1. M. Grosse Perdekamp, UIUC Transverse Spin Measurements at RHIC Workshop on Transverse Spin and the Transverse Structure of the Nucleon 3 rd Joint Meeting of the DNP and the JPS in Waikola, Hawaii, October 13h -17th, 2009 STAR

2. M. Grosse Perdekamp, UIUC Transverse Spin Measurements at RHIC Inclusive Single Spin Asymmetries A N in Hadron Introduction RHIC Measurements Interpretation Measurements to Isolate different Mechanisms Tansversity & Collins Sivers Future Measurements Drell Yan & Jet-Photon STAR

3. Single Spin Asymmetries (SSA) in Hadron Collisions Introduction

4. 4 Single Spin Asymmetries (SSA) A N in Polarized Proton-Proton Scattering spsp π p p π spsp = 0 ? AN =AN = N L - N R N L + N R N L : pions to the left N R : pions to the right Example: Inclusive π production in polarized p-p Correlation proton spin S p vs p π ⊥ π transverse momentum Single transverse spin asymmetries A N October 13 th Transverse Spin Measurements at RHIC

5. 5 Scaling Limit: A N  0, QCD Test !? October 13 th Transverse Spin Measurements at RHIC

6. 6 Experiment: Sizeable SSA Observed over Large Range of Scales ! Experiment: A N >> 10 -4 for 4 GeV < √s < 200 GeV for charged pions ! from Christine Aidala, Spin 2008 and Don Crabb & Alan Krisch in then Spin 2008 Summary, CERN Courier, 6-2009 ZGS √s=4.7 GeVAGS √s=6.5 GeVFNAL √s = 20 GeVRHIC √s = 200 GeV π+π-π+π- October 13 th Transverse Spin Measurements at RHIC Soft effects due to QCD dynamics in hadrons remain relevant up to scales where pQCD can be used to describe the scattering process!

7. 7 NLO pQCD Cross Sections vs RHIC data for Different √s and Rapidity Intervals √s = 200 GeV ∆ PHENIX π 0, η = 0 ∙ Brahms π +,η = 2.95 ⌷ STAR π 0,η = 0 - - - - - NLO pQCD √s = 62.4 GeV See analysis in De Florian, Vogelsang, Wagner PRD 76,094021 (2007) and Bourrely and Soffer Eur.Phys.J.C36:371-374 (2004) o PHENIX π 0, η = 0 -------- NLO pQCD Good agreement between inclusive hadron cross sections from RHIC data and pQCD calculations ! p T [GeV] October 13 th Transverse Spin Measurements at RHIC

8. 8 Origin of Large SSA  Inspect Factorized Cross Section at Hard Scales! Jet proton structure hard scattering reaction fragmentation process Final state – hadron fragmentation pQCD Initial state – proton structure Kane, Pumplin, Repko  a LL ~10 -4 ) Can initial and/or final state effects generate large transverse spin asymmetries? (A N ~10 -1 ) October 13 th Transverse Spin Measurements at RHIC

9. 9 Origin of Large SSA for Hard Scattering -- Two Solutions: Final State vs Initial State (I) “Transversity” quark-distributions and Collins fragmentation Correlation between proton- und quark-spin and spin dependent fragmentation (II) Sivers quark-distribution + Correlation between proton-spin and transverse quark momentum Collins FF Quark transverse spin distribution Sivers distribution (III) Initial or final state twist-3 + Qiu/Sterman and Koike STAR, PRL-92:171801, 2004 + unified picture: Ji, Qiu, Vogelsang and Yuan in PRL-97:082002, 2006 October 13 th Transverse Spin Measurements at RHIC First measurement at RHIC √s = 200 GeV

10. RHIC Measurements of A N for Inclusive Hadrons

11. 11 BRAHMS: A N for Charged Pions vs p T and x F at √s=62.4 GeV and √s=200 GeV 200 GeV √s=200 GeV √s=62.4 GeV 0.4<p T <0.6 GeV/c 0.5 p T <0.6 GeV/c0.6 p T <0.8 GeV/c 0.8 p T <1.0 GeV/c 1.0 p T <1.2 GeV/c 0.5<p T <0.75 GeV/c1.0<p T <1.25 GeV/c1.25<p T <1.5 GeV/c1.5<p T <2.0 GeV/c2.0<p T <2.5 GeV/c A N increases with x F (valence quarks) A N increases with p T (?) Possibly constant from p T =1.5 GeV/c ? October 13 th Transverse Spin Measurements at RHIC

12. PHENIX: A N vs X F for  0 ’s at √s=62.4 GeV A N = 0 for x F < 0 no sizeable asymmetries at small x! Larger forward asymmetries at higher pseudo-rapidity, η ? Limited by statistics and correlations between x F, p T and η ! October 13 th Transverse Spin Measurements at RHIC

13. 13 STAR Run 2006: p T Dependence of A N at √s=200 GeV PRL 101,222001 For given η strong correlation between x F and p T : A N (p T ) integrated over x F A N (p T, x F ) A N increases with p T up to p T ~ 3 GeV/c -- Models: A N ~ 1/p T October 13 th Transverse Spin Measurements at RHIC

14. Decrease as ~1/p T expected from initial state effects is not observed. A N constant from p T >2.5 GeV. Need more statistics to extend measurement to p T > 4 GeV ! Positive x F Negative x F Consistent with zero for all p T STAR Run 2008: p T Dependence of A N at √s=200 GeV Ogawa at CIPANP 2009 October 13 th Transverse Spin Measurements at RHIC

15.  K p Large A N for K-  significant Sivers asymmetries for sea quarks ?! Large A N for anti-Proton unexplained. BRAHMS: A N for Charged Pions, Kaons and Protons at √s=200 GeV October 13 th Transverse Spin Measurements at RHIC

16. Another Surprise: A N for Eta Mesons larger than for Pions ! STAR A N (η) > A N (π 0 ) for 0.55 < x F < 0.75 Does this point to large effects in the fragmentation? STAR arXiv:0905.2840 ( Heppelmann, DIS08) October 13 th Transverse Spin Measurements at RHIC

17. 17 Understanding of A N in terms of Collins and Sivers Effect: Work in Progress! Future goal: Extract Sivers and transversity quark distributions from global anlaysis to all SIDIS, pp and e+e- data! Present work: Extract Sivers + transversity from SIDIS and e+e- and predict A N in pp Presently: Poor agreement with many problems to solve! Universality, evolution, pdf and fragmentation functions not sufficiently known. For example, note the impact of un-polarized FFs thick line DSS thin line Kretzer October 13 th Transverse Spin Measurements at RHIC STAR π 0 BRAHMS π +,- Global analysis of SIDIS & e+e- Anselmino, Boglione, D’Alesio, Kotzinian, Murgia, Prokudin, Turk Phys. Rev. D75:05032,2007 A N calculation from D’Alesio

18. 18 A RHIC and US-Japan Contribution to Transverse Spin Analysis: Measurement of the Collins Effect in e + e - Annihilation into Quarks at Belle BNL-Illinois-RBRC-RIKEN q1q1 quark-1 spin electron positron q2q2 quark-2 spin e + +e -  π + + π - + X ~ Collins(z 1 ) x Collins (z 2 ) October 13 th Transverse Spin Measurements at RHIC Belle Collins asymmetries & global fit Collins FF extracted from Belle data. Measurement of the Collins effect in e+e- at Belle:

19. SSA in Very Forward Neutron Production neutron Large negative SSA observed for x F >0 Diffractive physics Highly useful as local polarimeter at PHENIX October 13 th Transverse Spin Measurements at RHIC

20. Measurements to Isolate Different Mechanisms o Transversity & Collins o Sivers

21. 21 Ideas for Measurements of Transversity Observables at RHIC Drell Yan: Required luminosity not available at RHIC. Spin dependent Lambda-FF unknown. Measure Λ-FF in e + e - ? Collins effect in jets: Forward calorimeter upgrade in PHENIX Di-hadron intereference fragmentation function. IFF data available from e + e - Belle ! October 13 th Transverse Spin Measurements at RHIC

22. 22 Interference Fragmentation –IFF- for Di-Hadrons at Mid-Rapidity in PHENIX A UT compatible ~0 Dilution from gg processes! Future:  Update with more statistics  Study possibility of forward measurements: enhance qg fraction and higher x. October 13 th Transverse Spin Measurements at RHIC

23. 23 IFF Measurement in e + e - at BELLE Artru and Collins, Z. Phys. C69, 277 (1996) Boer, Jakob, and Radici, PRD67, 094003 (2003) Vossen, Spin Conference in Dubna October 13 th Transverse Spin Measurements at RHIC q1q1 quark-1 spin electron positron q2q2 quark-2 spin z pair-1 z 1,2 relative pion-pair momenta ϕ pair-1 ϕ pair-2 θ

24. Preliminary Belle IFF- Asymmetries vs Hadron Pair Momentum Fraction z i 9x9 z 1 z 2 binning z1z1 a 12 BNL-Illinois-RBRC-RIKEN October 13 th Transverse Spin Measurements at RHIC

25. 25 Ideas for Measurements of Sivers Observables at RHIC Precision measurement of A N at mid-rapidity. Back-to-back correlations for jets. A N for inclusive jets. A N for heavy flavor. A N for direct photons. A N in jet-photon production. A N in Drell Yan. significant improve- ments from upgrades: forward calorimeters + silicon vertex detectors October 13 th Transverse Spin Measurements at RHIC

26. 26 A N from  0 and h +/- at Central Rapidity PRL 95, 202001 (2005) Analysis with high statistics 2006+2008 data in progress Statistical uncertainties will reduce by factor 7. PHENIX A N (η=0), Run 2002 PHENIX A N (η=0), Run 2005 Anselmino et al, Phys. Rev. D 74, 094011 Constrain gluon Sivers effect with PHENIX 2002  0 data ! October 13 th Transverse Spin Measurements at RHIC Process Contribution to  0, η=0,  s=200 GeV

27. 27 A N in Di-Jet Production in STAR z x y 180º proton spin Di-jet p T Additional k T kick to jet axis from Sivers effect  Boer & Vogelsang, PRD 69, 094025 (2004) parton Gluon radiation Di-jet p T STAR: PRL-99:142003,2007 Di-jet A N consistent with 0 and consistent with DIS October 13 th Transverse Spin Measurements at RHIC

28. Sivers Effect in Heavy Flavor Production Heavy flavor production gives sensitivity to gluon Sivers effect. Significant improvement with vertex detector upgrades. Work needed to connect theory and experimental observable. Anselmino et al, PRD 70, 074025 (2004) Gluon Sivers=0 Gluon Sivers=Max Calculations for D mesons Measurement for  -

29. Future Measurements of Sivers Asymmetries in the Drell Yan and Jet-Photon Channels

30. 30 Transverse Spin Drell Yan at RHIC vs π-Sivers Asymmetry in Deep Inelastic Scattering Important test at RHIC of the fundamental QCD prediction using gauge link formalism of the non-universality of the Sivers effect! Requires very high luminosity (~ 250pb -1 ) October 13 th Transverse Spin Measurements at RHIC

31. 31 Soft Gluon Interaction in the Initial and Final State of Hard Scattering Processes Integrate initial state gluon radiation: gauge link and insert gauge link in hard scattering matrix element Integrate final state gluon radiation: gauge link and insert gauge link in hard scattering matrix element October 13 th Transverse Spin Measurements at RHIC Unique predictions for process dependence: SIDIS vs Drell Yan or direct photon at RHIC!

32. 32 Drell Yan at RHIC ϒ-states J/Ψ Drell Yan Ψ’Ψ’ charm bottom FVTX enables DY measurement by rejecting heavy flavor background:  Measurement: 4 GeV < Q < 10 GeV yield in arbitrary units October 13 th Transverse Spin Measurements at RHIC Bland et al. “Transverse Spin Drell-Yan Physics at RHIC” http://thy.phy.bnl.gov/~vogelsan/drellyan1/dy_final.pdf

33. 33 0.1 0.2 0.3 x Sivers Amplitude 0 Experiment SIDIS vs Drell Yan: Sivers| DIS = − Sivers| DY Test Unique Prediction of Gauge Theory HERMES Sivers Results Markus Diefenthaler DIS Workshop Műnchen, April 2007 0 RHIC Drell Yan Projections October 13 th Transverse Spin Measurements at RHIC Bland et al. “Transverse Spin Drell-Yan Physics at RHIC” http://thy.phy.bnl.gov/~vogelsan/drellyan1/dy_final.pdf

34. 34 A N photon+Jet : An Alternative Test of the Process Dependence of the Sivers Effect at RHIC Bachhetta, Bomhof, D’Alesio, Mulders, Murgia Phys.Rev.Lett.99:212002,2007. Weighted moment of A N photon+Jet no process dependence Correct process dependence Measurement: A N in jet-photon production forward photon η > 2 jet -1 < η < 0 Much less luminosity hungry …  NSAC milestone for transverse spin (HP-13, 2015) ! Reachable at STAR. Requires FOCAL upgrade in PHENIX. October 13 th Transverse Spin Measurements at RHIC

35. 35 Summary Single spin asymmetries found in the past at low center of mass energies persist at the highest center of mass energies at RHIC. Precise A N data for inclusive hadrons are available from RHIC. More statistics is still needed to characterize the kinematic dependence of A N at high p T. The theoretical analysis of A N into Collins and Sivers contributions continues to be challenging. SSA in forward neutron production discovered at RHIC, are sizeable at all center of mass energies and used for local polarimetery at RHIC. Several observables exist that will permit to isolate Sivers and Collins effects at RHIC. These measurement will benefit from detector and luminosity upgrades in progress at RHIC. The newly developed gauge link formalism makes unique predictions for the process dependence of Sivers asymmetries that can be tested at RHIC in Drell Yan or Jet-Photon production. October 13 th Transverse Spin Measurements at RHIC

36. 36 Backup October 13 th Transverse Spin Measurements at RHIC

37. 37 Simple QED example: DIS: attractive Drell-Yan: repulsive Same in QCD: As a result: Non-universality of Sivers Asymmetries: Unique Prediction of Gauge Theory ! October 13 th Transverse Spin Measurements at RHIC

38. 38 Collins Effect in Quark Fragmentation J.C. Collins, Nucl. Phys. B396, 161(1993) q Collins Effect: Fragmentation of a transversely polarized quark q into spin-less hadron h carries an azimuthal dependence: October 13 th Transverse Spin Measurements at RHIC

39. 39 General Form of Fragmentation Functions Number density for finding hadron h from a transversely polarized quark, q: unpolarized FF Collins FF October 13 th Transverse Spin Measurements at RHIC

40. IFF- a 12 vs Invariant Mass 8x8 m 1 m 2 binning 40 Preliminary Systematic errors shown. a 12 increases with m 1 and m 2 reaches |a 12 | ~ 0.1 at large m i. m 1 [GeV/c 2 ] a 12

41. 41 The Sivers Effect proton SpSp SpSp Sivers function: D. Sivers 1990 Sivers: Correlation between the transverse spin of the proton and the transverse momentum k T of quarks and gluons in the proton (link to orbital angular momentum?) Observed asymmetry: October 13 th Transverse Spin Measurements at RHIC