efremov & al. (2009)] [Meißner & al. (2007)]

  12. Geometrical explanation [C.L., Pasquini (2011)] Preliminaries Conditions: • Quasi-free quarks • Spherical symmetry Wigner rotation (reduces to Melosh rotation in case of FREE quarks) Canonical spin Light-front helicity

  13. Geometrical explanation Axial symmetry about z

  14. Geometrical explanation Axial symmetry about z

  15. Summary • Exclusive vs. Semi-inclusive • DVCS vs. SIDIS • Factorizationapproach • GPDs vs. TMDs • Quark-quark correlator • Partonicinterpretation • 3D imaging • Probabilisticinterpretation • Twist-2 and Twist-3 • Helicity structure • Hadron structure • Angularmomentumdecompositions • Short overview • Quark spin and OAM • Relation with observables • Interesting relations • Sphericalsymmetry in quark models

  16. Quark polarization Quark polarization Nucleon polarization Nucleon polarization LC helicity and canonical spin [C.L., Pasquini (2011)] LC helicity Canonical spin

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