1. Transverse-Momentum Distributions and spherical symmetry Cédric Lorcé Mainz University Germany in collaboration with Barbara Pasquini Pavia University Italy [Lorcé, Pasquini (in preparation)] 30 years of strong interactions Three-day meeting in honour of J. Cugnon and H.-J. Pirner Sol Cress, Spa, Belgium 6-8 April 2011

2. Outline Semi-inclusive DIS and TMDs Model relations Light-cone helicity and canonical spin Spherical symmetry

3. Semi-inclusive DIS SIDIS 2 ~Im [Collins (1993)] [Bacchetta & al. (2007)]

4. Transverse-Momentum Distributions TMDs Dirac matrix selects quark polarization TMDs parametrize the quark-quark correlator Quark density in momentum space

5. Transverse-Momentum Distributions Convenient to think in terms of effective polarization Light-cone helicity Quark polarization Nucleon polarization

6. ** * * * * Model relations Flavor-dependent Flavor-independent Linear relationsQuadratic relation Bag  QSM LCCQM S Diquark AV Diquark Cov. Parton Quark Target [Jaffe & Ji (1991), Signal (1997), Barone & al. (2002), Avakian & al. (2008-2010)] [Lorcé & Pasquini (2011)] [Pasquini & al. (2005-2008)] [Ma & al. (1996-2009), Jakob & al. (1997), Bacchetta & al. (2008)] [Ma & al. (1996-2009), Jakob & al. (1997)] [Bacchetta & al. (2008)] [Efremov & al. (2009)] [Meißner & al. (2007)] *=SU(6) * * * * * *

7. LC helicity and canonical spin Canonical boost Light-cone boost

8. LC helicity and canonical spin Bag Model,  QSM, LCCQM, Quark-Diquark Model (Ma) and Covariant Parton Model Common assumption :Quasi-free quarks (reduces to Melosh rotation in case of FREE quarks) LC helicity Canonical spin Wigner rotation

9. LC helicity and canonical spin LC helicityCanonical spin Nucleon polarization Quark polarization Nucleon polarization

10. Spherical symmetry Common assumption :Explicit or implicit rotational symmetry Bag Model,  QSM, LCCQM, Quark-Diquark Model (Ma) and Covariant Parton Model The probability does not depend on the direction of canonical polarization

11. 2 + 2 =+ 22 = = 0 Spherical symmetry Axial symmetry about

12. 2 =+ 22 = = 0 Spherical symmetry Axial symmetry about

13. Why do relations appear in models? = = - Axial symmetry about

14. Why do relations appear in models? Spherical symmetryAxial symmetries Bag Model,  QSM, LCCQM, Quark-Diquark (Ma) and Covariant Parton Models Not independent!

15. Summary If a model assumes Quasi-free partons Spherical symmetry in canonical spin basis then it automatically implies the relations

16. Backup

17. Why do relations appear in models? What about Quark-Diquark models of Jakob & al. and Bacchetta & al.? Quark and diquark (a priori) not independent WF defined directly in Front Form Scalar diquark (Yukawa) Axial-vector diquark Jakob & al.Bacchetta & al. LCWFs without explicit dependence satisfy flavor-independent relations! ~ Independent constituents? Spherical symmetry? Instant Form WFs?

18. Formalism Light-Cone Quark Model Chiral Quark-Soliton Model Bag Model Independent quarks LC helicity Canonical spin (Melosh rotation) S-waveP-wave S-waveP-wave

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