Single Transverse Spin Asymmetries

1. Single Transverse Spin Asymmetries Jianwei Qiu Iowa State University RBRC Workshop on Single Spin Asymmetries June 1 – 3, 2005 Brookhaven National Lab, Upton, NY Jianwei Qiu, ISU

2. Outline • Single spin asymmetry – definition • Single spin asymmetry before QCD • Single spin asymmetry within the collinear factorization – high twist matrix elements • KT- factorization – Sivers and Collins effects • Connection between high twist matrix elements and Sivers and Collins functions • Open questions Jianwei Qiu, ISU

3. Spin-avg X-section: • Spin-dep X-section: • Single spin asymmetry: • single longitudinal spin asymmetry: • single transverse spin asymmetry: Single Spin Asymmetry – definition Jianwei Qiu, ISU

4. AL ≠ 0 for W+ production good for parton flavor separation Symmetry and Single Spin Asymmetry • Even though cross section is finite, single spin asymmetries can vanish if the polarized cross sections are independent of spin directions due to the fundamental symmetries of the interactions • AL vanishes for Parity conserved interactions: Jianwei Qiu, ISU

5. Single transverse spin asymmetry before QCD • Almost 40 years ago, AN in inclusive DIS was proposed • by Christ and Lee to test the Time-Reversal invariance: In the approximation of one-photon exchange, AN of inclusive DIS vanishes if Time-Reversal is invariant for EM and Strong interactions N. Christ and T.D. Lee, Phys. Rev. 143, 1310 (1966) Jianwei Qiu, ISU

6. AN = 0 for inclusive DIS • DIS cross section: • Leptionic tensor is symmetric:Lμν = Lνμ • Hadronic tensor: • Polarized cross section: • P and T invariance: Jianwei Qiu, ISU

7. s=23.5 GeV PT=0.5~2 GeV/c Large AN in hadronic collisions • process: only one hadron is transversely polarized: • Large asymmetries AN observed in hadron collisions: • decay of L • production of p’s FNAL - E704 Jianwei Qiu, ISU

8. Single spin asymmetry correspondsto a T-odd triple product Jianwei Qiu, ISU

9. = Chiral-odd helicity-flip density Single transverse spin asymmetry – AN in the parton model • transverse spin information at leading twist – transversity: • the operator for δq has even γ’s quark mass term • the phase requires an imaginary part loop diagram PQCD calculable partonic parts should not depend on light current quark mass – singals a high twist effect in pQCD Jianwei Qiu, ISU

10. Single transverse spin asymmetry – AN in collinear factorization approach • Leading twist PDF with transverse hadron spin: • need an even number g’s: Twist-3 matrix elements An extra transverse index extra gluon (its polarization) extra vector direction Jianwei Qiu, ISU

11. x • Unpinched pole to give the phase: High twist contribution to AN • Spin flip from interference between a quark state and a quark-gluon composite state • Observed hadron momentum provides the 3rd vector Q: pQCD factorization beyond leading twist? Jianwei Qiu, ISU

12. Multiple scales in hadronic collisions (3) (2) (1) • Hard collision: Q >> ΛQCD • Gluon shower: <kT>dynamic ~ F[Q2,log(s/Q2)] • Hadron wave function: <kT>intrinsic ~ 1/fm ~ ΛQCD • PQCD factorization: (1) Perturbative IR safe single hard partonic “cross section” (2) Leading log DGLAP evolution of PDFs (3) Nonperturbative PDFs Jianwei Qiu, ISU

13. H(Q) k k p p T Nonperturbative matrix element Short-distance Perturbative QCD factorization – (I) • Perturbative pinch poles: Parton state of momentum, k, lives much longer than the time of hard collision: |k2|<<|Q2| • Perturbative factorization: Remove soft interactions between different time scales Jianwei Qiu, ISU

14.  Perturbative QCD factorization (II) • KT –factorization Long lived parton state No all-order proof of kT – factorization for an arbitrary kT Leading Twist • Collinear factorization: Provides systematic ways to quantify high order corrections perturbative Factorization fails beyond the next-to-leading powers in hadronic collisions Power corrections Jianwei Qiu, ISU

15. Normal twist-2 distributions have different properties under the P and T transformation does not contribute to theAN is universal, x1=x2 for AN due to the pole AN from polarized twist-3 correlations • Factorization: • Twist-3 correlation functions: Jianwei Qiu, ISU

16. Single spin asymmetry within the collinear factorization • Generic twist-3 factorized contributions Provides hadron spin dependence transversity Even g’s ! Even g’s ! Calculated by Qiu and Sterman, Phys. Rev. D, 1999 Calculated by Kanazawa and Koike, Phys. Lett. B, 2000 Jianwei Qiu, ISU

17. Leading twist-3 contribution to AN • Minimal approach (within the collinear factorization): Jianwei Qiu, ISU

18. Predictive power of the factorization approach Jianwei Qiu, ISU

19. Represents a fundamental quantum correlation between quark and gluon inside a hadron What is the T(3)(x)? Jianwei Qiu, ISU

20. What the T(3)(x) tries to tells us? • Consider a classical (Abelian) situation: Jianwei Qiu, ISU

21. Model for TF(x,x) • TF(x,x) tells us something about quark’s transverse motion in a transversely polarized hadron • It is non-perturbative, has unknown x-dependence One parameter and one sign! Jianwei Qiu, ISU

22. Numerical results – (I)(compare apples with oranges) Qiu and Sterman Phy. Rev. D, 1999 Jianwei Qiu, ISU

23. Numerical results – (II)(compare apples with oranges) Qiu and Sterman Phy. Rev. D, 1999 Jianwei Qiu, ISU

24. Numerical results – (III)(comparison with RHIC data) • Comparison with STAR data • Too small PT value • to be comfortable • for initial state twist-3 • See Koike’s talk on final state twist-3 • New data from STAR, BRAHMS, PHENIX Jianwei Qiu, ISU

25. Twist-3 vs KT approach • Twist-3 contribution in collinear factorization – leading corrections from parton correlation (a minimal approach) • Effect of non-vanish parton kT (when kT ~ pT): M = Non-perturbative scale, e.g., di-quark mass, … Jianwei Qiu, ISU

26. Sivers’ functions • Sivers’ functions: Sivers’ functions are connected to a polarized hadron beam Sivers’ functions are T- odd, but do not need another T- odd function to produce nonvanish asymmetries – the extracted proportional factor is T- odd, proportional to AN • Polarized SIDIS cross section: Jianwei Qiu, ISU

27. Collins’ functions • Collins’ functions: Collins’ functions are connected to the unpolarized Fragmentation contributions to a hadron Collins’ functions are T- odd, need another T- odd function to produce nonvanish asymmetries • Polarized SIDIS cross section: Jianwei Qiu, ISU

28. KT - Factorization • kT-factorization measures parton kT directly, while twist-expansion gives integrated kT information • No formal proof of kT-factorization for hadronic collisions at kT ~ pT Q ~ pT >> kT • Factorization requires a separation of perturbative hard scale from nonperturbative hadronic scale a physical hard scale, Q, much larger than the kT • kT-factorization works for semi-inclusive DIS and Drell-Yan, or others with a large scale Q Jianwei Qiu, ISU

29. ℓ’ ℓ q k’ p q k’ P k sT k P Semi-inclusive deeply inelastic scattering Breit frame: Two scale problem: Q2=-q2, pT • Fixed order pQCD: • Single spin asym: • low pT data sensitive to parton kT If P is anti-parallel to p • Sudakov resummation: Jianwei Qiu, ISU

30. ℓ’ ℓ q k’ p k sT P Intrinsic vs dynamical kT In q-P frame, if • we can neglect in partonic part • But, we cannot neglect S • One can define kT-dependent and gauge invariant parton distributions • Soft interaction between the hadrons can spoil factorization • Sudakov resummation (done in b- or kT-space) resums dynamical kT from gluon shower • Parton orbital motion is more relevant to the intrinsic kT Jianwei Qiu, ISU

31. Twist-3 kT approach Sivers: Collins: Open questions – (I) • How much overlap between kT-approach at low pT and twist expansion at high pT? • What these nonperturbative functions try to tell us? “direct kT” vs “kT – moments” Jianwei Qiu, ISU

32. Open questions – (II) • If there is no KT – factorization, how universal are Sivers and Collins functions? • Although there is kT-factorization in SIDIS, Drell-Yan and the others, how to separate dynamical kT from intrinsic kT ? • How Sivers and Collins functions are affected by the process dependent gluon shower (resummation)? • … Jianwei Qiu, ISU

33. Backup transparencies Jianwei Qiu, ISU

34. ≠ Collinear approximation is important With collinear approximation: IR safe  = In general, matrix elements with different cuts are not equal: Jianwei Qiu, ISU

35. When does the factorization lose its predictive power? At the time when the nonperturbative functions lose their universality • For final-state fragmentation: Factorization breaks if the fragmentation took place inside the hadronic medium If the lifetime of the parton state of momentun k is shorter than the medium size Lifetime: Jianwei Qiu, ISU

36. Asymmetries • Single longitudinal spin asymmetries: • Double longitudinal spin asymmetries: Reduce under parity to: • Single transverse spin asymmetries: • Double transverse spin asymmetries: Jianwei Qiu, ISU

37. Measure Sivers’ and Collins’ functions • SIDIS: • Collins functions: Jianwei Qiu, ISU

38. Seperate Sivers’ and Collins’ functions Jianwei Qiu, ISU

39. Initial success of RHIC pp runs • p0cross section measured over 8 order of magnitude [PRL 91, 241803 (2003)] • Good agreement with NLO pQCD calculation at low pT • Can be used in interpretation • of spin-dependent results 9.6% normalization error not shown Jianwei Qiu, ISU