1. Nucleon Spin Structure 30 Years of Experiment: What have we learned? M. Grosse Perdekamp, University of Illinois and RBRC

2. Nucleon Spin Structure 2 June 6 th Overview o Scientific Motivation and Early Beginnings The Rabi School of Physics The SLAC – Bielefeld -- Tsukuba – Yale Collaboration Modern Experiments o Nucleon Helicity Structure Quark spin ΔΣ Gluon spin ΔG Orbital angular momentum L z  GPDs ! o Transverse Spin Transverse spin in hard scattering QCD Transversity and Collins Quark Fragmentation The Sivers Effect

3. Nucleon Spin Structure 3 June 6 th Scientific Motivation: Proton Structure Including Spin Degrees of Freedom Constituents: quarks = u, d, s and gluons

4. Nucleon Spin Structure 4 June 6 th Proton Spin Structure from Inclusive Deep Inelastic Lepton-Nucleon Scattering electron or muon probe spin proton target spin Extract spin dependent quark distribution functions from the spin structure function g 1 (x,Q 2 ) Large Q 2 : measure photon-quark absorption cross section double spin asymmetry

5. Nucleon Spin Structure 5 June 6 th The Rabi School of Physics N. F. Ramsey, Eur. J. Phys. 11 (1990) 137 J. Rigden, Physics World, Nov. 1999 (I) Molecular beam laboratory at Columbia University with strong emphasize on the development of new experimental technology. (II) Field new, precise instrumentation to study fundamental questions of physics. Example: Precision Measurements of “Hydrogen Spin Structure” g-2 of the electron, P. Kusch Lamb shift, W. E. Lamb Dirac Theory  QED Tomonaga, Schwinger, Feynman Nobel Prize 1955 Rabi, Nobel Prize 1944 Nobel Prize 1965

6. Nucleon Spin Structure 6 June 6 th SLAC: Quark Structure of the Proton Nucleon Quantum Chromo Dynamics Experiment: Deep inelastic electron nucleon scattering Theory: quark structure of hadrons, QCD Friedman, Kendall, Taylor Nobel Prize 1990 Gell Mann Nobel Prize 1969 also Nakano, Nishijima New instrumental method & fundamental physics !

7. Nucleon Spin Structure 7 June 6 th Polarized Deep Inelastic Scattering (I)Molecular beam technology as starting point for the development of polarized electron beams at Yale starting 1959. (II)Physics: (a) Proton spin structure (b) Test the Bjorken sum rule as fundamental QCD prediction Experiments E80+E130 at SLAC Bielefeld – CUNY – SLAC – Nagoya – Tsukuba – Yale (Coward, Kondo, Hughes) EMC experiment at CERN (Gabathuler, Sloan, Hughes) Vernon W. Hughes a contribution from the Rabi School of Physics !

8. Nucleon Spin Structure 8 June 6 th The Quark Spin Contribution ΔΣ Quark Spin Contribution to the Proton Spin. SLAC: 0.10 < x SLAC <0.7 CERN: 0.01 < x CERN <0.5 0.1 < x SLAC < 0.7 A 1 (x) x-Bjorken EMC, Phys.Lett.B206:364,1988 1338 citations in SPIRES 0.01 < x CERN < 0.5 “Proton Spin Crisis” First Thesis on Nucleon Spin Structure E80/Yale, 1977: Noboru Sasao

9. Nucleon Spin Structure 9 June 6 th DIS Nucleon Spin Structure: 30 Years of Experiment  2000 ongoing  1995  2007 ongoing polarized pp semi inclusive + exclusive processes, luminosity Quark Spin – Gluon Spin – Transverse Spin – GPDs – L z SLAC E80-E155 CERN EMC,SMC COMPASS FNAL E704 DESY HERMES JLAB Halls A, B, C RHIC BRAHMS, PHENIX, STAR polarized proton beams, polarized proton collider major experimental innovations

10. Nucleon Spin Structure June 6 th AGS LINAC BOOSTER Polarized Source Spin Rotators Partial Snake Siberian Snakes 200 MeV Polarimeter Rf Dipole RHIC pC Polarimeters Absolute Polarimeter (H jet) P HENIX P HOBOS B RAHMS & PP2PP S TAR Siberian Snakes AGS pC Polarimeter Helical Partial Snake Strong Snake Spin Flipper RHIC Spin Instrumentation Development 1995-2005 A novel experimental method: Probing Proton Spin Structure in High Energy Polarized Proton Collisions Instrumentation High current polarized proton source High energy proton polarimetry Control of spin coherence during acceleration + storage Spin sorted luminosity measurements Physics Probes directly sensitive to color charge Utilize Parity violation in W-production Large Q 2  clean pQCD interpretation US-Japanese collaboration at Brookhaven National Laboratory RIKEN Radiation Laboratory RIKEN BNL Research Center

11. Nucleon Spin Structure 11 June 6 th at ultra-relativistic energies the proton represents a jet of quark and gluon probes For example, direct photon production ~ probe gluon content with quark probes The related double spin asymmetry: RHIC SPIN: Proton Structure with Quark and Gluon Probes quark gluon quark photon experimental double spin asymmetry pQCD DIS ?

12. Nucleon Helicity Structure Quark spin ΔΣ, Δq(x) Gluon spin ΔG(x), ∫ ΔG(x)dx Orbital angular momentum L z  GPDs ?

13. Nucleon Spin Structure 13 June 6 th Inclusive Measurements of g 1 p, g 1 d and g 1 n ProtonNeutron HERMES ΔƩ = 0.33 ± 0.011(th) ± 0.025 (exp) ± 0.028 (evo) at 5 GeV 2 COMPASS ΔƩ = 0.35 ± 0.03 (stat) ± 0.05 (syst) at 3 GeV 2 Bjorken sum S. Paul, X. Lu, H. Gao, INPC 2007 0.1821 ∓ 0.0019 (NNNLO)

14. Nucleon Spin Structure 14 June 6 th Semi-Inclusive DIS: e+p  e+ h +X Quark & Anti-Quark Helicity Distributions u quarks large positive polarization d quark have negative polarization sea quarks (u, d, s,s) compatible with 0 in the measured x-range 0.02 < x < 0.6. [HERMES, PRL92(2004), PRD71(2005)] x Future: Precision DIS at JLAB-12 and at a possible electron – ion collider! xΔu(x) xΔd(x) xΔu(x) xΔd(x) xΔs(x) How well do we know hadron fragmentation functions ?  new analysis of e+e- data, Hirai, Kumano, Nagai, Sudo hep-ph/0612009, INPC 2007 Possible Improvements  include e-p, p-p and e+e- in fragmentation function analysis  done! De Florian, Sassot, Stratmann hep-ph/0703242  “add data” from b-factories e+e-  hadrons

15. Nucleon Spin Structure 15 June 6 th Belle MC <1% of data sample  work in progress Possible Impact on the Knowledge of Hadron FFs from Analysis of b-Factory Data FF Compilation of data available for the char- ged hadron FF Belle MC: Charged h +/-, pions, kaons, protons precision at high z!  h+,-  pions  kaons  protons Input for precision measurements of quark helicity distributions in SIDIS, with JLab-12 and a possible future electron- polarized proton collider.

16. Nucleon Spin Structure 16 June 6 th Another Alternative: W-production at RHIC SIDIS: large x-coverage uncertainties from knowing fragmentation functions Ws in polarized p-p: limited x-coverage high Q 2  theoretically clean no FF-info needed Hermes – 243 pb -1 PHENIX – 800 pb -1

17. Nucleon Spin Structure 17 June 6 th Gluon Spin Contribution ΔG(x) from scaling violation of world g 1 (x,Q 2 ): Hirai, Kumano, Saito Phys.Rev.D74:014015,2006 g P 1 (x,Q 2 ) ΔG=∫ΔG(x) dx = 0.47 ∓ 1.08, Q 2 =1GeV 2

18. Nucleon Spin Structure 18 June 6 th Gluon Polarization from Photon Gluon Fusion in DIS “direct” measurements Photon-Gluon Fusion (PGF) golden channel: charm production golden channel: charm production hadron production at high P T S. Paul, X. Lu INPC 2007 Favors small ΔG(x≈0.1)

19. Nucleon Spin Structure 19 June 6 th 2005 data A LL also for  ,  , J/  K.Aoki, R. Fatemi, B. Surrow INPC 2007 Gluon Polarization from Inclusive Hadrons and Jets in Polarized pp

20. Nucleon Spin Structure 20 June 6 th  2006: 7.5 pb -1 @ 60% polarisation projections Gluon Polarization from Inclusive Hadrons and Jets in Polarized pp

21. Nucleon Spin Structure 21 June 6 th NLO QCD Analysis of DIS A 1 + A LL (π 0 ) DIS A 1 + A LL (π 0 ) ACC03 x Only DIS ∫ΔG(x) dx = 0.47 ∓ 1.08, Q 2 =1GeV 2 Hirai, Kumano, Saito Phys.Rev.D74:014015,2006 DIS + pp ∫ΔG(x) dx = 0.31 ∓ 0.32, Q 2 =1GeV 2

22. Nucleon Spin Structure 22 June 6 th PHENIX π 0 A LL vs GSA-LO and GSC-NLO A LL p T [GeV] GSA-LO GSC-NLO PHENIX-2005 GSA-LO: ΔG = ∫ΔG(x)dx = 1.7 GSC-NLO: ΔG = ∫ΔG(x)dx = 1.0 Large uncertainties resulting from the functional form used for ΔG(x) in the QCD analysis! GSA-LO and GSC-NLO courtesy Marco Stratmann and Werner Vogelsang

23. Nucleon Spin Structure 23 June 6 th ΔG(x) A, B and C from Gehrmann Stirling present x-range Much of the first moment ΔG = ∫ΔG(x)dx might emerge from low x! Some theoretical guidance: ΔG(x) ≤ x G(x) but G(X) diverges faster than x -1 ! NEED TO EXTEND MEASUREMENTS TO LOW x !!

24. Nucleon Spin Structure 24 June 6 th Increase integrated luminosity by factor 10 (2008) Extend measurements to low x  Di-hadron Production extends (2008) measurements to x  0.01 NLO treatment available: Marco Stratmann -- INPC 2007 (EMC forward calorimeters available in STAR and PHENIX!) Forward detector upgrades for direct (2011) photons and heavy flavor + electron cooling reach x  0.001 Polarized Electron Ion Collider measure ΔG(x) through scaling violations Next Steps for ΔG(x) at RHIC

25. Nucleon Spin Structure 25 June 6 th      1 1 )0,, q(q()0,, q(q( 2 1 xE xHxdx J q X. Ji, Phy.Rev.Lett.78,610(1997) Generalized Parton Distributions vs Orbital Angular Momentum ? GPDs H u, H d, E u, E d provide access to total quark contribution to proton angular momentum in exclusive processes l + N  l’ + N + γ ½ = ½ (  u+  d+  s) + L q + J g J q Proton spin sum

26. Nucleon Spin Structure 26 June 6 th First Model Dependent Constraint of J u vs J d E. Burtin, P. Bertin, X. Lu, INPC 2007

27. Transverse Spin Transverse spin in hard scattering QCD Transversity and Collins Quark Fragmentation The Sivers Effect

28. Nucleon Spin Structure 28 June 6 th Transverse Spin Phenomena in Hard Scattering QCD QCD: Asymmetries for transverse spin are small at high energies (Kane, Pumplin, Repko, PRL 41, 1689–1692 (1978) ) π+π+ π-π- π0π0 Is QCD the correct theory of the strong interaction? Experiment (E704, Fermi National Laboratory): QCD Test !

29. Nucleon Spin Structure 29 June 6 th STAR Single Transverse Spin Asymmetries A N at √=62.4 GeV and 200 GeV Large single spin asymmetries persist at higher √s=62.4 and 200 GeV √s=62.4 PHENIX and BRAHMS √s=200 GeV STAR ANAN ANAN xFxF xFxF M. Chiu INPC 2007

30. Nucleon Spin Structure 30 June 6 th Inspect Factorized Expression for Cross Section Jet Proton Structure hard scattering reaction fragmentation process fragmentation function pQCD Proton Structure small spin dependence (a LL ~10 -4 ) Can initial and/or final state effects generate large transverse spin asymmetries? (A LL ~10 -1 )

31. Nucleon Spin Structure 31 June 6 th Transverse Spin in QCD: Two Solutions π+π+ π-π- π0π0 (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 ANAN xFxF Collins FF Quark transverse spin distribution Sivers distribution

32. Nucleon Spin Structure 32 June 6 th Collins Effect in the Quark- fragmentation into the Final State sqsq π q q π sqsq = 0 AN =AN = N L - N R N L + N R Collins Effect N L : pions to the left N R : pions to the right q Collins Effect: Fragmentation of a transversely polarized quark q into spin-less hadron h carries an azimuthal dependence:

33. Nucleon Spin Structure 33 June 6 th π + picks up L=-1 to compensate for the pair S=1 and is emitted up. u-quark absorbs photon/gluon and flips it’s Spin. Proton spin is pointing up! String breaks and a dd-pair with spin 1 is inserted. A simple model to illustrate that spin-orbital angular momentum coupling can lead to left right asymmetries in spin-dependent fragmentation: Artru Model for Collins Fragmentation L = -1

34. Nucleon Spin Structure 34 June 6 th Measurements of Quark Transversity Distributions and Collins Fragmentation Functions (I) SIDIS Collins Asymmetries in semi- inclusive deep inelastic scattering e+p  e + π + X ~ Transversity (x) x Collins(z) New HERMES results for Collins Asymmetries Diefenthaler, DIS 2007, Lu INPC 2007 A UT sin(  s )

35. Nucleon Spin Structure 35 June 6 th Collins Asymmetries in e + e - annihilation into hadrons e + +e -  π + + π - + X ~ Collins(z 1 ) x Collins (z 2 ) New Belle Collins Asymmetries Seidl, DIS 2007 Measurements of Quark Transversity Distributions and Collins Fragmentation Functions (II) e + e -      e-e- e+e+ A 12 cos(    2 ) PRELIMINARY

36. Nucleon Spin Structure 36 June 6 th Anselmino, Boglione, D’Alesio, Kotzinian, Murgia, Prokudin, Turk Phys. Rev. D75:05032,2007 HERMES SIDIS + COMPASS SIDIS + Belle e + e -  transversity dist. + Collins FF Fit includes: First Extraction of Quark Transversity Distributions and Collins Fragmentation Functions SIDIS + e + e -

37. Nucleon Spin Structure 37 June 6 th 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:

38. Nucleon Spin Structure 38 June 6 th Sivers Asymmetries at HERMES and COMPASS  implies non-zero L q    

39. Nucleon Spin Structure 39 June 6 th Sivers Effect and Orbital Angular Momentum M. Burkardt >

40. Nucleon Spin Structure 40 June 6 th The Sivers Effect : Needs Final State Soft Gluon Exchange M. Burkardt

41. Nucleon Spin Structure 41 June 6 th What have we learned from this? The Sivers effect arises from soft gluon interactions in the final state (SIDIS) or initial state (Drell Yan). Need to modify naïve concepts of factorization which reduce hard scattering to partonic processes and neglect soft gluon interactions in the initial or final state: hard scattering matrix elements are modified with gauge link integrals that account for initial and final state soft gluon exchange. A modified concept of universality has been obtained which shows how the presence of initial or final state interactions can impact transverse momentum dependent distribution; eg. the Sivers function changes sign between SIDS and Drell Yan! There may be exciting applications elsewhere, eg. other transverse momentum dependent effects or the understanding nuclear effects in hard scattering.

42. Nucleon Spin Structure 42 June 6 th Goals for the Future Quantitative understanding of transverse spin phenomena in QCD Do Sivers and Collins mechanisms reconcile QCD with transverse spin phenomena? Precision measurements of transversity distributions and Collins fragmentation function measurements. This will complete the experimental survey of the nucleon at leading twist. Determine sum of first moments (tensor charge) which can be compared to lattice calculations. Survey Sivers and Boer Mulders effects in SIDIS and pp Fundamental understanding of factorization and universality in hard scattering. Relation to orbital angular momentum ?! Future results expected from COMPASS, RHIC, JLAB, Belle, JLAB-12-GEV, JPARC FAIR and EIC. This includes high precision measurements in e-p, e-e and p-p  possibly first systematic study of factorization + universality

43. Nucleon Spin Structure 43 June 6 th Transversity : correlation between transverse proton spin and quark spin Sivers : correlation between transverse proton spin and quark transverse momentum Boer/Mulders: correlation between transverse quark spin and quark transverse momentum Transversity, Sivers and Boer Mulders in the Proton Wavefunction S p – S q – coupling ? S p - L q – coupling ?? S q - L q – coupling ??

44. Nucleon Spin Structure 44 June 6 th Summary Bjorken sum rule holds Integral quark spin contributions are well known Δq(x), Δq(x) only well known for up-quarks only Hints that ΔG(x) is small at x~0.1. ∫ ΔG(x)dx remains largely unconstraint  RHIC luminosity, low-x Possible route to OAM through Exp. Observation of Sivers and Collins asymmetries  Theoretical advance in understanding TMD + concepts of factorization and universality Plenty of work for theory + existing and future experimental tools!

45. Nucleon Spin Structure 45 June 6 th Sivers in SIDIS and Drell Yan vs Factorization and Universality

46. Nucleon Spin Structure 46 June 6 th Transverse Spin Drell Yan at RHIC vs π-Sivers Asymmetry in Deep Inelastic Scattering Important test at RHIC of the fundamental QCD prediction of the non-universality of the Sivers effect! requires very high luminosity (~ 250pb -1 )

47. Nucleon Spin Structure 47 June 6 th Simple QED example: DIS: attractive Drell-Yan: repulsive Same in QCD: As a result: Non-universality of Sivers Asymmetries: Unique Prediction of Gauge Theory !

48. Nucleon Spin Structure 48 June 6 th 0.1 0.2 0.3 x Sivers Amplitude 0 Experiment SIDIS vs Drell Yan: Sivers| DIS = − Sivers| DY *** Test QCD Prediction of Non-Universality *** HERMES Sivers Results Markus Diefenthaler DIS Workshop Műnchen, April 2007 0 RHIC II Drell Yan Projections

49. Nucleon Spin Structure 49 June 6 th I) Can one extract G(x,Q 2 ) from pp? II) NLO pQCD vs RHIC data Is pQCD applicable at RHIC?

50. Nucleon Spin Structure 50 June 6 th Global QCD Analysis for G(x,Q 2 ) and q(x,Q 2 ): J. Pumplin et.al JEHP 0207:012 (2002) 10 -4 10 -3 10 -2 10 -1 0.5 x gluon down up-quarks anti-down Quark and Gluon Distributions error on G(x,Q 2 ) error for u(x,Q 2 ) +/- 10% +/- 5% error for d(x,Q 2 ) 10 -4 10 -3 10 -2 10 -1 0.5 x CTEQ6: use DGLAP Q 2 -evolution of quark and gluon distributions to extract q(x,Q 2 ) and G(x,Q 2 ) from global fit to data sets at different scales Q 2. H1 + Zeus F 2 CDF + D0 Jets CTEQ5M1 CTEQ6M

51. Nucleon Spin Structure 51 June 6 th G(x,Q 2 ) and q(x,Q 2 ) + pQCD beautifully agree Tevatron + HERA! J. Pumplin et.al JEHP 0207:012 (2002) D0 Jet Cross Section ZEUS F 2

52. Nucleon Spin Structure 52 June 6 th and at RHIC ? q(x,Q 2 ), G(x,Q 2 ) and D(z,Q 2 ) + pQCD are nicely consistent with experiment! o Good agreement between NLO pQCD calculations and experiment  can use a NLO pQCD analysis to extract spin dependent quark and gluon distributions from RHIC data! PHENIX π 0 cross section a |η|<0.35 Phys.Rev.Lett.91:241803,2003 STAR π 0 cross section a 3.4<η<4.0 Phys.Rev.Lett.92:171801,2004 gluon fragmentation !?

53. Nucleon Spin Structure 53 June 6 th NLO-pQCD calculation –Private communication with W.Vogelsang –CTEQ6M PDF. –direct photon + fragmentation photon –Set Renormalization scale and factorization scale p T /2,p T,2p T Theory calculation show good agreement with the experimental cross section. Direct Photons: NLO pQCD vs RHIC data

54. Nucleon Spin Structure 54 June 6 th W Z W Production in Polarized pp Collisions Single Spin Asymmetry in the naive Quark Parton Model Experimental Requirements:  tracking at high p T  event selection for muons difficult due to hadron decays and beam backgrounds  control of all backgrounds Parity violation of the weak interaction in combination with control over the proton spin orientation gives access to the flavor spin structure in the proton!

55. Nucleon Spin Structure 55 June 6 th Extraction of quark polarizations at LO  Machine and detector requirements: –∫Ldt=800pb-1, P=0.7 at √s=500 GeV –trigger upgrade –Control of backgrounds  contributions both from FVTX and NCC! 2009 to 2012 running at √s=500 GeV is projected to yield ∫Ldt ~950pb -1

56. Nucleon Spin Structure 56 June 6 th Run 5 A LL (   ): First constraints for ∆G(x) ¨ standard ∆G from DIS ∆G =0 PHENIX max ∆G from DIS min ∆G possible curves: comparison with A LL obtained with ∆G from deep Inelastic lepton nucleon scattering ( M. Glück, E. Reya, M. Stratmann, und W. Vogelsang, Phys. Rev. D 53 (1996) 4775). PANIC, October 2005 Asymmetries are consistent with gluon spin contributions from ʃ∆G(x)dx ~ 0 to 0.5

57. Nucleon Spin Structure 57 June 6 th EMC-RICH Trigger (RBRC/UIUC, UCR, Tokyo) Information from EMC (172 elements with 4 energy thresholds) and RICH (256 ele- ments with one threshold) is used to tag high energy electrons and photons: Physics (p-p, d-Au) : EMC Trigger Efficiency

58. Nucleon Spin Structure 58 June 6 th  Final results on ∆G will come from combined NLO analysis of RHIC and DIS  RHIC measurements will span broad range in x with good precision. Multiple channels with independent theo. and exp. uncertainties.  s=200 GeV incl.  0 prod’n  s=500 GeV incl. jet prod’n ∆G Measurements by 2012 see Spin report to DOE http://spin.riken.bnl.gov/rsc/

59. Nucleon Spin Structure 59 June 6 th Sivers Function in PHENIX: The Muon Piston Calorimeter (MPC) Measure the Sivers function through the asymmetry A N in hadron-hadron correlationen, for neutral pions (Boer and Vogelsang Phys.Rev.D69:094025,2004 ) ANAN Jets Hadron Paare ∫Ldt = 0.35pb -1 (Run 3)

60. Nucleon Spin Structure 60 June 6 th First attempt at lower x: A LL (2π 0 ) from Les Bland (for STAR FMS) Measure A LL for neutral pion pairs: one in the central arm the second in the MPC  0.1 > x  0.001 ! MPC

61. Nucleon Spin Structure 61 June 6 th NCC direct photons ΔG(x) – x-range with Detector Upgrades

62. Nucleon Spin Structure 62 June 6 th K.Aoki, R. Fatemi, B. Surrow INPC 2007 Gluon Polarization from Inclusive Hadrons and Jets in Polarized pp