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June , Dipartimento di Fisica, Universita’ di Pavia, Italy

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Presentation on theme: "June , Dipartimento di Fisica, Universita’ di Pavia, Italy"— Presentation transcript:

1 June 25 2013, Dipartimento di Fisica, Universita’ di Pavia, Italy
Parton Wigner Distributions of the nucleon Cédric Lorcé IPN Orsay - LPT Orsay June , Dipartimento di Fisica, Universita’ di Pavia, Italy

2 The outline Zoo of parton distribution functions
Physical interpretation Wigner distributions and OAM Model calculations Conclusions

3 The outline Zoo of parton distribution functions
Physical interpretation Wigner distributions and OAM Model calculations Conclusions

4 The charges Charges Depends on : Polarization Vector Axial Tensor
Parton number Axial Parton helicity Tensor Parton transversity Charges

5 The parton distribution functions (PDFs)
Depends on : Polarization Longitudinal momentum (fraction) DIS PDFs PDFs Charges

6 The form factors (FFs) PDFs FFs Charges Depends on : Polarization
Longitudinal momentum (fraction) Momentum transfer Elastic scattering PDFs FFs FFs Charges

7 The generalized PDFs (GPDs)
Depends on : Polarization Longitudinal momentum (fraction) Momentum transfer GPDs DVCS PDFs FFs GPDs Charges

8 The transverse momentum-dependent PDFs (TMDs)
Depends on : Polarization Longitudinal momentum (fraction) Momentum transfer Transverse momentum No direct connection TMDs FFs PDFs Charges GPDs SIDIS TMDs

9 The generalized TMDs (GTMDs)
Depends on : GTMDs Polarization Longitudinal momentum (fraction) Momentum transfer Transverse momentum TMDs GPDs ??? PDFs FFs GTMDs Charges

10 The complete zoo GTMDs TMDs TMFFs GPDs TMCs PDFs FFs Charges
Depends on : GTMDs Polarization Longitudinal momentum (fraction) Momentum transfer Transverse momentum TMDs TMFFs GPDs ??? TMCs PDFs FFs GTMDs Charges [C.L., Pasquini, Vanderhaeghen (2011)]

11 The double parton scattering
Depends on : Polarization Longitudinal momentum (fraction) Momentum transfer Transverse momentum Inter-parton distance DPDFs DPDFs [Diehl, Ostermeier, Schäfer (2012)] [Thürman, Master thesis (2012)]

12 The outline Zoo of parton distribution functions
Physical interpretation Wigner distributions and OAM Model calculations Conclusions

13 The physical interpretation
Initial/final Average/difference Position Momentum Fourier-conjugated variables

14 The physical interpretation
[Ernst, Sachs, Wali (1960)] [Sachs (1962)] Breit frame Non-relativistic ! Position w.r.t. the CM Lorentz contraction Creation/annihilation of pairs

15 The physical interpretation
[Soper (1977)] [Burkardt (2000)] Drell-Yan frame Position w.r.t. the center of momentum Lorentz contraction Creation/annihilation of pairs

16 The physical interpretation
Dirac matrix ~ quark polarization Quark Wigner operator Wilson line Canonical momentum Either fix the gauge such that , i.e. work with boundary condition Or split the Wilson line to form Dirac variables

17 The physical interpretation
Quark Wigner operator Fixed light-front time No need for time-ordering ! Non-relativistic Wigner distribution [Ji (2003)] [Belitsky, Ji, Yuan (2004)] 3+3D Relativistic Wigner distribution [C.L., Pasquini (2011)] [C.L., Pasquini, Xiong, Yuan (2012)] 2+3D GTMDs

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

19 The outline Zoo of parton distribution functions
Physical interpretation Wigner distributions and OAM Model calculations Conclusions

20 Heisenberg’s uncertainty relations
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

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

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

23 The path dependence Orbital angular momentum Canonical Kinetic
[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 FSI ISI Drell-Yan SIDIS

24 The proton spin decompositions
[C.L. (2013)] [Leader, C.L. (in preparation)] Reviews : Canonical Kinetic [Jaffe, Manohar (1990)] [Ji (1997)] Pros: Satisfies canonical relations Complete decomposition Pros: Gauge-invariant decomposition Accessible in DIS and DVCS Cons: Gauge-variant decomposition Missing observables for the OAM Cons: Does not satisfy canonical relations Incomplete decomposition News: Gauge-invariant extension News: Complete decomposition [Chen et al. (2008)] [Wakamatsu (2009,2010)] OAM accessible via Wigner distributions [C.L., Pasquini (2012)] [C.L., Pasquini, Xiong, Yuan(2012)] [Hatta (2012)]

25 The outline Zoo of parton distribution functions
Physical interpretation Wigner distributions and OAM Model calculations Conclusions

26 The light-front overlap representation
[C.L., Pasquini, Vanderhaeghen (2011)] Overlap representation Momentum Polarization Light-front quark models Wigner rotation

27 The model results [C.L., Pasquini (2011)] Wigner distribution of unpolarized quark in unpolarized nucleon favored disfavored Left-right symmetry No net quark OAM

28 The model results [C.L., Pasquini (2011)] Distortion induced by the nucleon longitudinal polarization Proton spin u-quark OAM d-quark OAM

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

30 The model results [C.L., Pasquini (2011)] Distortion induced by the quark longitudinal polarization Quark spin u-quark OAM d-quark OAM

31 The model results Quark spin-nucleon spin correlation Proton spin
[C.L., Pasquini (2011)] Quark spin-nucleon spin correlation Proton spin u-quark spin d-quark spin

32 The model results [C.L., Pasquini (2011)]

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

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

35 The conclusions Twist-2 parton distributions provide
multidimensional pictures of the nucleon Relativistic phase-space distributions exist. Open question: how to access them? Both kinetic (Ji) and canonical (Jaffe-Manohar) are measurable (twist-2 and twist-3) Model calculations can test spin sum rules

36 Backup slides

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

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

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

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

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

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

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

44 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. ( )] [C.L., Pasquini, Vanderhaeghen (2011)] [Pasquini & al. ( )] [Ma & al. ( ), Jakob & al. (1997), Bacchetta & al. (2008)] [Ma & al. ( ), Jakob & al. (1997)] [Bacchetta & al. (2008)] [Efremov & al. (2009)] [Meißner & al. (2007)]

45 (reduces to Melosh rotation in case of FREE quarks)
Geometrical explanation [C.L., Pasquini (2011)] Preliminaries Conditions: Quasi-free quarks Spherical symmetry Wigner rotation Light-front helicity Canonical spin (reduces to Melosh rotation in case of FREE quarks)

46 Geometrical explanation
Axial symmetry about z

47 Geometrical explanation
Axial symmetry about z

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