Slide 1

Cdric Lorc IFPA Lige Multidimensional pictures of the nucleon (3/3) June 30-July 4, 2014, LPT, Paris-Sud University, Orsay, France Second International Summer School of the GDR PH-QCD Correlations between partons in nucleons N Slide 2 Reminder 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 Lecture 2 [GPD] PDF[FF] Energy density Momentum density Energy flux Momentum flux Shear stress Normal stress (pressure) Slide 3 Outline Nucleon 1D picture Nucleon 2D picture Nucleon 2+1D picture Energy-momentum tensor Lecture 2 Introduction Tour in phase space Galileo vs Lorentz Photon point of view Lecture 1 Another nucleon 3D picture Tour in Fock space 3D+3D= 5D ! Lecture 3 Slide 4 What about k T ? Large single-spin asymmetries have been observed at high energy ! Partonic origin ? Collinear twist-2 Intrinsic k T Too small ! [Kane, Pumplin, Repko (1978)] Price for helicity flip Collinear twist-3 1/32 Slide 5 Semi-inclusive DIS Inclusive DISSemi-inclusive DIS (SIDIS) Identified particles in final state 2/32 Slide 6 Transverse-momentum distributions (TMDs) Optical theorem TMDs Final-state cut [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)] Fragmentation Function FFs 3/32 Slide 7 Transverse-momentum distributions (TMDs) TMD correlator SIDIS modulations [Mulders, Tangermann (1996)] [Boer, Mulders (1998)] [Bacchetta et al. (2004)] [Bacchetta et al. (2007)] [Anselmino et al. (2011)] 4/32 Slide 8 FFs PDFs Charges GPDs Transverse-momentum distributions (TMDs) TMDs Spin-orbit correlations Momentum space Position space No direct relation ! Complementary hadron 3D pictures ! Average momentum Position shift Average position Momentum transfer Momentum-space imaging 5/32 Slide 9 Transverse-momentum distributions (TMDs) MonopoleDipoleQuadrupole Nucleon polarization Quark polarization Multipole structure 6/32 Slide 10 Transverse-momentum distributions (TMDs) MonopoleDipoleQuadrupole Nucleon polarization Quark polarization Multipole structure 7/32 Slide 11 Transverse-momentum distributions (TMDs) MonopoleDipoleQuadrupole Nucleon polarization Quark polarization Multipole structure 8/32 Slide 12 Transverse-momentum distributions (TMDs) MonopoleDipoleQuadrupole Nucleon polarization Quark polarization Multipole structure 9/32 Slide 13 Transverse-momentum distributions (TMDs) MonopoleDipoleQuadrupole Nucleon polarization Quark polarization Multipole structure Naive T-odd ! 10/32 Slide 14 FSIISI Drell-YanSIDIS Non-trivial gauge link CPT invariance [Buffing et al. (2012)] [Buffing et al. (2013)] UniversalProcess dependentCalculable Fundamental test ! [Belitsky et al. (2003)] [Boer et al. (2003)] Naive T-odd Transverse-momentum distributions (TMDs) Generalized universality 11/32 Slide 15 Color-induced phase ! Analogy: F. Pijlman Figure: K. Huyser Transverse-momentum distributions (TMDs) Quasi-classical interpretation ISIFSI [Sivers (2006)] [Sievert, Kovchegov (2014)] FSI ISI QED QCDQCD Attractive Repulsive 12/32 Slide 16 Clear experimental signalLattice QCD [Musch et al. (2012)] [Anselmino et al. (2012)] Courtesy of Alexei Prokudin Dipole shift uvuv Transverse-momentum distributions (TMDs) 13/32 Slide 17 Entangled color flow 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, k T factorization Sign mismatch with collinear twist-3 approach Factorization breaks down in some pp scattering [Rogers, Mulders (2011)] [Kang et al. (2011)] Direct extraction Via Sivers TMD Transverse-momentum distributions (TMDs) M. Buffing 14/32 Slide 18 Parton distribution zoo 2+1D 2+0D 0+3D 0+1D [C.L., Pasquini, Vanderhaeghen (2011)] TMDs FFsPDFs Charges GPDs Physical objects Theoretical tools 15/32 Slide 19 Parton distribution zoo 2+1D 2+0D 0+3D 0+1D [C.L., Pasquini, Vanderhaeghen (2011)] TMDs FFsPDFs Charges GPDs Physical objects Theoretical tools GTMDs 2+3D Phase-space (Wigner) distribution 16/32 Slide 20 Parton distribution zoo 2+1D 2+0D 0+3D 0+1D 2+3D [C.L., Pasquini, Vanderhaeghen (2011)] GTMDs TMDs FFsPDFs Charges GPDs Physical objects Theoretical tools Phase-space (Wigner) distribution 17/32 Slide 21 2+1D 2+0D 0+3D 0+1D 2+3D GTMDs TMDs FFsPDFs Charges GPDs LFWFs Phase-space (Wigner) distribution Parton distribution zoo [C.L., Pasquini, Vanderhaeghen (2011)] Physical objects Theoretical tools 18/32 Slide 22 Light-front wave functions (LFWFs) Fock expansion of the nucleon state Probability associated with the Fock states Momentum and angular momentum conservation gauge 19/32 Slide 23 [C.L., Pasquini, Vanderhaeghen (2011)] ~ Overlap representation Light-front wave functions (LFWFs) GTMDs MomentumPolarization 20/32 Slide 24 [C.L., Pasquini, Vanderhaeghen (2011)] Light-front wave functions (LFWFs) Light-front quark models Wigner rotation Light-front helicity Canonical spin SU(6) spin-flavor wave function 21/32 Slide 25 Parametrization GTMDs TMDsGPDs Nucleon polarization Quark polarization [Meissner, Metz, Schlegel (2009)] [C.L., Pasquini (2013)] Quarks & gluons Complete parametrizations : Quarks Twist-2 22/32 Slide 26 Parametrization GTMDs TMDsGPDs Nucleon polarization Quark polarization [Meissner, Metz, Schlegel (2009)] [C.L., Pasquini (2013)] Quarks & gluons Complete parametrizations : Quarks Twist-2 23/32 Slide 27 Parametrization GTMDs TMDsGPDs Nucleon polarization Quark polarization [Meissner, Metz, Schlegel (2009)] [C.L., Pasquini (2013)] Quarks & gluons Complete parametrizations : Quarks Twist-2 24/32 Slide 28 Parametrization GTMDs TMDsGPDs Nucleon polarization Quark polarization [Meissner, Metz, Schlegel (2009)] [C.L., Pasquini (2013)] Quarks & gluons Complete parametrizations : Quarks Twist-2 25/32 Slide 29 Parametrization GTMDs TMDsGPDs Nucleon polarization Quark polarization [Meissner, Metz, Schlegel (2009)] [C.L., Pasquini (2013)] Quarks & gluons Complete parametrizations : Quarks Twist-2 26/32 Slide 30 [C.L., Pasquini (2011)] Wigner distribution of unpolarized quark in unpolarized nucleon Model results favored disfavored Left-right symmetry 2+2D favoreddisfavored 27/32 Slide 31 Quark spin-nucleon spin correlation Model results Proton spin u-quark spin d-quark spin 2+2D [C.L., Pasquini (2011)] 28/32 Slide 32 Model results Proton spin u-quark OAM d-quark OAM 2+2D Distortion correlated to nucleon spin [C.L., Pasquini (2011)] 29/32 Slide 33 [C.L., Pasquini, Xiong, Yuan (2012)] Average transverse quark momentum correlated to nucleon spin Model results Vorticity 2+2D 30/32 Slide 34 Model results Quark spin u-quark OAM d-quark OAM 2+2D Distortion correlated to quark spin [C.L., Pasquini (2011)] 31/32 Slide 35 Model results [C.L., Pasquini (2011)] 32/32 Slide 36 Summary 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 Lecture 3 Nucleon FFsPDFsTMDsGPDs GTMDs LFWFs Slide 37 Backup slides Slide 38 Spin decompositions in a nutshell [Jaffe, Manohar (1990)][Ji (1997)] SqSq SgSg LgLg LqLq SqSq LqLq JgJg CanonicalKinetic Gauge non-invariant ! Incomplete Slide 39 FSIISI SIDISDrell-Yan OAM and path dependence [Ji, Xiong, Yuan (2012)] [Hatta (2012)] [C.L. (2013)] Coincides locally with kinetic quark OAM Naive T-even x-based Fock-SchwingerLight-front LqLq LqLq Quark generalized OAM operator Slide 40 Kinetic vs canonical OAM Quark naive canonical OAM (Jaffe-Manohar) Model-dependent ! Kinetic OAM (Ji) but No gluons and not QCD EOM ! Pure twist-3 Canonical OAM (Jaffe-Manohar) [C.L., Pasquini, PLB710 (2012) 486] [C.L., Pasquini, PRD84 (2011) 014015] [C.L., Pasquini, Xiong, Yuan, PRD85 (2012) 114006] [Kanazawa, C.L., Metz, Pasquini, Schlegel, PRD (2014)] Slide 41 Lattice results CIDI [Deka et al. (2013)]