SIDIS asymmetries in QuarkDiquark model for Distribution Functions

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SIDIS asymmetries in Quark-Diquark model for
Distribution Functions

Aram Kotzinian CEA-Saclay, IRFU/Service de
Physique Nucléaire, 91191 Gif-sur-Yvette, France
On leave in absence from YerPhI, Armenia and
JINR, Russia
PKU-RBRC Workshop on Transverse Spin Physics

• Introduction
• Quark-Diquark model of DFs
• Transverse target polarization depending
  asymmetries
• Sivers DF
• Helicity DFs
• Concluding remarks

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General expression for 1h production cross-section
This is a general expression which is also valid
for exclusive reactions and for entire phase
space of SIDIS (TFR, CFR) Azimuthal
modulations 2 polarization independent 1 single
beam polarization dependent 2 single target
longitudinal polarization dependent 1 double beam
target longitudinal polarization dependent 5
single target transverse polarization dependent 3
double beam target transverse polarization
dependent
A.K. NPB 441 (1995) 234 Bacchetta et al, JHEP
0702093,2007
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Measured Structure Functions and Asymmetries
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Twist-two TMD quark DFs
DFs from Q-DQ model
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Twist-two TMD quark FFs
FFs from DSS and Anselmino et al parameterisations
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Quark-Diquark model for DFs
R. Jakob, P. Mulders Rodrigues NP A626, 937
(1997)
Choose exponential form-factor
k, m
MR, Rs,a
Only few common parameters, mq0.36, MA0.8,
MS0.6, ?0.5 (GeV/c), for all DFs No x-kT
factorization and width of intrinsic transverse
momentum depends on x
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Quark-Diquark model, 2
Proton SU(6) wave function
And same for other DFs
Sivers and Boer-Mulders DFs are equal to zero
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Interpretation of target transverse spin
asymmetries
8 Structure Functions for target transverse spin
part
Parton model, Twist-2
Sivers
Collins
Comparison with x-dependence of COMPASS Deuteron
target data Nucl.Phys.B76531,2007
arXiv0705.2402  arXiv0709.3440 
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Sivers asymmetry
Further comments later
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Collins asymmetry _at_
COMPASS
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Collins asymmetry _at_
HERMES
We expect that Q-DQ model will work in the
valence quark region
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and
_at_ COMPASS
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Cahn kinematical corrections
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Interpretation of target transverse spin
asymmetries
Twist-2 DFs and FFs kT/Q kinematical
corrections
Works
Doesnt work
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and _at_
COMPASS
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and _at_
COMPASS
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Sivers effect
J.Ellis, D-S.Hwang, A.K. preliminary Sivers
function a la BHS from FSI
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Sivers effect 2
HERMES Proton target
as0.3
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Analyzing power of Sivers functions Positivity
Bound
Consider large kT limit
Brodsky, Hwang Schmidt
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Analyzing power of Sivers functions, 2
JMR model (dipole formfactor), J.Ellis,
D-S.Hwang, A.K.
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Analyzing power of Sivers functions, 3
Gaussian form-factor (J.Ellis, D.Hwang, A.K.)
Transverse Quark Spin Effects and the Flavor
Dependence of the Boer-Mulders Function L.Gamberg,
G.Goldstein M.Schlegel, 0708.0324v2
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Quark longitudinal polarization
For given x the sign of the polarization is
changing at high kT
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Quark longitudinal polarization
For given x the sign of the polarization is
changing at high kT
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Orbital momentum and g1L
Model by Brodsky, Hwang, Ma Schmidt, NPB 593
(2001) 311
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Positive and negative helicity DFs in Q-DQ model
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ALL _at_ JLab
Duak-Diquak model
M.Anselmino, A.Efremov, A.K B.Parsamyan PRD
74, 074015 (2006)
The case
is
very similar to Quark-Diquark model results
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HERMES, Vaness Mexner PhD (2005)
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Concluding remarks

• JMR q-dq model is a good tool for guidance
• The kT and pT dependences of (polarized) DFs and
  FFs can be nontrivial.
• No x-kT factorization in DFs, flavor dependence
  of kT(x), pT(z)
• The kT dependence of DF g1 is tightly related to
  quark orbital momentum
• In valence region this model is able to describe
  the x-dependence of new 6 transverse spin
  dependent azimuthal asymmetries
• Do we understand well dynamical origin of Sivers
  effect?
• FSI?
• Why changing form-factor of nucleon-quark-diquark
  vertex brings to unphysical kT behavior?
• How one can resolve this problem?
• Twist-four?
• More measurements are needed for better
  understanding TMD DFs
• HERMES 6 asymmetries transversely polarized
  proton target?
• For better understanding of SIDIS we need the
  data for unpolarized x-sections and asymmetries
  (Rh(x,z,pT), ALL(pT)) as a function of all
  kinematical variables (x, z, PT, Q2) or (x, PT)
  , (z, PT), (xF, PT)

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Additional slides
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cos(f) asymmetry in Q-DQ model (Cahn effect)
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cos(2f) asymmetry in Q-DQ model (Cahn effect)
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cos(2f) asymmetry in Q-DQ model (Cahn effect) 2
Different kT width for S and A form-factors
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Subleading twist
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Higher twist example 2 predictions for cos(fs)
asymmetry
Spectator model
Cahn correction for g1T contribution