1. HERMES results on azimuthal modulations in the spin-independent SIDIS cross section Francesca Giordano DESY, Hamburg For the collaboration Madrid, DIS 2009

2. 2 Collinear approximation Unpolarized Semi-Inclusive DIS Negative square four-momentum transfer to the target Fractional energy of the virtual photon Bjorken scaling variable Fractional energy transfer to the produced hadron

3. 3 Collinear approximation Unpolarized Semi-Inclusive DIS Negative square four-momentum transfer to the target Fractional energy of the virtual photon Bjorken scaling variable Fractional energy transfer to the produced hadron Beam polarization Virtual photon polarization Target polarization

4. 4 Unpolarized Semi-Inclusive DIS

5. 5

6. 6 DF FF Leading twist expansion

7. 7 DF FF Leading twist expansion N / qULT U L T Distribution Functions (DF) q/h U U T Fragmentation Functions (FF)

8. 8 DF FF Leading twist expansion N / qULT U L T q/h U U T Distribution Functions (DF) Fragmentation Functions (FF)

9. 9 = Boer-Mulders function CHIRAL-ODD Leading twist expansion CHIRAL-EVEN CHIRAL-EVEN! chiral-odd DF chiral-odd FF N / qULT U L T q/h U U T Distribution Functions (DF) Fragmentation Functions (FF)

10. 10 Leading twist azimuthal modulation (Implicit sum over quark flavours)

11. 11 (Implicit sum over quark flavours)...neglecting interaction dependent terms.... Leading & next to leading twist azimuthal modulation

12. 12 Cahn and Boer-Mulders effects CAHN EFFECT

13. 13 BOER-MULDERS EFFECT CAHN EFFECT Cahn and Boer-Mulders effects

14. 14 HERa MEasurement of Spin HERA storage ring @ DESY

15. 15 HERa MEasurement of Spin Lepton (Electron/Positron) HERA beam (27.6 GeV)

16. 16 HERMES spectrometer Resolution:  p/p ~ 1-2%  <~0.6 mrad Electron-hadron separation efficiency ~ 98-99% Hadron identification with dual-radiator RICH

17. 17 HERMES spectrometer Resolution:  p/p ~ 1-2%  <~0.6 mrad Electron-hadron separation efficiency ~ 98-99% Hadron identification with dual-radiator RICH

18. 18 HERMES spectrometer Resolution:  p/p ~ 1-2%  <~0.6 mrad Electron-hadron separation efficiency ~ 98-99% Hadron identification with dual-radiator RICH Aerogel n=1.03 C 4 F 10 n=1.0014

19. 19 Experimental extraction

20. 20 Experimental extraction

21. 21 unfolding procedure Experimental extraction

22. 22 Multidimensional ( ) unfolding procedure Experimental extraction

23. 23 The unfolding procedure

24. 24 Probability that an event generated with kinematics w  is measured with kinematics w’ (w) (w’) The unfolding procedure

25. 25 The unfolding procedure Accounts for acceptance, radiative and smearing effects depends only on instrumental and radiative effects Probability that an event generated with kinematics w  is measured with kinematics w’ (w) (w’)

26. 26 Includes the events smeared into the acceptance Accounts for acceptance, radiative and smearing effects depends only on instrumental and radiative effects The unfolding procedure Probability that an event generated with kinematics w  is measured with kinematics w’

27. 27 The unfolding procedure

28. 28 Monte Carlo + Cahn model Measured inside acceptance Generated in 4  Why a multi-dimensional analysis?

29. 29 Why a multi-dimensional analysis?

30. 30 Why a multi-dimensional analysis? 4D binned in

31. 31 BINNING 400 kinematical bins x 12   -bins VariableBin limits# x0.0230.0420.0780.1450.2715 y0.30.450.60.70.854 z0.20.30.450.60.7515 P h. 0.050.20.350.50.754 The multi-dimensional analysis x bin=2 x bin=3  x bin=1 x bin=5    hh First y bin x bin=4 z

32. 32 The multi-dimensional analysis unfolding+fit x bin=2 x bin=3  x bin=1 x bin=5    hh First y bin x bin=4 z

33. 33 projection The multi-dimensional analysis x bin=2 x bin=3  x bin=1 x bin=5    hh First y bin x bin=4 z

34. 34 The multi-dimensional analysis x bin=2 x bin=3  x bin=1 x bin=5    hh First y bin x bin=4 z

35. Results

36. 36 Hydrogen data

37. 37 Hydrogen data M. Anselmino et al., Phys. Rev. D75:054032, 2007

38. 38 Hydrogen data

39. 39 Hydrogen data

40. 40 cos2  h interpretation       L. P. Gamberg and G. R. Goldstein, Phys. Rev. D77:094016, 2008

41. 41 cos2  h interpretation Boer-Mulders All contributions Cahn (twist 4) V. Barone et al. Phys.Rev. D78:045022, 2008

42. 42 cos2  h interpretation B. Zhang et al., Phys. Rev. D78:034035, 2008

43. 43 cos  h interpretation M. Anselmino et al., Phys. Rev. D71:074006, 2005 Eur. Phys. J. A31:373, 2007

44. 44 cos  h interpretation

45. 45 h+h+ Hydrogen vs. Deuterium data

46. 46 h-h- Hydrogen vs. Deuterium data

47. 47 Summary The existence of an intrinsic quark transverse motion gives origin to an azimuthal asymmetry in the hadron production direction: Cahn effect: an (higher twist) azimuthal modulation related to the existence of intrinsic quark motion; Boer-Mulders effect: a leading twist asymmetry originated from the correlation between the quark transverse motion and transverse spin (a kind of spin-orbit effect).

48. 48 Summary Monte Carlo studies show that: A fully differential unfolding procedure is essential to disentangle the ‘physical’ azimuthal asymmetry from the acceptance and radiative modulations of the cross-section. The existence of an intrinsic quark transverse motion gives origin to an azimuthal asymmetry in the hadron production direction: Cahn effect: an (higher twist) azimuthal modulation related to the existence of intrinsic quark motion; Boer-Mulders effect: a leading twist asymmetry originated from the correlation between the quark transverse motion and transverse spin (a kind of spin-orbit effect).

49. 49 Flavour dependent experimental results: Negative moments are extracted for positive and negative hadrons, with a larger absolute value for the positive ones The results for the moments are negative for the positive hadrons and positive for the negative hadrons - Evidence of a non-zero Boer-Mulders function Summary Monte Carlo studies show that: A fully differential unfolding procedure is essential to disentangle the ‘physical’ azimuthal asymmetry from the acceptance and radiative modulations of the cross-section. The existence of an intrinsic quark transverse motion gives origin to an azimuthal asymmetry in the hadron production direction: Cahn effect: an (higher twist) azimuthal modulation related to the existence of intrinsic quark motion; Boer-Mulders effect: a leading twist asymmetry originated from the correlation between the quark transverse motion and transverse spin (a kind of spin-orbit effect).

50. 50 The existence of an intrinsic quark transverse motion gives origin to an azimuthal asymmetry in the hadron production direction: Cahn effect: an (higher twist) azimuthal modulation related to the existence of quark intrinsic motion; Boer-Mulders effect: a leading twist asymmetry originated by the correlation between the quark transverse motion and spin (a kind of spin-orbit effect). Summary Monte Carlo studies show that: A fully differential unfolding procedure is able to disentangle the ‘physical’ azimuthal asymmetry from the acceptance and radiative modulations of the cross-section. THANK YOU! Flavour dependent experimental results: Negative moments are extracted for positive and negative hadrons, with a larger absolute value for the positive ones The results for the moments are negative for the positive hadrons and positive for the negative hadrons - Evidence of a non-zero Boer-Mulders function

51. 51 Compass results

52. 52 Experimental status: EMC E665 ZEUS c) Negative results in all the existing measurements No distinction between hadron type or charge

53. 53 EMC ZEUS collaboration ZEUS Drell-Yan Experimental status: Positive results in all the existing measurements No distinction between hadron type or charge (in SIDIS experiments) Indication of small Boer-Mulders function for the sea quark (from Drell-Yan experiments)