1. 1  0 Transverse Single Spin Asymmetries at High x F in p  +p Collisions in Mickey Chiu SPIN2010 Sep 30, 2010

2. 2 A Brief Motivation E704 Polarization data has often been the graveyard of fashionable theories. If theorists had their way, they might just ban such measurements altogether out of self-protection. J.D. Bjorken St. Croix, 1987

3. 3 PHENIX at RHIC Spin Run02Run05Run06Run08  s (GeV/c 2 ) 200 62.4200  Ldt (pb -1 ) 0.15 2.70.025.2 0.150.470.570.500.46 P2LP2L0.00340.0330.870.051.3 STAR PHENIX Transversely Polarized p+p Data Set Central Arm Tracking |  | < 0.35, x F ~ 0 Drift Chamber (DC) momentum measurement Pad Chambers (PC) pattern recognition, 3d space point Time Expansion Chamber (TEC) additional resolution at high pt Central Arm Calorimetry PbGl and PbSc Very Fine Granularity Tower  x  ~ 0.01x0.01 Trigger Central Arm Particle Id RICH electron/hadron separation TOF  /K/p identification Global Detectors (Luminosity,Trigger) BBC 3.0 < |  | < 3.9 Quartz Cherenkov Radiators ZDC/SMD (Local Polarimeter) Forward Hadron Calorimeter Forward Calorimetry 3.1 < |  | < 3.7 MPC PbWO 4 Crystal Forward Muon Arms 1.2 < |  | < 2.4 MPC

4. 4 PHENIX Muon Piston Calorimeter Upgrade Small cylindrical hole in Muon Magnet Piston, Radius 22.5 cm and Depth 43.1 cm SOUTH 2.16Refractive Index 420-440, 500 nmMain Emission Lines 1000 GyRadiation Hardness -2% /  C Temp. Coefficient ~10 p.e./MeV @ 25  C Light Yield 22.4 cmInteraction Length 0.89 cmRadiation Length 2.0 cmMoliere radius 721.3 gWeight 20 X0, 0.92 Length 2.2x2.2x18 cm 3 Size 8.28 g/cm 3 Density PbWO 4

5. 5 Measuring  0 ’s with the MPC Clustering: 1.Groups towers together above an energy theshold 2.Fit energy and position of incident photon If two photons are separated by ~1 tower, they are reconstructed as a single cluster. Physics Impact: Photon merging effects prevent two-photon  0 analysis: for E pi0 >20 GeV (p T >2 GeV/c) At √s = 62 GeV 20 GeV  0.65 x F :Two-photon  0 analysis At √s = 200 GeV 20 GeV  0.20 x F for two-photon pi0 analysis Use merged Single clusters as proxy for pi0 Yields dominated by  0 ’s but subject to backgrounds Decay photon impact positions for low and high energy  0 ’s

6. 6 Muon Piston Calorimeter Performance Background subtracted All Pairs Mixed Events Photon Pair Cuts (pi0 62 GeV) Pair Energy > 8 GeV Asymmetry |E 1 -E 2 |/|E 1 +E 2 | < 0.6 Noisy Towers in Run06 (up to 25% of MPC) were excluded Cluster Cuts (200 GeV) Energy > 25 GeV Fiducial Radial Cuts to avoid edges Only ~4/416 noisy towers excluded in Run08 Width ~ 20 MeV at 62.4 GeV, but improved by factor two in Run08 using pi0 tower by tower calibration Shower Reconstruction Using Shower Shape Fits 62.4 GeV Energy scale set by MIP In noisy towers, used tower spectrum MIP Peak LED Monitoring for gain stability

7. 7 Left Right 2. Or, take the left-right difference between 2 detectors This is susceptible to detector Relative Acceptance differences 1. Yield difference between up/down proton in a single detector This is susceptible to Rel. Luminosity differences Transverse Single Spin Asymmetries Definition: where p is the 4-momentum of a particle (hadron, jet, photon, etc...) Mostly insensitive to Relative Luminosity and Detector Acceptance differences 3. Or, take the cross geometric mean (square-root formula) Experimentally, there are a variety of (~equivalent) ways this can be measured.

8. 8 3.0<  <4.0 p  +p  0 +X at  s=62.4 GeV/c 2  0 A N at High x F,  s=62.4 GeV Large asymmetries at forward x F Valence quark effect? x F, p T,  s, and  dependence provide quantitative tests for theories Complementary to other data, ie, Brahms  , which allows flavor study

9. 9 GeV/c Forward A N Cluster at  s=200 GeV Eta>3.3 xFxF η 3.3 Fraction of clusters xFxF Decay photon π 0 Direct photon process contribution to  0,  =3.3,  s=200 GeV PLB 603,173 (2004)

10. 10 Fraction of clusters Forward A N Cluster at  s=200 GeV Decay photon π 0 Direct photon

11. 11 p T Dependence pTpT Fraction of clusters Decay photon π 0 Direct photon So far, 1/p T has not been observed in proton-proton collisions p T =0  A N =0 p T large, A N ~ 1/p T Low p T (TMD regime) Figure of Merit: This analysis: 1.1 pb -1 Projected 2012+2013: 66. pb -1  Errors shrink by factor of 8. In addition, triggering system is being upgraded now.  Greater efficiency Graphic from Zhongbo Kang

12. 12 Isospin Dependence (“Collins”) Transversity PDF Sivers PDF Transversity  Collins:  + (ud)  - (du)  0 (uu+dd) Sign of A N seems consistent with sign of tranversity However, transversity larger for u, but A N is larger for  + Collins is symmetric between  + and  - so it doesn’t contribute to difference  0 not average of  + and  - What is  0 Collins? Might be 0 (Belle’s sees isospin symmetry in   Collins) (Preliminary)

13. 13 Isospin Dependence (“Sivers”) Transversity PDF Sivers PDF Sivers:  + (ud)  - (du)  0 (uu+dd) Sign also consistent with Sivers Again, Sivers larger for u, but A N is larger for  + Is A N (  0 ) ~ 2A N (  + ) + A N (  - )??? Factorization/Universality breaks down??? (Preliminary)

14. 14 PYTHIA 6.214 Studies Ongoing TuneA, CKIN(3)=2, describes  0 x- section well Extrapolation from known Sivers or Transversity/Collins depends on and x versus  s Want to know outgoing jet type (Collins) Same as incoming (Sivers) Soft vs Hard: @pT = 1 GeV, ~50/50 @pT = 2 GeV, ~90%  + : ~100%u,  - : 50/50 d/u,  0 : 25/75 d/u d u g ++ 00 --

15. 15  s Dependence of  0 A N No strong dependence on  s from 19.4 to 200 GeV Spread probably due to different acceptance in pseudorapidity and/or p T If purely Sivers, should have a strong  s dependence? x F ~ P jet /P L ~ x so maybe x F just scales it out. Collins  transversity should also depend on  s through and x dependence? (Preliminary)

16. 16  s Dependence of   A N A N (%)‏ ++ -- Features:   A N (x F ) are opposite in sign and symmetric in magnitude until  s = 62.4 GeV x F intercept (where x F  0) seems to saturate at ~0.2, but is ~0.5 at  s=6.6 GeV Maximum measured asymmetry the same (accident of where statistics runs out?)

17. 17 NLO pQCD FWD  0 Cross-section Bourrely and Soffer, Eur.Phys.J.C36:371-374,2004 Cross-sections generally better described at mid-rapidity and at higher  s NLL calculations are very promising for intermediate to lower  s PHENIX  s=62.4 GeV y=0  0 cross-section, arXiv:0810.0701arXiv:0810.0701 Understanding lower p T A N important for understanding A N at higher  s More remarkable because A N (x F ) are qualitatively similar across all  s

18. 18 Summary Single Transverse Spin Asymmetries of hadrons from p+p collisions is still not understood, after over 20 years Data coming from SIDIS (Hermes, Compass, JLab), and e + e - (Belle) helps tremendously Test of extrapolation from transversities/Sivers measured by other experiments and applied to hadron-hadron collisions Does universality hold in hadron-hadron collisions? Future prospects from the MPC in PHENIX  asymmetries, extending flavor dependence (D. Kleinjan’s talk Tuesday) Possibility of more differentiating measurements? back-to-back di-hadron angular asymmetry Correlations with very forward neutrons Direct photons at very high pT (>6 GeV)?? Etc… More 200 GeV transverse data, possibly in Runs 12 and 13 SSA in transversely polarized proton collisions might add information on proton structure, but are beset by theoretical difficulties Transversity extracted/applied to p+p collisions TMD factorization/universality breakdown in p+p  h+X Transition from Sivers to twist-3 description Information on magnitude of color Lorentz force in the proton? Orbital angular momentum? While GPD’s may be cleanest way to OAM, strongest asymmetries are in p+p, and are what started the field of transverse spin physics

19. 19 Backup Slides

20. 20 Transverse Proton Spin Physics quark helicity distribution – known transversity distribution – unknown gluon helicity distribution – poorly known Polarized parton distribution functions E704 Helicity violation term due to finite quark masses Naïve LO, Leading Twist, pQCD Result

21. 21 Transverse Proton Spin Physics Various possible explanations have been proposed to explain these asymmetries Transversity x Spin-dep fragmentation (e.g., Collins effect or IFF), Intrinsic-k T in proton (Transverse Momentum Dep Functions), Eg, Sivers Function Perturbative LO Twist-3 Calculations (Qiu-Sterman, Efremov, Koike) These calculations have been related to the Sivers function Or some combination of the above Caveat: The theory is still being actively worked out A Unified picture for single transverse-spin asymmetries in hard processes, Ji, Qiu, Vogelsang, Yuan PRL97:082002,2006 Anim. courtesy J. Kruhwel, JLAB

22. 22 Kinematic Cuts and A N eta<3.5 eta>3.5 Mean A N is measured to be lower for p T >1, even though mean x F is higher for this p T bin, and higher x F implies higher asymmetry This implies that A N is dropping with pt for a given x F slice The  cut, for a given x F slice, splits that slice into high pt and low pt, with the lower eta selecting higher pt This implies that A N at lower  should be smaller, consistent with predictions of PRD74:114013 However, at 62.4 GeV the p T are low (pQCD invalid?) Cross-section is being analyzed now Phys.Rev.D74:114013,2006.

23. 23 PHENIX Preliminary BRAHMS PRL 101, 042001 RHIC Forward Pion A N at 62.4 GeV Brahms Spectrometer at “2.3  ” and “3.0  ” setting  = 3.44, comparable to PHENIX all eta Qualitatively similar behavior to E704 data: pi0 is positive and between pi+ and pi-, and roughly similar magnitude: AN(pi+)/AN(pi0) ~ 25-50% Flavor dependence of identified pion asymmetries can help to distinguish between effects Kouvaris, Qiu, Vogelsang, Yuan, PRD74:114013, 2006 Twist-3 calculation for pions for pion  exactly at 3.3 Derived from fits to E704 data at  s=19.4 GeV and then extrapolated to 62.4 and 200 GeV E704, 19.4 GeV, PLB261, (1991) 201

24. 24 Carry Out Steps Analogous to QCD Analysis of Unpolarized Distributions (ii) Transversity PDF Sivers PDF Phys.Rev.D75:054032,2007, Nucl.Phys.Proc.Suppl.191:98-107,2009 Theoretical analysis: Umberto D’Alesio and collaborators, PKU/RBRC Transverse Spin Physics Workshop Experimental data: STAR Collaboration PRL 101, 222001 (2008) Disagreement between theory and experiment. Extract Distributions from SIDIS and e + e - Predict proton-proton observables

25. 25 Comparison to  0 at  s = 200 GeV/c 2 At higher , the scaling with  s is stronger? The  dependence is switched when going from 62 to 200 GeV?  <3.5  >3.5 PHENIX 62 GeV Preliminary STAR arxiv:0801.2990v1, p+p  0 @  s=200 GeV, accepted by PRL

26. 26 Sivers  n from Back2Back Analysis Boer and Vogelsang, Phys.Rev.D69:094025,2004, hep-ph/0312320 Bomhof,Mulders,Vogelsang,Yuan, PRD75:074019,2007 Boer and Vogelsang find that this parton asymmetry will lead to an asymmetry in the  distribution of back-to-back jets Should also be able to see this effect with fragments of jets, and not just with fully reconstructed jets Important analysis to decouple the effects in single inclusive A N MPC  0 Cent h,  0 * See also Feng Wei’s talk in previous session 

27. 27 Particle Fractions of Single Clusters 1.Generate simulated proton-proton collision (Pythia) Pick Pythia configuration using detailed comparison of measured cross-sections at RHIC 2.Propagate proton-proton collision products through realistic detector response simulation (GEANT3) 3.Produce simulated data files using realistic detector resolution/smearing 4.Contributions: –Electromagnetic Merged pi0’s Direct photons Decay photons (η, etc) –Hadronic: (  +/-, K+/-, etc.) small