1. Quark and Gluon Sivers Functions
S. Brodsky
D.S. Hwang
J. Soffer
Ivan Schmidt
Como 2005

2. Sivers Function New distribution functions:
Corrections to collinear approximation
Possible explanation of Single Spin Asymmetries
Among these:
Sivers distribution function:
Collins fragmentation function:
Distr. of unpolarized quark in trans. polarized target
Fragm. of trans. polarized quark into unpolarized hadron

3. Many times they appear together:
transversity
Sivers:
T-odd correlation
Azimuthal asymmetry with respect to
(1993) Incorrect.
Target rest frame
Azimuthal asymmetry
Transverse spin
Helicity basis

4. Final state interactions
Two spin amplitudes which couple to the same final state
Helicity flip
Helicity non-flip
Interference
(2) Non-trivial phase difference
Conclusions
SSA : QCD at amplitude level.
SSA : understanding L Similar to
Need Im : cannot be tree level.
Final state interactions

5. Sivers SSA shadowing Simple model Drell-Yan crossing
Initial state interactions
crossing
Drell-Yan
Final state interactions

6. How to obtain the Sivers function ?
Drell-Yan: initial state interactions
( different gauge links )
How to obtain the Sivers function ?
Weak interaction processes
Produced quark left-handed
Transversity cannot contribute
In more detail (Boer, Mulders):

7. Parametrization
which can be projected for the specific process.
1) Electromagnetic case :
result:
Drell-Yan
crossing

8. 2) Charged currents
SSAs in
get
only
Similar analysis for
only Sivers
3) Neutral currents
same SSA as in the em case
factor with respect to em case

9. Some phenomenology Sivers Factorized form (Anselmino et al.)
flavor separation

10. Only Sivers (photon does not fragment)
Gluon Sivers function
Gluon contribution to proton amm
(J. Soffer, I. S.)
Photon production
Jet correlations
D meson production
(Boer, Vogelsang)
Proposals
(Anselmino et al.)
Only Sivers (photon does not fragment)
Unpolarized
Gluon distribution
Hard process
dominant
t-channel

11. SSA for Sivers functions quark Sivers function gluon Sivers function
dominates
gluons cannot have transverse spin
Sivers functions
quark Sivers function
gluon Sivers function

12. Identify kinematic region where gluon Sivers function dominates :
Take
GeV
for
integrated
low values contribute

13. Other possibilities:
no integration
more difficult experimentally
quark annihilation dominates
Prompt photon production at high is a good probe for extracting the gluon Sivers function.
Conclusion:
The Sivers function has interesting physics information