1. Luciano L. Pappalardo University of Ferrara Selected TMD results from HERMES L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-18 2013

2. The full phase-space distribution of the partons encoded in the Wigner function 2 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013 The phase-space distribution of partons

3. The full phase-space distribution of the partons encoded in the Wigner function TMDs GPDs cannot be directly accessed experimentally  integrated quantities The phase-space distribution of partons 3 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

4. TMDs The non-collinear structure of the nucleon Sivers worm-gears Boer-Mulders pretzelosity helicity transversity momentum Sivers worm-gears GPDs The full phase-space distribution of the partons encoded in the Wigner function cannot be directly accessed experimentally  integrated quantities 4 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

5. The non-collinear structure of the nucleon Sivers worm-gears Boer-Mulders pretzelosity helicity transversity momentum Sivers worm-gears FF Fragmentation Functions (FF) hadronhadron Collins FF chiral-odd unpol. FF chiral-even 5 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

6. The SIDIS cross-section } 6 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013 FF

7. The SIDIS cross-section } beam polarization unpolarized beam and target polarization target polarization 7 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

8. The SIDIS cross-section } 8 L.L. Pappalardo - SPIN2012 – JINR, Dubna, Russia – September 17-22 2012 18 Structure Functions Leading twist Sub-leading Twist Distribution Functions Fragmentation Functions h

9. Selected twist-2 and twist-3 1-hadron SIDIS results 9 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

10. Distribution FunctionsFragmentation Functions h } Sivers function Describes correlation between quark transverse momentum and nucleon transverse polarization 10 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

11. Sivers amplitudes significantly positive slightly positive consistent with zero consistent with Sivers func. of opposite sign for u and d quarks (isospin-symmetry) [Anselmino et al.,Eur.Phys.J.A3,2009] [Airapetian et al., Phys. Rev. Lett. 103 (2009) 152002] 11 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

12. Sivers amplitudes significantly positive slightly positive consistent with zero (isospin-symmetry) [Anselmino et al.,Eur.Phys.J.A3,2009] consistent with Sivers func. of opposite sign for u and d quarks [Airapetian et al., Phys. Rev. Lett. 103 (2009) 152002] 12 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013 significantly positive slightly positive

13. Sivers kaons amplitudes: open questions  + /K + production dominated by u-quarks, but: 13 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

14. Sivers kaons amplitudes: open questions  + /K + production dominated by u-quarks, but: 14 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013 different role of various sea quarks ? ?

15. no effect for pions, but hint of a systematic shifts for kaons Sivers kaons amplitudes: open questions different role of various sea quarks ? ?  + /K + production dominated by u-quarks, but: 15 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013 ? Higher-twist contrib. for Kaons only in low-Q 2 region significant deviation each x-bin divided into two Q 2 bins

16. Distribution FunctionsFragmentation Functions h } Pretzelosity Describes correlation between quark transverse momentum and transverse spin in a transversely pol. nucleon  Sensitive to non-spherical shape of the nucleon 16 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

17. …suppressed by two powers of P h  w.r.t. Sivers amplitudes All amplitudes consistent with zero 17 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

18. Distribution FunctionsFragmentation Functions h } Describes the probability to find longitudinally polarized quarks in a transversely polarized nucleon!  Can be accessed in LT DSAs 18 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013 }

19. 19 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013 S. Boffi et al. (2009) Phys. Rev. D 79 094012 Light-cone constituent quark model dashed line: interf. L=0, L=1 dotted line: interf L=1, L=2  The only TMD that is both chiral-even and naïve-T-even  requires interference between wave function components that differ by 1 unit of OAM  quark orbital motion inside nucleons

20.  The only TMD that is both chiral-even and naïve-T-even  requires interference between wave function components that differ by 1 unit of OAM  quark orbital motion inside nucleons  Accessible in LT DSAs: 20 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013 S. Boffi et al. (2009) Phys. Rev. D 79 094012 Light-cone constituent quark model dashed line: interf. L=0, L=1 dotted line: interf L=1, L=2

21. 21 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013 S. Boffi et al. (2009) Phys. Rev. D 79 094012 Light-cone constituent quark model dashed line: interf. L=0, L=1 dotted line: interf L=1, L=2 Simplest way to probe  The only TMD that is both chiral-even and naïve-T-even  requires interference between wave function components that differ by 1 unit of OAM  quark orbital motion inside nucleons  Accessible in LT DSAs:

22. similar observations from Hall-A and COMPASS slightly positive ? consistent with zero positive!! 22 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

23. 23 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

24. Distribution FunctionsFragmentation Functions h } Describes the probability to find transversely polarized quarks in a longitudinally polarized nucleon 24 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013  some models support the simple relation

25. Amplitudes consistent with zero for all mesons and for both H and D targets Deuterium targetHydrogen target A. Airapetian et al, Phys. Lett. B562 (2003) A. Airapetian et al, Phys. Rev. Lett. 84 (2000) 25 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

26. A. Airapetian et al, Phys. Lett. B562 (2003) 26 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013 Positive: Hydrogen results larger than Deuteron (u-quark dominance) Positive: Hydrogen and Deuteron of same size Deuteron positive, Hydrogen  0 (u-quark dominance)

27. Distribution Functions } Subleading twist L.L. Pappalardo – Structure of Nucleons and Nuclei – Como – June 10-14 2013 Sensitive to worm-gear, sivers, transversity + higher-twist DF and FF 27 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

28. Subleading-twist sin(  S ) Fourier component sensitive to worm-gear, Sivers function, Transversity, etc significant non-zero signal for  - and K - ! Large and negative negative 28 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

29. Subleading-twist sin(  S ) Fourier component sensitive to worm-gear, Sivers function, Transversity, etc significant non-zero signal for  - and K - !  low-Q 2 amplitude larger  hint of Q 2 dependence for  - Large and negative negative 29 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

30. 2-hadron SIDIS results Following formalism developed by Steve Gliske Find details in Transverse Target Moments of Dihadron Production in Semi-inclusive Deep Inelastic Scattering at HERMES S. Gliske, PhD thesis, University of Michigan, 2011 30 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013 http://www-personal.umich.edu/~lorenzon/research/HERMES/PHDs/Gliske-PhD.pdf

31. A short digression on di-hadron fragmentation functions Standard definition of di-hadron FF assume no polarization of final state hadrons (pseudo-scalar mesons) or define mixtures of certain partial waves as new FFs The cross-section is identical to the ones in literature, the only difference is the interpretation of the FFs: 31 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

32. The di-hadron SIDIS cross-section 32 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

33. The di-hadron SIDIS cross-section 33 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013 JHEP 06 (2008) 017

34. The di-hadron SIDIS cross-section 34 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013 JHEP 06 (2008) 017

35. Conclusions A rich phenomenology and surprising effects arise when parton transverse momentum is not integrated out! Transverse effects and orbital motion of partons are now established as key ingredients of the nucleon internal dynamics 35 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

36. Conclusions A rich phenomenology and surprising effects arise when parton transverse momentum is not integrated out! Transverse effects and orbital motion of partons are now established as key ingredients of the nucleon internal dynamics The HERMES experiment has played a pioneering role in these studies: 36 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

37. Back-up 37 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

38. Distribution FunctionsFragmentation Functions h } Describes correlation between quark transverse momentum and transverse spin in unpolarized nucleon Boer-Mulders function 38 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

39. The cos2  amplitudes negative positive A. Airapetian et al, Phys. Rev. D 87 (2013) 012010 39 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

40. The cos2  amplitudes negative positive Large and negative A. Airapetian et al, Phys. Rev. D 87 (2013) 012010 http://www-hermes.desy.de/cosnphi/ Analysis multi-dimensional in x, y, z,and Pt Create your own projections of results through: 40 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

41. The cos  amplitudes negative Large and negative Consist. with 0 A. Airapetian et al, Phys. Rev. D 87 (2013) 012010 http://www-hermes.desy.de/cosnphi/ Analysis multi-dimensional in x, y, z,and Pt Create your own projections of results through: 41 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

42. Distribution FunctionsFragmentation Functions h } Transversity Describes probability to find transversely polarized quarks in a transversely polarized nucleon 42 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

43. Consistent with Belle/BaBar measurements in e + e - Collins amplitudes positive consistent with zero large and negative! (isospin-symmetry) significantly positive consistent with zero [Airapetian et al., Phys. Lett. B 693 (2010) 11-16] Soffer bound xh 1 (x) d u xh 1 (x, k ) T u T d Anselmino et al. Phys. Rev. D 75 (2007) 43 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

44. } Distribution Functions 44 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

45. } open circles 0.2<z<0.5 full circles 0.5<z<0.8 open squares: 0.8<z<1.0 A. Airapetian et al, Phys. Lett. B 648 (2007) 1996-2000 data 45 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

46. H target, 2000-2007 data 0.2<z<0.7 Released yesterday!! 46 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

47. Released yesterday!! D target, 2000-2007 data 0.2<z<0.7 47 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

48. The sin(2  +  S ) Fourier component arises solely from longitudinal (w.r.t. virtual photon direction) component of the target spin related to UL Fourier comp: sensitive to worm-gear suppressed by one power of P h  w.r.t. Collins and Sivers amplitudes no significant signal observed (except maybe for K+) 48 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

49. The subleading-twist sin(2  -  S ) Fourier component sensitive to worm-gear, Pretzelosity and Sivers function: suppressed by one power of P h  w.r.t. Collins and Sivers amplitudes no significant non-zero signal observed 49 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

50. (a phenomenological explanation of the Collins effect) In the cross-section the Collins FF is always paired withy a distrib. function involving a transv. pol. quark. A short digression on the Lund/Artru string fragmentation model 50 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

51. 1 pseudo-scalar meson (PSM) 1 Longitudinal VM 2 transvrse VM A short digression on the Lund/Artru string fragmentation model 51 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

52. “gluon radiaton model” vs. Lund/Artru model The Lund/Artru model only accounts for favored Collins fragmentation. An extension of the model (the gluon radiation model), elaborated by S. Gliske accounts for the disfavored case Lund/Artu Gluon radiation Di-quark has q.n. of vacuum Struck quark joins the anti-quark in the final state  favored fragment. Di-quark has q.n. of observed final state Produced quark joins the anti-quark in the final state  disfavored fragment. 52 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

53. …and now let’s look at the results Fragment. processFav/disfavDeflectionSign of amplitude fav PSM disfav PSM fav VM< 0 disfav VM< 0 mixed VM0 or < 0 from data from models u dominance 53 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

54. …and now let’s look at the results Fragment. processFav/disfavDeflectionSign of amplitude fav PSM disfav PSM fav VM< 0 disfav VM< 0 mixed VM0 or < 0 from data from models u dominance 54 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

55. Aerogel n=1.03 C 4 F 10 n=1.0014 hadron separation lepton-hadron > 98% TRD, Calorimeter, preshower, RICH:  ~ 98%, K ~ 88%, P ~ 85% The HERMES experiment at HERA 55 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

56. Siver amplitudes: additional studies No systematic shifts observed between high and low Q 2 amplitudes for both  + and K + No indication of important contributions from exclusive VM 56 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013

57. The pion-difference asymmetry Contribution from exclusive  0 largely cancels out! significantly positive Sivers and Collins amplitudes are obtained measured amplitudes are not generated by exclusive VM contribution Contribution by decay of exclusively produced vector mesons (  0, ,  ) is not negligible (6-7% for pions and 2-3% for kaons), though substatially limited by the requirement z<0.7. a new observable 57 L.L. Pappalardo – Baryons 2013 – Glasgow – June 24-28 2013