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Energy Evolution of Sivers asymmetry in Hard Processes

Energy Evolution of Sivers asymmetry in Hard Processes. Feng Yuan Lawrence Berkeley National Laboratory. Outlines. General theory background Implement the TMD evolution from low Q SIDIS to Drell-Yan Match to high Q Drell-Yan/W/Z Collins asymmetries. Hard processes.

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Energy Evolution of Sivers asymmetry in Hard Processes

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  1. Energy Evolution of Sivers asymmetry in Hard Processes Feng Yuan Lawrence Berkeley National Laboratory

  2. Outlines • General theory background • Implement the TMD evolution from low Q SIDIS to Drell-Yan • Match to high Q Drell-Yan/W/Z • Collins asymmetries

  3. Hard processes • In the context of this talk, the hard processes means low transverse momentum hard processes • Semi-inclusive DIS at low pt • Drell-Yan/W/Z production • Higgs production • …

  4. Collinear vs TMD factorization • TMD factorization is an extension and simplification to the collinear factorization • Extends to the region where collinear fails • Simplifies the kinematics • Power counting, correction 1/Q neglected (PT,Q)=H(Q) f1(k1T,Q) f2(k2T, Q) S(T) • There is no x- and kt-dependence in the hard factor

  5. DGLAP vs CSS • DGLAP for integrated parton distributions • One hard scale (Q)=H(Q/) f1()… • CSS for TMDs • Two scales, large double logs

  6. Evolution vs resummation • Any evolution is to resum large logarithms • DGLPA resum single large logarithms • CSS evolution resum double logarithms

  7. Energy Evolution • CS evolution for TMD distribution/fragmentation functions, scheme-dependent • Collins-Soper 81, axial gauge • Ji-Ma-Yuan 04, Feynman gauge, off-light • Collins 11, cut-off • SCET, quite a few • CSS evolution on the cross sections • TMD factorization implicit

  8. Energy dependence • Collins-Soper Evolution, 1981 • Collins-Soper-Sterman, 1985 • Boer, 2001 • Idilbi-Ji-Ma-Yuan, 2004 • Kang-Xiao-Yuan, 2011 • Collins 2010 • Aybat-Collins-Rogers-Qiu, 2011 • Aybat-Prokudin-Rogers,2012 • Idilbi, et al., 2012

  9. Semi-inclusive DIS • Fourier transform • Evolution

  10. Calculate at small-b • Sudakov

  11. b*-prescription and non-perturbative form factor • b* always in perturbative region • This will introduce a non-perturbative form factors • Generic behavior

  12. Rogers et al. • Calculate the structure at two Q, • Relate high Q to low Q • Low Q parameterized as Gaussian

  13. BLNY form factors • Fit to Drell-Yan and W/Z boson production bmax=0.5GeV-1

  14. BLNY form can’t describe SIDIS • Log Q dependence is so strong, leading to a≈0.08 at HERMES energy • Hermes data require a≈0.2 BLNY will be even Worse Any modification will Introduce new problem

  15. It could be that the functional form is not adequate to describe large-b physics • In particular, for \ln Q term (see follows) • Or evolution has to be reconsidered in the relative (still perturbative) low Q range around HERMES/COMPASS • Q>~Q0~1/b*~2GeV (for bmax=0.5GeV-1)

  16. One solution: back to old way • Parameterize at scale Q0

  17. Limitations • It’s an approximation: both Q0 and Q are restricted to a limited range, definitely not for W/Z boson • Log(Q0 b) in the evolution kernel • Do not have correct behavior at small-b (could be improved), will have uncertainties at large pt • x-dependence is not integrated into the formalism

  18. Advantages • 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

  19. Almost parameter-free prediction • SIDIS Drell-Yan in similar x-range

  20. Fit to Sivers asymmetries • With the evolution effects taken into account. • Not so large Q difference

  21. Systematics of the SIDIS experiments are well understood • Q range is large to apply perturbative QCD • Sivers functions are only contributions to the observed asymmetries

  22. Predictions at RHIC • About a factor of 2 reduction, as compared to previous order of magnitude difference

  23. Cross checks • Re-fit Rogers et al’s parameterization to the pt-distributions, and calculate the SSA, in similar range • Assume a simple Gaussian for both SIDIS and Drell-Yan (Schweitzer et al.), and again obtain similar size SSA for Drell-Yan

  24. Match to higher Q • Extract the transverse momentum-moment of the Sivers function, and use the b* prescription and resummation, and again obtain similar size of SSA for Drell-Yan • This can be used to calculate the asymmetries up to W/Z boson production

  25. High energies w/o evolution b*-prescription Q=5.5GeV with evolution Z boson PT(GeV)

  26. Collins asymmetries • Ec.m.≈10GeV, di-hadron azimuthal asymmetric correlation in e+e- annihilation

  27. Collins asymmetries in SIDIS • asd

  28. Test the evolution at BEPC • Ec.m.=4.6GeV, di-hadron in e+e- annihilation BEPC-(Beijing electron-positron collider)

  29. It is extremely important to test this evolution effect • EIC will be perfect, because Q coverage • Anselm Vossen also suggests to do it at BELLE with ISR with various Q possible

  30. 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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