1. Measurement of azimuthal asymmetries of the unpolarized cross-section at HERMES Francesca Giordano Charlottesville, USA, SPIN2008 Università degli studi di Ferrara

2. Unpolarized Semi-Inclusive DIS (SIDIS)

3. Unpolarized SIDIS : collinear approximation

4. Unpolarized SIDIS : non-collinear cross-section

6. Leading twist expansion DF FF

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

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

9. Leading twist expansion = Boer-Mulders function CHIRAL-ODD 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. Structure functions expansion at leading twist (Implicit sum over quark flavours)

11. Structure functions expansion at twist 3 (Implicit sum over quark flavours)

12. Structure functions expansion at twist 3 (Implicit sum over quark flavours)

13. Structure functions expansion at twist 3 (Implicit sum over quark flavours)

14. Structure functions expansion at twist 3 (Implicit sum over quark flavours)...neglecting interaction dependent terms....

15. Cahn and Boer-Mulders effects (Implicit sum over quark flavours)...neglecting interaction dependent terms....

16. Cahn and Boer-Mulders effects kTkT kTkT CAHN EFFECT

17. BOER-MULDERS EFFECT Cahn and Boer-Mulders effects kTkT kTkT sTsT sTsT kTkT kTkT CAHN EFFECT

18. HERa MEasurement of Spin HERA storage ring @ DESY

19. HERMES spectrometer Resolution:  p/p ~ 1-2%  <~0.6 mrad Electron-hadron separation efficiency ~ 98-99%

20. HERMES spectrometer Resolution:  p/p ~ 1-2%  <~0.6 mrad Electron-hadron separation efficiency ~ 98-99%

21. Experimental extraction

26. Why a fully differential analysis?

27. Standard Monte Carlo Why a fully differential analysis? Measured inside acceptance Generated in 4 

28. Why a fully differential analysis?

29. 1- VS. Multi-dimensional analysis

31. MC1, FLAT MC2, FLAT 1- VS. Multi-dimensional analysis

32. One-dimensional analysis Multi-dimensional analysis

33. One-dimensional analysis Multi-dimensional analysis 1- VS. Multi-dimensional analysis Fully differential analysis is needed

34. The unfolding procedure

35. Probability that an event generated with kinematics  is measured with kinematics  ’   ’ 

36. The unfolding procedure Accounts for acceptance, radiative and smearing effects depends only on instrumental and radiative effects Probability that an event generated with kinematics  is measured with kinematics  ’   ’ 

37. The unfolding procedure Includes the events smeared within kinematical cuts Accounts for acceptance, radiative and smearing effects depends only on instrumental and radiative effects Probability that an event generated with kinematics  is measured with kinematics  ’

38. The unfolding procedure

39. x bin=2 x bin=3 The multi-dimensional analysis Z  x bin=1 x bin=5 ....x4 as the y binning is missing here! x bin=4 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 hT 0.050.20.350.50.754

40. Z ....x4 as the y binning is missing here! The multi-dimensional analysis x bin=2 x bin=3 x bin=1 x bin=5 x bin=4 unfolding

41. Z ....x4 as the y binning is missing here! The multi-dimensional analysis x bin=2 x bin=3 x bin=1 x bin=5 x bin=4 projection

42. Z  The multi-dimensional analysis x bin=2 x bin=3 x bin=1 x bin=5 x bin=4

43. Model for the ‘Cahn effect’ in Monte Carlo The multi-dimensional analysis Monte Carlo check

44. The multi-dimensional analysis Monte Carlo check Measured inside acceptance Generated in 4 

45. The multi-dimensional analysis Monte Carlo check Measured inside acceptance Generated in 4 

46. The multi-dimensional analysis Monte Carlo check Measured inside acceptance Generated in 4 

47. Monte Carlo Test Cahn Model Unfolded

48. Results

49. Statistics Target TypeHadron charge#SIDIS (Million) Hydrogenh+h+ 1.46 h-h- 0.82 Deuteriumh+h+ 1.53 h-h- 1.00

50. Hydrogen target

51. Cahn and Boer-Mulders effects (interaction dependent terms neglected)

52. Cahn and Boer-Mulders effects

53. cos2  interpretation

54.      

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

56. cos  interpretation

57. Hydrogen VS. Deuterium h+h+

58. h+h+

59. h-h-

60. Summary Accounting for the intrinsic quark transverse motion in the unpolarized cross- section gives origin to an azimuthal asymmetry in the hadron production direction; In particular it was stressed the existence of the 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).

61. Monte Carlo studies show that: A fully differential analysis together with an unfolding procedure is able to disentangle the ‘physical’ azimuthal asymmetry from the acceptance and radiative modulations of the cross-section. Summary Accounting for the intrinsic quark transverse motion in the unpolarized cross- section gives origin to an azimuthal asymmetry in the hadron production direction; In particular it was stressed the existence of the 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).

62. Monte Carlo studies show that: A fully differential analysis together with an unfolding procedure is able to disentangle the ‘physical’ azimuthal asymmetry from the acceptance and radiative modulations of the cross-section. Summary Accounting for the intrinsic quark transverse motion in the unpolarized cross- section gives origin to an azimuthal asymmetry in the hadron production direction; In particular it was stressed the existence of the 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). 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

63. Monte Carlo studies show that: A fully differential analysis together with an unfolding procedure is able to disentangle the ‘physical’ azimuthal asymmetry from the acceptance and radiative modulations of the cross-section. Summary Accounting for the intrinsic quark transverse motion in the unpolarized cross- section gives origin to an azimuthal asymmetry in the hadron production direction; In particular it was stressed the existence of the 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). 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 THANK YOU!

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

65. 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)

66. Compass results

67. Vector meson dilution