1. CCAST Workshop on RHIC Physics Transverse Spin Physics Beijing, August 13 th 2004 Transverse Spin Physics at RHIC o Introduction o Transverse Proton Spin Structure o Single Transverse Spin Asymmetries o Avenues to Measure Transversity at RHIC o Spin Dependent Fragmentation Functions o Summary Matthias Grosse Perdekamp, UIUC and RBRC

2. CCAST Workshop on RHIC Physics Transverse Spin Physics Beijing, August 13 th 2004 Proton (well known) (moderately well known) (unknown) (moderately well known) (unknown) Nucleon Structure Quark and Gluon (parton) Distribution Functions What is the origin of the Proton Spin? (and it’s mass??)

3. CCAST Workshop on RHIC Physics Transverse Spin Physics Beijing, August 13 th 2004 How Do We Study Proton Sub-Structure? Hard Scattering! Deep inelastic lepton nucleon scattering (“DIS”) High energetic proton-proton collisions Cross Section, example DIS of e-p: Measure: Cross sections/structure functions Extract: Quark- and Gluon Distribution Functions e-e- e-e- proton spectator system current quark jet

4. CCAST Workshop on RHIC Physics Transverse Spin Physics Beijing, August 13 th 2004 Factorization and Universality? Cross SectionForward Elastic Scattering Amplitude Optical Theorem e-e- e-e- proton spectator system current quark jet q(x,Q 2 ), G(x,Q 2 ) photon, gluon proton pQCD, hard scattering quark Process independent quark and gluon distri- butions  Universality? initial statefinal state Factorization?

5. CCAST Workshop on RHIC Physics Transverse Spin Physics Beijing, August 13 th 2004 Extracted q(x,Q 2 ) and G(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% 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. error for d(x,Q 2 ) 10 -4 10 -3 10 -2 10 -1 0.5 x

6. CCAST Workshop on RHIC Physics Transverse Spin Physics Beijing, August 13 th 2004 q(x,Q 2 ) and G(x,Q 2 ) + pQCD beautifully agree with HERA + Tevatron! J. Pumplin et.al JEHP 0207:012 (2002) D0 Jet Cross Section ZEUS F 2

7. CCAST Workshop on RHIC Physics Transverse Spin Physics Beijing, August 13 th 2004 q(x,Q 2 ), G(x,Q 2 ) and D(z,Q 2 ) + pQCD consistent with experiment at RHIC 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 uncertainty in gluon fragmentation

8. CCAST Workshop on RHIC Physics Transverse Spin Physics Beijing, August 13 th 2004 Jet Proton Structure Hard Scattering Process Fragmentation Access to Quark and Gluon Distributions in pp at RHIC pQCD Quark and Gluon distributions from DIS + pp  Universality! Fragmentation Function from e+e-  Universality! measure Can solve for one unknown parton dstrb. Observables: spin dependent cross sections, eg. the inclu- sive π 0 cross section. Factorizes: pdf x parton scattering x fragmentation cross section function Incoming protons Hard scattering

9. CCAST Workshop on RHIC Physics Transverse Spin Physics Beijing, August 13 th 2004 Double Spin Asymmetry Gluon Compton (85% of ) Example: Spin dependent Gluon Distribution ∆G(x,Q 2 ) in Prompt Photon Production I a LL Observable: prompt photon yields relative Luminosity

10. CCAST Workshop on RHIC Physics Transverse Spin Physics Beijing, August 13 th 2004 If projected future PHENIX Prompt Photon Data are included in a Global QCD Analysis the error on ∆G(x,Q 2 ) will be significantly reduced : AAC Preliminary M. Hirai, H.Kobayashi, M. Miyama et al. Example: Spin dependent Gluon Distribution ∆G(x,Q 2 ) in Prompt Photon Production II

11. CCAST Workshop on RHIC Physics Transverse Spin Physics Beijing, August 13 th 2004 Helicity Amplitudes in Hard Scattering proton, H f Forward Scattering Amplitude proton, H i initial statefinal state hard probe: gluon, photon Quark, h f Quark, h i h: quark helicity H: proton helicity In initial and final state H i h i H f h f Helicity is conserved helicity average helicity difference helicity flip transversity quark distributions

12. CCAST Workshop on RHIC Physics Transverse Spin Physics Beijing, August 13 th 2004 structure functions: The transversity function h 1 (x) quark distrb. Probability to probe a quark of flavor i and momentum fraction x that contributes to the spin of a transversely polarized proton Helicity flip! helicity amplitudes q spectators proton spin probe

13. CCAST Workshop on RHIC Physics Transverse Spin Physics Beijing, August 13 th 2004 Transversity distributions are the last unknown leading twist nucleon distribution functions. Helicity flip amplitude  no gluon transversity  pure quark observable avoid complicated coupling between gluon- and quark degrees of freedom we observe for longitudinal polarization: Lattice results suggest that the transverse quark spin sum is large. For example, Interesting properties: chiral odd, does not mix with gluons under evolution For non-relativistic quarks : Difference provides information on quark dynamics in the nucleon. Soffer’s bound: not small! Possibly Some Observations S. Aoki, M. Doui, T. Hatsuda and Y. Kuramashi Phys.Rev. D56 (1997)433

14. CCAST Workshop on RHIC Physics Transverse Spin Physics Beijing, August 13 th 2004 Transversity in Inclusive Processes Does not contribute in leading twist inclusive DIS q chirality unchanged by strong interaction or electromagnetic current Higher twist contributions are suppressed by Semi-inclusive DIS with chiral odd frag- mentation function: Collins fragmen- tation function J.C. Collins, Nucl. Phys. B396, 161(1993)

15. CCAST Workshop on RHIC Physics Transverse Spin Physics Beijing, August 13 th 2004 The Collins Fragmentation function z = E h / E q  angle between S and k T around quark-jet axis SqSq π A T = q kTkT kTkT q q J.C. Collins, Nucl. Phys. B396, 161(1993) π π Scatter hard probe on trans- versely polarized protons and observe left-right assymmetry A T for pions in the final state! SqSq SqSq quark which has absorbed the hard probe and fragments into a pion. The quark carries spin S q.

16. CCAST Workshop on RHIC Physics Transverse Spin Physics Beijing, August 13 th 2004 The Collins Effect in the Artru Fragmentation Model π + picks up L=1 to compensate for the pair S=1 and is emitted to the right. 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:

17. CCAST Workshop on RHIC Physics Transverse Spin Physics Beijing, August 13 th 2004 First Measurements of A N in E704 ANAN ANAN ANAN π+π+ π-π- π0π0 π-π- π-π- π+π+ π+π+ π0π0 Theory: Collins only Theory: Sivers only Theory: higher twist Anselmino et al. Qiu- Sterman No discriminative power!

18. CCAST Workshop on RHIC Physics Transverse Spin Physics Beijing, August 13 th 2004 What is the Sivers Effect? Sivers Effect: k T distribution of quarks depends on the transverse proton spin direction. proton SpSp SpSp Sivers function: J. Collins, 1993 : Sivers function is forbidden by symmetry properties (T-odd) Brodsky, Hwang and Schmidt 2002: Sivers function can arise from interference with diagrams with soft final state gluon exchange. D. Sivers 1990

19. CCAST Workshop on RHIC Physics Transverse Spin Physics Beijing, August 13 th 2004 Sivers Effect and Orbital Angular Momentum (Hide Tanaka at Trento, June 2004) M. Burkardt

20. CCAST Workshop on RHIC Physics Transverse Spin Physics Beijing, August 13 th 2004 The Sivers Effect in DIS (Hide Tanaka at Trento, June 2004) M. Burkardt

21. CCAST Workshop on RHIC Physics Transverse Spin Physics Beijing, August 13 th 2004 Collins Asymmetry Sivers Asymmetry New Hermes Results (A. Miller, Trento June 2004) π + appears to be positive!!Relative sign between π + and π 0 requires H 1 (favored)=-H 1 (unfavored)

22. CCAST Workshop on RHIC Physics Transverse Spin Physics Beijing, August 13 th 2004 First RHIC Results on A N (I) o Our ability to distinguish between possible sources of the observed asymmetry is limited by statistics. Run 2005 with P=0.5 and ∫Ldt > 3.0pb-1 will reduce improve errors by factor 10.  Brahms!! PHENIX A N (π 0 ) and A N (π0) at |η|<0.35 C. Aidala, DIS 2004, to be published STAR A N (π 0 ) at 3.4<η<4.0 Phys.Rev.Lett.92:171801,2004 Run 02, ∫Ldt ~ 0.2pb -1, P~0.15 o First spin results from RHIC  A N sizeable in forward X F  A N compatible with 0 at η~0 (as expected from pQCD)

23. CCAST Workshop on RHIC Physics Transverse Spin Physics Beijing, August 13 th 2004 First RHIC Results on A N (II) STAR A N for leading charged hadrons in the central rapidity region A N compatible with 0 consistent with pQCD STAR Preliminary

24. CCAST Workshop on RHIC Physics Transverse Spin Physics Beijing, August 13 th 2004 (A) Physics Channels for Low Luminosity (2005/2006) The Transverse Spin Program at RHIC STAR Phys. Rev. Lett. 92:171801, 2004 Boer and Vogelsang (hep-ph/0312320): azimuthal back to back correlation between hadrons in opposite hemisphere jets: Separation of intrinsic transverse quark spin (transversity) from trans- verse momentum effects (Sivers)? Clean channel for Sivers effect! STAR, PHENIX and BRAHMS STAR and PHENIX (I) (II)

25. CCAST Workshop on RHIC Physics Transverse Spin Physics Beijing, August 13 th 2004 (B) Physics Channels for high L Transverse Spin at RHIC J.C. Collins, Nucl. Phys. B396, 161(1993) R. Jaffe, X.Jin, J. Tang Phys. Rev. D57 (1999)5920 J. Collins, S. Heppelmann, G. Ladinsky, Nucl.Phys. B420 (1994)565 Statistical sensitivity for A T with 32pb -1 Brahms A N measurements from 2004 and 2005 polarized proton runs! Brief PHENIX and STAR runs on A N and back-to-back correlations as ∫ Ldt/week>1pb -1 /week (2006?) STAR and PHENIX M. Anselmino J.Ralston and D.E. Soper, Nucl. Phys. B152, 109(1979)

26. CCAST Workshop on RHIC Physics Transverse Spin Physics Beijing, August 13 th 2004 O.Martin, A. Schafer, M. Stratmann, W. Vogelsang Phys.Rev. D60, 117502(1999) Drell Yan J.Ralston and D.E. Soper, Nucl. Phys. B152, 109(1979) Luminosity limited!

27. CCAST Workshop on RHIC Physics Transverse Spin Physics Beijing, August 13 th 2004 The PHENIX Detector 2 central arms: electrons, photons, hadrons –charmonium J/ ,  ’  e  e  –vector meson   e  e  –high p T       –direct photons –open charm –hadron physics 2 muon arms: muons –“onium” J/ ,  ’,      –vector meson      –open charm combined central and muon arms: charm production DD  e  global detectors forward energy and multiplicity –event characterization designed to measure rare probes: + high rate capability & granularity + good mass resolution and particle ID - limited acceptance Au-Au & p-p spin

28. CCAST Workshop on RHIC Physics Transverse Spin Physics Beijing, August 13 th 2004 The PHENIX Detector: Central Arms

29. CCAST Workshop on RHIC Physics Transverse Spin Physics Beijing, August 13 th 2004 Two Collisions seen by the PHENIX Central Arms Au-Au d-Au

30. CCAST Workshop on RHIC Physics Transverse Spin Physics Beijing, August 13 th 2004 RHIC Schedule for Future Runs 2004 2005 2006 2007 2008 2009 …. pp 5+1 5+10 5+11 0 5+9  156pb -1 √s= ……………………….. 200 GeV ………………….........| P= 0.45 0.5 0.7 …………………………………………. Inclusive hadrons + Jets Transverse Physics Charm Physics direct photons Bottom physics W-physics A LL (hadrons, Jets)A LL (charm) A LL (γ) AL(W)AL(W) L= 6x10 30 cm -2 s -1 8x10 31 cm -2 s -1

31. CCAST Workshop on RHIC Physics Transverse Spin Physics Beijing, August 13 th 2004 Polarized pp, SIDIS, e + e - : Global Analysis global analysis for best results… Single transverse spin asymmetries in SIDIS HERMES COMPASS JLAB Belle in polarized pp: A N, A T, A TT BRAHMS PHENIX STAR I II III IV Lattice calculation of the tensor charge RBRC and elsewhere

32. CCAST Workshop on RHIC Physics Transverse Spin Physics Beijing, August 13 th 2004 Spin Fragmentation Functions from Belle Raw charged pion Fragmentation (no corrections!) scanning about 0.3% of total sample “World Data” for charged hadrons NLO QCD parametrizations: (Kretzer and Kniehl Kraemer, Poetter)  Belle FFs consistent with LEP  *VERY* large sample: Goal: measure Collins and interference fragmentation functions

33. CCAST Workshop on RHIC Physics Transverse Spin Physics Beijing, August 13 th 2004 Event Structure at Belle e -, 8 GeV e +, 3.5 GeV Jet axis: Thrust = 6.4 Near-side Hemisphere: h i, i=1,N n with z i Far-side: h j, j=1,N f with z j Correlation Analysis: Collins Interference Fragmentation z i vs z j z i 1, z i 2 vs z j 1, z j 2

34. CCAST Workshop on RHIC Physics Transverse Spin Physics Beijing, August 13 th 2004 e + e -   + jet1  - jet2 X Reaction plane defined with beam (z-axis) and jet axis Hadron plane defined with  and jet axis on each side:  i  angle between the planes A    (z 1 )    (z 2 )cos(     ) Example: Collins Fragmentation Function in e+e- 0 Schedule: Measure spin dependent fragmentation function by the end of 2005 as input for future transversity measurements.

35. CCAST Workshop on RHIC Physics Transverse Spin Physics Beijing, August 13 th 2004 Summary First evidence from HERMES that Transversity and Sivers functions may be different from zero. Exciting connections to orbital angular momentum and quark dynamics in the nucleon. Many complementary channels to explore transverse spin phenomena at RHIC. Unique Sivers signature! All experimental tools required are in place in STAR, PHENIX and BRAHMS.

36. CCAST Workshop on RHIC Physics Transverse Spin Physics Beijing, August 13 th 2004 AGS LINAC BOOSTER Polarized Source Spin Rotators Partial Snake Siberian Snakes 200 MeV Polarimeter AGS Internal Polarimeter Rf Dipole RHIC pC Polarimeters Absolute Polarimeter (H jet) P HENIX P HOBOS B RAHMS & PP2PP S TAR Siberian Snakes Run 04 achieved: P b ~45%, 55 bunches New working point with long beam and polarization lifetimes Run 05 planned: Time to tune accelerator complex Measure: A LL (jets), A LL (π 0 ) Commission strong supercon- ducting AGS snake (see M. Bai’s talk) AGS pC Polarimeter The successful Development of a novel Experimental Method: Polarized Proton Collisions! Helical Partial Snake Strong Snake Spin Flipper source: Thomas Roser, BNL

37. CCAST Workshop on RHIC Physics Transverse Spin Physics Beijing, August 13 th 2004 Jet Proton Structure Hard Scattering Process Interference Fragmentation Jian Tang, Thesis MIT, June 1999 R. Jaffe, X.Jin, J. Tang Phys. Rev. D57 (1999)5920 X. Ji, Phys. Rev. D49 (1994)114 J. Collins, S. Heppelmann, G. Ladinsky, Nucl.Phys. B420 (1994)565 Nucleon transversity through Interference Fragmentation Currently unknown: Model Calculations LEP Measurement(s) Model Calculations (RBRC Workshop on Future Transversity: Delphi, Jakob et.al., Polyakov, Weiss et.al. Leader et.al ) pQCD measured parton dis. ρ,σρ,σ

38. CCAST Workshop on RHIC Physics Transverse Spin Physics Beijing, August 13 th 2004 Interference fragmentation s-p wave interference fragmentation: Parton emits followed by absorption of a forming a parton

39. CCAST Workshop on RHIC Physics Transverse Spin Physics Beijing, August 13 th 2004 200 GeV 500 GeV Transverse Single Spin Asymmetry (Jian Tang, Thesis, MIT) Maximum Asymmetry

40. CCAST Workshop on RHIC Physics Transverse Spin Physics Beijing, August 13 th 2004 Strong interaction phase shifts s-wave p-wave Bin + Bin - Non-vanishing “support” only in the mass region! Sufficient mass Resolution? Great for systematics! Where: P. Estabrooks and A.D. Martin, Nucl. Phys. B79 (1974)301 Interference Fragmentation