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Quark phase-space distributions and orbital angular momentum

Quark phase-space distributions and orbital angular momentum. Cédric Lorcé. and. 19 Apr 2012, Ecole Polytechnique, Palaiseau, France. Outline. [C.L., Pasquini, Vanderhaeghen (2011)] [C.L., Pasquini (2011)] [C.L., Pasquini, Xiong, Yuan (2011)]. Introduction Parton distribution functions

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Quark phase-space distributions and orbital angular momentum

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  1. Quark phase-space distributionsand orbital angular momentum Cédric Lorcé and 19 Apr 2012, Ecole Polytechnique, Palaiseau, France

  2. Outline [C.L., Pasquini, Vanderhaeghen (2011)] [C.L., Pasquini (2011)] [C.L., Pasquini, Xiong, Yuan (2011)] • Introduction • Parton distribution functions • Model results and discussion • Wigner distributions • Link with OAM

  3. Charges Charges Forward, local Vector Axial Tensor

  4. PDFs Charges Parton Distribution Functions Forward, non-local DIS

  5. PDFs FFs Charges Form Factors Non-forward, local ES 2D Fourier transform!

  6. PDFs FFs GPDs Charges Generalized PDFs Hadron 3D picture ! Non-forward, non-local DVCS [Burkardt (2000,2003)] [Belitsky et al. (2004)]

  7. TMDs PDFs FFs GPDs Charges Transverse-Momentum PDFs Complementary hadron 3D picture ! Forward, non-local SIDIS No direct connection Mean momentum Displacement Momentum space Position space Momentum transfer Mean position

  8. GTMDs TMDs PDFs FFs GPDs Charges Generalized TMDs Hadron 5D picture ! Non-forward, non-local Quasi-probabilistic interpretation in phase-space [Wigner (1932)] [Belitsky , Ji, Yuan(2004)] [C.L., Pasquini, Vanderhaeghen (2011)]

  9. Unpol. quark in unpol. proton [C.L., Pasquini (2011)] Based on LFCQM disfavored favored Left-right symmetry no net quark OAM

  10. Unpol. quark in long. pol. proton [C.L., Pasquini (2011)] Based on LFCQM Proton spin u-quark OAM d-quark OAM

  11. Unpol. quark in long. pol. proton [C.L., Pasquini, Xiong, Yuan (2011)] Based on LFCQM Proton spin u-quark OAM d-quark OAM

  12. Long. pol. quark in unpol. proton [C.L., Pasquini (2011)] Based on LFCQM Quark spin u-quark OAM d-quark OAM

  13. Long. pol. quark in long. pol. proton [C.L., Pasquini (2011)] Based on LFCQM Proton spin u-quark spin d-quark spin

  14. Angular momentum decompositions 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)]

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

  16. Summary [C.L., Pasquini, Vanderhaeghen (2011)] [C.L., Pasquini (2011)] [C.L., Pasquini, Xiong, Yuan (2011)] • Introduction • Parton distribution functions • 3D and 5D partonic pictures • Model results and discussion • Wigner distributions • Unpolarized/polarized quark in unpolarized/polarized nucleon • Link with OAM • Kinematic and canonical decompositions • Relations to parton distributions

  17. Backup

  18. Decompositions of total OAM Fock expansion of the proton state Fock states Simultaneous eigenstates of Momentum Light-front helicity

  19. How can one access to OAM? Overlap representation [Hägler, Mukherjee, Schäfer (2004)] [C.L., Pasquini, Xiong, Yuan (2011)] [C.L., Pasquini (2011)] Flavor contribution TMDs TMDs GTMDs GPDs Pure quark system [C.L., Pasquini (2011)] Conservation of transverse momentum NB: also valid for N,b Fock states Conservation of longitudinal momentum Anomalous gravitomagnetic sum rule! [Brodsky, Hwang, Ma, Schmidt (2001)]

  20. Physical interpretation Models Chiral quark-soliton model [Wakamatsu, Tsujimoto (2005)] [Wakamatsu (2010)] Non-perturbative sea contribution Scalar quark-diquark [Burkardt, Hikmat (2009)] Regularization-dependent 3Q light-front wave functions [C.L., Pasquini (2011)] Artifacts?

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