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HERMES results on azimuthal modulations in the spin-independent SIDIS cross section. Madrid, DIS 2009. Francesca Giordano DESY, Hamburg For the collaboration. Negative square four-momentum transfer to the target Fractional energy of the virtual photon
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HERMES results on azimuthal modulations in the spin-independent SIDIS cross section Madrid, DIS 2009 Francesca Giordano DESY, Hamburg For the collaboration
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
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
Leading twist expansion FF DF
Leading twist expansion FF Distribution Functions (DF) DF Fragmentation Functions (FF)
Leading twist expansion FF Distribution Functions (DF) DF Fragmentation Functions (FF)
Leading twist expansion = Boer-Mulders function CHIRAL-ODD Distribution Functions (DF) Fragmentation Functions (FF) chiral-odd FF chiral-odd DF CHIRAL-EVEN!
Leading twist azimuthal modulation (Implicit sum over quark flavours)
Leading & next to leading twist azimuthal modulation ...neglecting interaction dependent terms.... (Implicit sum over quark flavours)
Cahn and Boer-Mulders effects CAHN EFFECT
Cahn and Boer-Mulders effects BOER-MULDERS EFFECT CAHN EFFECT
HERa MEasurementof Spin HERA storage ring @ DESY
HERa MEasurementof Spin Lepton (Electron/Positron) HERA beam (27.6 GeV)
HERMESspectrometer Resolution: Dp/p ~ 1-2% Dq <~0.6 mrad Electron-hadron separation efficiency ~ 98-99% Hadron identification with dual-radiator RICH
HERMESspectrometer Resolution: Dp/p ~ 1-2% Dq <~0.6 mrad Electron-hadron separation efficiency ~ 98-99% Hadron identification with dual-radiator RICH
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
Experimental extraction unfolding procedure
Experimental extraction Multidimensional ( ) unfolding procedure
The unfolding procedure Probability that an event generated with kinematics wis measured with kinematics w’ (w’) (w)
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)
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’
Measured inside acceptance Generated in 4p Why a multi-dimensional analysis? Monte Carlo + Cahn model
4D binned in Why a multi-dimensional analysis?
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
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
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
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
Hydrogen data M. Anselmino et al., Phys. Rev. D75:054032, 2007
cos2fh interpretation p- p- p- p+ p+ p+ L. P. Gamberg and G. R. Goldstein, Phys. Rev. D77:094016, 2008
All contributions Boer-Mulders Cahn (twist 4) cos2fh interpretation V. Barone et al. Phys.Rev. D78:045022, 2008
cos2fh interpretation B. Zhang et al., Phys. Rev. D78:034035, 2008
cosfh interpretation M. Anselmino et al., Phys. Rev. D71:074006, 2005 Eur. Phys. J. A31:373, 2007
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).
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.
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
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