1. Oct 3 Spin2006 J.H. Lee (BNL) 1/29 SSA in BRAHMS J.H. Lee and F. Videbaek Physics Department Brookhaven National Laboratory for BRAHMS Collaboration Preliminary Results on x F -dependent ,K,p Transverse Single Spin Asymmetries  at √s = 200 GeV and 62 GeV Spin2006, Oct. 3, Kyoto, Japan

2. Oct 3 Spin2006 J.H. Lee (BNL) 2/29 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. Oct 3 Spin2006 J.H. Lee (BNL) 3/29 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 parton correlations -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. Oct 3 Spin2006 J.H. Lee (BNL) 4/29 SSA measurements in p  +p ->  /K/p + X at 200/62 GeV BRAHMS measures identified hadrons ( ,K,p,pbar) in the kinematic ranges of - 0 < x F < 0.35 and 0.2 < p T < 3.5 GeV/c at √s=200 GeV - 0 < x F < 0.6 and 0.2 < p T < 1.5 GeV/c at √s=62 GeV for x F, p T, flavor, √s dependent SSA cross-section of unpolarized hadron production (constraint for theoretically consistent description) Data: Run-5: √s = 200 GeV 2.5 pb -1 recorded (polarization:45-50%) Run-6: √s = 62 GeV 0.21 pb -1 recorded (polarization:45-65%) Data from Forward Spectrometer at 2.3-4 deg. covering “high”-x F (0.15 < x F < 0.6) are presented.

5. Oct 3 Spin2006 J.H. Lee (BNL) 5/29 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). Most of the systematics in N + /N - cancel out Uncertainties on relative luminosity L estimated to be < 0.3% Beam polarization P from on-line measurements: systematic uncertainty of ~18% Overall systematic error on A N : ~ 25%-30%

6. Oct 3 Spin2006 J.H. Lee (BNL) 6/29 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

7. Oct 3 Spin2006 J.H. Lee (BNL) 7/29 BRAHMS FS Acceptance at 2.3 deg. and 4 deg. /Full Field (7.2 Tm) at √s = 200 GeV FS @4deg. FS @2.3deg. Strong x F -p T correlation due to limited spectrometer solid angle acceptance

8. Oct 3 Spin2006 J.H. Lee (BNL) 8/29 Calculations compared at the BRAHMS kinematic region Twist-3 parton correlation calculation provide by F. Yuan - Kouvarius, Qiu, Vogelsang, Yuan - “Extended” with non-derivative terms (“moderate” effects at BRAHMS kinematics) - Two flavor (u,d) fit and valence+sea+antiquarks fit 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 by Vogelsang (Mon.) D’Alesio (Tues.) )

9. Oct 3 Spin2006 J.H. Lee (BNL) 9/29 Sivers Function description of FNAL/E704 (talk by U. D’Alesio) Collins function Sivers function talk by U. D’Alesio

10. Oct 3 Spin2006 J.H. Lee (BNL) 10/29 Twist-3 calculation compared with FNAL/E704 talk by W. Vogelsang

11. Oct 3 Spin2006 J.H. Lee (BNL) 11/29 A N (  ) at 2.3 deg. at √s = 200 GeV A N (   ): positive ~(<) A N (   ): negative: 4-6% in 0.15 <x F < 0.3

12. Oct 3 Spin2006 J.H. Lee (BNL) 12/29 A N (  ) at 2.3 deg. at √s = 200 GeV compared with Twist-3 Solid lines: two-flavor (u, d) fit Dashed lines: valence + sea, anti-quark Calculations done only for > 1 GeV/c Curves: Twist-3 by F. Yuan

13. Oct 3 Spin2006 J.H. Lee (BNL) 13/29 A N (  ) at 2.3 deg. at √s = 200 GeV compared with Sivers effect Curves: Sivers effect by U. D’Alesio

14. Oct 3 Spin2006 J.H. Lee (BNL) 14/29 A N (  ) at 4 deg. at √s = 200 GeV (high-p T setting) A N (  ) decreases with p T especially at lower x F -p T

15. Oct 3 Spin2006 J.H. Lee (BNL) 15/29 A N (  ) at 4 deg. at √s = 200 GeV (high-p T setting) compared with Twist-3 calculations Curves: Twist-3 by F. Yuan

16. Oct 3 Spin2006 J.H. Lee (BNL) 16/29 A N (  ) at 4 deg. at √s = 200 GeV (high-p T setting) + Sivers Curves: Sivers effect by U. D’Alesio

17. Oct 3 Spin2006 J.H. Lee (BNL) 17/29 A N (K  ) ~ A N (K  ): positive 2-5% for 0.15 <x F <0.3 If main contribution to A N at large x F is from valence quarks: A N (K + )~A N (  + ), A N (K - ) ~0: disagreement with naïve expectations A N (K) at 2.3 deg at √s = 200 GeV

18. Oct 3 Spin2006 J.H. Lee (BNL) 18/29 A N (K) at 2.3 deg at √s = 200 GeV compared with Twist-3 Curves: Twist-3 by F. Yuan Solid lines: two-flavor (u, d) fit Dashed lines: valence + sea, anti-quark Calculations done only for > 1 GeV/c

19. Oct 3 Spin2006 J.H. Lee (BNL) 19/29 A N (pbar), A N (K - ) > 0: Accidental? Or contribution from sea-quarks A N (p) ~ 0: At this kinematic region, significant fraction of proton are mostly from polarized beam proton, but only ones showing A N ~0 proton at 2.3 deg. at √s = 200 GeV

20. Oct 3 Spin2006 J.H. Lee (BNL) 20/29 Kinematic coverage at √s = 62 GeV (FS at 2.3 and 3 deg.)

21. Oct 3 Spin2006 J.H. Lee (BNL) 21/29 A N (  ) at √s = 62 GeV Large A N (  ): 40% at x F ~0.6 p T ~1.3 GeV/c Strong x F -p T dependence (“Alligator”) |A N (   )/A N (   )| decreases with x F -p T

22. Oct 3 Spin2006 J.H. Lee (BNL) 22/29 A N (  ) at √s = 62 GeV compared with Twist-3 Curves: Twist-3 by F. Yuan

23. Oct 3 Spin2006 J.H. Lee (BNL) 23/29 A N (  ) at √s = 62 GeV compared with Sivers Curves: Sivers effect by U. D’Alesio

24. Oct 3 Spin2006 J.H. Lee (BNL) 24/29 A N (  ) vs –x F at √s = 62 GeV

25. Oct 3 Spin2006 J.H. Lee (BNL) 25/29 A N (K) at √s = 62 GeV

26. Oct 3 Spin2006 J.H. Lee (BNL) 26/29 A N (K) at √s = 62 GeV compared with Twist-3 Curves: Twist-3 by F. Yuan Solid lines: two-flavor (u, d) fit Dashed lines: valence + sea, anti-quark Calculations done only for > 1 GeV/c

27. Oct 3 Spin2006 J.H. Lee (BNL) 27/29 A N (K) vs –x F at √s = 62 GeV

28. Oct 3 Spin2006 J.H. Lee (BNL) 28/29 BRAHMS measures A N of identified hadrons at √s=62 GeV and 200 GeV , K cross-sections at 200 GeV described by NLO pQCD Large x F dependent 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 √s=62 GeV? (cross-section analysis at 62 GeV in progress) - 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? - What are the theoretical uncertainties? Is p T ~ 1 GeV/c valid for pQCD description? Summary

29. Oct 3 Spin2006 J.H. Lee (BNL) 29/29 “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!

30. Oct 3 Spin2006 J.H. Lee (BNL) 30/29 Backup Backup

31. Oct 3 Spin2006 J.H. Lee (BNL) 31/29 Braod RAnge Hadron Magnetic Spectrometers Designed to study nuclear reactions in broad kinematic range (y-p T ) 2 movable spectrometers with small solid angle measuring charged identified hardrons precisely Min-Bias Trigger Detector for pp: ”CC” counter 53 people from 12 institutions from 5 countries

32. Oct 3 Spin2006 J.H. Lee (BNL) 32/29 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

33. Oct 3 Spin2006 J.H. Lee (BNL) 33/29 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)

34. Oct 3 Spin2006 J.H. Lee (BNL) 34/29 Particle Identification using RICH Multiple settings PID for the analysis: Ring Image Cherenkov Counter ,K identification 17 GeV/c with efficiency ~ 97%