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Cédric Lorcé

CLAS12 3rd European Workshop. Cédric Lorcé. Observability of the different proton spin decompositions. IPN Orsay - LPT Orsay. June 21 2013, University of Glasgow, UK. The outline. Summary of the decompositions Gauge-invariant extensions Observability Accessing the OAM Conclusions.

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Cédric Lorcé

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  1. CLAS12 3rd European Workshop Cédric Lorcé Observability of the different proton spin decompositions IPN Orsay - LPT Orsay June 21 2013, University of Glasgow, UK

  2. The outline • Summary of the decompositions • Gauge-invariant extensions • Observability • Accessing the OAM • Conclusions Quark spin ? Dark spin ~ 30 % Reviews: [C.L. (2013)] [Leader, C.L. (in preparation)]

  3. The decompositions in a nutshell Canonical Kinetic [Ji (1997)] [Jaffe-Manohar (1990)] Lq Lq Sq Sq Sg Jg Lg Gauge non-invariant! [Chen et al. (2008)] [Wakamatsu (2010)] Lq Lq Sq Sq Lg Sg Sg Lg Gauge-invariant extension (GIE)

  4. The decompositions in a nutshell Canonical Kinetic [Ji (1997)] [Jaffe-Manohar (1990)] Lq Lq Sq Sq Sg Jg Lg Gauge non-invariant! [Chen et al. (2008)] [Wakamatsu (2010)] Lq Lq Sq Sq Lg Sg Sg Lg Gauge-invariant extension (GIE)

  5. The Stueckelberg symmetry [Stoilov (2010)] [C.L. (2013)] Ambiguous! Infinitely many possibilities! Coulomb GIE Lq Lq Sq Sq Lpot Lg Sg Sg Lg [Chen et al. (2008)] [Wakamatsu (2010)] Light-front GIE Lq Sq Lq Sq Lpot Lg Lg Sg Sg [Hatta (2011)] [C.L. (2013)]

  6. The gauge-invariant extension (GIE) [Ji, Xu, Zhao (2012)] [C.L. (2013)] Gauge-variant operator GIE2 GIE1 Gauge « Natural » gauges Rest Center-of-mass Infinite momentum Lorentz-invariant extensions ~ « Natural » frames

  7. The geometrical interpretation [C.L. (2013)] Parallel transport Non-local! Path dependence Stueckelberg dependence

  8. The semantic ambiguity Quid ? « physical » « measurable » « gauge invariant » Observables Measurable, physical, gauge invariant and local E.g. cross-sections Path Stueckelberg Background Expansion scheme dependent but fixed by the process E.g. collinear factorization Light-front gauge links Quasi-observables « Measurable », « physical », gauge invariant but non-local E.g. parton distributions

  9. The observability Observable Quasi-observable Not observable Canonical Kinetic [Ji (1997)] [Jaffe-Manohar (1990)] Lq Lq Sq Sq Sg Jg Lg [Chen et al. (2008)] [Wakamatsu (2010)] Lq Lq Sq Sq Lg Sg Sg Lg

  10. The gluon spin Gluon helicity distribution « Measurable », gauge invariant but non-local Light-front gauge Light-front GIE [Jaffe-Manohar (1990)] [Hatta (2011)] Local fixed-gauge interpretation Non-local gauge-invariant interpretation

  11. The kinetic and canonical OAM Kinetic OAM (Ji) [Ji (1997)] [Penttinen et al. (2000)] [Kiptily, Polyakov (2004)] [Hatta (2012)] Pure twist-3 Quark naive canonical OAM (Jaffe-Manohar) [Burkardt (2007)] [Efremov et al. (2008,2010)] [She, Zhu, Ma (2009)] [Avakian et al. (2010)] [C.L., Pasquini (2011)] Model-dependent ! Canonical OAM (Jaffe-Manohar) [C.L., Pasquini (2011)] [C.L., Pasquini, Xiong, Yuan (2012)] [Hatta (2012)] No gluons and not QCD EOM! but [C.L., Pasquini (2011)]

  12. The orbital motion in a model • [C.L., Pasquini, Xiong, Yuan (2012)] Average transverse quark momentum in a longitudinally polarized nucleon « Vorticity »

  13. The conclusions • Kinetic and canonical decompositions are physically inequivalent and are both interesting • Measurability requires gauge invariance but not necessarily locality • Jaffe-Manohar OAM and gluon spin are measurable (also on a lattice) Reviews: [C.L. (2013)] [Leader, C.L. (in preparation)]

  14. Backup slides

  15. The path dependence [C.L., Pasquini, Xiong, Yuan (2012)] [Hatta (2012)] [Ji, Xiong, Yuan (2012)] [C.L. (2013)] Orbital angular momentum Reference point [Jaffe, Manohar (1990)] [Ji (1997)] Canonical Kinetic ISI FSI Drell-Yan SIDIS

  16. The quark orbital angular momentum [C.L., Pasquini (2011)] GTMD correlator Wigner distribution Orbital angular momentum Unpolarized quark density Parametrization [Meißner, Metz, Schlegel (2009)]

  17. The emerging picture Longitudinal Transverse Cf. Bacchetta [Burkardt (2005)] [Barone et al. (2008)] [C.L., Pasquini (2011)]

  18. The Chen et al. approach [Chen et al. (2008,2009)] [Wakamatsu (2010,2011)] Gauge transformation (assumed) Pure-gauge covariant derivatives Field strength

  19. The gauge symmetry [C.L. (2013)] Quantum electrodynamics « Physical » « Background » Stueckelberg Passive Active Activex (Passive)-1

  20. The phase-space picture GTMDs TMDs PDFs FFs GPDs Charges 2+3D 2+1D 0+3D 0+1D 2+0D

  21. The phase-space distribution [Wigner (1932)] [Moyal (1949)] Wigner distribution Galilei covariant • Either non-relativistic • Or restricted to transverse position Probabilistic interpretation Heisenberg’s uncertainty relations Expectation value Position space Momentum space Phase space

  22. The parametrization @ twist-2 and x=0 GTMDs TMDs GPDs [Meißner, Metz, Schlegel (2009)] Parametrization : Quark polarization Nucleon polarization Monopole Dipole Quadrupole

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

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

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

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