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Cédric Lorcé

Second International Summer School of the GDR PH-QCD “Correlations between partons in nucleons”. N. Cédric Lorcé. Multidimensional pictures of the nucleon (3/3). IFPA Liège. June 30-July 4, 2014, LPT, Paris-Sud University, Orsay, France. Reminder. Lecture 2.

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Cédric Lorcé

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  1. Second International Summer School of the GDR PH-QCD “Correlations between partons in nucleons” N Cédric Lorcé Multidimensional pictures of the nucleon (3/3) IFPA Liège June 30-July 4, 2014, LPT, Paris-Sud University, Orsay, France

  2. Reminder Lecture 2 • PDFs provide 1D pictures of the nucleon • FFs provide 2D pictures of the nucleon • GPDs generalize both PDFs and FFs and give access to the EMT Energy density Momentum density Shear stress [GPD] Normal stress (pressure) Energy flux Momentum flux PDF [FF]

  3. Outline • Introduction • Tour in phase space • Galileo vs Lorentz • Photon point of view Lecture 1 • Nucleon 1D picture • Nucleon 2D picture • Nucleon 2+1D picture • Energy-momentumtensor Lecture 2 • Another nucleon 3D picture • Tour in Fock space • 3D+3D=… 5D ! Lecture 3

  4. What about kT ? 1/32 Large single-spin asymmetries have been observed at high energy ! Partonic origin ? Price for helicity flip Collinear twist-2 [Kane, Pumplin, Repko (1978)] Too small ! Intrinsic kT Collinear twist-3

  5. Semi-inclusive DIS 2/32 Inclusive DIS Semi-inclusive DIS (SIDIS) Identified particles in final state

  6. Transverse-momentum distributions (TMDs) 3/32 Optical theorem Final-state cut FFs TMDs Fragmentation Function [Collins, Soper, Sterman (1985)] [Ji, Ma, Yuan (2004)] [Idilbi et al. (2004)] [Cherednikov, Stefanis (2008)] [Trentadue, Ceccopieri (2008)] [Hautman (2008)] [Echevarria, Idilbi, Scimemi (2011)] [Collins (2011)]

  7. Transverse-momentum distributions (TMDs) 4/32 TMD correlator SIDIS modulations [Mulders, Tangermann (1996)] [Boer, Mulders (1998)] [Bacchetta et al. (2004)] [Bacchetta et al. (2007)] [Anselmino et al. (2011)]

  8. Transverse-momentum distributions (TMDs) TMDs PDFs FFs GPDs Charges 5/32 Average momentum Position shift Spin-orbit correlations Momentum space Position space Momentum transfer Average position No direct relation ! Complementary hadron 3D pictures ! Momentum-space imaging

  9. Transverse-momentum distributions (TMDs) 6/32 Multipole structure Quark polarization Nucleon polarization Monopole Dipole Quadrupole

  10. Transverse-momentum distributions (TMDs) 7/32 Multipole structure Quark polarization Nucleon polarization Monopole Dipole Quadrupole

  11. Transverse-momentum distributions (TMDs) 8/32 Multipole structure Quark polarization Nucleon polarization Monopole Dipole Quadrupole

  12. Transverse-momentum distributions (TMDs) 9/32 Multipole structure Quark polarization Nucleon polarization Monopole Dipole Quadrupole

  13. Transverse-momentum distributions (TMDs) 10/32 Multipole structure Quark polarization Nucleon polarization Monopole Dipole Quadrupole Naive T-odd !

  14. Transverse-momentum distributions (TMDs) 11/32 Non-trivial gauge link [Belitsky et al. (2003)] [Boer et al. (2003)] Drell-Yan SIDIS ISI FSI CPT invariance Fundamental test ! Naive T-odd Generalized universality [Buffing et al. (2012)] [Buffing et al. (2013)] Process dependent Calculable Universal

  15. Transverse-momentum distributions (TMDs) 12/32 Color-induced phase ! FSI ISI QED QCD Analogy: F. Pijlman Figure: K. Huyser Attractive Repulsive Quasi-classical interpretation ISI FSI [Sivers (2006)] [Sievert, Kovchegov (2014)]

  16. Transverse-momentum distributions (TMDs) 13/32 Clear experimental signal Lattice QCD [Musch et al. (2012)] Dipole shift uv [Anselmino et al. (2012)] Courtesy of Alexei Prokudin

  17. Transverse-momentum distributions (TMDs) 14/32 Open questions and problems • Tests of universality (e.g. with DY) and evolution • Model dependence and extrapolations • Precise determination of polarized TMDs • Extraction of gluon TMDs • Accessing higher-twist distributions • Link with low x, kT factorization • Sign mismatch with collinear twist-3 approach • Factorization breaks down in some pp scattering • … Entangled color flow Via Sivers TMD Direct extraction [Kang et al. (2011)] M. Buffing [Rogers, Mulders (2011)]

  18. Parton distribution zoo TMDs PDFs FFs GPDs Charges 15/32 Theoretical tools 2+1D 0+3D « Physical » objects 2+0D 0+1D [C.L., Pasquini, Vanderhaeghen (2011)]

  19. Parton distribution zoo GTMDs TMDs PDFs FFs GPDs Charges 16/32 Phase-space (Wigner) distribution Theoretical tools 2+3D 2+1D 0+3D « Physical » objects 2+0D 0+1D [C.L., Pasquini, Vanderhaeghen (2011)]

  20. Parton distribution zoo GTMDs TMDs PDFs FFs GPDs Charges 17/32 Phase-space (Wigner) distribution Theoretical tools 2+3D 2+1D 0+3D « Physical » objects 2+0D 0+1D [C.L., Pasquini, Vanderhaeghen (2011)]

  21. Parton distribution zoo LFWFs GTMDs TMDs PDFs FFs GPDs Charges 18/32 Phase-space (Wigner) distribution Theoretical tools 2+3D 2+1D 0+3D « Physical » objects 2+0D 0+1D [C.L., Pasquini, Vanderhaeghen (2011)]

  22. Light-front wave functions (LFWFs) 19/32 Fock expansion of the nucleon state Probability associated with the Fock states Momentum and angular momentum conservation gauge

  23. Light-front wave functions (LFWFs) 20/32 Overlap representation ~ GTMDs Momentum Polarization [C.L., Pasquini, Vanderhaeghen (2011)]

  24. Light-front wave functions (LFWFs) 21/32 Light-front quark models SU(6) spin-flavor wave function Wigner rotation Canonical spin Light-front helicity [C.L., Pasquini, Vanderhaeghen (2011)]

  25. Parametrization GTMDs TMDs GPDs 22/32 Twist-2 Quark polarization Nucleon polarization Complete parametrizations : Quarks [Meissner, Metz, Schlegel (2009)] [C.L., Pasquini (2013)] Quarks & gluons

  26. Parametrization GTMDs TMDs GPDs 23/32 Twist-2 Quark polarization Nucleon polarization Complete parametrizations : Quarks [Meissner, Metz, Schlegel (2009)] [C.L., Pasquini (2013)] Quarks & gluons

  27. Parametrization GTMDs TMDs GPDs 24/32 Twist-2 Quark polarization Nucleon polarization Complete parametrizations : Quarks [Meissner, Metz, Schlegel (2009)] [C.L., Pasquini (2013)] Quarks & gluons

  28. Parametrization GTMDs TMDs GPDs 25/32 Twist-2 Quark polarization Nucleon polarization Complete parametrizations : Quarks [Meissner, Metz, Schlegel (2009)] [C.L., Pasquini (2013)] Quarks & gluons

  29. Parametrization GTMDs TMDs GPDs 26/32 Twist-2 Quark polarization Nucleon polarization Complete parametrizations : Quarks [Meissner, Metz, Schlegel (2009)] [C.L., Pasquini (2013)] Quarks & gluons

  30. Model results 27/32 Wigner distribution of unpolarized quark in unpolarized nucleon 2+2D favored disfavored Left-right symmetry [C.L., Pasquini (2011)] favored disfavored

  31. Model results 28/32 Quark spin-nucleon spin correlation 2+2D Proton spin u-quark spin d-quark spin [C.L., Pasquini (2011)]

  32. Model results 29/32 Distortion correlated to nucleon spin 2+2D Proton spin u-quark OAM d-quark OAM [C.L., Pasquini (2011)]

  33. Model results 30/32 Average transverse quark momentum correlated to nucleon spin 2+2D « Vorticity » [C.L., Pasquini, Xiong, Yuan (2012)]

  34. Model results 31/32 Distortion correlated to quark spin 2+2D Quark spin u-quark OAM d-quark OAM [C.L., Pasquini (2011)]

  35. Model results 32/32 [C.L., Pasquini (2011)]

  36. Summary Lecture 3 • TMDs provide complementary 3D pictures of the nucleon • All distributions can be seen as overlaps of light-front wave functions • Models constrained by data give access to Wigner distributions Nucleon GTMDs LFWFs GPDs TMDs FFs PDFs

  37. Backup slides

  38. Spin decompositions in a nutshell Canonical Kinetic Lq Lq Sq Sq Sg Lg Jg « Incomplete » Gauge non-invariant ! [Jaffe, Manohar (1990)] [Ji (1997)]

  39. OAM and path dependence [Ji, Xiong, Yuan (2012)] [Hatta (2012)] [C.L. (2013)] Quark generalized OAM operator Light-front x-based Fock-Schwinger Lq Lq ISI FSI Drell-Yan SIDIS Coincides locally with kinetic quark OAM Naive T-even

  40. Kinetic vs canonical OAM Kinetic OAM (Ji) Pure twist-3 Quark naive canonical OAM (Jaffe-Manohar) [C.L., Pasquini, PLB710 (2012) 486] Model-dependent ! Canonical OAM (Jaffe-Manohar) [C.L., Pasquini, PRD84 (2011) 014015] [C.L., Pasquini, Xiong, Yuan, PRD85 (2012) 114006] [Kanazawa, C.L., Metz, Pasquini, Schlegel, PRD (2014)] No gluons and not QCD EOM ! but

  41. Lattice results CI DI [Deka et al. (2013)]

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