1. OAM in transverse densities and resonances Cédric Lorcé and 09 Feb 2012, INT, Seattle, USA INT Workshop INT-12-49W Orbital Angular Momentum in QCD February 6 - 17, 2012

2. Outline Part one  Electromagnetic form factors  Transverse charge densities Part two  Decompositions of total OAM  How can one access to OAM?  Physical interpretation

3. Outline Part one  Electromagnetic form factors  Transverse charge densities Part two  Decompositions of total OAM  How can one access to OAM?  Physical interpretation

4. Electromagnetic form factors Textbook interpretation Breit frame Spatial charge density Lorentz contraction No probabilistic/charge interpretation Creation/annihilation of pairs Spin-1/2 [Ernst, Sachs, Wali (1960)] [Sachs (1962)]

5. Electromagnetic form factors Light-front interpretation Drell-Yan-West frame Transverse charge density Probabilistic/charge interpretation [Soper (1977)] [Burkardt (2000)] Number operator

6. Transverse charge densities Longitudinally polarized target + - [Miller (2007)] ProtonNeutron Monopole Negative core does not fit naive picture

7. Transverse charge densities Transversely polarized target + - [Carlson, Vanderhaeghen (2008)] + MonopoleDipole + ProtonNeutron

8. Transverse charge densities Induced electric dipole [Burkardt (2003)] B int S d u d X Orbital angular momentum Light-front « artifact » Induced electric dipole moment Anomalous magnetic moment Helicity flip Distorted transverse densities

9. Transverse charge densities Deuteron [Carlson, Vanderhaeghen (2009)] Delta(1232) [Alexandrou et al. (2009)] Monopole =+++ DipoleOctupoleQuadrupole Lattice QCD J z =0J z =1J x =0J x =1 Dip

10. Transverse charge densities Arbitrary spin Orbital angular momentum Induced electric moments Anomalous moments 2j+1 multipoles Standard Model Supergravity Structureless particle Natural EM moments No OAM No distortions No anomalous moments Charge normalization Universal g=2 factor [C.L. (2009)]

11. Transverse charge densities Pion [Miller, Strikman, Weiss (2011)] Based on dispersion integral of imaginary part of timelike pion FF Singular!

12. Transverse charge densities N to N* transitions [Carlson, Vanderhaeghen (2008)] [Tiator, Vanderhaeghen (2009)] [Tiator, Drechsel, Kamalov, Vanderhaeghen (2011)] P 11 (1440) Proton Neutron S 11 (1535) MAID No probabilistic interpretation

13. Transverse charge densities N to Delta transitions [Carlson, Vanderhaeghen (2008)] [Tiator, Vanderhaeghen (2009)] [Tiator, Drechsel, Kamalov, Vanderhaeghen (2011)] P 33 (1232) Proton D 13 (1520) MAID Small quadrupole No probabilistic interpretation

14. Outline Part one  Electromagnetic form factors  Transverse charge densities Part two  Decompositions of total OAM  How can one access to OAM?  Physical interpretation

15. Species space Position space Momentum space Phase space Spin-orbit space Well-defined, unambiguous, conserved Ambiguous! Gauge symmetry! Crucial importance of the interpretation Position of the problem Decompositions of total OAM

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

17. Light-front wave functions Proton state Eigenstates of parton light-front helicity Eigenstates of total OAM Probability associated with the N,  Fock state Normalization NB: A + =0 gauge Decompositions of total OAM

18. RelativeIntrinsicNaive Interparton distance Impact parameter Transverse center of momentum Physical interpretation ? Depends on proton position Not intrinsic !

19. Decompositions of total OAM Equivalence IntrinsicRelativeNaive Due to the momentum constraint Flavor contribution Fock states Active partons Parton contribution Flavor projector

20. How can one access to OAM? TMDs But no exact extraction of OAM is known Most TMDs vanish in absence of OAM No information on quark position NB: Quark polarization Nucleon polarization In spherically symmetric (independent) quark models: Naive OAM density Pretzelosity TMD [Burkardt (2007)] [Efremov, Schweitzer, Teryaev, Zavada (2008,2010)] [She, Zhu, Ma (2009)] [Avakian, Efremov, Schweitzer, Yuan (2010)] [C.L., Pasquini (2011)]

21. How can one access to OAM? GPDs Most GPDs vanish in absence of OAM Quark OAM Ji’s sum rule for quark angular momentum Quark polarization Nucleon polarization [Ji (1997)] Divergence terms

22. How can one access to OAM? GTMDs Most GTMDs vanish in absence of OAM Quark polarization Nucleon polarization Absent in GPDs and TMDs Spin-orbit correlation OAM Consequence of axial symmetry [Meißner, Metz, Schlegel (2009)] [C.L., Pasquini, Vanderhaeghen (2011)] [C.L., Pasquini (2011)]

23. No wave packetsNo infinite normalization factors How can one access to OAM? Standard definition Canonical quark OAM operator Expectation value Singular normalization Link with GTMDs Wigner or phase-space distributions GTMD correlator [C.L., Pasquini (2011)] [Hatta (2011)] [C.L., Pasquini, Xiong, Yuan (2011)]

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

25. Physical interpretation Interpretation Operator representations Position spaceMomentum space Momentum Position Impact parameter Naive Intrinsic ??? Intrinsic? Question:

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

27. Physical interpretation Back to theory Canonical Belinfante OAMSpin Energy-momentum form factors Total angular momentum

28. Physical interpretation Link with GPDs QCD energy-momentum tensor Generalized Parton Distributions « Skewing » relies on QCD Lorentz covariance and

29. Physical interpretation Model artifacts? Models are not QCD Truncation of Fock space spoils Lorentz covariance In model calculations, one would expectbut [Carbonell, Desplanques, Karmanov, Mathiot (1998)] The genuine quark OAM is

30. Physical interpretation Sum rule GTMD version of Ji sum rule Canonical decomposition Based on QCD Lorentz covariance and

31. Summary Part one  Electromagnetic form factors 2D Fourier transform for physical intepretation  Transverse charge densities Distortions due to OAM Natural EM moments for any spin Part two  Decompositions of total OAM Different types of OAM  How can one access to OAM? TMDs, GPDs, GTMDs Overlap representation  Physical interpretation Model artifacts

32. Backup

33. C omplete picture @ PDFsFFs TMDs Charges GTMDs GPDs TMSDs TMFFs Transverse density in momentum space Transverse density in position space Longitudinal Transverse Momentum space Position space

34. Formalism Assumption :  in instant form (automatic w/ spherical symmetry) More convenient to work in canonical spin basis