Flemming Videbaek Physics Department, BNL for the BRAHMS collaboration

1. Transverse Single Spin Asymmetries from BRAHMS in pp collisions at 62 and 200 GeV Flemming Videbaek Physics Department, BNL for the BRAHMS collaboration Partonic description of inclusive cross section Single spin asymmetries for p+- Single spin asymmetries for kaons Comparisons to pQCD models DIS, London, April 7-11, 2008

2. Partonic description of hadronic dynamics in p+p at RHIC • Description of partonic dynamics without understanding of spin independent cross-section is incomplete • Large SSA have been observed at forward rapidities in hadronic reactions in a wide energy range. √S ~ 20-200 GeV • SSA: Probing internal degree of freedom. May reveal information on internal orbital angular momentum in the proton • Present energy and flavor dependent SSA and cross section at large xF measured by BRAHMS at RHIC DIS, London, April 7-11, 2008

3. Partonic description of hadronic dynamics in p+p at RHIC E704 • Description of partonic dynamics without understanding of spin independent cross-section is incomplete. • Large SSA have been observed at forward rapidities in hadronic reactions in a wide energy range. √S ~ 20-200 GeV • SSA: Probing internal degree of freedom. May reveal information on internal orbital angular momentum in the proton. • Present energy and flavor dependent SSA and cross section at large xF measured by BRAHMS at RHIC DIS, London, April 7-11, 2008

4. Beyond Naïve Parton Models • 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 ( Koike (final state) -Qiu, Sterman (initial state) , -Ji, Qiu, Vogelsang, Yuan… Challenge to have a consistent partonic description: - Cross-section pi K at large y. • Energy dependent SSA vs. xF, pT, -Flavor dependent SSA DIS, London, April 7-11, 2008

5. DIS, London, April 7-11, 2008

6. Un-polarized Cross-sections at √s=200 GeV . Good description at 200 GeV over all rapidities down to pT of 1-2 GeV/c. DIS, London, April 7-11, 2008

7. Charged separated fragmentation functions Recently deFlorian, Sassot and Stratman performed a global fit including new data from Brahms at high rapidity. PRD 75, 114010 (2007) Brahms data: PRL 98, 252001 (2007) DIS, London, April 7-11, 2008

8. Comparison of NLO pQCD calculations (Vogelsang) with BRAHMS p- data at high rapidity. The calculations are for KKP (solid) and a scale factor of m=pT, DSS with CTEQ5 and CTEQ6.5 are also shown. The agreement is surprisingly good, in apparent disagreement with earlier analysis of ISR podata at 53 GeV. DIS, London, April 7-11, 2008

9. Kaon 62 GeV at y=3.2 The K- data are suppressed due order of magnitude (valence quark effect). NLO pQCD using the recent DSS fragmentation functions give approximately same yield (?) Related to fragmentation or PDFs? DIS, London, April 7-11, 2008

10. Determination of Single Spin Asymmetry: AN • Asymmetries are defined as • AN= (s+ - s- )/(s+ + s-) = e /P • For non-uniform bunch intensities e = (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 systematic uncertainties for N+/N- cancels Uncertainties on relative luminosity L estimated to be < 0.3% • Beam polarization P ~50% with systematic uncertainty dP/P of ~7.2% for blue beam DIS, London, April 7-11, 2008

11. Calculations compared at the BRAHMS kinematic region • Twist-3 parton correlationcalculation 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 calculations provided by U. D’Alesio - Anselmino, Boglione, Leader, Melis, Murgia “Sivers effect with complete and consistent kT kinematics plus description of un-polarized cross-section” DIS, London, April 7-11, 2008

12. AN(p) at √s = 62 GeV Submitted to Physical Review LettersarXiv:0801.1078 Twist 3 sivers • Large AN(p): 0.3-0.4 at xF~0.6 pT~1.3 GeV • Strong xF -pTdependence. Though|AN(p+)| ~ !AN(p-)| |AN(p+)/AN(p-)| decreases with xF-pT DIS, London, April 7-11, 2008

13. 2.3o 4o AN(p) at √s = 200 GeV • AN(p+): positive ~(<) AN(p-): negative: 4-6% in 0.15 <xF< 0.3 • Behavior consistent with a slight decrease with increasing pT as evident in going from ~4 deg to 2.3 deg setting. • Good agreement with twist-3 calculations which also has the 1/pt-dependence at higher pT. DIS, London, April 7-11, 2008

14. AN xF-pT dependence at √s = 62, 200 GeV 62.4 GeV acceptance , 3 angle settings of spectrometer (2,3 and 6 deg) DIS, London, April 7-11, 2008

15. xF dependence in pT slices • To gain more insight the data are separated in pT bin to study xF dependence 200 GeV p+ and p- • At all pT increasing AN with xF. • Magnitude is approximately constant at pT>1.5 GeV/c DIS, London, April 7-11, 2008

16. AN xF-pT dependence at √s = 62 GeV At low-pT AN(π) increases from low pT. (Constraint must be 0 at pT=0) DIS, London, April 7-11, 2008

17. Viewing pT dependence differently Ratio of 2.3 vs 3 deg AN vs. xF at 62.4 GeV. R < 1 : Increasing AN with pT R > 1: Decreasing => AN flat or decreasing above 0.5 (~pT~1) DIS, London, April 7-11, 2008

18. Unifying 62 and 200 GeV DIS, London, April 7-11, 2008

19. Unifying 62 and 200 GeVBRAHMS + E704 E704 data – all pt (small star) pt>0.7 red star. DIS, London, April 7-11, 2008

20. Kaon SSA at 62 GeV • AN ~0 at negative xF • AN(K+) ~ AN(K-): positive ~20% at xF< 0.5-0.6 DIS, London, April 7-11, 2008

21. If main contribution to AN at large xF is from valence quark: AN(K+) ~ AN(p+) and AN(K-) ~0 • Observation clearly different • Show different models comparisons (only pT>1) DIS, London, April 7-11, 2008

22. Sensitivity to fragmentation functions DIS, London, April 7-11, 2008

23. 200 GeV Kaons Data shown at DIS 2007. DIS, London, April 7-11, 2008

24. Summary • BRAHMS measured AN of identified hadrons at 62 GeV and 200 GeV. p, K cross-section at large rapidities at 200 GeV are described by NLO pQCD . • At 62 GeV results shows that pQCD may actually still be valid at large y, and moderate pT. This make plausible the use pQCD approach to SSA at this energy. • Large SSAs seen for pions and kaons • Increases with pT to ~ 1.0 GeV/c Suggesting: - described (qualitatively) by Twist-3 - main contributions are from leading (favored) quarks Open Questions - where the large positive AN(K-) come from? - What are the theoretical uncertainties; pT ~ 1 GeV valid for QCD description? • What is pT dependence at larger values above 1 GeV/c? DIS, London, April 7-11, 2008

25. Backup Slides. DIS, London, April 7-11, 2008

26. NLO pQCD comparisons to BRAHMS data KKP FF does a better job compared to Kretzer, Pi and Kaon production still dominated by gg and gq at these rapidities apart from the highest pT KKP has only 0 frag. Modifications were needed to produce charged pions Calculations done by W. Vogelsang. Only one scale =pT and the same fragmentation functions as used for the PHENIX/STAR comparisons. DIS, London, April 7-11, 2008

27. AN for Kaons BKK FF BKK FF rescaled K+ K- Anselmino and Murgia PLB442 (1998) 470-478 • Strong strangeness FF dependence in prediction • If main contribution to AN at large xF is from valence quarks: AN(K+)~AN(p+), K- ~0 • BKK (Binnewies, Kniehl, Kramer 1995) DIS, London, April 7-11, 2008

28. Owen et al ISR DIS, London, April 7-11, 2008