TMD Evolution: Matching SIDIS to Drell-Yan/W/Z Production in pp collisions

1. TMD Evolution: Matching SIDIS to Drell-Yan/W/Z Production in pp collisions Feng Yuan Lawrence Berkeley National Laboratory Refs: Sun, Yuan, arXiv: 1304.5037; to be submitted

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. 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

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

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

6. 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, y-cut-off • SCET, quite a few, … • CSS evolution on the cross sections • TMD factorization implicit

7. Energy dependence • Collins-Soper Evolution, 1981 • Collins-Soper-Sterman, 1985 • Boer, 2001 • Idilbi-Ji-Ma-Yuan, 2004 • Kang-Xiao-Yuan, 2011 • Collins 2011 • Aybat-Collins-Rogers-Qiu, 2011 • Aybat-Prokudin-Rogers,2012 • Idilbi, et al., 2012 IJMY04

8. Semi-inclusive DIS • Fourier transform • Evolution

9. Calculate at small-b • Sudakov

10. b*-prescription and non-perturbative form factor • b* always in perturbative region • This will introduce a non-perturbative form factors • Generic behavior Collins-Soper-Sterman 85

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

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

13. Very successful phenomenology • Most quoted comparisons at the LHC for W/Z production ResBos: Nadolsky, et al., PRD 2003 CSS resummation built in

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 Ji, Ma, Yuan, 2004 • 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. Assumptions • Systematics of the SIDIS experiments are well understood • Q range is large to apply perturbative QCD and TMD factorization • 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. Matching Arbitrary unit b*-prescription Q=5.5GeV with evolution PT(GeV)

26. High energies Q=5.5GeV Arbitrary unit Q=7.5GeV Q=9.5GeV Q=20GeV Z boson PT(GeV) DGLAP evolution (1/b*) yet to be included See also D. Boer talk

27. Uncertainties in the Sivers functions Up Down Ubar

28. SSA for W at RHIC • x-range similar to HERMES/COMPASS • Early calculations by Kang-Qiu, Metz-Zhou W+ W- 500GeV, y=0

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

30. Collins asymmetries in SIDIS • asd

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

32. 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

33. 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