1. 1 Transverse Spin Measurements at PHENIX John Koster for the PHENIX collaboration University of Illinois at Urbana-Champaign DIS2009 2009/04/27

2. 2 π+π+ π-π- π0π0 Experiment: (E704, Fermi National Laboratory, 1991) Single Transverse Spin Asymmetries in pp Collisions E704: Left-right asymmetries A N for pions: A N difference in cross-section between particles produced to the left and right Theory Expectation: Small asymmetries at high energies (Kane, Pumplin, Repko, PRL 41, 1689–1692 (1978) ) Right Left A N O(10 -1 ) Measured A N O(10 -4 ) Theory ANAN xFxF

3. 3 fragmentation function pQCD Proton Structure small spin dependence Can initial and/or final state effects generate large transverse spin asymmetries? (A N ~10 -1 ) Possible Origin of Large Single Spin Asymmetries h X’ q fbfb fafa σ FF q

4. 4 Transverse Spin Effects in p ↑ p Collisions (I) Transversity quark distributions and Collins fragmentation function Correlation between proton & quark spin + spin dependant fragmentation function Collins FF Quark transverse spin distribution (II) Sivers quark-distribution Correlation between proton-spin and transverse quark momentum Sivers distribution π+π+ π-π- π0π0 ANAN xFxF E704: Left-right asymmetries A N for pions: D. Sivers, Phys. Rev. D 41, 83 (1990) J. C. Collins, Nucl. Phys. B396, 161 (1993)

5. 5 RHIC Polarized Proton Collider AGS LINAC BOOSTER Polarized Source Spin Rotators 200 MeV Polarimeter AGS Internal Polarimeter Rf Dipole RHIC pC Polarimeters Absolute Polarimeter (H jet) P HENIX P HOBOS B RAHMS & PP2PP S TAR AGS pC Polarimeter Partial Snake Siberian Snakes Helical Partial Snake Strong Snake Spin Flipper 2009 Run: Excellent performance during first 500 GeV run at RHIC ~10pb -1 200 GeV run ongoing

6. 6 RHIC ∫L* and Polarization RunEnergyPolarizationLongitudinalTransverse [GeV][%]L [pb -1 ]LP 4 [pb -1 ]L [pb -1 ]LP 2 [pb -1 ] 200220015--0.153.4 x 10 -3 2003200270.351.9 x 10 -3 -- 2004200400.129 x 10 -3 -- 200520049 (47)3.42 x 10 -1 0.163.5 x 10 -2 200620057 (51)7.57.9 x 10 -1 2.77.0 x 10 -1 200662480.084.2 x 10 -3 0.024.6 x 10 -3 200820046--5.21.1 x 10 0 2009500~35~10 2009200In progress Steadily increasing polarization and luminosity * integrated luminosity for PHENIX central arm

7. 7  0 Cross-Sections at y = 0 Experiment vs Theory  √s=200 GeV (RHIC)Agreement  √s=19.4 GeV (FNAL/E704)Different Process Contribution to  0, η=0,  s=200 GeV Neutral Pion Cross-Sections Experiment vs pQCD Guzey et al, PLB 603,173 (2004) Bourrely et al, Eur.Phys.J.C36:371-374,2004 de Florian et al, PRD:76,094021  0 Cross-Sections at y = 0 Experiment vs Theory  √s=200 GeV (RHIC)Agreement  √s=19.4 GeV (FNAL/E704)Different  √s=62.4 GeV (RHIC) Agreement More work needed to understand lower energies

8. 8 p  +p  0 +X at  s=200 GeV/c 2 PRL 95, 202001 (2005) PHENIX Data at Mid-Rapidity Helps Constrain gluon Sivers Function Experimental Measurement at y~=0Comparison of Exp. To Theory Anselmino et al, Phys. Rev. D 74, 094011 Cyan: Gluon Sivers Function at positivity bound, no sea quark Sivers Thick Red: Gluon Sivers parameterized to be 1 sigma from PHENIX  0 A N Blue: Asymmetry from Sea quark Sivers at positivity bound Green: Asymmetry from Gluon Sivers for case of sea quark at positivity bound High statistics 2006+2008 data coming. Smaller statistical errors (factor 23 improvement for  0 ’s) Higher p T Possible ANAN ANAN p T (GeV/c)

9. 9 PHENIX Detector at RHIC Muon Arms 1.2 < | η | < 2.4 J/Psi Unidentified charged hadrons Heavy Flavor Central Arms | η | < 0.35 Identified charged hadrons Neutral Pions Direct Photon J/Psi Heavy Flavor MPC 3.1 < | η | < 3.9 Neutral Pion’s Eta’s PHENIX strategy: Measure several observables each sensitive to different transverse spin effects (i) Forward SSA  Sivers & Collins Neutral Pions (ii) Transversity-type Asymmetries Interference Frag. Func. Analysis (iii) Sivers-type Asymmetries Heavy Flavor Back to Back Hadrons Pion A N for y~0

10. 10 (i) Forward SSA A N  0 in MPC Forward asymmetries contain mixture of contributions from  Sivers  Transversity x Collins  Twist-3 PHENIX  0 results available for √s=62 GeV Coming soon from 2008 √s=200 GeV dataset –  0 and  5.2 pb -1, 46% Polarization Asymmetries could enter a global analysis on transverse spin asymmetries Guzey et al, PLB 603,173 (2004) Process contribution to  0,  =3.3,  s=200 GeV 3.1 < η < 3.7 η > 3.5 η < 3.5

11. 11 (ii) Constraints on Transversity: Dihadron IFF Analysis Interference Fragmentation Function Analysis Measure di-hadron asymmetry with hadron pairs in central arm (  0,h + ) (  0,h - ), (h +,h - )  Measures δq(x) x H 1 Transversity extraction will become possible with Interference Fragmentation Function (H 1 ) measurement in progress at BELLE + + _ _ IFF

12. 12 Models for Interference Fragmentation Function  Use partial wave analysis of  phase shift data to model IFF   Sign change around  mass  Jaffe, Jin and Tang, PRL 80 (1998) 1166  Breit-Wigner shape for p wave  No sign change around  mass  Trend consistent with HERMES results  Bacchetta and Radici, Phys. Rev. D 74, 114007 (2006) Analysis done in mass bins above and below the ρ mass

13. 13 vs mass of the pair Added statistics from 2008 running NEW No significant asymmetries seen at mid-rapidity.

14. 14 vs invariant mass of the pair Added statistics from 2008 running NEW No significant asymmetries seen at mid-rapidity.

15. 15 (iii) Constraints on Sivers Function: Heavy Flavor D meson A N Production dominated by gluon-gluon fusion at RHIC energy Gluon transversity zero  Asymmetry cannot originate from Transversity x Collins Sensitive to gluon Sivers effect Anselmino et al, Phys. Rev. D 70, 074025 (2004) p ↑ p  DX Gluon Sivers=Max Quark Sivers=0 Gluon Sivers=0 Quark Sivers=Max Theoretical prediction:

16. 16 (iii) Constraints on Sivers Function: Heavy Flavor PHENIX: no reconstruction of D meson Exploratory measurements of A N for single muons  Dominated by charm production in current kinematic range  Predicted asymmetry smeared by decay kinematics

17. 17 (iii) Constraints on Sivers Function: J/Psi Exploratory measurement of A N J/Psi  J/Psi production mechanism not well understood  Single spin asymmetries may shed light on production mechanism Constraints on gluon Sivers function Yuan, PRD78:014024,2008

18. 18 (iii) Constraints on Sivers Function: DiJet Production Azimuthal distribution of Di-Jet production in pp Suggested in: Boer, Vogelsang, Phys. Rev. D 69, 094025 δφ Counts Beam is in and out of page Look at back-to-back jet opening angles δφ Proton Spin k T Sensitive to Sivers function only! No Collins-type effects

19. 19 (iii) Constraints on Sivers Function: DiHadron Production PHENIX Result from 2006 data:  Done with di-hadrons at y 1 =y2~=0  Asymmetry consistent with zero Large 2008 data set available! η min η max -3.7 -3.1 -2.0 -1.4 -0.35 +0.35 1.4 2.0 3.1 3.9 Similar analysis possible in different combinations of rapidity Works in progress… pi0 h +/-

20. 20 Near Term Outlook -- Large 2008 Dataset  Initial constraints on gluon Sivers function  Dedicated transversity channels: –IFF Analysis –Future analysis with Collins asymmetry (See next slide)  Sivers function constraints possible with more data –Connection to orbital angular momentum? Summary (i) Forward SSA A N  0 at √s=200 GeV soon. Exploring η, K 0 short, Direct γ (ii) Transversity-type measurements IFF results already preliminary Exploration Forward IFF (iii) Sivers-type measurements A N  for y~0 smaller errors and higher p T A N Heavy Flavor -- Forward open heavy flavor, J/Psi -- Mid-rapidity open heavy flavor Di-Jet analyses will expand to rapidity-separated hadron pairs

21. 21 Long Term Outlook -- Upgrades  Vertex Detectors (2011-2012) Large acceptance precision tracking –Heavy flavor tagging –Jets –Drell-Yan –Electrons from charm decays and beauty decays separately –c,b-Jet Correlations  Forward Calorimetery (2012-2013) Proposed PHENIX Upgrade ( 1 < eta < 3 ) –A N  0, Direct γ, γ-Jet –Collins-type analyses

22. 22 Backup

23. 23 IFF: Definition of Vectors and Angles Bacchetta and Radici, PRD70, 094032 (2004)

24. 24 IFF: Transversity from di-hadron SSA Physics asymmetry IFF + Di-hadron FF to be measured in e+e- Transversity to be extracted Hard scattering cross section from pQCD Unpolarized quark distribution Known from DIS

25. 25 Ongoing IFF measurement at BELLE (RBRC/Illinois)  2   1 e+ e- thrust axis Artru and Collins, Z. Phys. C69, 277 (1996) Boer, Jakob, and Radici, PRD67, 094003 (2003) IFF sensitivity projection from data

26. 26  Use partial wave analysis of  phase shift data to model IFF   Sign change around  mass  Jaffe, Jin and Tang, PRL 80 (1998) 1166 Models for IFF  Breit-Wigner shape for p wave  No sign change around  mass  Trend consistent with HERMES results  Bacchetta and Radici, Phys. Rev. D 74, 114007 (2006)