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Wigner distributions and quark orbital angular momentum

Wigner distributions and quark orbital angular momentum. Cédric Lorcé. and. May 14 2012, JLab, Newport News, VA, USA. Outline. Parton distribution zoo PDFs, FFs, GPDs, TMDs, GTMDs Partonic interpretation Proton spin puzzle Decompositions Relations with observables Model results

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Wigner distributions and quark orbital angular momentum

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  1. Wigner distributions and quark orbital angular momentum Cédric Lorcé and May 14 2012, JLab, Newport News, VA, USA

  2. Outline • Parton distribution zoo • PDFs, FFs, GPDs, TMDs, GTMDs • Partonic interpretation • Proton spin puzzle • Decompositions • Relations with observables • Model results • Overlap representation • Wigner distributions

  3. Outline • Parton distribution zoo • PDFs, FFs, GPDs, TMDs, GTMDs • Partonicinterpretation • Proton spin puzzle • Decompositions • Relations with observables • Model results • Overlaprepresentation • Wigner distributions

  4. Charges Parton distribution zoo Charges Partonic interpretation (twist-2) Vector Axial Tensor 0D Picture

  5. PDFs Charges Parton distribution zoo Parton Distribution Functions DIS Partonic interpretation (twist-2) 1D Picture

  6. PDFs FFs Charges Parton distribution zoo Form Factors ES Partonic interpretation (twist-2) Transverse center of momentum Impact parameter 2D Picture

  7. PDFs FFs GPDs Charges Parton distribution zoo Generalized PDFs DVCS Partonic interpretation (twist-2) [Soper (1977)] [Burkardt (2000,2003)] [Diehl, Hägler (2005)] 3D Picture

  8. TMDs PDFs FFs GPDs Charges Parton distribution zoo Transverse-Momentum dependent PDFs SIDIS No direct connection Partonic interpretation (twist-2) Mean momentum Displacement Momentum space Position space Momentum transfer Mean position 3D Picture gauge

  9. GTMDs TMDs PDFs FFs GPDs Charges Parton distribution zoo Generalized TMDs ??? ??? Partonic interpretation (twist-2) Quasi-probabilistic interpretation [Wigner (1932)] [Belitsky , Ji, Yuan(2004)] [C.L., Pasquini (2011)] 5D Picture

  10. GTMDs TMDs TMFFs TMCs PDFs TMFFs TMFFs TMCs TMCs FFs GPDs Charges Parton distribution zoo Complete set [C.L., Pasquini, Vanderhaeghen (2011)] Partonic interpretation (twist-2) 4D Picture 2D Picture

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

  12. Twist-2 structure Monopole Dipole GTMDs [Meißner, Metz, Schlegel (2009)] Quadrupole Quark polarization Nucleon polarization Naive OAM

  13. Twist-3 structure Monopole Dipole GPDs TMDs Quadrupole Quark polarization Quark polarization Nucleon polarization Nucleon polarization -odd Naive T-odd

  14. Outline • Parton distribution zoo • PDFs, FFs, GPDs, TMDs, GTMDs • Partonicinterpretation • Proton spin puzzle • Decompositions • Relations with observables • Model results • Overlaprepresentation • Wigner distributions

  15. Proton spin puzzle Ji Jaffe-Manohar [Ji (1997)] [Jaffe, Manohar (1990)] Kinetic 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)]

  16. Quark spin and OAM GPDs TMDs GTMDs Quark spin ALL Quark spin ALL Quark spin ALL Quark kinetic OAM Quark canonical OAM Quark canonical OAM AUU+AUT ATT AUL Twist-2 [Burkardt (2007)] [Efremov et al. (2008,2010)] [She, Zhu, Ma (2009)] [Avakian et al. (2010)] [C.L., Pasquini (2011)] [Ji (1997)] [C.L., Pasquini (2011)] [Hatta (2011)] [C.L. et al. (2012)] AUL Twist-3 • Model-dependent • Not intrinsic! Pure twist-3! [Penttinen et al. (2000)]

  17. OAM and origin dependence Naive Relative Intrinsic Depends on proton position Momentum conservation Transverse center of momentum Physical interpretation ? Equivalence Intrinsic Naive Relative

  18. Outline • Parton distribution zoo • PDFs, FFs, GPDs, TMDs, GTMDs • Partonicinterpretation • Proton spin puzzle • Decompositions • Relations with observables • Model results • Overlaprepresentation • Wigner distributions

  19. Overlap representation Fock expansion of the proton state Fock states Simultaneous eigenstates of Momentum Light-front helicity

  20. Overlap representation Light-front wave functions Eigenstates of parton light-front helicity Eigenstates of total OAM gauge Proton state Probabilityassociated with the N,b Fock state Normalization

  21. GTMDs TMDs GPDs Overlap representation Fock-state contributions [C.L., Pasquini (2011)] [C.L. et al. (2012)] Kinetic OAM Naive canonical OAM Canonical OAM

  22. GTMDs TMDs GPDs Model calculations Light-front 3Q models [C.L., Pasquini (2011)] Models are notQCD Truncation of Fock space spoils Lorentz covariance [Carbonell, Desplanques, Karmanov, Mathiot (1998)] In model calculations, one would expect but

  23. Model calculations Unpold quark in unpold nucleon [C.L., Pasquini (2011)] favored disfavored Left-right symmetry No net quark OAM

  24. Model calculations Unpold quark in longitudinally pold nucleon [C.L., Pasquini (2011)] Proton spin u-quark OAM d-quark OAM

  25. Model calculations Unpold quark in longitudinally pold nucleon [C.L. et al. (2012)] Proton spin u-quark OAM d-quark OAM

  26. Model calculations Longitudinally pold quark in unpold nucleon [C.L., Pasquini (2011)] Quark spin u-quark OAM d-quark OAM

  27. Model calculations Longitudinally pold quark in longitudinally pold nucleon [C.L., Pasquini (2011)] Proton spin u-quark spin d-quark spin

  28. Emerging picture Longitudinal Transverse [Burkardt (2005)] [Barone et al. (2008)] [C.L., Pasquini (2011)]

  29. Summary • Parton distribution zoo • PDFs, FFs, GPDs, TMDs, GTMDs • Partonic interpretation • Twist-2 phase-space distributions • Proton spin puzzle • Decompositions • Kinetic versus canonical • Relations with observables • Model results • Overlap representation • Wigner distributions • Consistent emerging picture

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

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

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

  33. 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)]

  34. 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

  35. Geometrical explanation Axial symmetry about z

  36. Geometrical explanation Axial symmetry about z

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