1. 1 SSA in BRAHMS J.H. Lee (BNL) for BRAHMS Collaboration Preliminary Results on ,K,p Transverse Single Spin Asymmetries  at 200 GeV and 62 GeV  at high-x F Sep. 29 th 2006 RHIC-SPIN Collaboration Meeting

2. 2 Single transverse Spin Asymmetry (SSA): Introduction Large SSAs have been observed at forward rapidities in hadronic reactions: E704/FNAL and STAR/RHIC SSA is suppressed in naïve parton models (~  s m q /Q ) Non-zero SSA at partonic level requires -Spin Flip Amplitude, and -Relative phase SSA: Unravelling the spin-orbital motion of partons?

3. 3 Beyond Naïve Parton Models to accommodate large SSA Spin and Transverse-Momentum-Dependent parton distributions -”Final state” in Fragmentation (Collins effect), -”Initial state” in PDF (Sivers effect) Twist-3 matrix effects -Hadron spin-flip through gluons and hence the quark mass is replaced by Λ QCD -Efremov,Teryaev (final state) -Qiu,Sterman (initial state) Or combination of above -Ji, Qiu, Vogelsang, Yuan… Challenge to have a consistent partonic description: -Energy dependent SSA vs x F,p T, -Flavor dependent SSA -Cross-section

4. 4 SSA measurements in BRAHMS at 200 GeV BRAHMS measures identified hadrons ( ,K,p,pbar) in kinematic ranges of 0<Y<3.5 and 0.2 <p T <4 GeV/c p T dependent SSA in x F 0 - ±0.35 (x F, p T, flavor-dependent A N ) Cross-section of hadron production (Theoretical consistency) Data: Run-5: pp at √s = 200 GeV 2.5 pb -1 recorded

5. 5 SSA measurements in BRAHMS at 62 GeV Measurements at 62 GeV offers an opportunity to address an intermediate energy (RHIC-FNAL) to clarify to what degree the SSA are describable by pQCD, or is a ‘soft’ physics effect. p T dependent SSA in x F 0 – ±0.6 (x F, p T, flavor-dependent A N ) Cross-section (not shown today) Data: Run-6: pp at √s = 62 GeV 0.21 pb -1 recorded with polarization at 50-65% (see Vadim’s talk)

6. 6 Determination of Single Spin Asymmetry: A N Asymmetries are defined as A N          =  / P For non-uniform bunch intensities  = (N + / L + - N - / L - ) / (N + / L + + N - / L - ) = (N + - L *N - ) / (N + + L *N - ) where L = relative luminosity = L + / L - and the yield of in a given kinematic bin with the beam spin direction is N + (up) and N - (down). The polarization P of the beam was ~50% in the RHIC Run-5 (Blue beam) Beam polarization P from on-line measurements: (systematic uncertainty ~18%)

7. 7 Covers ~70% (~45%) of pp inelastic cross-section 41mb (36 mb) at 200 GeV (62 GeV) 3.25 < |  |  < 5.25 range Vertex resolution  (z)~ 1.6cm Main relative luminosity monitor for SSA analysis Min-Bias Trigger / Normalization Counter: “CC” (Cherenkov Radiators)

8. 8 Relative luminosity determination Relative luminosity L = L + / L - determination Using CC in spin scaler ±80cm Consistent with CC recorded in data stream Relative luminosity calculated by Beam-Beam Counter and CC: < 0.3% Systematic effect on bunch number dependent beam width: negligible

9. 9 Particle Identification using RICH Multiple settings PID for the analysis: Ring Image Cherenkov Counter ,K identification 17 GeV/c with efficiency ~ 97%

10. 10 A N (  ±,K ±,p,pbar) presented at DIS2006 (April 2006)

11. 11 Charged Hadron production at Forward vs NLO pQCD NLO pQCD describes data at forward rapidity at 200 GeV  -,K + are described best by mKKP (Kniehl-Kramer-Potter) than Kretzer FF pbar is described best by AKK (Albino-Kniehl-Kramer) FF (light flavor separated) (NLO pQCD Calculations done by W. Vogelsang. mKKP: “modified” KKP for charge separations for  and K) BRAHMS Preliminary

12. 12 Summary at DIS2006 BRAHMS has obtained particle spectra and single transverse spin asymmetries for  ±,K ±, p, and pbar in √s =200 GeV pp collisions at RHIC in the x F range of 0.1 to 0.35 Cross-section described by NLO pQCD (with updated/modified FFs) Proton production requires extra production mechanism in addition to fragmentation even at high-p T A N (   ): positive ~(<) A N (   ): negative: 5-10% in 0.1 < x F < 0.3 increasing with x F and decreasing with p T A N (   ) in agreement with Twist-3 calculations First SSA Results on K, p in 0.1 < x F < 0.3 - A N (K  ) ~ A N (K  ): positive - A N (p) ~0, A N (pbar): positive A N (K) in disagreement with naïve expectation of small sea quark polarization. Lack of understanding of p, pbar polarization: Need more theoretical inputs.

13. 13 vs x F (200 GeV) at 2.3 and 4 deg with various field settings vs x F (200 GeV) at 2.3 and 4 deg with various field settings

14. 14 BRAHMS FS Acceptance at 2.3 deg. and 4 deg. /Full Field (7.2 Tm) 4deg. 2.3deg. Strong x F -p T correlation due to limited spectrometer solid angle acceptance

15. 15 Calculations compared at the BRAHMS kinematic region Twist-3 calculation provide by F. Yuan - Kouvarius, Qiu, Vogelsang, Yuan - “Extended” with non-derivative terms (“moderate” effects at BRAHMS kinematics) - Two flavor (u,d) and valence+sea+antiquarks Fits Sivers effect calculation provided by U. D’Alesio - Anselmino, Boglione, Leader, Melis, Murgia “Sivers effect with complete and consistent k T kinematics plus description of unpolarized cross- section” (Details: Talks at this afternoon: D’Alesio, Vogelsang)

16. 16 A N (  ) at 2.3 deg. at 200 GeV

17. 17 A N (  ) at 2.3 deg. at 200 GeV + Twist-3 Solid line: two-flavor (u, d) fit Dashed line: valence + sea, anti-quark Calculations shown only for p T (  ) > 1 GeV/c

18. 18 A N (  ) at 2.3 deg. at 200 GeV + Sivers

19. 19 A N (  ) at 4 deg. at 200 GeV (high-pt setting)

20. 20 A N (  ) at 4 deg. at 200 GeV (high-pt setting) + Twist-3

21. 21 A N (  ) at 4 deg. at 200 GeV (high-pt setting) + Sivers

22. 22 A N (K) at 2.3 deg at 200 GeV

23. 23 A N (K) at 2.3 deg at 200 GeV + Twist-3

24. 24 proton 2.3 deg at 200 GeV

25. 25 62 GeV kinematic coverage at 2.3+3deg/half field setting

26. 26 A N (  ) at 62 GeV

27. 27 A N (  ) at 62 GeV + Twist-3

28. 28 A N (  ) vs –x F at 62 GeV

29. 29 A N (K) at 62 GeV

30. 30 A N (K) at 62 GeV + Twist-3

31. 31 A N (K) vs –x F at 62 GeV

32. 32 Summary BRAHMS measures A N of identified hadrons at 62 GeV and 200 GeV Large SSAs seen for pions and kaons Suggesting: - Sivers mechanism plays an important role. - described (qualitatively) by Twist-3 - main contributions are from leading (favored) quarks - power-suppression 1/p T set the scale Questioning: - where the large positive A N (K - ) come from then? - Sea quark contributions not well understood: A N (K-) and A N (pbar) - how well pQCD applicable at 62 GeV (cross-sections at 62 GeV will be delivered) - what can (not) be learned from A N at p T < 1 GeV/c - A N (-x F ) ~ 0 set limits on Sivers-gluon contribution? - can A N (p, pbar) be described in the consistent framework? We plan to finalize the SSA analysis (+ cross-section analysis) in the next few months

33. 33 “Despite the conceptual simplicity of A N, the theoretical analysis of SSA of hadronic scattering is remarkably complex.” (hep-ph/0609242) Looks like theorists are having all the fun. Enjoy!