1. Energy Evolution for the Sivers Asymmetries in Hard Processes
Peng Sun
LBNL
in collaboration with F Yuan
arXiv:

2. Outlines TMD factorization Energy evolution
Fit the sivers function with SIDIS experiments
Implement the TMD evolution from low Q SIDIS to Drell-Yan
Collins asymmetries
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3. TMD factorization
TMD factorization is an extension and simplification to the collinear factorization
Simplifies the kinematics
Power counting, correction 1/Q neglected
(PT,Q)=H(Q) f1(x1,k1T,Q) f2(x2,k2T, Q) S(T)
There is no x- and kT-dependence in the hard factor
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4. Energy evolution
By solving CSS evolution equations
At the leading order of ɑs

6. There is no Landau pole singularity in the integral
Almost parameter-free
No Q-dependent non-perturbative form factor
Gaussian assumption at lower scale Q0
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7. SIDIS SIDIS at HERMES g0=0.1, gh=0.045 Q2=3.14GeV2, x=0.16 Q2=3.14GeV2
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8. SIDIS at COMPASS, Q2=7.75, x=0.1

9. Drell-Yan
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10. Fit to Sivers asymmetries
With the evolution effects taken into account.
Not so large Q difference
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14. Uncertainties in the Sivers functions: moments
Up quark most constrained in the moderate x
Large uncertainties in small-x region and sea quark
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15. Predictions at RHIC
About a factor of 2 reduction, as compared to previous order of magnitude difference
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16. Collins asymmetries in e+e- →hh
The collins effect is porprotianal to cos(2ɸ0)

17. Collins asymmetries
Ec.m.≈10GeV, di-hadron azimuthal asymmetric correlation in e+e- annihilation
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18. Test the evolution at BEPC
Ec.m.=4.6GeV, di-hadron in e+e- annihilation BEPC-(Beijing electron-positron collider)
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19. Conclusion
We evaluate the energy dependence for Sivers asymmetries in hard processes, from HERMES/COMPASS to typical Drell-Yan process
The same evolution procedure consistently describes the Collins asymmetries from HERMES/COMPASS and BELLE
Further tests are needed to nail down this issue
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20. Thank you very much!

21. Ji Ma Yuan scheme, in SIDIS
Structure function is
It depends on ρ

22. Collins scheme
This version is much simpler than that of Ji Ma Yuan

23. In Aybat-Collins-Qiu-Rogers framework
And then
Here gK(b) is gc×b2

24. Energy Evolution in TMD factorization scheme
Aybat-Collins-Qiu-Rogers, 2011

25. Q2-dependence Aybat-Prokudin-Rogers, 2011 Needs a cross check!
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26. Collins asymmetries in SIDIS
asd
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27. Energy evolution
In our framework
At the leading order of ɑs