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Transverse Spin Measurements in Spin Physics at RHIC

Explore transversity and TMD measurements at University of Massachusetts Amherst, covering data sets from 2002-2008 and beyond. Learn about polarization-averaged cross sections, forward pions analysis, and determinations of transverse single spin asymmetries. Discover the insights into twist-3 Sivers effects and calculations compared to BRAHMS data.

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Transverse Spin Measurements in Spin Physics at RHIC

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  1. Transversity and TMD Measurements from and University of Massachusetts Amherst Christine Aidala Transversity 2008, Ferrara May 29, 2008

  2. Transverse spin only (No rotators) Spin physics at RHIC • Variety of results out from STAR, PHENIX, and BRAHMS from 2002-2006 data sets • 2006: STAR and PHENIX took significant transverse as well as longitudinally polarized data • 2006: Polarized data at Ös = 200 and 62.4 GeV • Beyond 2006, only STAR and PHENIX • 2008: Short run with transverse collisions at 200 GeV at STAR and PHENIX Longitudinal or transverse spin Longitudinal or transverse spin C. Aidala, Transversity 2008, May 29, 2008

  3. Machine performance: Transverse spin running at PHENIX C. Aidala, Transversity 2008, May 29, 2008

  4. BRAHMS detector • Philosophy: Small acceptance spectrometer arms designed with good charged particle ID. C. Aidala, Transversity 2008, May 29, 2008

  5. The PHENIX detector • Philosophy: High rate capability to measure rare probes, limited acceptance. • 2 central spectrometers • Track charged particles and detect electromagnetic processes • 2 forward muon spectrometers • Identify and track muons • 2 forward calorimeters (as of 2007!) • Measure forward pions • Relative Luminosity • Beam-Beam Counter (BBC) • Zero-Degree Calorimeter (ZDC) C. Aidala, Transversity 2008, May 29, 2008

  6. Polarization-averaged cross sections at √s=200 GeV Good description at 200 GeV over all rapidities down to pT of 1-2 GeV/c. C. Aidala, Transversity 2008, May 29, 2008

  7. From good to even better:Now charge-separated fragmentation functions! Recently de Florian, Sassot and Stratmann performed a global fit including new data from BRAHMS at 200 GeV and high rapidity (PRD 75, 114010 (2007)). K+ K- h = 2.95 BRAHMS data: PRL 98, 252001 (2007) C. Aidala, Transversity 2008, May 29, 2008

  8. How about √s=62.4 GeV?Midrapidity pions Comparisons to NLO and NLL pQCD calculations using m=pT shown. Unlike at 200 GeV, scale choice of m=pT underpredicts the data.  Threshold logarithm effects still relevant at this intermediate energy? 11% normalization uncertainty not included But—overall, pretty good agreement! Data points from arXiv:0801.4555, submitted to PRL C. Aidala, Transversity 2008, May 29, 2008

  9. √s=62.4 GeVForward pions Comparison of NLO pQCD calculations with BRAHMS pdata at high rapidity. The calculations are for a scale factor of m=pT, KKP (solid) and DSS (dashed) with CTEQ5 and CTEQ6.5. Surprisingly good description of data, in apparent disagreement with earlier analysis of ISR p0data at 53 GeV. Still not so bad! C. Aidala, Transversity 2008, May 29, 2008

  10. √s=62.4 GeVForward kaons K-data suppressed ~order of magnitude (valence quark effect). NLO pQCD using recent DSS FF’s gives ~same yield for both charges(??). Related to FF’s? PDF’s?? K+: Not bad! K-: Hmm… C. Aidala, Transversity 2008, May 29, 2008

  11. Determination of transverse single spin asymmetries AN N.B. Detector acceptance only on one side of beam for BRAHMS  Square-root formula not an option • Look at left-right asymmetries relative to one transversely polarized proton beam • To cancel acceptance and luminosity effects use so-called square root formula C. Aidala, Transversity 2008, May 29, 2008

  12. BRAHMS xF-pT acceptance at √s = 62.4 GeV Strong xF-pT correlation due to limited spectrometer solid angle acceptance. Three angle settings of spectrometer used: 2, 3, and 6 deg C. Aidala, Transversity 2008, May 29, 2008

  13. AN(p) at √s = 62.4 GeV Submitted to PRL arXiv:0801.1078 Twist 3 Sivers • Large AN(p): 0.3-0.4 at xF~0.6, pT~1.3 GeV • Strong xF-pT dependence. Though |AN(p+)| ~ |AN(p-)|, |AN(p+)/AN(p-)| decreases with xF-pT C. Aidala, Transversity 2008, May 29, 2008

  14. Calculations compared to BRAHMS data • Twist-3 parton correlationcalculation provided by F. Yuan - Kouvaris, Qiu, Vogelsang, Yuan - “Extended” with non-derivative terms (“moderate” effects at BRAHMS kinematics) - Two flavor (u,d) and valence+sea+antiquark fits • Sivers effect calculations provided by U. D’Alesio - Anselmino, Boglione, D’Alesio, Leader, Melis, Murgia “Sivers effect with complete and consistent kT kinematics plus description of unpolarized cross section” C. Aidala, Transversity 2008, May 29, 2008

  15. 2.3o 4o AN(p) at √s = 200 GeV pT xF • AN(p+) positive; AN(p-) negative • 4-6% in 0.15 <xF< 0.3 • Behavior consistent with slight decrease with increasing pT as evident in going from 2.3 deg to 4 deg setting • Good agreement with twist-3 calculations which also have the 1/pT-dependence at higher pT C. Aidala, Transversity 2008, May 29, 2008

  16. xF dependence in pT slices, 200 GeV • To gain more insight the data are separated into pT bins to study xF dependence • At all pT, increasing AN with xF. • Magnitude is approximately constant at pT>1.5 GeV/c 200 GeV BRAHMS Preliminary C. Aidala, Transversity 2008, May 29, 2008

  17. AN xF-pT dependence at √s = 62.4 GeV arXiv:0801.1078 At low-pT AN(π) increases with pT. (Constrained to be 0 at pT=0) C. Aidala, Transversity 2008, May 29, 2008

  18. Unifying 62.4 and 200 GeV,BRAHMS + E704 E704 data – all pT (small stars); pT>0.7 GeV/c (large stars). C. Aidala, Transversity 2008, May 29, 2008

  19. Kaon SSA at 62.4 GeV • AN ~0 at negative xF • AN(K+) ~ AN(K-): positive ~20% at xF< 0.5-0.6 • Calculations get signs correct but underpredict K- Thick lines: Twist-3 w/sea quark contrib. Medium lines: Twist-3 w/o sea quarks Thin lines: Sivers arXiv:0801.1078 C. Aidala, Transversity 2008, May 29, 2008

  20. Sensitivity to fragmentation functions KKP DSS KKP DSS C. Aidala, Transversity 2008, May 29, 2008

  21. p p Comparing 200 and 62.4 GeV 200 GeV 62.4 GeV Note different scales K K K- asymmetries underpredicted 200 GeV 62.4 GeV p p Large antiproton asymmetry?? Unfortunately no 62.4 GeV measurement 200 GeV 62.4 GeV C. Aidala, Transversity 2008, May 29, 2008

  22. AN of midrapidity p0 and h+/-at Ös=200 GeV AN p0 PRL 95, 202001 (2005) AN h+/- Run-05 Run-02 |h| < 0.35 hep-ex/0507073 |h| < 0.35 pT (GeV/c) pT (GeV/c) • AN is zero within 1% contrast with forward pions • Constrains Sivers distribution function for gluons (Anselmino et al., PRD74, 094011 (2006)) • Updated p0 analysis with ~200x improvement(!) in statistical figure-of-merit underway . . . C. Aidala, Transversity 2008, May 29, 2008

  23. p0 AN xF<0 p0 AN xF>0 62.4 GeV f f Improving forward coverage at PHENIX • Muon Piston Calorimeter (MPC): PbWO4 calorimeter • 3.1 < |h| < 3.7 • Region of large observed asymmetries • Single arm commissioned in 2006 • Second arm took data in 2008 Full azimuthal coverage for 3.1  h  3.7 and 2 < E(p0) < 25 GeV C. Aidala, Transversity 2008, May 29, 2008

  24. Forward p0 SSA’s at √s=62.4 GeV PHENIX, Chiu et al., nucl-ex/0701031 pT xF Sizable asymmetries in forward direction. Need more data to understand pT dependence . . . C. Aidala, Transversity 2008, May 29, 2008

  25. Forward p0’s at √s=62.4 GeV:Pseudorapidity dependence Indication of larger forward asymmetries at higher pseudorapidity C. Aidala, Transversity 2008, May 29, 2008

  26. PHENIX and BRAHMS preliminary Charged vs. neutral pions at 62.4 GeV • BRAHMS <> = 3.44, comparable to PHENIX “all eta” = black circles. • Qualitatively similar behavior to E704 data: • p0 positive, between p+ and p- • Roughly similar magnitude: AN(p0)/AN(p+) ~ 25-50% • Quantitative comparison between identified pion asymmetries should provide strong test of theories! • Calculations: Kouvaris, Qiu, Vogelsang, Yuan, PRD74:114013, 2006 • Twist-3 calculation for pions at  = 3.3 • Derived from fits to E704 data at s~20 GeV and then evolved to 62.4 and 200 GeV • Beware that kinematics not exactly matched, since AN strong function of pT and xF. C. Aidala, Transversity 2008, May 29, 2008

  27. Forward Backward Heavy flavor single spin asymmetries • Open charm single spin asymmetries sensitive to gluon Sivers function • Anselmino et al, PRD70, 074025 (2004) • PHENIX data now available for AN of prompt muons from heavy flavor decays C. Aidala, Transversity 2008, May 29, 2008

  28. SSA of heavy flavor vs. xF Qualitative conclusion: Data constrain the gluon Sivers function to be significantly smaller than the maximal allowed. Caveat: Need to obtain updated calculation reflecting what has been learned since 2004. Translation between D meson and muon kinematics and estimate of charm vs. bottom components underway such that more quantitative comparison can be made in the future. Calculations: D mesons Data: Prompt muons C. Aidala, Transversity 2008, May 29, 2008

  29. What about charmonium? xF J/y complicated by unknown production mechanism! Recent calculations for charmonium from F.Yuan, arXiv:0801.4357 [hep-ph] C. Aidala, Transversity 2008, May 29, 2008

  30. New “rough” calculation for J/Y AN at RHIC AN 0.03 0.02 F. Yuan 0.01 Error bars currently too large to draw any conclusions -0.1 0 0.1 0.2 0.3 0.4 xF • Assumed gluon Sivers function ~ 0.5 x(1-x) times unpolarized gluon distribution • Assumed 30% J/Y from cc decays • No direct contributions! • Color-singlet is small in the cross section • Color-octet, FSI/ISI cancel out, SSA vanishes in the limit of pT<<MQ • Origin of potential non-zero asymmetry is through cc! • But beware: Production mechanism remains poorly understood! C. Aidala, Transversity 2008, May 29, 2008

  31. Forward neutrons at Ös=200 GeV at PHENIX Cross section at 200 GeV consistent with ISR data  suggests Feynman scaling holds C. Aidala, Transversity 2008, May 29, 2008

  32. charged particles neutron neutron Forward neutrons at Ös=200 GeV at PHENIX Large negative SSA observed for xF>0, enhanced by requiring concidence with forward charged particles (“MinBias” trigger). No xF dependence seen. Mean pT (Estimated by simulation assuming ISR pT dist.) 0.4<|xF|<0.6 0.088 GeV/c 0.6<|xF|<0.8 0.118 GeV/c 0.8<|xF|<1.0 0.144 GeV/c C. Aidala, Transversity 2008, May 29, 2008

  33. Forward neutrons at other energies Significant forward neutron asymmetries observed down to 62.4 and up to 410 GeV! √s=62.4 GeV √s=410 GeV C. Aidala, Transversity 2008, May 29, 2008

  34. To come • Sadly, beyond publication of 200 GeV asymmetries, no new polarized results expected from BRAHMS  • But thanks to BRAHMS for stepping up and expanding their physics program beyond heavy ions!  A variety of new results expected from PHENIX: • Interference fragmentation function • 62.4 GeV p0 forward cross section and final SSA • Updated midrapidity asymmetries for neutral pions • Updated heavy flavor asymmetries, HF tagging ~2011 • Forward neutron SSA pT dependence • Forward neutron results for other energies • Antilambda DNN C. Aidala, Transversity 2008, May 29, 2008

  35. Summary • Various SSA results for identified particles now available from PHENIX and BRAHMS over a wide kinematic range • Cross section measurements at 62.4 GeV show that pQCD may in fact still be valid at large y and moderate pT plausible to use pQCD approaches to describe forward SSA’s at this energy as well as at 200 GeV • Direct, quantitative comparisons to theoretical calculations performed in the same kinematics as the asymmetry data will be necessary to extract maximal information from the experimental measurements • Significant transverse data set taken by PHENIX earlier this year promises a variety of improved results! C. Aidala, Transversity 2008, May 29, 2008

  36. Extra Slides C. Aidala, Transversity 2008, May 29, 2008

  37. Absolute Polarimeter (H jet) Helical Partial Snake Strong Snake RHIC as a Polarized p+p Collider RHIC pC Polarimeters Siberian Snakes BRAHMS & PP2PP PHOBOS Siberian Snakes Spin Flipper PHENIX STAR Spin Rotators Various equipment to maintain and measure beam polarization through acceleration and storage Partial Snake Polarized Source LINAC AGS BOOSTER 200 MeV Polarimeter Rf Dipole AGS Internal Polarimeter AGS pC Polarimeter C. Aidala, Transversity 2008, May 29, 2008

  38. RHIC Specifications • 3.83 km circumference • Two independent rings • Up to 120 bunches/ring • 106 ns crossing time • Energy: • Up to 500 GeV for p+p • Up to 200 GeV for Au+Au(per N+N collision) • Luminosity • Au+Au: 2 x 1026 cm-2 s-1 • p+p : 2 x 1032 cm-2 s-1(70%polarized) C. Aidala, Transversity 2008, May 29, 2008

  39. RHIC Polarimetry • Proton-carbon (pC) polarimeter • For fast measurements (< 10 s!) of beam polarization • Take several measurements during each fill • Polarized hydrogen-jet polarimeter • Dedicated measurements (weeks) to calibrate the pC polarimeter • Three-fold purpose of polarimeters • Measurement of beam polarization to provide feedback to accelerator physicists • Measurement of beam polarization as input for spin-dependent measurements at the various experiments • Study of polarized elastic scattering C. Aidala, Transversity 2008, May 29, 2008

  40. scattered proton (polarized) proton beam polarized proton target or Carbon target recoil proton or Carbon Polarimetry (cont.) • E950 experiment at AGS became RHIC pC polarimeter • Measure Pbeam to ~30% • H jet polarimeter expected to determine Pbeam to 6-8% for final release of 2005 data • Both take advantage of previously measured spin asymmetries to determine the beam polarization See H. Okada et al., hep-ex/0601001, for most recent published jet polarimeter measurements. C. Aidala, Transversity 2008, May 29, 2008

  41. Blue Yellow Spin Rotators ON Up-down asymmetry  Radial polarization Blue Yellow Spin Rotators ON No asymmetry  Longitudinal polarization Blue Yellow Single-Spin Asymmetries for Local Polarimetry Take advantage of previously measured transverse single-spin asymmetry in forward neutron production (PHENIX); forward charged hadron production (STAR) AN Spin Rotators OFF Left-right asymmetry  Vertical polarization f f C. Aidala, Transversity 2008, May 29, 2008

  42. Polarized Collider Development C. Aidala, Transversity 2008, May 29, 2008

  43. |h| < 0.35 PRL 95, 202001 (2005) STAR STAR Midrapidity Hadron Production at Ös=200 GeV NLO pQCD (calc. by W. Vogelsang) p0 |h| < 0.35 p0 Fraction pions produced h~0 C. Aidala, Transversity 2008, May 29, 2008

  44. Midrapidity Prompt g Production at Ös=200 GeV • Gluon Compton scattering dominates • At LO no fragmentation function • Small contribution from annihilation Run-05 Run-3 PRL 98, 012002 (2007) C. Aidala, Transversity 2008, May 29, 2008

  45. Direct photon cross section at 62.4 GeV C. Aidala, Transversity 2008, May 29, 2008

  46. STAR Forward Hadron Production at Ös=200 GeV Good agreement between data and NLO pQCD at Ös=200 GeV, even at larger rapidities PRL 97 (2006) 152302 BRAHMS Preliminary Fraction pions produced C. Aidala, Transversity 2008, May 29, 2008

  47. xT xT Scaling • xT scaling—can parametrize cross sections for particle production in hadronic collisions by: • Lower energy has higher yield at fixed xT We can probe higher xT with better statistics even with a short run at 62.4 GeV!! (compared to 200 GeV) C. Aidala, Transversity 2008, May 29, 2008

  48. p/K/p SSA Measurements at 200 and 62 GeV BRAHMS measures identified hadrons (p,K,p,pbar) in the kinematic ranges of - 0 < xF < 0.35 and 0.2 < pT < 3.5 GeV/c at √s=200 GeV - 0 < xF < 0.6 and 0.2 < pT < 1.5 GeV/c at √s=62 GeV for • xF, pT, 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”-xF (0.15 < xF< 0.6) are presented. C. Aidala, Transversity 2008, May 29, 2008

  49. AN(p) at 4 deg. at √s = 200 GeV Curves: Twist-3 by F. Yuan Curves: Sivers effect by U. D’Alesio C. Aidala, Transversity 2008, May 29, 2008

  50. AN(K) at 2.3 deg at √s = 200 GeV Curves: Twist-3 by F. Yuan • Solid lines: two-flavor (u, d) fit • Dashed lines: valence + sea, anti-quark • Calculations done only for <pT(p)> > 1 GeV/c C. Aidala, Transversity 2008, May 29, 2008

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