1. Proton spin structure in phase-space May 17, FSU Alumni Center, Tallahassee, Florida, USA Cédric Lorcé CPhT Baryons 2016 16-20 May 2016 Florida State University Alumni Center

2. Outline Phase-space distribution Multipole decomposition Angular correlations Conclusions Nucleon « tomography »

3. Physical processes (low resolution) (Semi-)inclusive Exclusive Deep Inelastic ScatteringElastic Scattering Deeply Virtual Compton ScatteringSemi-Inclusive DIS 1D picture2D picture 3D picture

4. Physical processes (high resolution) (Semi-)inclusive Exclusive Deep Inelastic ScatteringElastic Scattering Deeply Virtual Compton ScatteringSemi-Inclusive DIS 1D picture2D picture 3D picture PDFs TMDs FFs GPDs

5. Parton distribution zoo TMDs FFsPDFs Charges GPDs [C.L., Pasquini, Vanderhaeghen (2011)] 2+1D 2+0D 0+3D 0+1D

6. 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 distribution LFWF

7. Phase-space distributions Wigner distribution Probabilistic interpretation Expectation value Heisenberg’s uncertainty relations Position space Momentum space Phase space [Wigner (1932)] [Moyal (1949)]

8. Phase-space distributions Quark Wigner operator Non-relativistic Wigner distribution [Ji (2003)] [Belitsky, Ji, Yuan (2004)] [C.L., Pasquini, PRD84 (2011) 014015] [C.L., Pasquini, Xiong, Yuan, PRD85 (2012) 114006] 3+3D GTMDs 2+3D Relativistic Wigner distribution [Echevarria et al., arXiv:1602.06953] Consistent pQCD definition :

9. Phase-space transverse modes Parametrization of a correlator is not unique Natural modes ? [C.L., Pasquini, PRD93 (2016)]

10. Phase-space transverse modes Parametrization of a correlator is not unique Natural modes ? [C.L., Pasquini, PRD93 (2016)]

11. Phase-space transverse modes Properties under parity and time-reversal Parametrization of a correlator is not unique Natural modes ? [C.L., Pasquini, PRD93 (2016)]

12. Phase-space transverse modes Unpolarized quark in unpolarized target UU

13. Phase-space transverse modes Unpolarized quark in longitudinally polarized target LU [C.L., Pasquini, PRD84 (2011)] OAM

14. Phase-space transverse modes Unpolarized quark in transversely polarized target (1) TU

15. Phase-space transverse modes Unpolarized quark in transversely polarized target (2) TU

16. Phase-space transverse modes Unpolarized quark in transversely polarized target (1+2) TU

17. Angular correlations Phase-space distributions TMDs GPDs [C.L., Pasquini, PRD93 (2016)]

18. Conclusions Quark/gluon phase space can be explored by tomography (DIS, SIDIS, DVCS, …) Multipole decomposition is a natural basis constrained by space-time symmetries All leading-twist parton distributions can be understood as encoding particular angular correlation