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Azimuthal Modulations in Spin-Independent SIDIS Cross Section Study

This study examines azimuthal modulations in the spin-independent SIDIS cross section results. The investigation focuses on the fractional energy transfer, Bjorken scaling variable, and target polarization effects in unpolarized Semi-Inclusive DIS. The research delves into the leading twist azimuthal modulation and the effects of Cahn and Boer-Mulders in hadron production. Experimental extraction, multidimensional unfolding procedures, and the significance of a multi-dimensional analysis approach are explored, along with the interpretation of hydrogen and deuterium data. The study concludes by discussing the Cahn effect related to higher twist azimuthal modulation and the Boer-Mulders effect originating from the correlation of quark transverse motion and spin.

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Azimuthal Modulations in Spin-Independent SIDIS Cross Section Study

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

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

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

  4. Unpolarized Semi-Inclusive DIS

  5. Unpolarized Semi-Inclusive DIS

  6. Leading twist expansion FF DF

  7. Leading twist expansion FF Distribution Functions (DF) DF Fragmentation Functions (FF)

  8. Leading twist expansion FF Distribution Functions (DF) DF Fragmentation Functions (FF)

  9. Leading twist expansion = Boer-Mulders function CHIRAL-ODD Distribution Functions (DF) Fragmentation Functions (FF) chiral-odd FF chiral-odd DF CHIRAL-EVEN!

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

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

  12. Cahn and Boer-Mulders effects CAHN EFFECT

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

  14. HERa MEasurementof Spin HERA storage ring @ DESY

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

  16. HERMESspectrometer Resolution: Dp/p ~ 1-2% Dq <~0.6 mrad Electron-hadron separation efficiency ~ 98-99% Hadron identification with dual-radiator RICH

  17. HERMESspectrometer Resolution: Dp/p ~ 1-2% Dq <~0.6 mrad Electron-hadron separation efficiency ~ 98-99% Hadron identification with dual-radiator RICH

  18. Aerogel n=1.03 C4F10 n=1.0014 HERMESspectrometer Resolution: Dp/p ~ 1-2% Dq <~0.6 mrad Electron-hadron separation efficiency ~ 98-99% Hadron identification with dual-radiator RICH

  19. Experimental extraction

  20. Experimental extraction

  21. Experimental extraction unfolding procedure

  22. Experimental extraction Multidimensional ( ) unfolding procedure

  23. The unfolding procedure

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

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

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

  27. The unfolding procedure

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

  29. Why a multi-dimensional analysis?

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

  31. z x bin=1 x bin=2 x bin=3 x bin=4 x bin=5 f f f f fh First y bin The multi-dimensional analysis

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

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

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

  35. Results

  36. Hydrogen data

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

  38. Hydrogen data

  39. Hydrogen data

  40. cos2fh interpretation p- p- p- p+ p+ p+ L. P. Gamberg and G. R. Goldstein, Phys. Rev. D77:094016, 2008

  41. All contributions Boer-Mulders Cahn (twist 4) cos2fh interpretation V. Barone et al. Phys.Rev. D78:045022, 2008

  42. cos2fh interpretation B. Zhang et al., Phys. Rev. D78:034035, 2008

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

  44. cosfh interpretation

  45. Hydrogen vs. Deuterium data h+

  46. Hydrogen vs. Deuterium data h-

  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. 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). • Monte Carlo studies show that: • A fully differentialunfolding procedure is essential to disentangle the ‘physical’ azimuthal asymmetry from the acceptance and radiative modulations of the cross-section.

  49. 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). • Monte Carlo studies show that: • A fully differentialunfolding procedure is essential to disentangle the ‘physical’ azimuthal asymmetry from the acceptance and radiative modulations of the cross-section. • Flavour dependent experimental results: • Negative <cosfh> moments are extracted for positive and negative hadrons, with a largerabsolute value for the positive ones • The results for the <cos2fh> moments are negative for the positive hadrons and positive for the negative hadrons • - Evidence of a non-zero Boer-Mulders function

  50. 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 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). • Monte Carlo studies show that: • A fully differentialunfolding 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 <cosfh> moments are extracted for positive and negative hadrons, with a largerabsolute value for the positive ones • The results for the <cos2fh> moments are negative for the positive hadrons and positive for the negative hadrons • - Evidence of a non-zero Boer-Mulders function

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